Subgroups — #72230291

Order 2688.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)×#546	C₂	1	1	yes	maximal, characteristic, complemented
4	#90520⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×(C₂²⋊D₇)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#90367⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#90365⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#90345⋊C₃	C₂	1	2	yes	maximal, complemented
9	#90344⋊C₃	C₂	1	2	yes	maximal, complemented
10	#90321⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#90318⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#90300⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#90300⋊C₃	C₂	1	2	yes	maximal, complemented
14	#90298⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#90296⋊C₃	C₂	1	2	yes	maximal, complemented
16	#90281⋊C₃	C₂	1	2	yes	maximal, complemented
17	#120×AGL(1,𝔽₇)	C₂	1	2	yes	maximal, complemented
18	D₄×C₄⋊AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×C₄⋊AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
20	#90238⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#90236⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#90181⋊C₃	C₂	1	2	yes	maximal, complemented
23	C₂×#6445⋊C₃	C₂	1	2	yes	maximal, complemented
24	#11743730	C₃	1	1	yes	maximal, characteristic, complemented, Hall
25	C₂⁴×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
26	C₂×#41×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
28	C₂²×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	complemented
29	C₂²×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	complemented
30	#10621518	—	2	8	no	—
31	C₂×#66659	C₂²	1	1	yes	characteristic, complemented
32	C₂×#66659	C₂²	1	1	yes	characteristic, complemented
33	C₂×D₄×AGL(1,𝔽₇)	—	2	8	no	—
34	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
35	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
36	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
37	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
39	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
41	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
42	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
43	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
45	C₂×#1157⋊C₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×#1157⋊C₃	C₂²	1	2	yes	complemented
47	C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
48	C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
49	C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
51	C₂²×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
52	ΓL(1,𝔽₈)×#124	C₂²	1	1	yes	characteristic, complemented
53	ΓL(1,𝔽₈)×#123	C₂²	1	2	yes	complemented
54	ΓL(1,𝔽₈)×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	ΓL(1,𝔽₈)×#121	C₂²	1	2	yes	complemented
56	ΓL(1,𝔽₈)×#121	C₂²	1	1	yes	characteristic, complemented
57	ΓL(1,𝔽₈)×#120	C₂²	1	2	yes	complemented
58	C₄×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
59	C₄×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	2	yes	complemented
61	#10620789	C₂²	1	2	yes	complemented
62	#6510⋊C₃	C₂²	1	1	yes	characteristic, complemented
63	#6509⋊C₃	C₂²	1	1	yes	characteristic, complemented
64	#6503⋊C₃	C₂²	1	2	yes	complemented
65	#6503⋊C₃	C₂²	1	1	yes	characteristic, complemented
66	#6502⋊C₃	C₂²	1	1	yes	characteristic, complemented
67	#6502⋊C₃	C₂²	1	2	yes	complemented
68	#6502⋊C₃	C₂²	1	2	yes	complemented
69	#6501⋊C₃	C₂²	1	1	yes	characteristic, complemented
70	#6500⋊C₃	C₂²	1	1	yes	characteristic, complemented
71	#6500⋊C₃	C₂²	1	2	yes	complemented
72	#6500⋊C₃	C₂²	1	2	yes	complemented
73	#6500⋊C₃	C₂²	1	2	yes	complemented
74	#6500⋊C₃	C₂²	1	2	yes	complemented
75	D₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic, complemented
76	#6493⋊C₃	C₂²	1	1	yes	characteristic, complemented
77	#6493⋊C₃	C₂²	1	1	yes	characteristic, complemented
78	#6493⋊C₃	C₂²	1	2	yes	complemented
79	#6492⋊C₃	C₂²	1	2	yes	complemented
80	C₄×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	complemented
83	C₂×(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	complemented
84	C₂×(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	complemented
85	#6459⋊C₃	C₂²	1	1	yes	characteristic, complemented
86	#6458⋊C₃	C₂²	1	1	yes	characteristic, complemented
87	#6458⋊C₃	C₂²	1	1	yes	characteristic, complemented
88	#6458⋊C₃	C₂²	1	2	yes	complemented
89	#6458⋊C₃	C₂²	1	2	yes	complemented
90	#6457⋊C₃	C₂²	1	1	yes	characteristic, complemented
91	#6457⋊C₃	C₂²	1	2	yes	complemented
92	#6457⋊C₃	C₂²	1	2	yes	complemented
93	#6456⋊C₃	C₂²	1	2	yes	complemented
94	#6456⋊C₃	C₂²	1	1	yes	characteristic, complemented
95	#6455⋊C₃	C₂²	1	1	yes	characteristic, complemented
96	#6448⋊C₃	C₂²	1	2	yes	complemented
97	#6447⋊C₃	C₂²	1	1	yes	characteristic, complemented
98	#6447⋊C₃	C₂²	1	2	yes	complemented
99	#6447⋊C₃	C₂²	1	2	yes	complemented
100	#6447⋊C₃	C₂²	1	2	yes	complemented
101	#6447⋊C₃	C₂²	1	2	yes	complemented
102	#6446⋊C₃	C₂²	1	1	yes	characteristic, complemented
103	#6446⋊C₃	C₂²	1	2	yes	complemented
104	#6445⋊C₃	C₂²	1	1	yes	characteristic, complemented
105	#6445⋊C₃	C₂²	1	2	yes	complemented
106	#6445⋊C₃	C₂²	1	2	yes	complemented
107	#6445⋊C₃	C₂²	1	2	yes	complemented
108	#6445⋊C₃	C₂²	1	2	yes	complemented
109	#6445⋊C₃	C₂²	1	2	yes	complemented
110	#6445⋊C₃	C₂²	1	2	yes	complemented
111	#6445⋊C₃	C₂²	1	2	yes	complemented
112	#6445⋊C₃	C₂²	1	2	yes	complemented
113	#6445⋊C₃	C₂²	1	2	yes	complemented
114	#6445⋊C₃	C₂²	1	2	yes	complemented
115	#6445⋊C₃	C₂²	1	2	yes	complemented
116	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂²	1	2	yes	complemented
117	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂²	1	2	yes	complemented
118	C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
119	C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
120	C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
121	#6441⋊C₃	C₂²	1	1	yes	characteristic, complemented
122	#10620710	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
124	C₄×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
125	#6435⋊C₃	C₂²	1	1	yes	characteristic, complemented
126	C₂×#6553	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂²×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
128	C₇×#546	C₂×C₃	1	1	yes	characteristic, complemented
129	#90520	C₂×C₃	1	1	yes	characteristic, complemented
130	D₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
131	#90367	C₂×C₃	1	1	yes	characteristic, complemented
132	#90365	C₂×C₃	1	1	yes	characteristic, complemented
133	#90345	C₂×C₃	1	2	yes	complemented
134	#90344	C₂×C₃	1	2	yes	complemented
135	#90321	C₂×C₃	1	1	yes	characteristic, complemented
136	#90318	C₂×C₃	1	1	yes	characteristic, complemented
137	#90300	C₂×C₃	1	1	yes	characteristic, complemented
138	#90300	C₂×C₃	1	2	yes	complemented
139	#90298	C₂×C₃	1	1	yes	characteristic, complemented
140	#90296	C₂×C₃	1	2	yes	complemented
141	#90281	C₂×C₃	1	2	yes	complemented
142	D₇×#120	C₂×C₃	1	2	yes	complemented
143	D₄×D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
144	D₄×D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
145	#90238	C₂×C₃	1	1	yes	characteristic, complemented
146	#90236	C₂×C₃	1	1	yes	characteristic, complemented
147	#90181	C₂×C₃	1	2	yes	complemented
148	C₂×#6445	C₂×C₃	1	2	yes	complemented
149	C₃×#3484	—	7	1	no	maximal, Hall
150	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
151	C₂³×AGL(1,𝔽₇)	—	2	8	no	—
152	C₂³×AGL(1,𝔽₇)	—	4	4	no	—
153	C₂³×AGL(1,𝔽₇)	—	4	4	no	—
154	C₂³×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
155	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	—
156	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	—
157	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	—
158	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	—
159	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	—
160	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
161	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
162	#41×ΓL(1,𝔽₈)	—	2	4	no	—
163	C₂×Q₈×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
164	C₂×D₄×ΓL(1,𝔽₈)	—	2	4	no	—
165	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
166	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
167	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
168	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
169	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
170	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
171	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
172	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
173	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
174	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
175	C₂×(C₂²⋊D₇)⋊C₃	—	2	8	no	—
176	C₂×(C₂²⋊D₇)⋊C₃	—	4	4	no	—
177	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
178	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	1	yes	characteristic
179	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
180	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
181	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	1	yes	characteristic
182	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
183	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	1	yes	characteristic
184	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
185	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	complemented
186	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	1	yes	characteristic, complemented
