Subgroups — #72276718

Order 2688.

2672 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)×#534	C₂	1	1	yes	maximal, characteristic, complemented
2	#90496⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×(C₂²⋊D₇)⋊C₃	C₂	1	2	yes	maximal, complemented
4	C₂×#6500⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#90357⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#90350⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#90349⋊C₃	C₂	1	2	yes	maximal, complemented
8	#90348⋊C₃	C₂	1	2	yes	maximal, complemented
9	#90345⋊C₃	C₂	1	2	yes	maximal, complemented
10	#90311⋊C₃	C₂	1	2	yes	maximal, complemented
11	#90304⋊C₃	C₂	1	2	yes	maximal, complemented
12	#90303⋊C₃	C₂	1	2	yes	maximal, complemented
13	#90298⋊C₃	C₂	1	2	yes	maximal, complemented
14	#13057328	C₂	1	1	yes	maximal, characteristic, complemented
15	#90284⋊C₃	C₂	1	2	yes	maximal, complemented
16	#90281⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#90280⋊C₃	C₂	1	2	yes	maximal, complemented
18	#120×AGL(1,𝔽₇)	C₂	1	2	yes	maximal, complemented
19	#90181⋊C₃	C₂	1	2	yes	maximal, complemented
20	#11743378	C₃	1	1	yes	maximal, characteristic, complemented, Hall
21	C₂⁴×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
23	C₂²×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
24	C₂²×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	complemented
25	C₂²×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	complemented
26	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
27	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
28	C₂×D₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
29	C₂×#1157⋊C₃	C₂²	1	2	yes	complemented
30	C₂×#1157⋊C₃	C₂²	1	1	yes	characteristic, complemented
31	ΓL(1,𝔽₈)×#123	C₂²	1	1	yes	characteristic, complemented
32	ΓL(1,𝔽₈)×#123	C₂²	1	1	yes	characteristic, complemented
33	ΓL(1,𝔽₈)×#123	C₂²	1	2	yes	complemented
34	ΓL(1,𝔽₈)×#121	C₂²	1	2	yes	complemented
35	ΓL(1,𝔽₈)×#121	C₂²	1	2	yes	complemented
36	ΓL(1,𝔽₈)×#120	C₂²	1	2	yes	complemented
37	ΓL(1,𝔽₈)×#120	C₂²	1	1	yes	characteristic, complemented
38	ΓL(1,𝔽₈)×#120	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
40	#10620789	C₂²	1	2	yes	complemented
41	#10620789	C₂²	1	2	yes	complemented
42	#10620789	C₂²	1	2	yes	complemented
43	C₂×(C₂²⋊Dic₇)⋊C₃	C₂²	1	1	yes	characteristic, complemented
44	#6503⋊C₃	C₂²	1	2	yes	complemented
45	#6503⋊C₃	C₂²	1	1	yes	characteristic, complemented
46	#6503⋊C₃	C₂²	1	1	yes	characteristic, complemented
47	#6502⋊C₃	C₂²	1	2	yes	complemented
48	#6502⋊C₃	C₂²	1	2	yes	complemented
49	#6502⋊C₃	C₂²	1	2	yes	complemented
50	#6501⋊C₃	C₂²	1	2	yes	complemented
51	#6501⋊C₃	C₂²	1	2	yes	complemented
52	#6501⋊C₃	C₂²	1	2	yes	complemented
53	#6501⋊C₃	C₂²	1	2	yes	complemented
54	#6500⋊C₃	C₂²	1	2	yes	—
55	#6500⋊C₃	C₂²	1	1	yes	characteristic
56	#6500⋊C₃	C₂²	1	2	yes	complemented
57	#6500⋊C₃	C₂²	1	2	yes	complemented
58	#6500⋊C₃	C₂²	1	2	yes	complemented
59	#6500⋊C₃	C₂²	1	1	yes	characteristic, complemented
60	#6500⋊C₃	C₂²	1	2	yes	complemented
61	#6500⋊C₃	C₂²	1	1	yes	characteristic, complemented
62	#6500⋊C₃	C₂²	1	1	yes	characteristic, complemented
63	#6500⋊C₃	C₂²	1	2	yes	complemented
64	#6499⋊C₃	C₂²	1	1	yes	characteristic, complemented
65	#6499⋊C₃	C₂²	1	1	yes	characteristic, complemented
66	#6499⋊C₃	C₂²	1	2	yes	complemented
67	#6498⋊C₃	C₂²	1	2	yes	complemented
68	D₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	2	yes	complemented
69	#6493⋊C₃	C₂²	1	2	yes	complemented
70	#6493⋊C₃	C₂²	1	2	yes	complemented
71	#6492⋊C₃	C₂²	1	2	yes	complemented
72	C₄×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	complemented
73	C₄×(C₂²⋊D₇)⋊C₃	C₂²	1	2	yes	complemented
74	C₂×(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	2	yes	complemented
75	#6489⋊C₃	C₂²	1	1	yes	characteristic, complemented
76	#6461⋊C₃	C₂²	1	2	yes	complemented
77	#6461⋊C₃	C₂²	1	2	yes	complemented
78	#6460⋊C₃	C₂²	1	2	yes	complemented
79	#6459⋊C₃	C₂²	1	2	yes	complemented
80	#6458⋊C₃	C₂²	1	2	yes	complemented
81	#6457⋊C₃	C₂²	1	2	yes	complemented
82	#6456⋊C₃	C₂²	1	2	yes	complemented
83	#6455⋊C₃	C₂²	1	2	yes	complemented
84	#6449⋊C₃	C₂²	1	2	yes	complemented
85	#6448⋊C₃	C₂²	1	2	yes	complemented
86	#6448⋊C₃	C₂²	1	2	yes	complemented
87	#6448⋊C₃	C₂²	1	2	yes	complemented
88	#6448⋊C₃	C₂²	1	2	yes	complemented
89	#6447⋊C₃	C₂²	1	2	yes	complemented
90	#6447⋊C₃	C₂²	1	2	yes	complemented
91	#6447⋊C₃	C₂²	1	2	yes	complemented
92	#6446⋊C₃	C₂²	1	2	yes	complemented
93	#6446⋊C₃	C₂²	1	2	yes	complemented
94	#6446⋊C₃	C₂²	1	2	yes	complemented
95	#6445⋊C₃	C₂²	1	2	yes	complemented
96	#6445⋊C₃	C₂²	1	2	yes	complemented
97	#6445⋊C₃	C₂²	1	2	yes	complemented
98	#6445⋊C₃	C₂²	1	2	yes	complemented
99	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂²	1	2	yes	complemented
100	((C₂²⋊D₇)⋊C₃)⋊C₄	C₂²	1	2	yes	complemented
101	C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
102	C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
104	C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	1	2	yes	complemented
105	#6442⋊C₃	C₂²	1	2	yes	complemented
106	#6442⋊C₃	C₂²	1	2	yes	complemented
107	#6441⋊C₃	C₂²	1	2	yes	complemented
108	C₇×#534	C₂×C₃	1	1	yes	characteristic, complemented
109	#90496	C₂×C₃	1	1	yes	characteristic, complemented
110	D₄×C₂²⋊D₇	C₂×C₃	1	2	yes	complemented
111	C₂×#6500	C₂×C₃	1	1	yes	characteristic, complemented
112	#90357	C₂×C₃	1	1	yes	characteristic, complemented
113	#90350	C₂×C₃	1	1	yes	characteristic, complemented
114	#90349	C₂×C₃	1	2	yes	complemented
115	#90348	C₂×C₃	1	2	yes	complemented
116	#90345	C₂×C₃	1	2	yes	complemented
117	#90311	C₂×C₃	1	2	yes	complemented
118	#90304	C₂×C₃	1	2	yes	complemented
119	#90303	C₂×C₃	1	2	yes	complemented
120	#90298	C₂×C₃	1	2	yes	complemented
121	#90285	C₂×C₃	1	1	yes	characteristic, complemented
122	#90284	C₂×C₃	1	2	yes	complemented
123	#90281	C₂×C₃	1	1	yes	characteristic, complemented
124	#90280	C₂×C₃	1	2	yes	complemented
125	D₇×#120	C₂×C₃	1	2	yes	complemented
126	#90181	C₂×C₃	1	2	yes	complemented
127	C₃×#3532	—	7	1	no	maximal, Hall
128	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
129	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
130	C₂⁴×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
131	C₂³×AGL(1,𝔽₇)	—	4	4	no	—
132	C₂³×AGL(1,𝔽₇)	—	4	2	no	—
133	C₂³×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
134	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	—
135	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	—
136	C₂³×AGL(1,𝔽₇)	C₂³	1	2	yes	—
137	C₂³×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
138	C₂×D₄×ΓL(1,𝔽₈)	—	4	2	no	—
139	C₂×D₄×ΓL(1,𝔽₈)	—	4	2	no	—
140	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
141	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