187	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	complemented
188	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	complemented
189	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	complemented
190	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	complemented
191	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
192	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	complemented
193	#66659	—	2	4	no	—
194	#66659	—	2	4	no	—
195	D₄×AGL(1,𝔽₇)	—	2	8	no	—
196	D₄×AGL(1,𝔽₇)	—	2	8	no	—
197	D₄×AGL(1,𝔽₇)	—	2	4	no	—
198	D₄×AGL(1,𝔽₇)	—	2	4	no	—
199	D₄×AGL(1,𝔽₇)	—	2	8	no	—
200	D₄×AGL(1,𝔽₇)	—	2	8	no	—
201	D₄×AGL(1,𝔽₇)	—	2	4	no	—
202	D₄×AGL(1,𝔽₇)	—	2	4	no	—
203	D₄×AGL(1,𝔽₇)	—	4	4	no	—
204	D₄×AGL(1,𝔽₇)	—	4	4	no	—
205	D₄×AGL(1,𝔽₇)	D₄	1	8	yes	complemented
206	#1157⋊C₃	—	2	8	no	—
207	#1157⋊C₃	—	2	4	no	—
208	C₂×C₄⋊AGL(1,𝔽₇)	—	2	8	no	—
209	C₂×C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
210	C₂×C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
211	C₂×C₄⋊AGL(1,𝔽₇)	—	4	4	no	—
212	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	—
215	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	—
217	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	—
218	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic, complemented
220	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
221	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
222	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
223	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
224	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
225	C₂×C₄×AGL(1,𝔽₇)	—	2	4	no	—
226	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
227	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
228	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
229	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
230	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic, complemented
231	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
232	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
233	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
234	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
235	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂³	1	1	yes	characteristic, complemented
236	C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
237	C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
238	C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
239	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
240	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
241	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
242	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
243	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
244	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
245	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
246	C₄²×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
247	(C₂²⋊Dic₇)⋊C₃	C₂³	1	1	yes	characteristic
248	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	complemented
249	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	complemented
250	(C₂²⋊Dic₇)⋊C₃	C₂³	1	1	yes	characteristic, complemented
251	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	1	yes	characteristic
252	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	1	yes	characteristic
253	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	1	yes	characteristic
254	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
255	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
256	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	1	yes	characteristic
257	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
258	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	1	yes	characteristic, complemented
259	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
260	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
261	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
262	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
263	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
264	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
265	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
266	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	1	yes	characteristic, complemented
267	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	1	1	yes	characteristic, complemented
268	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	1	1	yes	characteristic, complemented
269	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	1	1	yes	characteristic, complemented
270	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	1	1	yes	characteristic, complemented
271	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	1	1	yes	characteristic, complemented
272	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	1	2	yes	complemented
273	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	1	1	yes	characteristic, complemented
274	C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic, complemented
275	C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	complemented
276	C₂⁴×D₇	C₂²×C₃	1	2	yes	complemented
277	C₂×C₇×#41	C₂²×C₃	1	1	yes	characteristic, complemented
278	C₂²×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
279	C₂²×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
280	C₂²×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
281	#6553	—	2	8	no	—
282	C₂×#1161	C₂²×C₃	1	1	yes	characteristic, complemented
283	C₂×#1161	C₂²×C₃	1	1	yes	characteristic, complemented
284	C₂×D₄×D₇	—	2	8	no	—
285	C₂×D₄×D₇	C₂²×C₃	1	1	yes	characteristic
286	C₂×D₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
287	C₂×D₄×D₇	C₂²×C₃	1	2	yes	complemented
288	C₂×D₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
289	C₂×D₄×D₇	C₂²×C₃	1	2	yes	complemented
290	C₂×D₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
291	C₂×D₄×D₇	C₂²×C₃	1	2	yes	complemented
292	C₂×D₄×D₇	C₂²×C₃	1	2	yes	complemented
293	C₂×D₄×D₇	C₂²×C₃	1	2	yes	complemented
294	C₂×D₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
295	C₂×D₄×D₇	C₂²×C₃	1	2	yes	complemented
296	C₂×#1157	C₂²×C₃	1	1	yes	characteristic, complemented
297	C₂×#1157	C₂²×C₃	1	2	yes	complemented
298	C₂²×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
299	C₂²×D₂₈	C₂²×C₃	1	2	yes	complemented
300	C₂²×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
301	C₂²×D₂₈	C₂²×C₃	1	2	yes	complemented
302	C₂²×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
303	C₇×#124	C₂²×C₃	1	1	yes	characteristic, complemented
304	C₇×#123	C₂²×C₃	1	2	yes	complemented
305	C₇×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
306	C₇×#121	C₂²×C₃	1	2	yes	complemented
307	C₇×#121	C₂²×C₃	1	1	yes	characteristic, complemented
308	C₇×#120	C₂²×C₃	1	2	yes	complemented
309	C₄×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
310	C₄×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
311	C₂×C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
312	#6516	C₂²×C₃	1	2	yes	complemented
313	#6510	C₂²×C₃	1	1	yes	characteristic, complemented
314	#6509	C₂²×C₃	1	1	yes	characteristic, complemented
315	#6503	C₂²×C₃	1	2	yes	complemented
316	#6503	C₂²×C₃	1	1	yes	characteristic, complemented
317	#6502	C₂²×C₃	1	1	yes	characteristic, complemented
318	#6502	C₂²×C₃	1	2	yes	complemented
319	#6502	C₂²×C₃	1	2	yes	complemented
320	#6501	C₂²×C₃	1	1	yes	characteristic, complemented
321	#6500	C₂²×C₃	1	1	yes	characteristic, complemented
322	#6500	C₂²×C₃	1	2	yes	complemented
323	#6500	C₂²×C₃	1	2	yes	complemented
324	#6500	C₂²×C₃	1	2	yes	complemented
325	#6500	C₂²×C₃	1	2	yes	complemented
326	D₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
327	#6493	C₂²×C₃	1	1	yes	characteristic, complemented
328	#6493	C₂²×C₃	1	1	yes	characteristic, complemented
329	#6493	C₂²×C₃	1	2	yes	complemented
330	#6492	C₂²×C₃	1	2	yes	complemented
331	C₄×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic, complemented
332	C₄×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic, complemented
333	C₄×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
334	C₂×(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
335	C₂×(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
336	#6459	C₂²×C₃	1	1	yes	characteristic, complemented
337	#6458	C₂²×C₃	1	1	yes	characteristic, complemented
338	#6458	C₂²×C₃	1	1	yes	characteristic, complemented
339	#6458	C₂²×C₃	1	2	yes	complemented
340	#6458	C₂²×C₃	1	2	yes	complemented
341	#6457	C₂²×C₃	1	1	yes	characteristic, complemented
342	#6457	C₂²×C₃	1	2	yes	complemented
343	#6457	C₂²×C₃	1	2	yes	complemented
344	#6456	C₂²×C₃	1	2	yes	complemented
345	#6456	C₂²×C₃	1	1	yes	characteristic, complemented
346	#6455	C₂²×C₃	1	1	yes	characteristic, complemented
347	#6448	C₂²×C₃	1	2	yes	complemented
348	#6447	C₂²×C₃	1	1	yes	characteristic, complemented
349	#6447	C₂²×C₃	1	2	yes	complemented
350	#6447	C₂²×C₃	1	2	yes	complemented
351	#6447	C₂²×C₃	1	2	yes	complemented
352	#6447	C₂²×C₃	1	2	yes	complemented
353	#6446	C₂²×C₃	1	1	yes	characteristic, complemented
354	#6446	C₂²×C₃	1	2	yes	complemented
355	#6445	C₂²×C₃	1	1	yes	characteristic, complemented
356	#6445	C₂²×C₃	1	2	yes	complemented
357	#6445	C₂²×C₃	1	2	yes	complemented
358	#6445	C₂²×C₃	1	2	yes	complemented
359	#6445	C₂²×C₃	1	2	yes	complemented
360	#6445	C₂²×C₃	1	2	yes	complemented
361	#6445	C₂²×C₃	1	2	yes	complemented
362	#6445	C₂²×C₃	1	2	yes	complemented
363	#6445	C₂²×C₃	1	2	yes	complemented
364	#6445	C₂²×C₃	1	2	yes	complemented
365	#6445	C₂²×C₃	1	2	yes	complemented
366	#6445	C₂²×C₃	1	2	yes	complemented
367	(C₂²⋊D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
368	(C₂²⋊D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
369	D₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
370	D₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
371	D₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
372	#6441	C₂²×C₃	1	1	yes	characteristic, complemented
373	#6437	C₂²×C₃	1	1	yes	characteristic, complemented
374	C₄×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
375	C₄×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
376	#6435	C₂²×C₃	1	1	yes	characteristic, complemented
377	C₂×C₃×H(5,𝔽₂)	—	7	1	no	—
378	C₂³×C₃×D₄	—	7	1	no	—
379	C₃×#546	—	7	1	no	—
380	C₃×#546	—	7	1	no	—
381	C₃×#546	—	7	2	no	—
382	C₃×#546	—	7	1	no	—
383	C₃×#546	—	7	2	no	—
384	C₃×#546	—	14	1	no	—
385	C₃×D₄²	—	7	1	no	—
386	C₃×D₄²	—	7	2	no	—
387	C₃×D₄²	—	7	1	no	—
388	C₃×D₄²	—	7	2	no	—
389	C₃×D₄²	—	7	1	no	—
390	C₃×D₄²	—	7	1	no	—
391	C₃×#535	—	7	1	no	—
392	C₃×#535	—	7	1	no	—
393	C₃×#534	—	7	2	no	—
394	C₃×#534	—	7	2	no	—
395	C₃×#525	—	7	1	no	—
396	C₃×#525	—	7	1	no	—
397	C₂×C₃×#120	—	7	2	no	—
398	C₂×C₃×#120	—	7	2	no	—
399	C₃×#518	—	7	1	no	—
400	C₂³×ΓL(1,𝔽₈)	—	2	4	no	—
401	C₂³×ΓL(1,𝔽₈)	—	2	4	no	—
402	C₂³×ΓL(1,𝔽₈)	—	4	2	no	—
403	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	2	yes	—
404	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
405	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	2	yes	—
406	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
407	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
408	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
409	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
410	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
411	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
412	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
413	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
414	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
415	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
416	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
417	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
418	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
419	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
420	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
421	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
422	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
423	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
424	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
425	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
426	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
427	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
428	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
429	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
430	C₂²×AGL(1,𝔽₇)	—	4	32	no	—
431	C₂²×AGL(1,𝔽₇)	C₂×D₄	1	8	yes	complemented
432	C₂²×AGL(1,𝔽₇)	C₂⁴	1	1	yes	characteristic
433	C₂²×AGL(1,𝔽₇)	C₂⁴	1	2	yes	—
434	C₂²×AGL(1,𝔽₇)	C₂⁴	1	2	yes	—
435	C₂²×AGL(1,𝔽₇)	C₂⁴	1	1	yes	characteristic
436	C₂²×AGL(1,𝔽₇)	C₂⁴	1	2	yes	—
437	C₂²×AGL(1,𝔽₇)	C₂⁴	1	1	yes	characteristic
438	Q₈×ΓL(1,𝔽₈)	—	2	2	no	—
439	D₄×ΓL(1,𝔽₈)	—	2	4	no	—
440	D₄×ΓL(1,𝔽₈)	—	2	4	no	—
441	D₄×ΓL(1,𝔽₈)	—	2	2	no	—
442	D₄×ΓL(1,𝔽₈)	—	2	2	no	—
443	D₄×ΓL(1,𝔽₈)	—	4	2	no	—
444	D₄×ΓL(1,𝔽₈)	C₂×D₄	1	4	yes	complemented
445	C₂×C₄×ΓL(1,𝔽₈)	—	2	4	no	—
446	C₂×C₄×ΓL(1,𝔽₈)	—	2	2	no	—
447	C₂×C₄×ΓL(1,𝔽₈)	—	2	2	no	—
448	C₂×C₄×ΓL(1,𝔽₈)	—	4	2	no	—
449	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
450	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
451	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	2	yes	—
452	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
453	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	2	yes	—
454	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
455	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
456	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
457	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
458	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
459	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
460	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
461	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
462	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
463	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
464	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
465	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
466	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
467	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
468	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
469	(C₂²⋊D₇)⋊C₃	C₂×D₄	1	8	yes	complemented
470	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
471	C₂×ΓL(1,𝔽₈)⋊C₄	—	4	2	no	—
472	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	1	yes	characteristic
473	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	1	yes	characteristic
474	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	1	yes	characteristic
475	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	2	yes	—
476	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	1	yes	characteristic
477	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	1	yes	characteristic
478	C₄⋊AGL(1,𝔽₇)	—	2	2	no	—
479	C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
480	C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
481	C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
482	C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
483	C₄⋊AGL(1,𝔽₇)	—	2	2	no	—
484	C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
485	C₄⋊AGL(1,𝔽₇)	—	2	2	no	—
486	C₄⋊AGL(1,𝔽₇)	—	2	2	no	—
487	C₄⋊AGL(1,𝔽₇)	—	4	2	no	—
488	C₄⋊AGL(1,𝔽₇)	—	4	2	no	—
489	C₄⋊AGL(1,𝔽₇)	—	4	2	no	—
490	C₄⋊AGL(1,𝔽₇)	C₂×D₄	1	4	yes	complemented
491	C₄×AGL(1,𝔽₇)	—	2	2	no	—
492	C₄×AGL(1,𝔽₇)	—	2	4	no	—
493	C₄×AGL(1,𝔽₇)	—	2	2	no	—
494	C₄×AGL(1,𝔽₇)	—	2	2	no	—
495	C₄×AGL(1,𝔽₇)	—	2	2	no	—
496	C₄×AGL(1,𝔽₇)	—	2	4	no	—
497	C₄×AGL(1,𝔽₇)	—	4	2	no	—
498	C₄×AGL(1,𝔽₇)	—	4	2	no	—
499	C₄×AGL(1,𝔽₇)	C₂×D₄	1	4	yes	complemented
500	ΓL(1,𝔽₈)⋊Q₈	—	2	2	no	—
501	#3484	—	7	1	no	Sylow
502	C₂⁴×C₇	C₂³×C₃	1	2	yes	—
503	C₂³×D₇	—	2	8	no	—
504	C₂³×D₇	—	4	4	no	—
505	C₂³×D₇	—	4	4	no	—
506	C₂³×D₇	C₂³×C₃	1	1	yes	characteristic
507	C₂³×D₇	C₂³×C₃	1	2	yes	—
508	C₂³×D₇	C₂³×C₃	1	2	yes	—
509	C₂³×D₇	C₂³×C₃	1	2	yes	—
510	C₂³×D₇	C₂³×C₃	1	2	yes	—
511	C₂³×D₇	C₂³×C₃	1	2	yes	—
512	C₂³×D₇	C₂³×C₃	1	2	yes	complemented
513	C₂³×D₇	C₂³×C₃	1	2	yes	complemented
514	C₇×#41	—	2	4	no	—
515	C₂×C₇×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
516	C₂×C₇×D₄	—	2	4	no	—
517	C₂×C₇×D₄	C₂³×C₃	1	1	yes	characteristic
518	C₂×C₇×D₄	C₂³×C₃	1	2	yes	—
519	C₂×C₇×D₄	C₂³×C₃	1	1	yes	characteristic
520	C₂×C₇×D₄	C₂³×C₃	1	1	yes	characteristic
521	C₂×C₇×D₄	C₂³×C₃	1	2	yes	complemented
522	C₂×C₇×D₄	C₂³×C₃	1	2	yes	complemented
523	C₂²×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
524	C₂²×C₄×C₇	C₂³×C₃	1	2	yes	complemented
525	C₂²×C₄×C₇	C₂³×C₃	1	1	yes	characteristic, complemented
526	C₂²×C₄×C₇	C₂³×C₃	1	2	yes	complemented
527	C₂×C₂²⋊D₇	—	2	8	no	—
528	C₂×C₂²⋊D₇	—	4	4	no	—
529	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
530	C₂×C₂²⋊D₇	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
532	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
533	C₂×C₂²⋊D₇	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊D₇	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
537	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	complemented
538	C₂×C₂²⋊D₇	C₂³×C₃	1	1	yes	characteristic, complemented
539	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	complemented
540	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	complemented
541	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	complemented
542	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	complemented
543	C₂²×Dic₇	C₂³×C₃	1	1	yes	characteristic
544	C₂²×Dic₇	C₂³×C₃	1	2	yes	complemented
545	#1161	—	2	4	no	—
546	#1161	—	2	4	no	—
547	D₄×D₇	—	2	8	no	—
548	D₄×D₇	—	2	8	no	—
549	D₄×D₇	—	2	4	no	—
550	D₄×D₇	—	2	4	no	—
551	D₄×D₇	—	2	8	no	—
552	D₄×D₇	—	2	8	no	—
553	D₄×D₇	—	2	4	no	—
554	D₄×D₇	—	2	4	no	—
555	D₄×D₇	—	4	4	no	—
556	D₄×D₇	—	4	4	no	—
557	D₄×D₇	C₃×D₄	1	8	yes	complemented
558	#1157	—	2	8	no	—
559	#1157	—	2	4	no	—
560	C₂×D₂₈	—	2	8	no	—
561	C₂×D₂₈	—	2	4	no	—
562	C₂×D₂₈	—	2	4	no	—
563	C₂×D₂₈	—	4	4	no	—
564	C₂×D₂₈	C₂³×C₃	1	1	yes	characteristic
565	C₂×D₂₈	C₂³×C₃	1	1	yes	characteristic
566	C₂×D₂₈	C₂³×C₃	1	2	yes	—
567	C₂×D₂₈	C₂³×C₃	1	1	yes	characteristic
568	C₂×D₂₈	C₂³×C₃	1	2	yes	—
569	C₂×D₂₈	C₂³×C₃	1	2	yes	—
570	C₂×D₂₈	C₂³×C₃	1	1	yes	characteristic
571	C₂×D₂₈	C₂³×C₃	1	1	yes	characteristic, complemented
572	C₂×D₂₈	C₂³×C₃	1	2	yes	complemented
573	C₂×D₂₈	C₂³×C₃	1	2	yes	complemented
574	C₂×D₂₈	C₂³×C₃	1	2	yes	complemented
575	C₂×D₂₈	C₂³×C₃	1	2	yes	complemented
576	C₂×D₂₈	C₂³×C₃	1	2	yes	complemented
577	C₂×C₄×D₇	—	2	4	no	—
578	C₂×C₄×D₇	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₄×D₇	C₂³×C₃	1	1	yes	characteristic
580	C₂×C₄×D₇	C₂³×C₃	1	1	yes	characteristic
581	C₂×C₄×D₇	C₂³×C₃	1	1	yes	characteristic
582	C₂×C₄×D₇	C₂³×C₃	1	1	yes	characteristic, complemented
583	C₂×C₄×D₇	C₂³×C₃	1	2	yes	complemented