142	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
143	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
144	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
145	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
146	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
147	C₂×D₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
148	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
149	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
150	C₂²×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
151	C₂×(C₂²⋊D₇)⋊C₃	—	4	4	no	—
152	C₂×(C₂²⋊D₇)⋊C₃	—	4	4	no	—
153	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
154	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
155	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
156	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
157	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
158	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
159	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
160	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
161	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
162	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	—
163	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	complemented
164	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	complemented
165	C₂×(C₂²⋊D₇)⋊C₃	C₂³	1	2	yes	complemented
166	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	—
167	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	complemented
168	D₄×AGL(1,𝔽₇)	—	4	4	no	—
169	D₄×AGL(1,𝔽₇)	—	4	4	no	—
170	D₄×AGL(1,𝔽₇)	—	4	4	no	—
171	#1157⋊C₃	—	4	4	no	—
172	#1157⋊C₃	—	4	2	no	—
173	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	—
174	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	—
175	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	2	yes	—
176	C₂×C₄⋊AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic, complemented
177	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	—
178	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	—
179	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	—
180	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
181	C₂×C₄×AGL(1,𝔽₇)	C₂³	1	2	yes	complemented
182	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂³	1	2	yes	complemented
183	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂³	1	1	yes	characteristic, complemented
184	C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
185	C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
186	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
187	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
188	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	—
189	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
190	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	2	yes	complemented
191	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
192	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic, complemented
193	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	—
194	(C₂²⋊Dic₇)⋊C₃	C₂³	1	1	yes	characteristic
195	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	—
196	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	—
197	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	—
198	(C₂²⋊Dic₇)⋊C₃	C₂³	1	1	yes	characteristic
199	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	complemented
200	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	complemented
201	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	complemented
202	(C₂²⋊Dic₇)⋊C₃	C₂³	1	2	yes	complemented
203	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
204	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
205	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
206	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
207	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
208	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
209	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
210	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
211	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
212	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	—
213	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
214	(C₂×AGL(1,𝔽₇))⋊C₄	C₂³	1	2	yes	complemented
215	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	1	2	yes	complemented
216	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	1	2	yes	complemented
217	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	1	2	yes	complemented
218	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	1	2	yes	complemented
219	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	1	2	yes	complemented
220	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	1	2	yes	complemented
221	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	1	2	yes	complemented
222	C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	complemented
223	C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	1	2	yes	complemented
224	C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic, complemented
225	C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic, complemented
226	C₂⁴×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
227	C₂²×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
228	C₂²×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
229	C₂²×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
230	C₂²×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
231	C₂×D₄×D₇	C₂²×C₃	1	2	yes	complemented
232	C₂×D₄×D₇	C₂²×C₃	1	2	yes	complemented
233	C₂×D₄×D₇	C₂²×C₃	1	2	yes	complemented
234	C₂×#1157	C₂²×C₃	1	2	yes	complemented
235	C₂×#1157	C₂²×C₃	1	1	yes	characteristic, complemented
236	C₇×#123	C₂²×C₃	1	1	yes	characteristic, complemented
237	C₇×#123	C₂²×C₃	1	1	yes	characteristic, complemented
238	C₇×#123	C₂²×C₃	1	2	yes	complemented
239	C₇×#121	C₂²×C₃	1	2	yes	complemented
240	C₇×#121	C₂²×C₃	1	2	yes	complemented
241	C₇×#120	C₂²×C₃	1	2	yes	complemented
242	C₇×#120	C₂²×C₃	1	1	yes	characteristic, complemented
243	C₇×#120	C₂²×C₃	1	1	yes	characteristic, complemented
244	C₂×C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
245	#6516	C₂²×C₃	1	2	yes	complemented
246	#6516	C₂²×C₃	1	2	yes	complemented
247	#6516	C₂²×C₃	1	2	yes	complemented
248	C₂×C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
249	#6503	C₂²×C₃	1	2	yes	complemented
250	#6503	C₂²×C₃	1	1	yes	characteristic, complemented
251	#6503	C₂²×C₃	1	1	yes	characteristic, complemented
252	#6502	C₂²×C₃	1	2	yes	complemented
253	#6502	C₂²×C₃	1	2	yes	complemented
254	#6502	C₂²×C₃	1	2	yes	complemented
255	#6501	C₂²×C₃	1	2	yes	complemented
256	#6501	C₂²×C₃	1	2	yes	complemented
257	#6501	C₂²×C₃	1	2	yes	complemented
258	#6501	C₂²×C₃	1	2	yes	complemented