584	C₂×C₄×D₇	C₂³×C₃	1	2	yes	complemented
585	C₂×C₄×D₇	C₂³×C₃	1	2	yes	complemented
586	C₂×C₄×D₇	C₂³×C₃	1	2	yes	complemented
587	C₂×Dic₁₄	C₂³×C₃	1	1	yes	characteristic, complemented
588	C₇×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
589	C₇×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
590	C₇×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
591	C₇×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
592	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
593	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	complemented
594	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	complemented
595	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	complemented
596	C₇×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
597	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	complemented
598	C₄²×C₇	C₂³×C₃	1	1	yes	characteristic, complemented
599	C₂²⋊Dic₇	C₂³×C₃	1	1	yes	characteristic
600	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	complemented
601	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	complemented
602	C₂²⋊Dic₇	C₂³×C₃	1	1	yes	characteristic, complemented
603	(C₂×D₇)⋊C₄	C₂³×C₃	1	1	yes	characteristic
604	(C₂×D₇)⋊C₄	C₂³×C₃	1	1	yes	characteristic
605	(C₂×D₇)⋊C₄	C₂³×C₃	1	1	yes	characteristic
606	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
607	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
608	(C₂×D₇)⋊C₄	C₂³×C₃	1	1	yes	characteristic
609	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
610	(C₂×D₇)⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
611	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
612	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
613	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
614	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
615	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
616	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
617	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
618	(C₂×D₇)⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
619	C₄⋊Dic₇	C₂³×C₃	1	1	yes	characteristic, complemented
620	C₄⋊Dic₇	C₂³×C₃	1	1	yes	characteristic, complemented
621	Dic₇⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
622	Dic₇⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
623	Dic₇⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
624	Dic₇⋊C₄	C₂³×C₃	1	2	yes	complemented
625	Dic₇⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
626	C₄×Dic₇	C₂³×C₃	1	1	yes	characteristic, complemented
627	C₄×Dic₇	C₂³×C₃	1	2	yes	complemented
628	C₂⁵×C₃	—	7	2	no	—
629	C₃×H(5,𝔽₂)	—	14	8	no	—
630	C₂×C₃×#41	—	7	1	no	—
631	C₂×C₃×#41	—	7	1	no	—
632	C₂×C₃×#41	—	7	1	no	—
633	C₂×C₃×#41	—	7	2	no	—
634	C₂×C₃×#41	—	14	1	no	—
635	C₂²×C₃×D₄	—	7	1	no	—
636	C₂²×C₃×D₄	—	7	2	no	—
637	C₂²×C₃×D₄	—	7	2	no	—
638	C₂²×C₃×D₄	—	7	2	no	—
639	C₂²×C₃×D₄	—	7	1	no	—
640	C₂²×C₃×D₄	—	7	2	no	—
641	C₂²×C₃×D₄	—	7	1	no	—
642	C₂²×C₃×D₄	—	7	1	no	—
643	C₂²×C₃×D₄	—	7	2	no	—
644	C₂²×C₃×D₄	—	7	1	no	—
645	C₂²×C₃×D₄	—	7	2	no	—
646	C₂²×C₃×D₄	—	7	2	no	—
647	C₂²×C₃×D₄	—	7	2	no	—
648	C₂²×C₃×D₄	—	7	1	no	—
649	C₂²×C₃×D₄	—	7	2	no	—
650	C₂²×C₃×D₄	—	7	1	no	—
651	C₂²×C₃×D₄	—	7	2	no	—
652	C₂²×C₃×D₄	—	14	8	no	—
653	C₂²×C₃×D₄	—	14	1	no	—
654	C₂³×C₃×C₄	—	7	1	no	—
655	C₃×#127	—	7	1	no	—
656	C₃×#127	—	7	2	no	—
657	C₃×#127	—	7	1	no	—
658	C₃×#124	—	7	1	no	—
659	C₃×#124	—	7	2	no	—
660	C₃×#124	—	14	1	no	—
661	C₃×#123	—	7	2	no	—
662	C₃×#123	—	7	2	no	—
663	C₃×#123	—	7	1	no	—
664	C₃×#123	—	7	2	no	—
665	C₃×#123	—	7	1	no	—
666	C₃×#123	—	7	2	no	—
667	C₃×#123	—	14	2	no	—
668	C₃×C₂²⋊Q₈	—	7	1	no	—
669	C₃×C₂²⋊Q₈	—	7	1	no	—
670	C₃×C₂²⋊Q₈	—	7	1	no	—
671	C₃×C₂²⋊Q₈	—	14	1	no	—
672	C₃×#121	—	7	1	no	—
673	C₃×#121	—	7	1	no	—
674	C₃×#121	—	7	2	no	—
675	C₃×#121	—	7	2	no	—
676	C₃×#121	—	7	1	no	—
677	C₃×#121	—	7	2	no	—
678	C₃×#121	—	7	1	no	—
679	C₃×#121	—	7	1	no	—
680	C₃×#121	—	7	2	no	—
681	C₃×#121	—	7	2	no	—
682	C₃×#121	—	7	1	no	—
683	C₃×#121	—	7	1	no	—
684	C₃×#121	—	7	2	no	—
685	C₃×#121	—	7	2	no	—
686	C₃×#121	—	7	2	no	—
687	C₃×#121	—	7	2	no	—
688	C₃×#121	—	14	2	no	—
689	C₃×#121	—	14	1	no	—
690	C₃×#120	—	7	2	no	—
691	C₃×#120	—	7	1	no	—
692	C₃×#120	—	7	2	no	—
693	C₃×#120	—	7	2	no	—
694	C₃×#120	—	7	2	no	—
695	C₃×#120	—	7	2	no	—
696	C₃×#120	—	7	2	no	—
697	C₃×#120	—	7	1	no	—
698	C₃×#120	—	7	2	no	—
699	C₃×#120	—	7	2	no	—
700	C₃×#120	—	7	2	no	—
701	C₃×#120	—	7	2	no	—
702	C₃×#120	—	7	2	no	—
703	C₃×#120	—	7	2	no	—
704	C₃×#120	—	7	2	no	—
705	C₃×#120	—	7	2	no	—
706	C₃×#120	—	7	2	no	—
707	C₃×#120	—	7	2	no	—
708	C₃×#120	—	14	2	no	—
709	C₃×C₄×D₄	—	7	1	no	—
710	C₃×C₄×D₄	—	7	2	no	—
711	C₃×C₄×D₄	—	7	1	no	—
712	C₃×C₄×D₄	—	7	1	no	—
713	C₃×C₄×D₄	—	7	1	no	—
714	C₃×C₄×D₄	—	7	2	no	—
715	C₃×C₄×D₄	—	7	2	no	—
716	C₃×C₄×D₄	—	7	2	no	—
717	C₃×C₄×D₄	—	7	1	no	—
718	C₃×C₄×D₄	—	7	1	no	—
719	C₃×C₄×D₄	—	14	1	no	—
720	C₃×C₄×D₄	—	14	1	no	—
721	C₃×#117	—	7	1	no	—
722	C₃×#117	—	7	1	no	—
723	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
724	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
725	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
726	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
727	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
728	C₂×C₃×C₂²⋊C₄	—	14	2	no	—
729	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
730	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
731	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
732	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
733	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
734	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
735	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
736	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
737	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
738	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
739	C₂²×ΓL(1,𝔽₈)	—	4	8	no	—
740	C₂²×ΓL(1,𝔽₈)	C₂²×D₄	1	4	yes	—
741	C₂²×ΓL(1,𝔽₈)	H(5,𝔽₂)	1	2	yes	complemented
742	C₂²×ΓL(1,𝔽₈)	C₂⁵	1	1	yes	characteristic
743	C₂×AGL(1,𝔽₇)	—	2	8	no	—
744	C₂×AGL(1,𝔽₇)	—	2	1	no	—
745	C₂×AGL(1,𝔽₇)	—	2	2	no	—
746	C₂×AGL(1,𝔽₇)	—	2	2	no	—
747	C₂×AGL(1,𝔽₇)	—	2	1	no	—
748	C₂×AGL(1,𝔽₇)	—	2	1	no	—
749	C₂×AGL(1,𝔽₇)	—	2	1	no	—
750	C₂×AGL(1,𝔽₇)	—	2	1	no	—
751	C₂×AGL(1,𝔽₇)	—	2	2	no	—
752	C₂×AGL(1,𝔽₇)	—	2	2	no	—
753	C₂×AGL(1,𝔽₇)	—	2	1	no	—
754	C₂×AGL(1,𝔽₇)	—	2	2	no	—
755	C₂×AGL(1,𝔽₇)	—	2	2	no	—
756	C₂×AGL(1,𝔽₇)	—	2	2	no	—
757	C₂×AGL(1,𝔽₇)	—	2	2	no	—
758	C₂×AGL(1,𝔽₇)	—	2	1	no	—
759	C₂×AGL(1,𝔽₇)	—	4	8	no	—
760	C₂×AGL(1,𝔽₇)	—	4	8	no	—
761	C₂×AGL(1,𝔽₇)	—	4	8	no	—
762	C₂×AGL(1,𝔽₇)	—	4	8	no	—
763	C₂×AGL(1,𝔽₇)	—	4	8	no	—
764	C₂×AGL(1,𝔽₇)	—	8	4	no	—
765	C₂×AGL(1,𝔽₇)	—	8	4	no	—
766	C₂×AGL(1,𝔽₇)	C₂²×D₄	1	2	yes	—
767	C₂×AGL(1,𝔽₇)	C₂²×D₄	1	4	yes	—
768	C₂×AGL(1,𝔽₇)	H(5,𝔽₂)	1	2	yes	complemented
769	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
770	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
771	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
772	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
773	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
774	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
775	C₄×ΓL(1,𝔽₈)	C₂²×D₄	1	2	yes	—
776	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
777	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
778	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
779	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
780	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
781	ΓL(1,𝔽₈)⋊C₄	C₂²×D₄	1	2	yes	—
782	C₂×H(5,𝔽₂)	—	7	1	no	—
783	C₂³×D₄	—	7	1	no	—
784	#546	—	7	1	no	—
785	#546	—	7	1	no	—
786	#546	—	7	2	no	—
787	#546	—	7	1	no	—
788	#546	—	7	2	no	—
789	#546	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
790	D₄²	—	7	1	no	—
791	D₄²	—	7	2	no	—
792	D₄²	—	7	1	no	—
793	D₄²	—	7	2	no	—
794	D₄²	—	7	1	no	—
795	D₄²	—	7	1	no	—
796	#535	—	7	1	no	—
797	#535	—	7	1	no	—
798	#534	—	7	2	no	—
799	#534	—	7	2	no	—
800	#525	—	7	1	no	—
801	#525	—	7	1	no	—
802	C₂×#120	—	7	2	no	—
803	C₂×#120	—	7	2	no	—
804	#518	—	7	1	no	—
805	C₂³×C₇	—	2	4	no	—
806	C₂³×C₇	—	2	4	no	—
807	C₂³×C₇	—	4	2	no	—
808	C₂³×C₇	C₂⁴×C₃	1	2	yes	—
809	C₂³×C₇	C₂⁴×C₃	1	1	yes	characteristic
810	C₂³×C₇	C₂⁴×C₃	1	2	yes	—
811	C₂³×C₇	C₂⁴×C₃	1	1	yes	characteristic
812	C₂²×D₇	—	2	2	no	—
813	C₂²×D₇	—	2	2	no	—
814	C₂²×D₇	—	2	2	no	—
815	C₂²×D₇	—	2	4	no	—
816	C₂²×D₇	—	2	4	no	—
817	C₂²×D₇	—	2	4	no	—
818	C₂²×D₇	—	2	4	no	—
819	C₂²×D₇	—	2	4	no	—
820	C₂²×D₇	—	2	4	no	—
821	C₂²×D₇	—	2	4	no	—
822	C₂²×D₇	—	2	4	no	—
823	C₂²×D₇	—	2	4	no	—
824	C₂²×D₇	—	4	2	no	—
825	C₂²×D₇	—	4	2	no	—
826	C₂²×D₇	—	4	2	no	—
827	C₂²×D₇	—	4	2	no	—
828	C₂²×D₇	—	4	2	no	—
829	C₂²×D₇	—	4	2	no	—
830	C₂²×D₇	—	4	2	no	—
831	C₂²×D₇	—	4	2	no	—
832	C₂²×D₇	—	4	2	no	—
833	C₂²×D₇	—	4	2	no	—
834	C₂²×D₇	—	4	2	no	—
835	C₂²×D₇	—	4	32	no	—
836	C₂²×D₇	C₂×C₃×D₄	1	8	yes	complemented
837	C₂²×D₇	C₂⁴×C₃	1	2	yes	—
838	C₂²×D₇	C₂⁴×C₃	1	1	yes	characteristic
839	C₂²×D₇	C₂⁴×C₃	1	2	yes	—
840	C₂²×D₇	C₂⁴×C₃	1	1	yes	characteristic
841	C₂²×D₇	C₂⁴×C₃	1	2	yes	—
842	C₂²×D₇	C₂⁴×C₃	1	1	yes	characteristic
843	C₇×Q₈	—	2	2	no	—
844	C₇×D₄	—	2	4	no	—
845	C₇×D₄	—	2	4	no	—
846	C₇×D₄	—	2	2	no	—
847	C₇×D₄	—	2	2	no	—
848	C₇×D₄	—	4	2	no	—
849	C₇×D₄	C₂×C₃×D₄	1	4	yes	complemented
850	C₂×C₄×C₇	—	2	4	no	—
851	C₂×C₄×C₇	—	2	2	no	—
852	C₂×C₄×C₇	—	2	2	no	—
853	C₂×C₄×C₇	—	4	2	no	—
854	C₂×C₄×C₇	C₂⁴×C₃	1	2	yes	—
855	C₂×C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
856	C₂×C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