259	#6500	C₂²×C₃	1	1	yes	characteristic
260	#6500	C₂²×C₃	1	2	yes	—
261	#6500	C₂²×C₃	1	2	yes	complemented
262	#6500	C₂²×C₃	1	1	yes	characteristic, complemented
263	#6500	C₂²×C₃	1	2	yes	complemented
264	#6500	C₂²×C₃	1	1	yes	characteristic, complemented
265	#6500	C₂²×C₃	1	1	yes	characteristic, complemented
266	#6500	C₂²×C₃	1	2	yes	complemented
267	#6500	C₂²×C₃	1	2	yes	complemented
268	#6500	C₂²×C₃	1	2	yes	complemented
269	#6499	C₂²×C₃	1	1	yes	characteristic, complemented
270	#6499	C₂²×C₃	1	1	yes	characteristic, complemented
271	#6499	C₂²×C₃	1	2	yes	complemented
272	#6498	C₂²×C₃	1	2	yes	complemented
273	D₄×Dic₇	C₂²×C₃	1	2	yes	complemented
274	#6493	C₂²×C₃	1	2	yes	complemented
275	#6493	C₂²×C₃	1	2	yes	complemented
276	#6492	C₂²×C₃	1	2	yes	complemented
277	C₄×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
278	C₄×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
279	C₂×(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
280	#6489	C₂²×C₃	1	1	yes	characteristic, complemented
281	#6461	C₂²×C₃	1	2	yes	complemented
282	#6461	C₂²×C₃	1	2	yes	complemented
283	#6460	C₂²×C₃	1	2	yes	complemented
284	#6459	C₂²×C₃	1	2	yes	complemented
285	#6458	C₂²×C₃	1	2	yes	complemented
286	#6457	C₂²×C₃	1	2	yes	complemented
287	#6456	C₂²×C₃	1	2	yes	complemented
288	#6455	C₂²×C₃	1	2	yes	complemented
289	#6449	C₂²×C₃	1	2	yes	complemented
290	#6448	C₂²×C₃	1	2	yes	complemented
291	#6448	C₂²×C₃	1	2	yes	complemented
292	#6448	C₂²×C₃	1	2	yes	complemented
293	#6448	C₂²×C₃	1	2	yes	complemented
294	#6447	C₂²×C₃	1	2	yes	complemented
295	#6447	C₂²×C₃	1	2	yes	complemented
296	#6447	C₂²×C₃	1	2	yes	complemented
297	#6446	C₂²×C₃	1	2	yes	complemented
298	#6446	C₂²×C₃	1	2	yes	complemented
299	#6446	C₂²×C₃	1	2	yes	complemented
300	#6445	C₂²×C₃	1	2	yes	complemented
301	#6445	C₂²×C₃	1	2	yes	complemented
302	#6445	C₂²×C₃	1	2	yes	complemented
303	#6445	C₂²×C₃	1	2	yes	complemented
304	(C₂²⋊D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
305	(C₂²⋊D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
306	D₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
307	D₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
308	D₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
309	D₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
310	#6442	C₂²×C₃	1	2	yes	complemented
311	#6442	C₂²×C₃	1	2	yes	complemented
312	#6441	C₂²×C₃	1	2	yes	complemented
313	C₃×H(3,𝔽₄)	—	7	1	no	—
314	C₃×#560	—	7	2	no	—
315	C₃×#560	—	7	1	no	—
316	C₃×#551	—	7	2	no	—
317	C₃×#551	—	7	1	no	—
318	C₃×#546	—	7	2	no	—
319	C₃×#546	—	7	2	no	—
320	C₃×#546	—	7	2	no	—
321	C₃×D₄²	—	7	2	no	—
322	C₃×D₄²	—	7	1	no	—
323	C₃×#538	—	7	2	no	—
324	C₃×#538	—	7	2	no	—
325	C₃×#538	—	7	2	no	—
326	C₃×#535	—	7	1	no	—
327	C₃×#535	—	7	2	no	—
328	C₃×#534	—	7	2	no	—
329	C₃×#534	—	7	1	no	—
330	C₂×C₃×#120	—	7	2	no	—
331	C₂×C₃×#120	—	7	1	no	—
332	C₂³×ΓL(1,𝔽₈)	—	2	2	no	—
333	C₂³×ΓL(1,𝔽₈)	—	2	2	no	—
334	C₂³×ΓL(1,𝔽₈)	—	4	2	no	—
335	C₂³×ΓL(1,𝔽₈)	—	4	2	no	—
336	C₂³×ΓL(1,𝔽₈)	—	4	2	no	—
337	C₂³×ΓL(1,𝔽₈)	—	4	1	no	—
338	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
339	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
340	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	2	yes	—
341	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
342	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
343	C₂³×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
344	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
345	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
346	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
347	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
348	C₂²×AGL(1,𝔽₇)	—	2	4	no	—
349	C₂²×AGL(1,𝔽₇)	—	4	1	no	—
350	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
351	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
352	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
353	C₂²×AGL(1,𝔽₇)	—	4	1	no	—
354	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
355	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
356	C₂²×AGL(1,𝔽₇)	—	4	2	no	—
357	C₂²×AGL(1,𝔽₇)	—	4	16	no	—
358	C₂²×AGL(1,𝔽₇)	C₂⁴	1	2	yes	—
359	C₂²×AGL(1,𝔽₇)	C₂⁴	1	2	yes	—
360	C₂²×AGL(1,𝔽₇)	C₂⁴	1	2	yes	—
361	D₄×ΓL(1,𝔽₈)	—	2	4	no	—
362	D₄×ΓL(1,𝔽₈)	—	4	2	no	—
363	D₄×ΓL(1,𝔽₈)	—	4	2	no	—
364	D₄×ΓL(1,𝔽₈)	—	4	1	no	—
365	D₄×ΓL(1,𝔽₈)	—	4	1	no	—
366	D₄×ΓL(1,𝔽₈)	—	4	1	no	—
367	D₄×ΓL(1,𝔽₈)	—	4	1	no	—
368	D₄×ΓL(1,𝔽₈)	—	4	2	no	—
369	C₂×C₄×ΓL(1,𝔽₈)	—	2	2	no	—
370	C₂×C₄×ΓL(1,𝔽₈)	—	4	2	no	—
371	C₂×C₄×ΓL(1,𝔽₈)	—	4	1	no	—
372	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	2	yes	—
373	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	2	yes	—
374	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	2	yes	—
375	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
377	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
378	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
379	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
380	(C₂²⋊D₇)⋊C₃	—	2	4	no	—
381	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
382	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
383	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
384	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
385	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
386	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
387	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
388	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
389	(C₂²⋊D₇)⋊C₃	—	4	2	no	—
390	C₂×ΓL(1,𝔽₈)⋊C₄	—	4	2	no	—
391	C₂×ΓL(1,𝔽₈)⋊C₄	—	4	2	no	—
392	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	2	yes	—
393	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	2	yes	—
394	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	2	yes	—
395	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	2	yes	—
396	C₂×ΓL(1,𝔽₈)⋊C₄	C₂⁴	1	2	yes	—
397	C₄⋊AGL(1,𝔽₇)	—	2	4	no	—
398	C₄⋊AGL(1,𝔽₇)	—	4	2	no	—
399	C₄⋊AGL(1,𝔽₇)	—	4	2	no	—
400	C₄⋊AGL(1,𝔽₇)	—	4	1	no	—
401	C₄×AGL(1,𝔽₇)	—	2	4	no	—
402	C₄×AGL(1,𝔽₇)	—	4	2	no	—
403	C₄×AGL(1,𝔽₇)	—	4	2	no	—
404	C₄×AGL(1,𝔽₇)	—	4	2	no	—
405	C₄×AGL(1,𝔽₇)	—	4	2	no	—
406	ΓL(1,𝔽₈)⋊Q₈	—	4	2	no	—
407	ΓL(1,𝔽₈)⋊Q₈	—	4	1	no	—
408	#3532	—	7	1	no	Sylow
409	C₂⁴×C₇	C₂³×C₃	1	1	yes	characteristic
410	C₂⁴×C₇	C₂³×C₃	1	1	yes	characteristic
411	C₂⁴×C₇	C₂³×C₃	1	1	yes	characteristic, complemented
412	C₂³×D₇	—	4	4	no	—
413	C₂³×D₇	—	4	2	no	—
414	C₂³×D₇	C₂³×C₃	1	1	yes	characteristic
415	C₂³×D₇	C₂³×C₃	1	2	yes	—
416	C₂³×D₇	C₂³×C₃	1	2	yes	—
417	C₂³×D₇	C₂³×C₃	1	2	yes	—
418	C₂³×D₇	C₂³×C₃	1	1	yes	characteristic
419	C₂×C₇×D₄	—	4	2	no	—
420	C₂×C₇×D₄	—	4	2	no	—
421	C₂×C₇×D₄	C₂³×C₃	1	2	yes	—
422	C₂×C₇×D₄	C₂³×C₃	1	2	yes	—
423	C₂×C₇×D₄	C₂³×C₃	1	1	yes	characteristic