857	C₂×C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
858	C₂×C₄×C₇	C₂⁴×C₃	1	2	yes	—
859	C₂×C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
860	C₂×C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
861	C₂²⋊D₇	—	2	4	no	—
862	C₂²⋊D₇	—	2	4	no	—
863	C₂²⋊D₇	—	2	4	no	—
864	C₂²⋊D₇	—	2	2	no	—
865	C₂²⋊D₇	—	2	2	no	—
866	C₂²⋊D₇	—	2	4	no	—
867	C₂²⋊D₇	—	2	2	no	—
868	C₂²⋊D₇	—	2	2	no	—
869	C₂²⋊D₇	—	2	4	no	—
870	C₂²⋊D₇	—	4	2	no	—
871	C₂²⋊D₇	—	4	2	no	—
872	C₂²⋊D₇	—	4	2	no	—
873	C₂²⋊D₇	—	4	2	no	—
874	C₂²⋊D₇	C₂×C₃×D₄	1	8	yes	complemented
875	C₂×Dic₇	—	2	2	no	—
876	C₂×Dic₇	—	4	2	no	—
877	C₂×Dic₇	C₂⁴×C₃	1	1	yes	characteristic
878	C₂×Dic₇	C₂⁴×C₃	1	1	yes	characteristic
879	C₂×Dic₇	C₂⁴×C₃	1	2	yes	—
880	C₂×Dic₇	C₂⁴×C₃	1	1	yes	characteristic
881	C₂×Dic₇	C₂⁴×C₃	1	1	yes	characteristic
882	C₂×Dic₇	C₂⁴×C₃	1	1	yes	characteristic
883	D₂₈	—	2	2	no	—
884	D₂₈	—	2	4	no	—
885	D₂₈	—	2	4	no	—
886	D₂₈	—	2	4	no	—
887	D₂₈	—	2	4	no	—
888	D₂₈	—	2	2	no	—
889	D₂₈	—	2	4	no	—
890	D₂₈	—	2	2	no	—
891	D₂₈	—	2	2	no	—
892	D₂₈	—	4	2	no	—
893	D₂₈	—	4	2	no	—
894	D₂₈	—	4	2	no	—
895	D₂₈	C₂×C₃×D₄	1	4	yes	complemented
896	C₄×D₇	—	2	2	no	—
897	C₄×D₇	—	2	4	no	—
898	C₄×D₇	—	2	2	no	—
899	C₄×D₇	—	2	2	no	—
900	C₄×D₇	—	2	2	no	—
901	C₄×D₇	—	2	4	no	—
902	C₄×D₇	—	4	2	no	—
903	C₄×D₇	—	4	2	no	—
904	C₄×D₇	C₂×C₃×D₄	1	4	yes	complemented
905	Dic₁₄	—	2	2	no	—
906	C₂⁴×C₃	—	7	2	no	—
907	C₂⁴×C₃	—	7	1	no	—
908	C₂⁴×C₃	—	7	2	no	—
909	C₂⁴×C₃	—	7	2	no	—
910	C₂⁴×C₃	—	7	2	no	—
911	C₂⁴×C₃	—	7	2	no	—
912	C₂⁴×C₃	—	7	2	no	—
913	C₂⁴×C₃	—	7	2	no	—
914	C₂⁴×C₃	—	14	8	no	—
915	C₂⁴×C₃	—	14	2	no	—
916	C₂⁴×C₃	—	28	4	no	—
917	C₂⁴×C₃	—	28	4	no	—
918	C₃×#41	—	14	4	no	—
919	C₃×#41	—	14	4	no	—
920	C₃×#41	—	14	4	no	—
921	C₃×#41	—	14	8	no	—
922	C₃×#41	—	28	4	no	—
923	C₂×C₃×Q₈	—	7	1	no	—
924	C₂×C₃×Q₈	—	14	1	no	—
925	C₂×C₃×D₄	—	7	2	no	—
926	C₂×C₃×D₄	—	7	8	no	—
927	C₂×C₃×D₄	—	7	1	no	—
928	C₂×C₃×D₄	—	7	2	no	—
929	C₂×C₃×D₄	—	7	1	no	—
930	C₂×C₃×D₄	—	7	1	no	—
931	C₂×C₃×D₄	—	7	2	no	—
932	C₂×C₃×D₄	—	7	2	no	—
933	C₂×C₃×D₄	—	7	2	no	—
934	C₂×C₃×D₄	—	7	2	no	—
935	C₂×C₃×D₄	—	7	1	no	—
936	C₂×C₃×D₄	—	7	2	no	—
937	C₂×C₃×D₄	—	7	2	no	—
938	C₂×C₃×D₄	—	7	2	no	—
939	C₂×C₃×D₄	—	7	2	no	—
940	C₂×C₃×D₄	—	7	1	no	—
941	C₂×C₃×D₄	—	7	2	no	—
942	C₂×C₃×D₄	—	7	1	no	—
943	C₂×C₃×D₄	—	7	2	no	—
944	C₂×C₃×D₄	—	7	1	no	—
945	C₂×C₃×D₄	—	7	2	no	—
946	C₂×C₃×D₄	—	7	1	no	—
947	C₂×C₃×D₄	—	7	2	no	—
948	C₂×C₃×D₄	—	7	2	no	—
949	C₂×C₃×D₄	—	7	1	no	—
950	C₂×C₃×D₄	—	7	2	no	—
951	C₂×C₃×D₄	—	7	2	no	—
952	C₂×C₃×D₄	—	7	2	no	—
953	C₂×C₃×D₄	—	14	4	no	—
954	C₂×C₃×D₄	—	14	8	no	—
955	C₂×C₃×D₄	—	14	8	no	—
956	C₂×C₃×D₄	—	14	4	no	—
957	C₂×C₃×D₄	—	14	8	no	—
958	C₂×C₃×D₄	—	14	4	no	—
959	C₂×C₃×D₄	—	14	4	no	—
960	C₂×C₃×D₄	—	14	8	no	—
961	C₂×C₃×D₄	—	14	8	no	—
962	C₂×C₃×D₄	—	14	4	no	—
963	C₂×C₃×D₄	—	14	4	no	—
964	C₂×C₃×D₄	—	14	8	no	—
965	C₂×C₃×D₄	—	14	1	no	—
966	C₂×C₃×D₄	—	14	1	no	—
967	C₂×C₃×D₄	—	14	2	no	—
968	C₂×C₃×D₄	—	14	1	no	—
969	C₂×C₃×D₄	—	14	2	no	—
970	C₂×C₃×D₄	—	14	2	no	—
971	C₂×C₃×D₄	—	28	4	no	—
972	C₂×C₃×D₄	—	28	4	no	—
973	C₂×C₃×D₄	—	28	4	no	—
974	C₂×C₃×D₄	—	28	4	no	—
975	C₂×C₃×D₄	—	28	4	no	—
976	C₂²×C₃×C₄	—	7	1	no	—
977	C₂²×C₃×C₄	—	7	1	no	—
978	C₂²×C₃×C₄	—	7	2	no	—
979	C₂²×C₃×C₄	—	7	1	no	—
980	C₂²×C₃×C₄	—	7	1	no	—
981	C₂²×C₃×C₄	—	7	1	no	—
982	C₂²×C₃×C₄	—	7	2	no	—
983	C₂²×C₃×C₄	—	7	2	no	—
984	C₂²×C₃×C₄	—	7	1	no	—
985	C₂²×C₃×C₄	—	7	2	no	—
986	C₂²×C₃×C₄	—	7	2	no	—
987	C₂²×C₃×C₄	—	14	4	no	—
988	C₂²×C₃×C₄	—	14	1	no	—
989	C₂²×C₃×C₄	—	14	2	no	—
990	C₂²×C₃×C₄	—	14	1	no	—
991	C₂²×C₃×C₄	—	14	2	no	—
992	C₃×C₄⋊C₄	—	7	1	no	—
993	C₃×C₄⋊C₄	—	7	1	no	—
994	C₃×C₄⋊C₄	—	7	1	no	—
995	C₃×C₄⋊C₄	—	7	1	no	—
996	C₃×C₄⋊C₄	—	7	2	no	—
997	C₃×C₄⋊C₄	—	7	1	no	—
998	C₃×C₄⋊C₄	—	7	1	no	—
999	C₃×C₄⋊C₄	—	14	1	no	—
1000	C₃×C₄⋊C₄	—	14	2	no	—
1001	C₃×C₄⋊C₄	—	14	1	no	—
1002	C₃×C₂²⋊C₄	—	7	1	no	—
1003	C₃×C₂²⋊C₄	—	7	2	no	—
1004	C₃×C₂²⋊C₄	—	7	2	no	—
1005	C₃×C₂²⋊C₄	—	7	1	no	—
1006	C₃×C₂²⋊C₄	—	7	2	no	—
1007	C₃×C₂²⋊C₄	—	7	1	no	—
1008	C₃×C₂²⋊C₄	—	7	1	no	—
1009	C₃×C₂²⋊C₄	—	7	2	no	—
1010	C₃×C₂²⋊C₄	—	7	1	no	—
1011	C₃×C₂²⋊C₄	—	7	1	no	—
1012	C₃×C₂²⋊C₄	—	7	2	no	—
1013	C₃×C₂²⋊C₄	—	7	2	no	—
1014	C₃×C₂²⋊C₄	—	7	2	no	—
1015	C₃×C₂²⋊C₄	—	7	2	no	—
1016	C₃×C₂²⋊C₄	—	7	2	no	—
1017	C₃×C₂²⋊C₄	—	7	2	no	—
1018	C₃×C₂²⋊C₄	—	7	1	no	—
1019	C₃×C₂²⋊C₄	—	7	2	no	—
1020	C₃×C₂²⋊C₄	—	7	2	no	—
1021	C₃×C₂²⋊C₄	—	7	1	no	—
1022	C₃×C₂²⋊C₄	—	14	2	no	—
1023	C₃×C₂²⋊C₄	—	14	1	no	—
1024	C₃×C₂²⋊C₄	—	14	2	no	—
1025	C₃×C₂²⋊C₄	—	14	2	no	—
1026	C₃×C₂²⋊C₄	—	14	2	no	—
1027	C₃×C₂²⋊C₄	—	14	2	no	—
1028	C₃×C₂²⋊C₄	—	14	1	no	—
1029	C₃×C₄²	—	7	2	no	—
1030	C₃×C₄²	—	7	1	no	—
1031	C₃×C₄²	—	14	1	no	—
1032	C₂×ΓL(1,𝔽₈)	—	2	2	no	—
1033	C₂×ΓL(1,𝔽₈)	—	2	4	no	—
1034	C₂×ΓL(1,𝔽₈)	—	4	2	no	—
1035	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
1036	C₂×ΓL(1,𝔽₈)	C₂³×D₄	1	1	yes	characteristic
1037	C₂×ΓL(1,𝔽₈)	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1038	C₂×ΓL(1,𝔽₈)	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1039	AGL(1,𝔽₇)	—	2	2	no	—
1040	AGL(1,𝔽₇)	—	2	2	no	—
1041	AGL(1,𝔽₇)	—	2	4	no	—
1042	AGL(1,𝔽₇)	—	4	2	no	—
1043	AGL(1,𝔽₇)	—	4	1	no	—
1044	AGL(1,𝔽₇)	—	4	2	no	—
1045	C₂⁵	—	7	2	no	—
1046	H(5,𝔽₂)	—	14	8	no	—
1047	C₂×#41	—	7	1	no	—
1048	C₂×#41	—	7	1	no	—
1049	C₂×#41	—	7	1	no	—
1050	C₂×#41	—	7	2	no	—
1051	C₂×#41	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1052	C₂²×D₄	—	7	1	no	—
1053	C₂²×D₄	—	7	2	no	—
1054	C₂²×D₄	—	7	2	no	—
1055	C₂²×D₄	—	7	2	no	—
1056	C₂²×D₄	—	7	1	no	—
1057	C₂²×D₄	—	7	1	no	—
1058	C₂²×D₄	—	7	2	no	—
1059	C₂²×D₄	—	7	1	no	—
1060	C₂²×D₄	—	7	1	no	—
1061	C₂²×D₄	—	7	2	no	—
1062	C₂²×D₄	—	7	2	no	—
1063	C₂²×D₄	—	7	2	no	—
1064	C₂²×D₄	—	7	2	no	—
1065	C₂²×D₄	—	7	1	no	—
1066	C₂²×D₄	—	7	2	no	—
1067	C₂²×D₄	—	7	1	no	—
1068	C₂²×D₄	—	7	2	no	—
1069	C₂²×D₄	—	14	8	no	—
1070	C₂²×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1071	C₂³×C₄	—	7	1	no	—
1072	#127	—	7	1	no	—
1073	#127	—	7	2	no	—
1074	#127	—	7	1	no	—
1075	#124	—	7	1	no	—
1076	#124	—	7	2	no	—
1077	#124	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1078	#123	—	7	2	no	—
1079	#123	—	7	2	no	—
1080	#123	—	7	1	no	—
1081	#123	—	7	2	no	—
1082	#123	—	7	1	no	—
1083	#123	—	7	2	no	—
1084	#123	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
1085	C₂²⋊Q₈	—	7	1	no	—
1086	C₂²⋊Q₈	—	7	1	no	—
1087	C₂²⋊Q₈	—	7	1	no	—
1088	C₂²⋊Q₈	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1089	#121	—	7	1	no	—
1090	#121	—	7	2	no	—
1091	#121	—	7	1	no	—
1092	#121	—	7	2	no	—
1093	#121	—	7	1	no	—
1094	#121	—	7	2	no	—
1095	#121	—	7	1	no	—
1096	#121	—	7	1	no	—
1097	#121	—	7	2	no	—
1098	#121	—	7	2	no	—
1099	#121	—	7	1	no	—
1100	#121	—	7	1	no	—
1101	#121	—	7	2	no	—
1102	#121	—	7	2	no	—
1103	#121	—	7	2	no	—
1104	#121	—	7	2	no	—
1105	#121	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
1106	#121	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1107	#120	—	7	2	no	—
1108	#120	—	7	1	no	—
1109	#120	—	7	2	no	—
1110	#120	—	7	2	no	—
1111	#120	—	7	2	no	—
1112	#120	—	7	2	no	—
1113	#120	—	7	2	no	—
1114	#120	—	7	1	no	—
1115	#120	—	7	2	no	—
1116	#120	—	7	2	no	—
1117	#120	—	7	2	no	—
1118	#120	—	7	2	no	—
1119	#120	—	7	2	no	—
1120	#120	—	7	2	no	—
1121	#120	—	7	2	no	—
1122	#120	—	7	2	no	—
1123	#120	—	7	2	no	—
1124	#120	—	7	2	no	—
1125	#120	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
1126	C₄×D₄	—	7	1	no	—
1127	C₄×D₄	—	7	1	no	—
1128	C₄×D₄	—	7	2	no	—
1129	C₄×D₄	—	7	1	no	—
1130	C₄×D₄	—	7	1	no	—
1131	C₄×D₄	—	7	2	no	—
1132	C₄×D₄	—	7	2	no	—
1133	C₄×D₄	—	7	2	no	—
1134	C₄×D₄	—	7	1	no	—
1135	C₄×D₄	—	7	1	no	—
1136	C₄×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1137	C₄×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1138	#117	—	7	1	no	—
1139	#117	—	7	1	no	—
1140	C₂×C₂²⋊C₄	—	7	2	no	—
1141	C₂×C₂²⋊C₄	—	7	2	no	—
1142	C₂×C₂²⋊C₄	—	7	2	no	—
1143	C₂×C₂²⋊C₄	—	7	2	no	—
1144	C₂×C₂²⋊C₄	—	7	2	no	—
1145	C₂×C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
1146	C₂²×C₇	—	2	1	no	—
1147	C₂²×C₇	—	2	2	no	—
1148	C₂²×C₇	—	2	2	no	—
1149	C₂²×C₇	—	2	1	no	—
1150	C₂²×C₇	—	2	1	no	—
1151	C₂²×C₇	—	2	2	no	—
1152	C₂²×C₇	—	2	1	no	—
1153	C₂²×C₇	—	2	1	no	—
1154	C₂²×C₇	—	2	2	no	—
1155	C₂²×C₇	—	2	2	no	—
1156	C₂²×C₇	—	4	8	no	—
1157	C₂²×C₇	C₂²×C₃×D₄	1	4	yes	—
1158	C₂²×C₇	C₃×H(5,𝔽₂)	1	2	yes	complemented
1159	C₂²×C₇	C₂⁵×C₃	1	1	yes	characteristic
1160	C₂×D₇	—	2	8	no	—
1161	C₂×D₇	—	2	1	no	—
1162	C₂×D₇	—	2	2	no	—
1163	C₂×D₇	—	2	2	no	—
1164	C₂×D₇	—	2	1	no	—
1165	C₂×D₇	—	2	1	no	—
1166	C₂×D₇	—	2	1	no	—
1167	C₂×D₇	—	2	1	no	—
1168	C₂×D₇	—	2	2	no	—
1169	C₂×D₇	—	2	2	no	—
1170	C₂×D₇	—	2	1	no	—
1171	C₂×D₇	—	2	2	no	—
1172	C₂×D₇	—	2	2	no	—
1173	C₂×D₇	—	2	2	no	—
1174	C₂×D₇	—	2	2	no	—
1175	C₂×D₇	—	2	1	no	—
1176	C₂×D₇	—	4	8	no	—
1177	C₂×D₇	—	4	8	no	—
1178	C₂×D₇	—	4	8	no	—
1179	C₂×D₇	—	4	8	no	—
1180	C₂×D₇	—	4	8	no	—
1181	C₂×D₇	—	8	4	no	—
1182	C₂×D₇	—	8	4	no	—
1183	C₂×D₇	C₂²×C₃×D₄	1	2	yes	—
1184	C₂×D₇	C₂²×C₃×D₄	1	4	yes	—
1185	C₂×D₇	C₃×H(5,𝔽₂)	1	2	yes	complemented
1186	C₄×C₇	—	2	1	no	—
1187	C₄×C₇	—	2	1	no	—
1188	C₄×C₇	—	2	2	no	—
1189	C₄×C₇	—	2	1	no	—
1190	C₄×C₇	—	2	2	no	—
1191	C₄×C₇	—	2	1	no	—
1192	C₄×C₇	C₂²×C₃×D₄	1	2	yes	—
1193	Dic₇	—	2	1	no	—
1194	Dic₇	—	2	1	no	—
1195	Dic₇	—	2	1	no	—
1196	Dic₇	—	2	2	no	—
1197	Dic₇	—	2	1	no	—
1198	Dic₇	C₂²×C₃×D₄	1	2	yes	—
1199	C₂³×C₃	—	7	1	no	—
1200	C₂³×C₃	—	7	1	no	—
1201	C₂³×C₃	—	7	2	no	—
1202	C₂³×C₃	—	7	8	no	—
1203	C₂³×C₃	—	7	2	no	—
1204	C₂³×C₃	—	7	2	no	—
1205	C₂³×C₃	—	7	1	no	—
1206	C₂³×C₃	—	14	2	no	—
1207	C₂³×C₃	—	14	2	no	—
1208	C₂³×C₃	—	14	4	no	—
1209	C₂³×C₃	—	14	4	no	—
1210	C₂³×C₃	—	14	4	no	—
1211	C₂³×C₃	—	14	4	no	—
1212	C₂³×C₃	—	14	4	no	—
1213	C₂³×C₃	—	14	4	no	—
1214	C₂³×C₃	—	14	2	no	—
1215	C₂³×C₃	—	14	4	no	—
1216	C₂³×C₃	—	14	4	no	—
1217	C₂³×C₃	—	14	4	no	—
1218	C₂³×C₃	—	14	1	no	—
1219	C₂³×C₃	—	14	2	no	—
1220	C₂³×C₃	—	14	2	no	—
1221	C₂³×C₃	—	14	1	no	—
1222	C₂³×C₃	—	28	4	no	—
1223	C₂³×C₃	—	28	4	no	—
1224	C₂³×C₃	—	28	2	no	—
1225	C₂³×C₃	—	28	2	no	—
1226	C₂³×C₃	—	28	2	no	—
1227	C₂³×C₃	—	28	2	no	—
1228	C₂³×C₃	—	28	2	no	—
1229	C₂³×C₃	—	28	2	no	—
1230	C₂³×C₃	—	28	2	no	—
1231	C₂³×C₃	—	28	2	no	—
1232	C₂³×C₃	—	28	2	no	—
1233	C₂³×C₃	—	28	2	no	—
1234	C₂³×C₃	—	28	2	no	—
1235	C₂³×C₃	—	28	32	no	—
1236	C₂³×C₃	—	56	2	no	—
1237	C₃×Q₈	—	14	2	no	—
1238	C₃×Q₈	—	28	2	no	—
1239	C₃×D₄	—	7	8	no	—
1240	C₃×D₄	—	7	4	no	—
1241	C₃×D₄	—	14	4	no	—
1242	C₃×D₄	—	14	2	no	—
1243	C₃×D₄	—	14	4	no	—
1244	C₃×D₄	—	14	2	no	—
1245	C₃×D₄	—	14	2	no	—
1246	C₃×D₄	—	14	2	no	—
1247	C₃×D₄	—	14	2	no	—
1248	C₃×D₄	—	14	4	no	—
1249	C₃×D₄	—	14	4	no	—
1250	C₃×D₄	—	14	4	no	—
1251	C₃×D₄	—	14	2	no	—
1252	C₃×D₄	—	14	4	no	—
1253	C₃×D₄	—	14	4	no	—
1254	C₃×D₄	—	14	4	no	—
1255	C₃×D₄	—	14	2	no	—
1256	C₃×D₄	—	14	4	no	—
1257	C₃×D₄	—	14	4	no	—
1258	C₃×D₄	—	14	2	no	—
1259	C₃×D₄	—	14	4	no	—
1260	C₃×D₄	—	28	2	no	—
1261	C₃×D₄	—	28	4	no	—
1262	C₃×D₄	—	28	4	no	—
1263	C₃×D₄	—	28	2	no	—
1264	C₃×D₄	—	28	2	no	—
1265	C₃×D₄	—	28	2	no	—
1266	C₃×D₄	—	28	2	no	—
1267	C₃×D₄	—	28	2	no	—
1268	C₃×D₄	—	28	2	no	—
1269	C₃×D₄	—	28	2	no	—
1270	C₃×D₄	—	28	2	no	—
1271	C₃×D₄	—	56	2	no	—
1272	C₂×C₃×C₄	—	7	1	no	—
1273	C₂×C₃×C₄	—	7	4	no	—
1274	C₂×C₃×C₄	—	7	1	no	—
1275	C₂×C₃×C₄	—	7	2	no	—
1276	C₂×C₃×C₄	—	7	1	no	—
1277	C₂×C₃×C₄	—	7	1	no	—
1278	C₂×C₃×C₄	—	7	1	no	—
1279	C₂×C₃×C₄	—	14	2	no	—
1280	C₂×C₃×C₄	—	14	2	no	—
1281	C₂×C₃×C₄	—	14	4	no	—
1282	C₂×C₃×C₄	—	14	2	no	—
1283	C₂×C₃×C₄	—	14	2	no	—
1284	C₂×C₃×C₄	—	14	2	no	—
1285	C₂×C₃×C₄	—	14	4	no	—
1286	C₂×C₃×C₄	—	14	1	no	—
1287	C₂×C₃×C₄	—	14	2	no	—
1288	C₂×C₃×C₄	—	14	1	no	—
1289	C₂×C₃×C₄	—	14	1	no	—
1290	C₂×C₃×C₄	—	14	2	no	—
1291	C₂×C₃×C₄	—	14	1	no	—
1292	C₂×C₃×C₄	—	14	1	no	—
1293	C₂×C₃×C₄	—	28	2	no	—
1294	C₂×C₃×C₄	—	28	2	no	—
1295	C₂×C₃×C₄	—	28	4	no	—
1296	C₂×C₃×C₄	—	28	2	no	—
1297	C₂×C₃×C₄	—	28	2	no	—
1298	C₂×C₃×C₄	—	28	2	no	—
1299	C₂×C₃×C₄	—	56	2	no	—
1300	ΓL(1,𝔽₈)	#3484	1	1	yes	characteristic, complemented, Hall
1301	C₂⁴	—	7	2	no	—
1302	C₂⁴	—	7	1	no	—
1303	C₂⁴	—	7	2	no	—
1304	C₂⁴	—	7	2	no	—
1305	C₂⁴	—	7	2	no	—
1306	C₂⁴	—	7	2	no	—
1307	C₂⁴	—	7	2	no	—
1308	C₂⁴	—	7	2	no	—
1309	C₂⁴	—	14	8	no	—
1310	C₂⁴	—	28	4	no	—
1311	C₂⁴	—	28	4	no	—
1312	C₂⁴	C₂²×AGL(1,𝔽₇)	1	2	yes	—
1313	#41	—	2	4	no	—
1314	#41	—	14	4	no	—
1315	#41	—	14	8	no	—
1316	#41	—	14	4	no	—
1317	#41	—	14	4	no	—
1318	C₂×Q₈	—	7	1	no	—
1319	C₂×Q₈	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1320	C₂×D₄	—	2	4	no	—
1321	C₂×D₄	—	7	2	no	—
1322	C₂×D₄	—	7	8	no	—
1323	C₂×D₄	—	7	1	no	—
1324	C₂×D₄	—	7	1	no	—
1325	C₂×D₄	—	7	2	no	—
1326	C₂×D₄	—	7	1	no	—
1327	C₂×D₄	—	7	2	no	—
1328	C₂×D₄	—	7	2	no	—
1329	C₂×D₄	—	7	2	no	—
1330	C₂×D₄	—	7	2	no	—
1331	C₂×D₄	—	7	1	no	—
1332	C₂×D₄	—	7	2	no	—
1333	C₂×D₄	—	7	2	no	—
1334	C₂×D₄	—	7	2	no	—
1335	C₂×D₄	—	7	2	no	—
1336	C₂×D₄	—	7	1	no	—
1337	C₂×D₄	—	7	2	no	—
1338	C₂×D₄	—	7	1	no	—
1339	C₂×D₄	—	7	2	no	—
1340	C₂×D₄	—	7	1	no	—
1341	C₂×D₄	—	7	2	no	—
1342	C₂×D₄	—	7	2	no	—
1343	C₂×D₄	—	7	2	no	—
1344	C₂×D₄	—	7	1	no	—
1345	C₂×D₄	—	7	1	no	—
1346	C₂×D₄	—	7	2	no	—
1347	C₂×D₄	—	7	2	no	—
1348	C₂×D₄	—	7	2	no	—
1349	C₂×D₄	—	14	4	no	—
1350	C₂×D₄	—	14	4	no	—
1351	C₂×D₄	—	14	8	no	—
1352	C₂×D₄	—	14	4	no	—
1353	C₂×D₄	—	14	8	no	—
1354	C₂×D₄	—	14	4	no	—
1355	C₂×D₄	—	14	8	no	—
1356	C₂×D₄	—	14	8	no	—
1357	C₂×D₄	—	14	8	no	—
1358	C₂×D₄	—	14	8	no	—
1359	C₂×D₄	—	14	4	no	—
1360	C₂×D₄	—	14	4	no	—
1361	C₂×D₄	—	28	4	no	—
1362	C₂×D₄	—	28	4	no	—
1363	C₂×D₄	—	28	4	no	—
1364	C₂×D₄	—	28	4	no	—
1365	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1366	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
1367	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1368	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1369	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1370	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1371	C₂²×C₄	—	7	1	no	—
1372	C₂²×C₄	—	7	1	no	—
1373	C₂²×C₄	—	7	2	no	—
1374	C₂²×C₄	—	7	2	no	—
1375	C₂²×C₄	—	7	2	no	—
1376	C₂²×C₄	—	7	1	no	—
1377	C₂²×C₄	—	7	1	no	—
1378	C₂²×C₄	—	7	1	no	—
1379	C₂²×C₄	—	7	1	no	—
1380	C₂²×C₄	—	7	2	no	—
1381	C₂²×C₄	—	7	2	no	—
1382	C₂²×C₄	—	14	4	no	—
1383	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1384	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1385	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1386	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1387	C₄⋊C₄	—	7	1	no	—
1388	C₄⋊C₄	—	7	1	no	—
1389	C₄⋊C₄	—	7	1	no	—
1390	C₄⋊C₄	—	7	2	no	—
1391	C₄⋊C₄	—	7	1	no	—
1392	C₄⋊C₄	—	7	1	no	—
1393	C₄⋊C₄	—	7	1	no	—
1394	C₄⋊C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1395	C₄⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1396	C₄⋊C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1397	C₂²⋊C₄	—	7	1	no	—
1398	C₂²⋊C₄	—	7	2	no	—
1399	C₂²⋊C₄	—	7	2	no	—
1400	C₂²⋊C₄	—	7	1	no	—
1401	C₂²⋊C₄	—	7	2	no	—
1402	C₂²⋊C₄	—	7	1	no	—
1403	C₂²⋊C₄	—	7	1	no	—
1404	C₂²⋊C₄	—	7	2	no	—
1405	C₂²⋊C₄	—	7	1	no	—
1406	C₂²⋊C₄	—	7	1	no	—
1407	C₂²⋊C₄	—	7	2	no	—
1408	C₂²⋊C₄	—	7	2	no	—
1409	C₂²⋊C₄	—	7	2	no	—
1410	C₂²⋊C₄	—	7	2	no	—
1411	C₂²⋊C₄	—	7	2	no	—
1412	C₂²⋊C₄	—	7	2	no	—
1413	C₂²⋊C₄	—	7	2	no	—
1414	C₂²⋊C₄	—	7	1	no	—
1415	C₂²⋊C₄	—	7	2	no	—
1416	C₂²⋊C₄	—	7	1	no	—
1417	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
1418	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1419	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1420	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1421	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1422	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1423	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1424	C₄²	—	7	2	no	—
1425	C₄²	—	7	1	no	—
1426	C₄²	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1427	C₂×C₇	—	2	2	no	—
1428	C₂×C₇	—	2	4	no	—
1429	C₂×C₇	—	4	2	no	—
1430	C₂×C₇	—	4	1	no	—
1431	C₂×C₇	C₂³×C₃×D₄	1	1	yes	characteristic
1432	C₂×C₇	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1433	C₂×C₇	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1434	D₇	—	2	2	no	—
1435	D₇	—	2	2	no	—
1436	D₇	—	2	4	no	—
1437	D₇	—	4	2	no	—
1438	D₇	—	4	1	no	—
1439	D₇	—	4	2	no	—
1440	C₂²×C₃	—	7	2	no	—
1441	C₂²×C₃	—	7	4	no	—
1442	C₂²×C₃	—	7	2	no	—
1443	C₂²×C₃	—	14	1	no	—
1444	C₂²×C₃	—	14	2	no	—
1445	C₂²×C₃	—	14	2	no	—
1446	C₂²×C₃	—	14	1	no	—
1447	C₂²×C₃	—	14	1	no	—
1448	C₂²×C₃	—	14	1	no	—
1449	C₂²×C₃	—	14	8	no	—
1450	C₂²×C₃	—	14	2	no	—
1451	C₂²×C₃	—	14	1	no	—
1452	C₂²×C₃	—	14	2	no	—
1453	C₂²×C₃	—	14	1	no	—
1454	C₂²×C₃	—	14	2	no	—
1455	C₂²×C₃	—	14	2	no	—
1456	C₂²×C₃	—	14	1	no	—
1457	C₂²×C₃	—	14	2	no	—
1458	C₂²×C₃	—	14	2	no	—
1459	C₂²×C₃	—	14	4	no	—
1460	C₂²×C₃	—	14	2	no	—
1461	C₂²×C₃	—	14	1	no	—
1462	C₂²×C₃	—	28	1	no	—
1463	C₂²×C₃	—	28	2	no	—
1464	C₂²×C₃	—	28	2	no	—
1465	C₂²×C₃	—	28	1	no	—
1466	C₂²×C₃	—	28	1	no	—
1467	C₂²×C₃	—	28	2	no	—
1468	C₂²×C₃	—	28	1	no	—
1469	C₂²×C₃	—	28	1	no	—
1470	C₂²×C₃	—	28	2	no	—
1471	C₂²×C₃	—	28	2	no	—
1472	C₂²×C₃	—	28	8	no	—
1473	C₂²×C₃	—	28	8	no	—
1474	C₂²×C₃	—	28	8	no	—
1475	C₂²×C₃	—	28	8	no	—
1476	C₂²×C₃	—	28	8	no	—
1477	C₂²×C₃	—	56	8	no	—
1478	C₂²×C₃	—	56	4	no	—
1479	C₂²×C₃	—	56	4	no	—
1480	C₃×C₄	—	7	2	no	—
1481	C₃×C₄	—	14	1	no	—
1482	C₃×C₄	—	14	1	no	—
1483	C₃×C₄	—	14	1	no	—
1484	C₃×C₄	—	14	2	no	—
1485	C₃×C₄	—	14	1	no	—
1486	C₃×C₄	—	14	2	no	—
1487	C₃×C₄	—	28	1	no	—
1488	C₃×C₄	—	28	2	no	—
1489	C₃×C₄	—	28	1	no	—
1490	C₃×C₄	—	28	1	no	—
1491	C₃×C₄	—	28	2	no	—
1492	C₃×C₄	—	28	1	no	—
1493	C₂³	—	2	4	no	—
1494	C₂³	—	2	4	no	—
1495	C₂³	—	4	2	no	—
1496	C₂³	—	7	1	no	—
1497	C₂³	—	7	1	no	—
1498	C₂³	—	7	2	no	—
1499	C₂³	—	7	8	no	—
1500	C₂³	—	7	2	no	—
1501	C₂³	—	7	2	no	—
1502	C₂³	—	7	1	no	—
1503	C₂³	—	14	2	no	—
1504	C₂³	—	14	2	no	—
1505	C₂³	—	14	4	no	—
1506	C₂³	—	14	4	no	—
1507	C₂³	—	14	4	no	—
1508	C₂³	—	14	4	no	—
1509	C₂³	—	14	4	no	—
1510	C₂³	—	14	4	no	—
1511	C₂³	—	14	2	no	—
1512	C₂³	—	14	4	no	—
1513	C₂³	—	14	4	no	—
1514	C₂³	—	14	4	no	—
1515	C₂³	—	28	2	no	—
1516	C₂³	—	28	2	no	—
1517	C₂³	—	28	2	no	—
1518	C₂³	—	28	2	no	—
1519	C₂³	—	28	2	no	—
1520	C₂³	—	28	2	no	—
1521	C₂³	—	28	2	no	—
1522	C₂³	—	28	2	no	—
1523	C₂³	—	28	2	no	—
1524	C₂³	—	28	2	no	—
1525	C₂³	—	28	2	no	—
1526	C₂³	—	28	32	no	—
1527	C₂³	C₂³×AGL(1,𝔽₇)	1	2	yes	—
1528	C₂³	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1529	C₂³	C₂³×AGL(1,𝔽₇)	1	2	yes	—
1530	C₂³	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1531	Q₈	—	2	2	no	—
1532	Q₈	—	14	2	no	—
1533	D₄	—	2	4	no	—
1534	D₄	—	2	4	no	—
1535	D₄	—	2	2	no	—
1536	D₄	—	2	2	no	—
1537	D₄	—	4	2	no	—
1538	D₄	—	7	8	no	—
1539	D₄	—	7	4	no	—
1540	D₄	—	14	4	no	—
1541	D₄	—	14	2	no	—
1542	D₄	—	14	4	no	—
1543	D₄	—	14	4	no	—
1544	D₄	—	14	4	no	—
1545	D₄	—	14	2	no	—
1546	D₄	—	14	4	no	—
1547	D₄	—	14	4	no	—
1548	D₄	—	14	2	no	—
1549	D₄	—	14	4	no	—
1550	D₄	—	14	2	no	—
1551	D₄	—	14	2	no	—
1552	D₄	—	14	4	no	—
1553	D₄	—	14	4	no	—
1554	D₄	—	14	4	no	—
1555	D₄	—	14	2	no	—
1556	D₄	—	14	2	no	—
1557	D₄	—	14	2	no	—
1558	D₄	—	28	2	no	—
1559	D₄	—	28	2	no	—
1560	D₄	—	28	2	no	—
1561	D₄	—	28	2	no	—
1562	D₄	—	28	2	no	—
1563	D₄	—	28	2	no	—
1564	D₄	—	28	2	no	—
1565	D₄	D₄×AGL(1,𝔽₇)	1	4	yes	complemented
1566	C₂×C₄	—	2	4	no	—
1567	C₂×C₄	—	2	2	no	—
1568	C₂×C₄	—	2	2	no	—
1569	C₂×C₄	—	4	2	no	—
1570	C₂×C₄	—	7	1	no	—
1571	C₂×C₄	—	7	4	no	—
1572	C₂×C₄	—	7	2	no	—