424	C₂×C₇×D₄	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₇×D₄	C₂³×C₃	1	2	yes	—
426	C₂×C₇×D₄	C₂³×C₃	1	1	yes	characteristic
427	C₂×C₇×D₄	C₂³×C₃	1	1	yes	characteristic
428	C₂×C₇×D₄	C₂³×C₃	1	2	yes	complemented
429	C₂²×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
430	C₂²×C₄×C₇	C₂³×C₃	1	1	yes	characteristic, complemented
431	C₂²×C₄×C₇	C₂³×C₃	1	2	yes	complemented
432	C₂×C₂²⋊D₇	—	4	4	no	—
433	C₂×C₂²⋊D₇	—	4	4	no	—
434	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
435	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
436	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
437	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
438	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
439	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
440	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
441	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
442	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
443	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	—
444	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	complemented
445	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	complemented
446	C₂×C₂²⋊D₇	C₂³×C₃	1	2	yes	complemented
447	C₂²×Dic₇	C₂³×C₃	1	2	yes	—
448	C₂²×Dic₇	C₂³×C₃	1	2	yes	complemented
449	D₄×D₇	—	4	4	no	—
450	D₄×D₇	—	4	4	no	—
451	D₄×D₇	—	4	4	no	—
452	#1157	—	4	4	no	—
453	#1157	—	4	2	no	—
454	C₂×D₂₈	C₂³×C₃	1	2	yes	—
455	C₂×D₂₈	C₂³×C₃	1	2	yes	—
456	C₂×D₂₈	C₂³×C₃	1	2	yes	—
457	C₂×D₂₈	C₂³×C₃	1	1	yes	characteristic, complemented
458	C₂×C₄×D₇	C₂³×C₃	1	2	yes	—
459	C₂×C₄×D₇	C₂³×C₃	1	2	yes	—
460	C₂×C₄×D₇	C₂³×C₃	1	2	yes	—
461	C₂×C₄×D₇	C₂³×C₃	1	2	yes	complemented
462	C₂×C₄×D₇	C₂³×C₃	1	2	yes	complemented
463	C₂×Dic₁₄	C₂³×C₃	1	2	yes	complemented
464	C₂×Dic₁₄	C₂³×C₃	1	1	yes	characteristic, complemented
465	C₇×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
466	C₇×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
467	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
468	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
469	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
470	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	complemented
471	C₇×C₂²⋊C₄	C₂³×C₃	1	2	yes	complemented
472	C₇×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
473	C₇×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic, complemented
474	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	—
475	C₂²⋊Dic₇	C₂³×C₃	1	1	yes	characteristic
476	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	—
477	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	—
478	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	—
479	C₂²⋊Dic₇	C₂³×C₃	1	1	yes	characteristic
480	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	complemented
481	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	complemented
482	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	complemented
483	C₂²⋊Dic₇	C₂³×C₃	1	2	yes	complemented
484	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
485	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
486	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
487	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
488	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
489	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
490	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
491	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
492	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
493	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	—
494	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
495	(C₂×D₇)⋊C₄	C₂³×C₃	1	2	yes	complemented
496	C₄⋊Dic₇	C₂³×C₃	1	2	yes	complemented
497	C₄⋊Dic₇	C₂³×C₃	1	2	yes	complemented
498	C₄⋊Dic₇	C₂³×C₃	1	2	yes	complemented
499	Dic₇⋊C₄	C₂³×C₃	1	2	yes	complemented
500	Dic₇⋊C₄	C₂³×C₃	1	2	yes	complemented
501	Dic₇⋊C₄	C₂³×C₃	1	2	yes	complemented
502	Dic₇⋊C₄	C₂³×C₃	1	2	yes	complemented
503	C₄×Dic₇	C₂³×C₃	1	2	yes	complemented
504	C₄×Dic₇	C₂³×C₃	1	2	yes	complemented
505	C₄×Dic₇	C₂³×C₃	1	1	yes	characteristic, complemented
506	C₄×Dic₇	C₂³×C₃	1	1	yes	characteristic, complemented
507	C₂⁵×C₃	—	7	1	no	—
508	C₂×C₃×#41	—	7	1	no	—
509	C₂×C₃×#41	—	7	2	no	—
510	C₂²×C₃×D₄	—	7	2	no	—
511	C₂²×C₃×D₄	—	7	2	no	—
512	C₂²×C₃×D₄	—	7	2	no	—
513	C₂²×C₃×D₄	—	7	2	no	—
514	C₂²×C₃×D₄	—	7	2	no	—
515	C₂²×C₃×D₄	—	7	1	no	—
516	C₂²×C₃×D₄	—	7	1	no	—
517	C₃×#127	—	7	1	no	—
518	C₃×#127	—	7	2	no	—
519	C₃×#127	—	7	1	no	—
520	C₃×#126	—	7	2	no	—
521	C₃×#126	—	7	2	no	—
522	C₃×#126	—	7	2	no	—
523	C₃×#126	—	7	2	no	—
524	C₃×#124	—	7	2	no	—
525	C₃×#124	—	7	2	no	—
526	C₃×#124	—	7	2	no	—
527	C₃×#124	—	7	1	no	—
528	C₃×#124	—	7	2	no	—
529	C₃×#124	—	7	2	no	—
530	C₃×#124	—	7	1	no	—
531	C₃×#123	—	7	2	no	—
532	C₃×#123	—	7	2	no	—
533	C₃×#123	—	7	2	no	—
534	C₃×#123	—	7	2	no	—
535	C₃×#123	—	7	2	no	—
536	C₃×#123	—	7	2	no	—
537	C₃×#123	—	7	2	no	—
538	C₃×#123	—	7	1	no	—
539	C₃×#123	—	7	1	no	—
540	C₃×#123	—	7	2	no	—
541	C₃×C₂²⋊Q₈	—	7	2	no	—
542	C₃×C₂²⋊Q₈	—	7	2	no	—
543	C₃×C₂²⋊Q₈	—	7	2	no	—
544	C₃×#121	—	7	2	no	—
545	C₃×#121	—	7	2	no	—
546	C₃×#121	—	7	2	no	—
547	C₃×#121	—	7	2	no	—
548	C₃×#121	—	7	2	no	—
549	C₃×#121	—	7	2	no	—
550	C₃×#121	—	7	2	no	—
551	C₃×#121	—	7	2	no	—
552	C₃×#121	—	7	2	no	—
553	C₃×#121	—	7	2	no	—
554	C₃×#121	—	7	2	no	—
555	C₃×#121	—	7	2	no	—
556	C₃×#121	—	7	2	no	—
557	C₃×#121	—	7	2	no	—
558	C₃×#121	—	7	2	no	—
559	C₃×#120	—	7	2	no	—
560	C₃×#120	—	7	1	no	—
561	C₃×#120	—	7	1	no	—
562	C₃×#120	—	7	2	no	—
563	C₃×#120	—	7	2	no	—
564	C₃×#120	—	7	2	no	—
565	C₃×#120	—	7	2	no	—
566	C₃×#120	—	7	2	no	—
567	C₃×#120	—	7	1	no	—
568	C₃×#120	—	7	2	no	—
569	C₃×#120	—	7	2	no	—
570	C₃×#120	—	7	2	no	—
571	C₃×#120	—	7	2	no	—
572	C₃×#120	—	7	1	no	—
573	C₃×#120	—	7	2	no	—
574	C₃×#120	—	7	2	no	—
575	C₃×#120	—	7	2	no	—
576	C₃×#120	—	7	1	no	—
577	C₃×#120	—	7	2	no	—
578	C₃×#120	—	7	1	no	—
579	C₃×C₄×D₄	—	7	2	no	—
580	C₃×C₄×D₄	—	7	2	no	—
581	C₃×C₄×D₄	—	7	2	no	—
582	C₃×C₄×D₄	—	7	2	no	—
583	C₃×C₄×D₄	—	7	2	no	—
584	C₃×C₄×D₄	—	7	2	no	—
585	C₃×#117	—	7	2	no	—
586	C₃×#117	—	7	1	no	—
587	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
588	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
589	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
590	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
591	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
592	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
593	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
594	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
595	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
596	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
597	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