1573	C₂×C₄	—	7	1	no	—
1574	C₂×C₄	—	7	1	no	—
1575	C₂×C₄	—	7	1	no	—
1576	C₂×C₄	—	7	1	no	—
1577	C₂×C₄	—	14	2	no	—
1578	C₂×C₄	—	14	4	no	—
1579	C₂×C₄	—	14	2	no	—
1580	C₂×C₄	—	14	4	no	—
1581	C₂×C₄	—	14	2	no	—
1582	C₂×C₄	—	14	2	no	—
1583	C₂×C₄	—	14	2	no	—
1584	C₂×C₄	—	28	2	no	—
1585	C₂×C₄	—	28	2	no	—
1586	C₂×C₄	—	28	2	no	—
1587	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	2	yes	—
1588	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1589	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1590	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	2	yes	—
1591	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1592	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1593	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1594	C₇	C₃×#3484	1	1	yes	characteristic, complemented, Sylow
1595	C₂×C₃	—	14	2	no	—
1596	C₂×C₃	—	14	2	no	—
1597	C₂×C₃	—	14	4	no	—
1598	C₂×C₃	—	14	1	no	—
1599	C₂×C₃	—	14	1	no	—
1600	C₂×C₃	—	14	1	no	—
1601	C₂×C₃	—	28	2	no	—
1602	C₂×C₃	—	28	4	no	—
1603	C₂×C₃	—	28	2	no	—
1604	C₂×C₃	—	28	2	no	—
1605	C₂×C₃	—	28	1	no	—
1606	C₂×C₃	—	56	2	no	—
1607	C₂×C₃	—	56	1	no	—
1608	C₂²	—	2	1	no	—
1609	C₂²	—	2	2	no	—
1610	C₂²	—	2	2	no	—
1611	C₂²	—	2	1	no	—
1612	C₂²	—	2	1	no	—
1613	C₂²	—	2	2	no	—
1614	C₂²	—	2	1	no	—
1615	C₂²	—	2	2	no	—
1616	C₂²	—	2	1	no	—
1617	C₂²	—	2	2	no	—
1618	C₂²	—	4	8	no	—
1619	C₂²	—	7	2	no	—
1620	C₂²	—	7	4	no	—
1621	C₂²	—	7	2	no	—
1622	C₂²	—	14	8	no	—
1623	C₂²	—	14	1	no	—
1624	C₂²	—	14	2	no	—
1625	C₂²	—	14	1	no	—
1626	C₂²	—	14	1	no	—
1627	C₂²	—	14	2	no	—
1628	C₂²	—	14	1	no	—
1629	C₂²	—	14	2	no	—
1630	C₂²	—	14	1	no	—
1631	C₂²	—	14	2	no	—
1632	C₂²	—	14	2	no	—
1633	C₂²	—	14	1	no	—
1634	C₂²	—	14	2	no	—
1635	C₂²	—	14	1	no	—
1636	C₂²	—	14	2	no	—
1637	C₂²	—	14	2	no	—
1638	C₂²	—	28	8	no	—
1639	C₂²	—	28	8	no	—
1640	C₂²	—	28	8	no	—
1641	C₂²	—	28	8	no	—
1642	C₂²	—	28	8	no	—
1643	C₂²	—	56	4	no	—
1644	C₂²	—	56	4	no	—
1645	C₂²	C₂×D₄×AGL(1,𝔽₇)	1	4	yes	—
1646	C₂²	#10621518	1	2	yes	complemented
1647	C₂²	C₂⁴×AGL(1,𝔽₇)	1	1	yes	characteristic
1648	C₄	—	2	1	no	—
1649	C₄	—	2	1	no	—
1650	C₄	—	2	2	no	—
1651	C₄	—	2	1	no	—
1652	C₄	—	2	1	no	—
1653	C₄	—	2	2	no	—
1654	C₄	—	7	2	no	—
1655	C₄	—	14	1	no	—
1656	C₄	—	14	1	no	—
1657	C₄	—	14	2	no	—
1658	C₄	—	14	1	no	—
1659	C₄	—	14	1	no	—
1660	C₄	C₂×D₄×AGL(1,𝔽₇)	1	2	yes	—
1661	C₃	—	14	1	no	Sylow
1662	C₂	—	2	2	no	—
1663	C₂	—	2	4	no	—
1664	C₂	—	4	2	no	—
1665	C₂	—	4	1	no	—
1666	C₂	—	14	2	no	—
1667	C₂	—	14	2	no	—
1668	C₂	—	14	4	no	—
1669	C₂	—	28	2	no	—
1670	C₂	—	28	1	no	—
1671	C₂	—	28	2	no	—
1672	C₂	C₂²×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
1673	C₂	C₂×#10621518	1	1	yes	characteristic
1674	C₂	H(5,𝔽₂)×AGL(1,𝔽₇)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₇	C₂⁵×C₃
Fitting	C₇×#546	C₂×C₃
hypercenter	#546	AGL(1,𝔽₇)
hypocenter	C₇	C₃×#3484
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#10621518	C₂	semidirect
2. C₂²×D₄×AGL(1,𝔽₇)	C₂	semidirect
3. ΓL(1,𝔽₈)×#546	C₂	semidirect
4. #90520⋊C₃	C₂	semidirect
5. D₄×(C₂²⋊D₇)⋊C₃	C₂	semidirect
6. #90367⋊C₃	C₂	semidirect
7. #90365⋊C₃	C₂	semidirect
8. #90345⋊C₃	C₂	semidirect
9. #90344⋊C₃	C₂	semidirect
10. #90321⋊C₃	C₂	semidirect
11. #90318⋊C₃	C₂	semidirect
12. #90300⋊C₃	C₂	semidirect
13. #90300⋊C₃	C₂	semidirect
14. #90298⋊C₃	C₂	semidirect
15. #90296⋊C₃	C₂	semidirect
16. #90281⋊C₃	C₂	semidirect
17. #120×AGL(1,𝔽₇)	C₂	semidirect
18. D₄×C₄⋊AGL(1,𝔽₇)	C₂	semidirect
19. D₄×C₄⋊AGL(1,𝔽₇)	C₂	semidirect
20. #90238⋊C₃	C₂	semidirect
21. #90236⋊C₃	C₂	semidirect
22. #90181⋊C₃	C₂	semidirect
23. C₂×#6445⋊C₃	C₂	semidirect
24. #11743730	C₃	semidirect
25. C₂⁴×AGL(1,𝔽₇)	C₂²	semidirect
26. C₂×#41×ΓL(1,𝔽₈)	C₂²	semidirect
27. C₂²×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
28. C₂²×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
29. C₂²×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
31. C₂×#66659	C₂²	semidirect
32. C₂×#66659	C₂²	semidirect
35. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
36. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
37. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
38. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
39. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
40. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
41. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
42. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
43. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
44. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
45. C₂×#1157⋊C₃	C₂²	semidirect
46. C₂×#1157⋊C₃	C₂²	semidirect
47. C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
48. C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
49. C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
50. C₂²×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
51. C₂²×C₄×AGL(1,𝔽₇)	C₂²	semidirect
52. ΓL(1,𝔽₈)×#124	C₂²	semidirect
53. ΓL(1,𝔽₈)×#123	C₂²	semidirect
54. ΓL(1,𝔽₈)×C₂²⋊Q₈	C₂²	semidirect
55. ΓL(1,𝔽₈)×#121	C₂²	semidirect
56. ΓL(1,𝔽₈)×#121	C₂²	semidirect
57. ΓL(1,𝔽₈)×#120	C₂²	semidirect
58. C₄×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
59. C₄×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
60. C₂×C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
61. #10620789	C₂²	semidirect
62. #6510⋊C₃	C₂²	semidirect
63. #6509⋊C₃	C₂²	semidirect
64. #6503⋊C₃	C₂²	semidirect
65. #6503⋊C₃	C₂²	semidirect
66. #6502⋊C₃	C₂²	semidirect
67. #6502⋊C₃	C₂²	semidirect
68. #6502⋊C₃	C₂²	semidirect
69. #6501⋊C₃	C₂²	semidirect
70. #6500⋊C₃	C₂²	semidirect
71. #6500⋊C₃	C₂²	semidirect
72. #6500⋊C₃	C₂²	semidirect
73. #6500⋊C₃	C₂²	semidirect
74. #6500⋊C₃	C₂²	semidirect
75. D₄×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
76. #6493⋊C₃	C₂²	semidirect
77. #6493⋊C₃	C₂²	semidirect
78. #6493⋊C₃	C₂²	semidirect
79. #6492⋊C₃	C₂²	semidirect
80. C₄×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
81. C₄×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
82. C₄×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
83. C₂×(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	semidirect
84. C₂×(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	semidirect
85. #6459⋊C₃	C₂²	semidirect
86. #6458⋊C₃	C₂²	semidirect
87. #6458⋊C₃	C₂²	semidirect
88. #6458⋊C₃	C₂²	semidirect
89. #6458⋊C₃	C₂²	semidirect
90. #6457⋊C₃	C₂²	semidirect
91. #6457⋊C₃	C₂²	semidirect
92. #6457⋊C₃	C₂²	semidirect
93. #6456⋊C₃	C₂²	semidirect
94. #6456⋊C₃	C₂²	semidirect
95. #6455⋊C₃	C₂²	semidirect
96. #6448⋊C₃	C₂²	semidirect
97. #6447⋊C₃	C₂²	semidirect
98. #6447⋊C₃	C₂²	semidirect
99. #6447⋊C₃	C₂²	semidirect
100. #6447⋊C₃	C₂²	semidirect
101. #6447⋊C₃	C₂²	semidirect
102. #6446⋊C₃	C₂²	semidirect
103. #6446⋊C₃	C₂²	semidirect
104. #6445⋊C₃	C₂²	semidirect
105. #6445⋊C₃	C₂²	semidirect
106. #6445⋊C₃	C₂²	semidirect
107. #6445⋊C₃	C₂²	semidirect
108. #6445⋊C₃	C₂²	semidirect
109. #6445⋊C₃	C₂²	semidirect
110. #6445⋊C₃	C₂²	semidirect
111. #6445⋊C₃	C₂²	semidirect
112. #6445⋊C₃	C₂²	semidirect
113. #6445⋊C₃	C₂²	semidirect
114. #6445⋊C₃	C₂²	semidirect
115. #6445⋊C₃	C₂²	semidirect
116. ((C₂²⋊D₇)⋊C₃)⋊C₄	C₂²	semidirect
117. ((C₂²⋊D₇)⋊C₃)⋊C₄	C₂²	semidirect
118. C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	semidirect
119. C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	semidirect
120. C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	semidirect
121. #6441⋊C₃	C₂²	semidirect
122. #10620710	C₂²	semidirect
123. C₄×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
124. C₄×C₄⋊AGL(1,𝔽₇)	C₂²	semidirect
125. #6435⋊C₃	C₂²	semidirect
126. C₂×#6553	C₂×C₃	semidirect
127. C₂²×D₄×D₇	C₂×C₃	semidirect
128. C₇×#546	C₂×C₃	semidirect
129. #90520	C₂×C₃	semidirect
130. D₄×C₂²⋊D₇	C₂×C₃	semidirect
131. #90367	C₂×C₃	semidirect
132. #90365	C₂×C₃	semidirect
133. #90345	C₂×C₃	semidirect
134. #90344	C₂×C₃	semidirect
135. #90321	C₂×C₃	semidirect
136. #90318	C₂×C₃	semidirect
137. #90300	C₂×C₃	semidirect
138. #90300	C₂×C₃	semidirect
139. #90298	C₂×C₃	semidirect
140. #90296	C₂×C₃	semidirect
141. #90281	C₂×C₃	semidirect
142. D₇×#120	C₂×C₃	semidirect
143. D₄×D₂₈	C₂×C₃	semidirect
144. D₄×D₂₈	C₂×C₃	semidirect
145. #90238	C₂×C₃	semidirect
146. #90236	C₂×C₃	semidirect
147. #90181	C₂×C₃	semidirect
148. C₂×#6445	C₂×C₃	semidirect
160. C₂³×AGL(1,𝔽₇)	C₂³	semidirect
161. C₂³×AGL(1,𝔽₇)	C₂³	semidirect
163. C₂×Q₈×ΓL(1,𝔽₈)	C₂³	semidirect
169. C₂×D₄×ΓL(1,𝔽₈)	C₂³	semidirect
170. C₂×D₄×ΓL(1,𝔽₈)	C₂³	semidirect
172. C₂²×C₄×ΓL(1,𝔽₈)	C₂³	semidirect
173. C₂²×C₄×ΓL(1,𝔽₈)	C₂³	semidirect
174. C₂²×C₄×ΓL(1,𝔽₈)	C₂³	semidirect
185. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
186. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
187. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
188. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
189. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
190. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
192. C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
205. D₄×AGL(1,𝔽₇)	D₄	semidirect
219. C₂×C₄⋊AGL(1,𝔽₇)	C₂³	semidirect
220. C₂×C₄⋊AGL(1,𝔽₇)	C₂³	semidirect
221. C₂×C₄⋊AGL(1,𝔽₇)	C₂³	semidirect
222. C₂×C₄⋊AGL(1,𝔽₇)	C₂³	semidirect
223. C₂×C₄⋊AGL(1,𝔽₇)	C₂³	semidirect
224. C₂×C₄⋊AGL(1,𝔽₇)	C₂³	semidirect
230. C₂×C₄×AGL(1,𝔽₇)	C₂³	semidirect
231. C₂×C₄×AGL(1,𝔽₇)	C₂³	semidirect
232. C₂×C₄×AGL(1,𝔽₇)	C₂³	semidirect
233. C₂×C₄×AGL(1,𝔽₇)	C₂³	semidirect
234. C₂×C₄×AGL(1,𝔽₇)	C₂³	semidirect
235. C₂×ΓL(1,𝔽₈)⋊Q₈	C₂³	semidirect
236. C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
237. C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
238. C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
241. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
242. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
243. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
244. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
245. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
246. C₄²×ΓL(1,𝔽₈)	C₂³	semidirect
248. (C₂²⋊Dic₇)⋊C₃	C₂³	semidirect
249. (C₂²⋊Dic₇)⋊C₃	C₂³	semidirect
250. (C₂²⋊Dic₇)⋊C₃	C₂³	semidirect
257. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
258. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
259. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
260. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
261. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
262. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
263. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
264. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
265. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
266. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
267. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	semidirect
268. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	semidirect
269. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	semidirect
270. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	semidirect
271. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	semidirect
272. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	semidirect
273. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	semidirect
274. C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
275. C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
276. C₂⁴×D₇	C₂²×C₃	semidirect
277. C₂×C₇×#41	C₂²×C₃	semidirect
278. C₂²×C₇×D₄	C₂²×C₃	semidirect
279. C₂²×C₂²⋊D₇	C₂²×C₃	semidirect
280. C₂²×C₂²⋊D₇	C₂²×C₃	semidirect
282. C₂×#1161	C₂²×C₃	semidirect
283. C₂×#1161	C₂²×C₃	semidirect
286. C₂×D₄×D₇	C₂²×C₃	semidirect
287. C₂×D₄×D₇	C₂²×C₃	semidirect
288. C₂×D₄×D₇	C₂²×C₃	semidirect
289. C₂×D₄×D₇	C₂²×C₃	semidirect
290. C₂×D₄×D₇	C₂²×C₃	semidirect
291. C₂×D₄×D₇	C₂²×C₃	semidirect
292. C₂×D₄×D₇	C₂²×C₃	semidirect
293. C₂×D₄×D₇	C₂²×C₃	semidirect
294. C₂×D₄×D₇	C₂²×C₃	semidirect
295. C₂×D₄×D₇	C₂²×C₃	semidirect
296. C₂×#1157	C₂²×C₃	semidirect
297. C₂×#1157	C₂²×C₃	semidirect
298. C₂²×D₂₈	C₂²×C₃	semidirect
299. C₂²×D₂₈	C₂²×C₃	semidirect
300. C₂²×D₂₈	C₂²×C₃	semidirect
301. C₂²×D₂₈	C₂²×C₃	semidirect
302. C₂²×C₄×D₇	C₂²×C₃	semidirect
303. C₇×#124	C₂²×C₃	semidirect
304. C₇×#123	C₂²×C₃	semidirect
305. C₇×C₂²⋊Q₈	C₂²×C₃	semidirect
306. C₇×#121	C₂²×C₃	semidirect
307. C₇×#121	C₂²×C₃	semidirect
308. C₇×#120	C₂²×C₃	semidirect
309. C₄×C₇×D₄	C₂²×C₃	semidirect
310. C₄×C₇×D₄	C₂²×C₃	semidirect
311. C₂×C₇×C₂²⋊C₄	C₂²×C₃	semidirect
312. #6516	C₂²×C₃	semidirect
313. #6510	C₂²×C₃	semidirect
314. #6509	C₂²×C₃	semidirect
315. #6503	C₂²×C₃	semidirect
316. #6503	C₂²×C₃	semidirect
317. #6502	C₂²×C₃	semidirect
318. #6502	C₂²×C₃	semidirect
319. #6502	C₂²×C₃	semidirect
320. #6501	C₂²×C₃	semidirect
321. #6500	C₂²×C₃	semidirect
322. #6500	C₂²×C₃	semidirect
323. #6500	C₂²×C₃	semidirect
324. #6500	C₂²×C₃	semidirect
325. #6500	C₂²×C₃	semidirect
326. D₄×Dic₇	C₂²×C₃	semidirect
327. #6493	C₂²×C₃	semidirect
328. #6493	C₂²×C₃	semidirect
329. #6493	C₂²×C₃	semidirect
330. #6492	C₂²×C₃	semidirect
331. C₄×C₂²⋊D₇	C₂²×C₃	semidirect
332. C₄×C₂²⋊D₇	C₂²×C₃	semidirect
333. C₄×C₂²⋊D₇	C₂²×C₃	semidirect
334. C₂×(C₂×D₇)⋊C₄	C₂²×C₃	semidirect
335. C₂×(C₂×D₇)⋊C₄	C₂²×C₃	semidirect
336. #6459	C₂²×C₃	semidirect
337. #6458	C₂²×C₃	semidirect
338. #6458	C₂²×C₃	semidirect
339. #6458	C₂²×C₃	semidirect
340. #6458	C₂²×C₃	semidirect
341. #6457	C₂²×C₃	semidirect
342. #6457	C₂²×C₃	semidirect
343. #6457	C₂²×C₃	semidirect
344. #6456	C₂²×C₃	semidirect
345. #6456	C₂²×C₃	semidirect
346. #6455	C₂²×C₃	semidirect
347. #6448	C₂²×C₃	semidirect
348. #6447	C₂²×C₃	semidirect
349. #6447	C₂²×C₃	semidirect
350. #6447	C₂²×C₃	semidirect
351. #6447	C₂²×C₃	semidirect
352. #6447	C₂²×C₃	semidirect
353. #6446	C₂²×C₃	semidirect
354. #6446	C₂²×C₃	semidirect
355. #6445	C₂²×C₃	semidirect
356. #6445	C₂²×C₃	semidirect
357. #6445	C₂²×C₃	semidirect
358. #6445	C₂²×C₃	semidirect
359. #6445	C₂²×C₃	semidirect
360. #6445	C₂²×C₃	semidirect
361. #6445	C₂²×C₃	semidirect
362. #6445	C₂²×C₃	semidirect
363. #6445	C₂²×C₃	semidirect
364. #6445	C₂²×C₃	semidirect
365. #6445	C₂²×C₃	semidirect
366. #6445	C₂²×C₃	semidirect
367. (C₂²⋊D₇)⋊C₄	C₂²×C₃	semidirect
368. (C₂²⋊D₇)⋊C₄	C₂²×C₃	semidirect
369. D₇×C₂²⋊C₄	C₂²×C₃	semidirect
370. D₇×C₂²⋊C₄	C₂²×C₃	semidirect
371. D₇×C₂²⋊C₄	C₂²×C₃	semidirect
372. #6441	C₂²×C₃	semidirect
373. #6437	C₂²×C₃	semidirect
374. C₄×D₂₈	C₂²×C₃	semidirect
375. C₄×D₂₈	C₂²×C₃	semidirect
376. #6435	C₂²×C₃	semidirect
431. C₂²×AGL(1,𝔽₇)	C₂×D₄	semidirect
444. D₄×ΓL(1,𝔽₈)	C₂×D₄	semidirect
469. (C₂²⋊D₇)⋊C₃	C₂×D₄	semidirect
490. C₄⋊AGL(1,𝔽₇)	C₂×D₄	semidirect
499. C₄×AGL(1,𝔽₇)	C₂×D₄	semidirect
512. C₂³×D₇	C₂³×C₃	semidirect
513. C₂³×D₇	C₂³×C₃	semidirect
515. C₂×C₇×Q₈	C₂³×C₃	semidirect
521. C₂×C₇×D₄	C₂³×C₃	semidirect
522. C₂×C₇×D₄	C₂³×C₃	semidirect
524. C₂²×C₄×C₇	C₂³×C₃	semidirect
525. C₂²×C₄×C₇	C₂³×C₃	semidirect
526. C₂²×C₄×C₇	C₂³×C₃	semidirect
537. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
538. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
539. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
540. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
541. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
542. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
544. C₂²×Dic₇	C₂³×C₃	semidirect
557. D₄×D₇	C₃×D₄	semidirect
571. C₂×D₂₈	C₂³×C₃	semidirect
572. C₂×D₂₈	C₂³×C₃	semidirect
573. C₂×D₂₈	C₂³×C₃	semidirect
574. C₂×D₂₈	C₂³×C₃	semidirect
575. C₂×D₂₈	C₂³×C₃	semidirect
576. C₂×D₂₈	C₂³×C₃	semidirect
582. C₂×C₄×D₇	C₂³×C₃	semidirect
583. C₂×C₄×D₇	C₂³×C₃	semidirect
584. C₂×C₄×D₇	C₂³×C₃	semidirect
585. C₂×C₄×D₇	C₂³×C₃	semidirect
586. C₂×C₄×D₇	C₂³×C₃	semidirect
587. C₂×Dic₁₄	C₂³×C₃	semidirect
588. C₇×C₄⋊C₄	C₂³×C₃	semidirect
589. C₇×C₄⋊C₄	C₂³×C₃	semidirect
590. C₇×C₄⋊C₄	C₂³×C₃	semidirect
593. C₇×C₂²⋊C₄	C₂³×C₃	semidirect
594. C₇×C₂²⋊C₄	C₂³×C₃	semidirect
595. C₇×C₂²⋊C₄	C₂³×C₃	semidirect
596. C₇×C₂²⋊C₄	C₂³×C₃	semidirect
597. C₇×C₂²⋊C₄	C₂³×C₃	semidirect
598. C₄²×C₇	C₂³×C₃	semidirect
600. C₂²⋊Dic₇	C₂³×C₃	semidirect
601. C₂²⋊Dic₇	C₂³×C₃	semidirect
602. C₂²⋊Dic₇	C₂³×C₃	semidirect
609. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
610. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
611. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
612. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
613. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
614. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
615. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
616. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
617. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
618. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
619. C₄⋊Dic₇	C₂³×C₃	semidirect
620. C₄⋊Dic₇	C₂³×C₃	semidirect
621. Dic₇⋊C₄	C₂³×C₃	semidirect
622. Dic₇⋊C₄	C₂³×C₃	semidirect
623. Dic₇⋊C₄	C₂³×C₃	semidirect
624. Dic₇⋊C₄	C₂³×C₃	semidirect
625. Dic₇⋊C₄	C₂³×C₃	semidirect
626. C₄×Dic₇	C₂³×C₃	semidirect
627. C₄×Dic₇	C₂³×C₃	semidirect
741. C₂²×ΓL(1,𝔽₈)	H(5,𝔽₂)	semidirect
768. C₂×AGL(1,𝔽₇)	H(5,𝔽₂)	semidirect
789. #546	AGL(1,𝔽₇)	semidirect
836. C₂²×D₇	C₂×C₃×D₄	semidirect
849. C₇×D₄	C₂×C₃×D₄	semidirect
874. C₂²⋊D₇	C₂×C₃×D₄	semidirect
895. D₂₈	C₂×C₃×D₄	semidirect
904. C₄×D₇	C₂×C₃×D₄	semidirect
1051. C₂×#41	C₂×AGL(1,𝔽₇)	semidirect
1070. C₂²×D₄	C₂×AGL(1,𝔽₇)	semidirect
1077. #124	C₂×AGL(1,𝔽₇)	semidirect
1084. #123	C₂×AGL(1,𝔽₇)	semidirect
1088. C₂²⋊Q₈	C₂×AGL(1,𝔽₇)	semidirect
1105. #121	C₂×AGL(1,𝔽₇)	semidirect
1106. #121	C₂×AGL(1,𝔽₇)	semidirect
1125. #120	C₂×AGL(1,𝔽₇)	semidirect
1136. C₄×D₄	C₂×AGL(1,𝔽₇)	semidirect
1137. C₄×D₄	C₂×AGL(1,𝔽₇)	semidirect
1145. C₂×C₂²⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
1158. C₂²×C₇	C₃×H(5,𝔽₂)	semidirect
1185. C₂×D₇	C₃×H(5,𝔽₂)	semidirect
1300. ΓL(1,𝔽₈)	#3484	semidirect
1319. C₂×Q₈	C₂²×AGL(1,𝔽₇)	semidirect
1369. C₂×D₄	C₂²×AGL(1,𝔽₇)	semidirect
1370. C₂×D₄	C₂²×AGL(1,𝔽₇)	semidirect
1384. C₂²×C₄	C₂²×AGL(1,𝔽₇)	semidirect
1385. C₂²×C₄	C₂²×AGL(1,𝔽₇)	semidirect
1386. C₂²×C₄	C₂²×AGL(1,𝔽₇)	semidirect
1394. C₄⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1395. C₄⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1396. C₄⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1419. C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1420. C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1421. C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1422. C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1423. C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1426. C₄²	C₂²×AGL(1,𝔽₇)	semidirect
1565. D₄	D₄×AGL(1,𝔽₇)	semidirect
1594. C₇	C₃×#3484	semidirect
1646. C₂²	#10621518	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10621518	2
C₂²×D₄×AGL(1,𝔽₇)	2
ΓL(1,𝔽₈)×#546	2
#90520⋊C₃	2
D₄×(C₂²⋊D₇)⋊C₃	2
#90367⋊C₃	2
#90365⋊C₃	2
#90345⋊C₃	2
#90344⋊C₃	2
#90321⋊C₃	2
#90318⋊C₃	2
#90300⋊C₃	2
#90298⋊C₃	2
#90296⋊C₃	2
#90281⋊C₃	2
#120×AGL(1,𝔽₇)	2
D₄×C₄⋊AGL(1,𝔽₇)	2
#90238⋊C₃	2
#90236⋊C₃	2
#90181⋊C₃	2
C₂×#6445⋊C₃	2
#11743730	3
C₃×#3484	7