598	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
599	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
600	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
601	C₂²×ΓL(1,𝔽₈)	—	2	2	no	—
602	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
603	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
604	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
605	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
606	C₂²×ΓL(1,𝔽₈)	—	4	4	no	—
607	C₂²×ΓL(1,𝔽₈)	—	8	2	no	—
608	C₂²×ΓL(1,𝔽₈)	—	8	2	no	—
609	C₂²×ΓL(1,𝔽₈)	H(5,𝔽₂)	1	2	yes	—
610	C₂²×ΓL(1,𝔽₈)	C₂⁵	1	1	yes	characteristic
611	C₂×AGL(1,𝔽₇)	—	2	2	no	—
612	C₂×AGL(1,𝔽₇)	—	2	2	no	—
613	C₂×AGL(1,𝔽₇)	—	2	2	no	—
614	C₂×AGL(1,𝔽₇)	—	2	2	no	—
615	C₂×AGL(1,𝔽₇)	—	2	2	no	—
616	C₂×AGL(1,𝔽₇)	—	2	2	no	—
617	C₂×AGL(1,𝔽₇)	—	2	2	no	—
618	C₂×AGL(1,𝔽₇)	—	2	2	no	—
619	C₂×AGL(1,𝔽₇)	—	4	4	no	—
620	C₂×AGL(1,𝔽₇)	—	4	8	no	—
621	C₂×AGL(1,𝔽₇)	—	4	8	no	—
622	C₂×AGL(1,𝔽₇)	—	4	4	no	—
623	C₂×AGL(1,𝔽₇)	—	8	4	no	—
624	C₂×AGL(1,𝔽₇)	H(5,𝔽₂)	1	4	yes	—
625	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
626	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
627	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
628	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
629	C₄×ΓL(1,𝔽₈)	—	2	2	no	—
630	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
631	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
632	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
633	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
634	ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
635	H(3,𝔽₄)	—	7	1	no	—
636	#560	—	7	1	no	—
637	#560	—	7	2	no	—
638	#551	—	7	2	no	—
639	#551	—	7	1	no	—
640	#546	—	7	2	no	—
641	#546	—	7	2	no	—
642	#546	—	7	2	no	—
643	D₄²	—	7	2	no	—
644	D₄²	—	7	1	no	—
645	#538	—	7	2	no	—
646	#538	—	7	2	no	—
647	#538	—	7	2	no	—
648	#535	—	7	1	no	—
649	#535	—	7	2	no	—
650	#534	—	7	2	no	—
651	#534	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
652	C₂×#120	—	7	1	no	—
653	C₂×#120	—	7	2	no	—
654	C₂³×C₇	—	2	2	no	—
655	C₂³×C₇	—	2	2	no	—
656	C₂³×C₇	—	4	2	no	—
657	C₂³×C₇	—	4	2	no	—
658	C₂³×C₇	—	4	2	no	—
659	C₂³×C₇	—	4	1	no	—
660	C₂³×C₇	C₂⁴×C₃	1	1	yes	characteristic
661	C₂³×C₇	C₂⁴×C₃	1	1	yes	characteristic
662	C₂³×C₇	C₂⁴×C₃	1	2	yes	—
663	C₂³×C₇	C₂⁴×C₃	1	1	yes	characteristic
664	C₂³×C₇	C₂⁴×C₃	1	1	yes	characteristic
665	C₂³×C₇	C₂⁴×C₃	1	1	yes	characteristic
666	C₂²×D₇	—	2	4	no	—
667	C₂²×D₇	—	2	4	no	—
668	C₂²×D₇	—	2	4	no	—
669	C₂²×D₇	—	2	4	no	—
670	C₂²×D₇	—	2	4	no	—
671	C₂²×D₇	—	4	1	no	—
672	C₂²×D₇	—	4	2	no	—
673	C₂²×D₇	—	4	2	no	—
674	C₂²×D₇	—	4	2	no	—
675	C₂²×D₇	—	4	1	no	—
676	C₂²×D₇	—	4	2	no	—
677	C₂²×D₇	—	4	2	no	—
678	C₂²×D₇	—	4	2	no	—
679	C₂²×D₇	—	4	16	no	—
680	C₂²×D₇	C₂⁴×C₃	1	2	yes	—
681	C₂²×D₇	C₂⁴×C₃	1	2	yes	—
682	C₂²×D₇	C₂⁴×C₃	1	2	yes	—
683	C₇×D₄	—	2	4	no	—
684	C₇×D₄	—	4	2	no	—
685	C₇×D₄	—	4	2	no	—
686	C₇×D₄	—	4	1	no	—
687	C₇×D₄	—	4	1	no	—
688	C₇×D₄	—	4	1	no	—
689	C₇×D₄	—	4	1	no	—
690	C₇×D₄	—	4	2	no	—
691	C₂×C₄×C₇	—	2	2	no	—
692	C₂×C₄×C₇	—	4	2	no	—
693	C₂×C₄×C₇	—	4	1	no	—
694	C₂×C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
695	C₂×C₄×C₇	C₂⁴×C₃	1	2	yes	—
696	C₂×C₄×C₇	C₂⁴×C₃	1	2	yes	—
697	C₂×C₄×C₇	C₂⁴×C₃	1	2	yes	—
698	C₂×C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
699	C₂²⋊D₇	—	2	4	no	—
700	C₂²⋊D₇	—	2	4	no	—
701	C₂²⋊D₇	—	2	4	no	—
702	C₂²⋊D₇	—	2	4	no	—
703	C₂²⋊D₇	—	4	2	no	—
704	C₂²⋊D₇	—	4	2	no	—
705	C₂²⋊D₇	—	4	2	no	—
706	C₂²⋊D₇	—	4	2	no	—
707	C₂²⋊D₇	—	4	2	no	—
708	C₂²⋊D₇	—	4	2	no	—
709	C₂²⋊D₇	—	4	2	no	—
710	C₂²⋊D₇	—	4	2	no	—
711	C₂²⋊D₇	—	4	2	no	—
712	C₂×Dic₇	—	4	2	no	—
713	C₂×Dic₇	—	4	2	no	—
714	C₂×Dic₇	C₂⁴×C₃	1	2	yes	—
715	C₂×Dic₇	C₂⁴×C₃	1	2	yes	—
716	C₂×Dic₇	C₂⁴×C₃	1	2	yes	—
717	C₂×Dic₇	C₂⁴×C₃	1	2	yes	—
718	C₂×Dic₇	C₂⁴×C₃	1	2	yes	—
719	D₂₈	—	2	4	no	—
720	D₂₈	—	4	2	no	—
721	D₂₈	—	4	2	no	—
722	D₂₈	—	4	1	no	—
723	C₄×D₇	—	2	4	no	—
724	C₄×D₇	—	4	2	no	—
725	C₄×D₇	—	4	2	no	—
726	C₄×D₇	—	4	2	no	—
727	C₄×D₇	—	4	2	no	—
728	Dic₁₄	—	4	2	no	—
729	Dic₁₄	—	4	1	no	—
730	C₂⁴×C₃	—	7	1	no	—
731	C₂⁴×C₃	—	7	2	no	—
732	C₂⁴×C₃	—	7	2	no	—
733	C₂⁴×C₃	—	7	2	no	—
734	C₂⁴×C₃	—	7	1	no	—
735	C₂⁴×C₃	—	7	1	no	—
736	C₂⁴×C₃	—	7	1	no	—
737	C₂⁴×C₃	—	7	1	no	—
738	C₂⁴×C₃	—	28	2	no	—
739	C₂⁴×C₃	—	28	4	no	—
740	C₃×#41	—	28	2	no	—
741	C₃×#41	—	28	4	no	—
742	C₂×C₃×Q₈	—	7	2	no	—
743	C₂×C₃×Q₈	—	7	1	no	—
744	C₂×C₃×D₄	—	7	2	no	—
745	C₂×C₃×D₄	—	7	2	no	—
746	C₂×C₃×D₄	—	7	2	no	—
747	C₂×C₃×D₄	—	7	2	no	—
748	C₂×C₃×D₄	—	7	2	no	—
749	C₂×C₃×D₄	—	7	2	no	—
750	C₂×C₃×D₄	—	7	2	no	—
751	C₂×C₃×D₄	—	7	1	no	—
752	C₂×C₃×D₄	—	7	2	no	—
753	C₂×C₃×D₄	—	7	2	no	—
754	C₂×C₃×D₄	—	7	2	no	—
755	C₂×C₃×D₄	—	7	2	no	—
756	C₂×C₃×D₄	—	7	2	no	—
757	C₂×C₃×D₄	—	7	2	no	—
758	C₂×C₃×D₄	—	7	2	no	—
759	C₂×C₃×D₄	—	7	2	no	—
760	C₂×C₃×D₄	—	7	2	no	—
761	C₂×C₃×D₄	—	7	2	no	—
762	C₂×C₃×D₄	—	7	1	no	—
763	C₂×C₃×D₄	—	7	2	no	—
764	C₂×C₃×D₄	—	7	2	no	—
765	C₂×C₃×D₄	—	7	1	no	—
766	C₂×C₃×D₄	—	7	1	no	—
767	C₂×C₃×D₄	—	7	1	no	—
768	C₂×C₃×D₄	—	7	2	no	—
769	C₂×C₃×D₄	—	28	2	no	—
770	C₂×C₃×D₄	—	28	2	no	—
771	C₂×C₃×D₄	—	28	4	no	—
772	C₂×C₃×D₄	—	28	4	no	—
773	C₂×C₃×D₄	—	28	4	no	—
774	C₂×C₃×D₄	—	28	4	no	—
775	C₂×C₃×D₄	—	28	4	no	—
776	C₂²×C₃×C₄	—	7	2	no	—
777	C₂²×C₃×C₄	—	7	2	no	—
778	C₂²×C₃×C₄	—	7	2	no	—
779	C₂²×C₃×C₄	—	7	2	no	—
780	C₂²×C₃×C₄	—	7	2	no	—
781	C₂²×C₃×C₄	—	7	2	no	—
782	C₂²×C₃×C₄	—	7	2	no	—
783	C₂²×C₃×C₄	—	7	1	no	—
784	C₂²×C₃×C₄	—	7	2	no	—
785	C₂²×C₃×C₄	—	7	1	no	—
786	C₃×C₄⋊C₄	—	7	2	no	—
787	C₃×C₄⋊C₄	—	7	2	no	—
788	C₃×C₄⋊C₄	—	7	2	no	—
789	C₃×C₄⋊C₄	—	7	2	no	—
790	C₃×C₄⋊C₄	—	7	2	no	—
791	C₃×C₄⋊C₄	—	7	2	no	—
792	C₃×C₄⋊C₄	—	7	2	no	—
793	C₃×C₄⋊C₄	—	7	2	no	—
794	C₃×C₄⋊C₄	—	7	2	no	—
795	C₃×C₂²⋊C₄	—	7	2	no	—
796	C₃×C₂²⋊C₄	—	7	2	no	—
797	C₃×C₂²⋊C₄	—	7	2	no	—
798	C₃×C₂²⋊C₄	—	7	2	no	—
799	C₃×C₂²⋊C₄	—	7	2	no	—
800	C₃×C₂²⋊C₄	—	7	2	no	—
801	C₃×C₂²⋊C₄	—	7	1	no	—
802	C₃×C₂²⋊C₄	—	7	2	no	—
803	C₃×C₂²⋊C₄	—	7	2	no	—
804	C₃×C₂²⋊C₄	—	7	2	no	—
805	C₃×C₂²⋊C₄	—	7	2	no	—
806	C₃×C₂²⋊C₄	—	7	2	no	—
807	C₃×C₂²⋊C₄	—	7	2	no	—
808	C₃×C₂²⋊C₄	—	7	2	no	—
809	C₃×C₂²⋊C₄	—	7	2	no	—
810	C₃×C₂²⋊C₄	—	7	1	no	—
811	C₃×C₂²⋊C₄	—	7	2	no	—
812	C₃×C₂²⋊C₄	—	7	2	no	—
813	C₃×C₂²⋊C₄	—	7	2	no	—
814	C₃×C₂²⋊C₄	—	7	2	no	—
815	C₃×C₂²⋊C₄	—	7	2	no	—
816	C₃×C₂²⋊C₄	—	7	2	no	—
817	C₃×C₂²⋊C₄	—	7	2	no	—
818	C₃×C₂²⋊C₄	—	7	2	no	—
819	C₃×C₂²⋊C₄	—	7	2	no	—
820	C₃×C₂²⋊C₄	—	7	2	no	—
821	C₃×C₂²⋊C₄	—	7	1	no	—
822	C₃×C₂²⋊C₄	—	7	1	no	—
823	C₃×C₂²⋊C₄	—	7	2	no	—
824	C₃×C₄²	—	7	1	no	—
825	C₃×C₄²	—	7	2	no	—
826	C₃×C₄²	—	7	1	no	—
827	C₃×C₄²	—	7	2	no	—
828	C₂×ΓL(1,𝔽₈)	—	2	2	no	—
829	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
830	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
831	C₂×ΓL(1,𝔽₈)	—	4	2	no	—
832	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
833	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
834	C₂×ΓL(1,𝔽₈)	C₂×H(5,𝔽₂)	1	2	yes	—
835	C₂×ΓL(1,𝔽₈)	C₂×H(5,𝔽₂)	1	1	yes	characteristic
836	AGL(1,𝔽₇)	—	2	4	no	—
837	AGL(1,𝔽₇)	—	4	2	no	—
838	AGL(1,𝔽₇)	—	4	2	no	—
839	C₂⁵	—	7	1	no	—
840	C₂×#41	—	7	1	no	—
841	C₂×#41	—	7	2	no	—
842	C₂²×D₄	—	7	2	no	—
843	C₂²×D₄	—	7	2	no	—
844	C₂²×D₄	—	7	2	no	—
845	C₂²×D₄	—	7	2	no	—
846	C₂²×D₄	—	7	2	no	—
847	C₂²×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
848	C₂²×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
849	#127	—	7	1	no	—
850	#127	—	7	1	no	—
851	#127	—	7	2	no	—
852	#126	—	7	2	no	—
853	#126	—	7	2	no	—
854	#126	—	7	2	no	—
855	#126	—	7	2	no	—
856	#124	—	7	1	no	—
857	#124	—	7	1	no	—
858	#124	—	7	2	no	—
859	#124	—	7	2	no	—
860	#124	—	7	2	no	—
861	#124	—	7	2	no	—
862	#124	—	7	2	no	—
863	#123	—	7	2	no	—
864	#123	—	7	2	no	—
865	#123	—	7	2	no	—
866	#123	—	7	2	no	—
867	#123	—	7	2	no	—
868	#123	—	7	2	no	—
869	#123	—	7	2	no	—
870	#123	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
871	#123	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
872	#123	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
873	C₂²⋊Q₈	—	7	2	no	—
874	C₂²⋊Q₈	—	7	2	no	—
875	C₂²⋊Q₈	—	7	2	no	—
876	#121	—	7	2	no	—
877	#121	—	7	2	no	—
878	#121	—	7	2	no	—
879	#121	—	7	2	no	—
880	#121	—	7	2	no	—
881	#121	—	7	2	no	—
882	#121	—	7	2	no	—
883	#121	—	7	2	no	—
884	#121	—	7	2	no	—
885	#121	—	7	2	no	—
886	#121	—	7	2	no	—
887	#121	—	7	2	no	—
888	#121	—	7	2	no	—
889	#121	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
890	#121	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
891	#120	—	7	2	no	—
892	#120	—	7	2	no	—
893	#120	—	7	2	no	—
894	#120	—	7	2	no	—
895	#120	—	7	2	no	—
896	#120	—	7	2	no	—
897	#120	—	7	2	no	—
898	#120	—	7	1	no	—
899	#120	—	7	1	no	—
900	#120	—	7	1	no	—
901	#120	—	7	2	no	—
902	#120	—	7	1	no	—
903	#120	—	7	2	no	—
904	#120	—	7	2	no	—
905	#120	—	7	2	no	—
906	#120	—	7	2	no	—
907	#120	—	7	2	no	—
908	#120	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
909	#120	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
910	#120	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
911	C₄×D₄	—	7	2	no	—
912	C₄×D₄	—	7	2	no	—
913	C₄×D₄	—	7	2	no	—
914	C₄×D₄	—	7	2	no	—
915	C₄×D₄	—	7	2	no	—
916	C₄×D₄	—	7	2	no	—
917	#117	—	7	1	no	—
918	#117	—	7	2	no	—
919	C₂×C₂²⋊C₄	—	7	1	no	—
920	C₂×C₂²⋊C₄	—	7	2	no	—
921	C₂×C₂²⋊C₄	—	7	2	no	—
922	C₂×C₂²⋊C₄	—	7	2	no	—
923	C₂×C₂²⋊C₄	—	7	2	no	—
924	C₂×C₂²⋊C₄	—	7	2	no	—
925	C₂×C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
926	C₂²×C₇	—	2	2	no	—
927	C₂²×C₇	—	2	2	no	—
928	C₂²×C₇	—	2	2	no	—
929	C₂²×C₇	—	2	2	no	—
930	C₂²×C₇	—	2	2	no	—
931	C₂²×C₇	—	2	2	no	—
932	C₂²×C₇	—	2	2	no	—
933	C₂²×C₇	—	2	2	no	—
934	C₂²×C₇	—	2	1	no	—
935	C₂²×C₇	—	2	1	no	—
936	C₂²×C₇	—	2	1	no	—
937	C₂²×C₇	—	2	1	no	—
938	C₂²×C₇	—	4	4	no	—
939	C₂²×C₇	—	8	2	no	—
940	C₂²×C₇	—	8	2	no	—
941	C₂²×C₇	C₃×H(5,𝔽₂)	1	2	yes	—
942	C₂²×C₇	C₂⁵×C₃	1	1	yes	characteristic
943	C₂×D₇	—	2	2	no	—
944	C₂×D₇	—	2	2	no	—
945	C₂×D₇	—	2	2	no	—
946	C₂×D₇	—	2	2	no	—
947	C₂×D₇	—	2	2	no	—
948	C₂×D₇	—	2	2	no	—
949	C₂×D₇	—	2	2	no	—
950	C₂×D₇	—	2	2	no	—
951	C₂×D₇	—	4	4	no	—
952	C₂×D₇	—	4	8	no	—
953	C₂×D₇	—	4	8	no	—
954	C₂×D₇	—	4	4	no	—
955	C₂×D₇	—	8	4	no	—
956	C₂×D₇	C₃×H(5,𝔽₂)	1	4	yes	—
957	C₄×C₇	—	2	2	no	—
958	C₄×C₇	—	2	1	no	—
959	C₄×C₇	—	2	2	no	—
960	C₄×C₇	—	2	1	no	—
961	C₄×C₇	—	2	2	no	—
962	Dic₇	—	2	2	no	—
963	Dic₇	—	2	2	no	—
964	Dic₇	—	2	2	no	—
965	Dic₇	—	2	2	no	—
966	Dic₇	—	2	2	no	—
967	C₂³×C₃	—	7	2	no	—
968	C₂³×C₃	—	7	2	no	—
969	C₂³×C₃	—	7	2	no	—
970	C₂³×C₃	—	7	1	no	—
971	C₂³×C₃	—	7	1	no	—
972	C₂³×C₃	—	7	1	no	—
973	C₂³×C₃	—	7	2	no	—
974	C₂³×C₃	—	7	1	no	—
975	C₂³×C₃	—	7	1	no	—
976	C₂³×C₃	—	14	2	no	—
977	C₂³×C₃	—	14	2	no	—
978	C₂³×C₃	—	14	4	no	—
979	C₂³×C₃	—	14	4	no	—
980	C₂³×C₃	—	14	4	no	—
981	C₂³×C₃	—	14	4	no	—
982	C₂³×C₃	—	14	4	no	—
983	C₂³×C₃	—	28	2	no	—
984	C₂³×C₃	—	28	1	no	—
985	C₂³×C₃	—	28	2	no	—
986	C₂³×C₃	—	28	2	no	—
987	C₂³×C₃	—	28	2	no	—
988	C₂³×C₃	—	28	1	no	—
989	C₂³×C₃	—	28	2	no	—
990	C₂³×C₃	—	28	2	no	—
991	C₂³×C₃	—	28	1	no	—
992	C₂³×C₃	—	28	2	no	—
993	C₂³×C₃	—	28	2	no	—
994	C₂³×C₃	—	28	2	no	—
995	C₂³×C₃	—	28	16	no	—
996	C₃×Q₈	—	28	1	no	—
997	C₃×Q₈	—	28	2	no	—
998	C₃×D₄	—	14	4	no	—
999	C₃×D₄	—	14	4	no	—
1000	C₃×D₄	—	14	4	no	—
1001	C₃×D₄	—	14	4	no	—
1002	C₃×D₄	—	14	4	no	—
1003	C₃×D₄	—	14	4	no	—
1004	C₃×D₄	—	28	1	no	—
1005	C₃×D₄	—	28	1	no	—
1006	C₃×D₄	—	28	1	no	—
1007	C₃×D₄	—	28	1	no	—
1008	C₃×D₄	—	28	2	no	—
1009	C₃×D₄	—	28	2	no	—
1010	C₃×D₄	—	28	2	no	—
1011	C₃×D₄	—	28	2	no	—
1012	C₃×D₄	—	28	2	no	—
1013	C₃×D₄	—	28	1	no	—
1014	C₃×D₄	—	28	2	no	—
1015	C₃×D₄	—	28	2	no	—
1016	C₃×D₄	—	28	2	no	—
1017	C₃×D₄	—	28	2	no	—
1018	C₃×D₄	—	28	2	no	—
1019	C₃×D₄	—	28	2	no	—
1020	C₃×D₄	—	28	2	no	—
1021	C₃×D₄	—	28	2	no	—
1022	C₃×D₄	—	28	2	no	—
1023	C₂×C₃×C₄	—	7	2	no	—
1024	C₂×C₃×C₄	—	7	2	no	—
1025	C₂×C₃×C₄	—	7	2	no	—
1026	C₂×C₃×C₄	—	7	2	no	—
1027	C₂×C₃×C₄	—	7	2	no	—
1028	C₂×C₃×C₄	—	7	1	no	—
1029	C₂×C₃×C₄	—	7	2	no	—
1030	C₂×C₃×C₄	—	7	2	no	—
1031	C₂×C₃×C₄	—	7	1	no	—
1032	C₂×C₃×C₄	—	7	2	no	—
1033	C₂×C₃×C₄	—	14	2	no	—
1034	C₂×C₃×C₄	—	14	4	no	—
1035	C₂×C₃×C₄	—	28	1	no	—
1036	C₂×C₃×C₄	—	28	2	no	—
1037	C₂×C₃×C₄	—	28	2	no	—
1038	C₂×C₃×C₄	—	28	2	no	—
1039	C₂×C₃×C₄	—	28	2	no	—
1040	C₂×C₃×C₄	—	28	2	no	—
1041	C₂×C₃×C₄	—	28	2	no	—
1042	C₂×C₃×C₄	—	28	2	no	—
1043	ΓL(1,𝔽₈)	#3532	1	1	yes	characteristic, complemented, Hall
1044	C₂⁴	—	7	1	no	—
1045	C₂⁴	—	7	2	no	—
1046	C₂⁴	—	7	2	no	—
1047	C₂⁴	—	7	2	no	—
1048	C₂⁴	—	7	1	no	—
1049	C₂⁴	—	28	2	no	—
1050	C₂⁴	—	28	4	no	—
1051	C₂⁴	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1052	C₂⁴	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1053	C₂⁴	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1054	#41	—	28	2	no	—
1055	#41	—	28	4	no	—
1056	C₂×Q₈	—	7	2	no	—
1057	C₂×Q₈	—	7	1	no	—
1058	C₂×D₄	—	4	2	no	—
1059	C₂×D₄	—	4	2	no	—
1060	C₂×D₄	—	7	2	no	—
1061	C₂×D₄	—	7	2	no	—
1062	C₂×D₄	—	7	2	no	—
1063	C₂×D₄	—	7	2	no	—
1064	C₂×D₄	—	7	2	no	—
1065	C₂×D₄	—	7	2	no	—
1066	C₂×D₄	—	7	2	no	—
1067	C₂×D₄	—	7	2	no	—
1068	C₂×D₄	—	7	2	no	—
1069	C₂×D₄	—	7	2	no	—
1070	C₂×D₄	—	7	2	no	—
1071	C₂×D₄	—	7	2	no	—
1072	C₂×D₄	—	7	2	no	—
1073	C₂×D₄	—	7	2	no	—
1074	C₂×D₄	—	7	2	no	—
1075	C₂×D₄	—	7	2	no	—
1076	C₂×D₄	—	7	1	no	—
1077	C₂×D₄	—	28	4	no	—
1078	C₂×D₄	—	28	4	no	—
1079	C₂×D₄	—	28	4	no	—
1080	C₂×D₄	—	28	4	no	—
1081	C₂×D₄	—	28	4	no	—
1082	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
1083	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1084	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1085	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1086	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1087	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
1088	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
1089	C₂×D₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1090	C₂²×C₄	—	7	2	no	—
1091	C₂²×C₄	—	7	2	no	—
1092	C₂²×C₄	—	7	2	no	—
1093	C₂²×C₄	—	7	2	no	—
1094	C₂²×C₄	—	7	2	no	—
1095	C₂²×C₄	—	7	2	no	—
1096	C₂²×C₄	—	7	2	no	—
1097	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
1098	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1099	C₂²×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1100	C₄⋊C₄	—	7	2	no	—
1101	C₄⋊C₄	—	7	2	no	—
1102	C₄⋊C₄	—	7	2	no	—
1103	C₄⋊C₄	—	7	2	no	—
1104	C₄⋊C₄	—	7	2	no	—
1105	C₄⋊C₄	—	7	2	no	—
1106	C₄⋊C₄	—	7	2	no	—
1107	C₄⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1108	C₄⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1109	C₂²⋊C₄	—	7	2	no	—
1110	C₂²⋊C₄	—	7	1	no	—
1111	C₂²⋊C₄	—	7	2	no	—
1112	C₂²⋊C₄	—	7	2	no	—
1113	C₂²⋊C₄	—	7	2	no	—
1114	C₂²⋊C₄	—	7	1	no	—
1115	C₂²⋊C₄	—	7	2	no	—
1116	C₂²⋊C₄	—	7	2	no	—
1117	C₂²⋊C₄	—	7	2	no	—
1118	C₂²⋊C₄	—	7	2	no	—
1119	C₂²⋊C₄	—	7	2	no	—
1120	C₂²⋊C₄	—	7	2	no	—
1121	C₂²⋊C₄	—	7	2	no	—
1122	C₂²⋊C₄	—	7	2	no	—
1123	C₂²⋊C₄	—	7	2	no	—
1124	C₂²⋊C₄	—	7	2	no	—
1125	C₂²⋊C₄	—	7	2	no	—
1126	C₂²⋊C₄	—	7	2	no	—
1127	C₂²⋊C₄	—	7	2	no	—
1128	C₂²⋊C₄	—	7	2	no	—
1129	C₂²⋊C₄	—	7	2	no	—
1130	C₂²⋊C₄	—	7	2	no	—
1131	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
1132	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
1133	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	—
1134	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1135	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1136	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
1137	C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	1	2	yes	complemented
1138	C₄²	—	7	1	no	—
1139	C₄²	—	7	2	no	—
1140	C₄²	—	7	1	no	—
1141	C₄²	—	7	2	no	—
1142	C₂×C₇	—	2	2	no	—
1143	C₂×C₇	—	4	1	no	—
1144	C₂×C₇	—	4	1	no	—
1145	C₂×C₇	—	4	2	no	—
1146	C₂×C₇	—	4	1	no	—
1147	C₂×C₇	—	4	1	no	—
1148	C₂×C₇	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1149	C₂×C₇	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1150	D₇	—	2	4	no	—
1151	D₇	—	4	2	no	—
1152	D₇	—	4	2	no	—
1153	C₂²×C₃	—	7	4	no	—
1154	C₂²×C₃	—	7	2	no	—
1155	C₂²×C₃	—	7	1	no	—
1156	C₂²×C₃	—	14	2	no	—
1157	C₂²×C₃	—	14	2	no	—
1158	C₂²×C₃	—	14	1	no	—
1159	C₂²×C₃	—	14	2	no	—
1160	C₂²×C₃	—	14	2	no	—
1161	C₂²×C₃	—	14	2	no	—
1162	C₂²×C₃	—	14	2	no	—
1163	C₂²×C₃	—	14	1	no	—
1164	C₂²×C₃	—	14	1	no	—
1165	C₂²×C₃	—	14	1	no	—
1166	C₂²×C₃	—	14	2	no	—
1167	C₂²×C₃	—	14	2	no	—
1168	C₂²×C₃	—	14	2	no	—
1169	C₂²×C₃	—	14	2	no	—
1170	C₂²×C₃	—	14	2	no	—
1171	C₂²×C₃	—	14	2	no	—
1172	C₂²×C₃	—	14	2	no	—
1173	C₂²×C₃	—	14	2	no	—
1174	C₂²×C₃	—	14	2	no	—
1175	C₂²×C₃	—	14	2	no	—
1176	C₂²×C₃	—	28	4	no	—
1177	C₂²×C₃	—	28	8	no	—
1178	C₂²×C₃	—	28	4	no	—
1179	C₂²×C₃	—	28	8	no	—
1180	C₂²×C₃	—	28	4	no	—
1181	C₂²×C₃	—	56	2	no	—
1182	C₂²×C₃	—	56	2	no	—
1183	C₂²×C₃	—	56	4	no	—
1184	C₃×C₄	—	14	1	no	—
1185	C₃×C₄	—	14	2	no	—
1186	C₃×C₄	—	14	1	no	—
1187	C₃×C₄	—	14	2	no	—
1188	C₃×C₄	—	14	2	no	—
1189	C₃×C₄	—	14	2	no	—
1190	C₃×C₄	—	14	2	no	—
1191	C₃×C₄	—	14	2	no	—
1192	C₃×C₄	—	14	2	no	—
1193	C₃×C₄	—	14	2	no	—
1194	C₂³	—	2	2	no	—
1195	C₂³	—	2	2	no	—
1196	C₂³	—	4	2	no	—
1197	C₂³	—	4	1	no	—
1198	C₂³	—	4	2	no	—
1199	C₂³	—	4	2	no	—
1200	C₂³	—	7	2	no	—
1201	C₂³	—	7	2	no	—
1202	C₂³	—	7	2	no	—
1203	C₂³	—	14	4	no	—
1204	C₂³	—	14	4	no	—
1205	C₂³	—	14	4	no	—
1206	C₂³	—	14	4	no	—
1207	C₂³	—	14	4	no	—
1208	C₂³	—	28	2	no	—
1209	C₂³	—	28	1	no	—
1210	C₂³	—	28	2	no	—
1211	C₂³	—	28	1	no	—
1212	C₂³	—	28	2	no	—
1213	C₂³	—	28	2	no	—
1214	C₂³	—	28	2	no	—
1215	C₂³	—	28	2	no	—
1216	C₂³	—	28	16	no	—
1217	C₂³	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1218	C₂³	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1219	C₂³	C₂³×AGL(1,𝔽₇)	1	2	yes	—
1220	C₂³	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1221	C₂³	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1222	C₂³	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1223	Q₈	—	28	1	no	—
1224	Q₈	—	28	2	no	—
1225	D₄	—	2	4	no	—
1226	D₄	—	4	1	no	—
1227	D₄	—	4	1	no	—
1228	D₄	—	4	1	no	—
1229	D₄	—	4	1	no	—
1230	D₄	—	4	2	no	—
1231	D₄	—	4	2	no	—
1232	D₄	—	4	2	no	—
1233	D₄	—	14	4	no	—
1234	D₄	—	14	4	no	—
1235	D₄	—	14	4	no	—
1236	D₄	—	14	4	no	—
1237	D₄	—	14	4	no	—
1238	D₄	—	28	2	no	—
1239	D₄	—	28	2	no	—
1240	D₄	—	28	1	no	—
1241	D₄	—	28	2	no	—
1242	D₄	—	28	2	no	—
1243	D₄	—	28	2	no	—
1244	D₄	—	28	2	no	—
1245	D₄	—	28	2	no	—
1246	D₄	—	28	2	no	—
1247	D₄	—	28	2	no	—
1248	D₄	—	28	2	no	—
1249	D₄	—	28	2	no	—
1250	C₂×C₄	—	2	2	no	—
1251	C₂×C₄	—	4	1	no	—
1252	C₂×C₄	—	4	2	no	—
1253	C₂×C₄	—	7	2	no	—
1254	C₂×C₄	—	7	2	no	—
1255	C₂×C₄	—	7	2	no	—
1256	C₂×C₄	—	7	2	no	—
1257	C₂×C₄	—	7	2	no	—
1258	C₂×C₄	—	14	4	no	—
1259	C₂×C₄	—	28	2	no	—
1260	C₂×C₄	—	28	2	no	—
1261	C₂×C₄	—	28	2	no	—
1262	C₂×C₄	—	28	2	no	—
1263	C₂×C₄	—	28	2	no	—
1264	C₂×C₄	—	28	2	no	—
1265	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1266	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	2	yes	—
1267	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	2	yes	—
1268	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
1269	C₂×C₄	C₂³×AGL(1,𝔽₇)	1	2	yes	—
1270	C₇	C₃×#3532	1	1	yes	characteristic, complemented, Sylow
1271	C₂×C₃	—	7	1	no	—
1272	C₂×C₃	—	7	2	no	—
1273	C₂×C₃	—	14	2	no	—
1274	C₂×C₃	—	14	4	no	—
1275	C₂×C₃	—	28	1	no	—
1276	C₂×C₃	—	28	1	no	—
1277	C₂×C₃	—	28	1	no	—
1278	C₂×C₃	—	28	2	no	—
1279	C₂×C₃	—	28	1	no	—
1280	C₂×C₃	—	28	2	no	—
1281	C₂×C₃	—	28	2	no	—
1282	C₂²	—	2	2	no	—
1283	C₂²	—	2	1	no	—
1284	C₂²	—	2	2	no	—
1285	C₂²	—	2	1	no	—
1286	C₂²	—	2	1	no	—
1287	C₂²	—	2	1	no	—
1288	C₂²	—	2	2	no	—
1289	C₂²	—	2	2	no	—
1290	C₂²	—	2	2	no	—
1291	C₂²	—	2	2	no	—
1292	C₂²	—	2	2	no	—
1293	C₂²	—	2	2	no	—
1294	C₂²	—	4	4	no	—
1295	C₂²	—	7	4	no	—
1296	C₂²	—	8	2	no	—
1297	C₂²	—	8	2	no	—
1298	C₂²	—	14	2	no	—
1299	C₂²	—	14	2	no	—
1300	C₂²	—	14	2	no	—
1301	C₂²	—	14	2	no	—
1302	C₂²	—	14	2	no	—
1303	C₂²	—	14	2	no	—
1304	C₂²	—	14	2	no	—
1305	C₂²	—	14	2	no	—
1306	C₂²	—	28	8	no	—
1307	C₂²	—	28	4	no	—
1308	C₂²	—	28	8	no	—
1309	C₂²	—	28	4	no	—
1310	C₂²	—	56	4	no	—
1311	C₂²	#6548⋊C₃	1	2	yes	—
1312	C₂²	C₂⁴×AGL(1,𝔽₇)	1	1	yes	characteristic
1313	C₄	—	2	1	no	—
1314	C₄	—	2	1	no	—
1315	C₄	—	2	2	no	—
1316	C₄	—	2	2	no	—
1317	C₄	—	2	2	no	—
1318	C₄	—	14	2	no	—
1319	C₄	—	14	2	no	—
1320	C₄	—	14	2	no	—
1321	C₄	—	14	2	no	—
1322	C₄	—	14	2	no	—
1323	C₃	—	7	1	no	Sylow
1324	C₂	—	2	2	no	—
1325	C₂	—	4	1	no	—
1326	C₂	—	4	1	no	—
1327	C₂	—	4	1	no	—
1328	C₂	—	4	2	no	—
1329	C₂	—	4	1	no	—
1330	C₂	—	14	4	no	—
1331	C₂	—	28	2	no	—
1332	C₂	—	28	2	no	—
1333	C₂	C₂×#6548⋊C₃	1	1	yes	characteristic
1334	C₂	H(5,𝔽₂)×AGL(1,𝔽₇)	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₇	C₂⁵×C₃
Fitting	C₇×#534	C₂×C₃
hypercenter	#534	AGL(1,𝔽₇)
hypocenter	C₇	C₃×#3532
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #534

Complements

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

N	H ≅ G/N	type
1. ΓL(1,𝔽₈)×#534	C₂	semidirect
2. #90496⋊C₃	C₂	semidirect
3. D₄×(C₂²⋊D₇)⋊C₃	C₂	semidirect
4. C₂×#6500⋊C₃	C₂	semidirect
5. #90357⋊C₃	C₂	semidirect
6. #90350⋊C₃	C₂	semidirect
7. #90349⋊C₃	C₂	semidirect
8. #90348⋊C₃	C₂	semidirect
9. #90345⋊C₃	C₂	semidirect
10. #90311⋊C₃	C₂	semidirect
11. #90304⋊C₃	C₂	semidirect
12. #90303⋊C₃	C₂	semidirect
13. #90298⋊C₃	C₂	semidirect
14. #13057328	C₂	semidirect
15. #90284⋊C₃	C₂	semidirect
16. #90281⋊C₃	C₂	semidirect
17. #90280⋊C₃	C₂	semidirect
18. #120×AGL(1,𝔽₇)	C₂	semidirect
19. #90181⋊C₃	C₂	semidirect
20. #11743378	C₃	semidirect
21. C₂⁴×AGL(1,𝔽₇)	C₂²	semidirect
22. C₂²×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
23. C₂²×D₄×ΓL(1,𝔽₈)	C₂²	semidirect
24. C₂²×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
25. C₂²×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
26. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
27. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
28. C₂×D₄×AGL(1,𝔽₇)	C₂²	semidirect
29. C₂×#1157⋊C₃	C₂²	semidirect
30. C₂×#1157⋊C₃	C₂²	semidirect
31. ΓL(1,𝔽₈)×#123	C₂²	semidirect
32. ΓL(1,𝔽₈)×#123	C₂²	semidirect
33. ΓL(1,𝔽₈)×#123	C₂²	semidirect
34. ΓL(1,𝔽₈)×#121	C₂²	semidirect
35. ΓL(1,𝔽₈)×#121	C₂²	semidirect
36. ΓL(1,𝔽₈)×#120	C₂²	semidirect
37. ΓL(1,𝔽₈)×#120	C₂²	semidirect
38. ΓL(1,𝔽₈)×#120	C₂²	semidirect
39. C₂×C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
40. #10620789	C₂²	semidirect
41. #10620789	C₂²	semidirect
42. #10620789	C₂²	semidirect
43. C₂×(C₂²⋊Dic₇)⋊C₃	C₂²	semidirect
44. #6503⋊C₃	C₂²	semidirect
45. #6503⋊C₃	C₂²	semidirect
46. #6503⋊C₃	C₂²	semidirect
47. #6502⋊C₃	C₂²	semidirect
48. #6502⋊C₃	C₂²	semidirect
49. #6502⋊C₃	C₂²	semidirect
50. #6501⋊C₃	C₂²	semidirect
51. #6501⋊C₃	C₂²	semidirect
52. #6501⋊C₃	C₂²	semidirect
53. #6501⋊C₃	C₂²	semidirect
56. #6500⋊C₃	C₂²	semidirect
57. #6500⋊C₃	C₂²	semidirect
58. #6500⋊C₃	C₂²	semidirect
59. #6500⋊C₃	C₂²	semidirect
60. #6500⋊C₃	C₂²	semidirect
61. #6500⋊C₃	C₂²	semidirect
62. #6500⋊C₃	C₂²	semidirect
63. #6500⋊C₃	C₂²	semidirect
64. #6499⋊C₃	C₂²	semidirect
65. #6499⋊C₃	C₂²	semidirect
66. #6499⋊C₃	C₂²	semidirect
67. #6498⋊C₃	C₂²	semidirect
68. D₄×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
69. #6493⋊C₃	C₂²	semidirect
70. #6493⋊C₃	C₂²	semidirect
71. #6492⋊C₃	C₂²	semidirect
72. C₄×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
73. C₄×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
74. C₂×(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	semidirect
75. #6489⋊C₃	C₂²	semidirect
76. #6461⋊C₃	C₂²	semidirect
77. #6461⋊C₃	C₂²	semidirect
78. #6460⋊C₃	C₂²	semidirect
79. #6459⋊C₃	C₂²	semidirect
80. #6458⋊C₃	C₂²	semidirect
81. #6457⋊C₃	C₂²	semidirect
82. #6456⋊C₃	C₂²	semidirect
83. #6455⋊C₃	C₂²	semidirect
84. #6449⋊C₃	C₂²	semidirect
85. #6448⋊C₃	C₂²	semidirect
86. #6448⋊C₃	C₂²	semidirect
87. #6448⋊C₃	C₂²	semidirect
88. #6448⋊C₃	C₂²	semidirect
89. #6447⋊C₃	C₂²	semidirect
90. #6447⋊C₃	C₂²	semidirect
91. #6447⋊C₃	C₂²	semidirect
92. #6446⋊C₃	C₂²	semidirect
93. #6446⋊C₃	C₂²	semidirect
94. #6446⋊C₃	C₂²	semidirect
95. #6445⋊C₃	C₂²	semidirect
96. #6445⋊C₃	C₂²	semidirect
97. #6445⋊C₃	C₂²	semidirect
98. #6445⋊C₃	C₂²	semidirect
99. ((C₂²⋊D₇)⋊C₃)⋊C₄	C₂²	semidirect
100. ((C₂²⋊D₇)⋊C₃)⋊C₄	C₂²	semidirect
101. C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	semidirect
102. C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	semidirect
103. C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	semidirect
104. C₂²⋊C₄×AGL(1,𝔽₇)	C₂²	semidirect
105. #6442⋊C₃	C₂²	semidirect
106. #6442⋊C₃	C₂²	semidirect
107. #6441⋊C₃	C₂²	semidirect
108. C₇×#534	C₂×C₃	semidirect
109. #90496	C₂×C₃	semidirect
110. D₄×C₂²⋊D₇	C₂×C₃	semidirect
111. C₂×#6500	C₂×C₃	semidirect
112. #90357	C₂×C₃	semidirect
113. #90350	C₂×C₃	semidirect
114. #90349	C₂×C₃	semidirect
115. #90348	C₂×C₃	semidirect
116. #90345	C₂×C₃	semidirect
117. #90311	C₂×C₃	semidirect
118. #90304	C₂×C₃	semidirect
119. #90303	C₂×C₃	semidirect
120. #90298	C₂×C₃	semidirect
121. #90285	C₂×C₃	semidirect
122. #90284	C₂×C₃	semidirect
123. #90281	C₂×C₃	semidirect
124. #90280	C₂×C₃	semidirect
125. D₇×#120	C₂×C₃	semidirect
126. #90181	C₂×C₃	semidirect
130. C₂⁴×ΓL(1,𝔽₈)	C₂³	semidirect
147. C₂×D₄×ΓL(1,𝔽₈)	C₂³	semidirect
149. C₂²×C₄×ΓL(1,𝔽₈)	C₂³	semidirect
150. C₂²×C₄×ΓL(1,𝔽₈)	C₂³	semidirect
163. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
164. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
165. C₂×(C₂²⋊D₇)⋊C₃	C₂³	semidirect
167. C₂²×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
176. C₂×C₄⋊AGL(1,𝔽₇)	C₂³	semidirect
180. C₂×C₄×AGL(1,𝔽₇)	C₂³	semidirect
181. C₂×C₄×AGL(1,𝔽₇)	C₂³	semidirect
182. C₂×ΓL(1,𝔽₈)⋊Q₈	C₂³	semidirect
183. C₂×ΓL(1,𝔽₈)⋊Q₈	C₂³	semidirect
184. C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
185. C₄⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
189. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
190. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
191. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
192. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂³	semidirect
199. (C₂²⋊Dic₇)⋊C₃	C₂³	semidirect
200. (C₂²⋊Dic₇)⋊C₃	C₂³	semidirect
201. (C₂²⋊Dic₇)⋊C₃	C₂³	semidirect
202. (C₂²⋊Dic₇)⋊C₃	C₂³	semidirect
213. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
214. (C₂×AGL(1,𝔽₇))⋊C₄	C₂³	semidirect
215. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	semidirect
216. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	semidirect
217. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂³	semidirect
218. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	semidirect
219. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	semidirect
220. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	semidirect
221. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂³	semidirect
222. C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
223. C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
224. C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
225. C₄×ΓL(1,𝔽₈)⋊C₄	C₂³	semidirect
226. C₂⁴×D₇	C₂²×C₃	semidirect
227. C₂²×C₇×D₄	C₂²×C₃	semidirect
228. C₂²×C₇×D₄	C₂²×C₃	semidirect
229. C₂²×C₂²⋊D₇	C₂²×C₃	semidirect
230. C₂²×C₂²⋊D₇	C₂²×C₃	semidirect
231. C₂×D₄×D₇	C₂²×C₃	semidirect
232. C₂×D₄×D₇	C₂²×C₃	semidirect
233. C₂×D₄×D₇	C₂²×C₃	semidirect
234. C₂×#1157	C₂²×C₃	semidirect
235. C₂×#1157	C₂²×C₃	semidirect
236. C₇×#123	C₂²×C₃	semidirect
237. C₇×#123	C₂²×C₃	semidirect
238. C₇×#123	C₂²×C₃	semidirect
239. C₇×#121	C₂²×C₃	semidirect
240. C₇×#121	C₂²×C₃	semidirect
241. C₇×#120	C₂²×C₃	semidirect
242. C₇×#120	C₂²×C₃	semidirect
243. C₇×#120	C₂²×C₃	semidirect
244. C₂×C₇×C₂²⋊C₄	C₂²×C₃	semidirect
245. #6516	C₂²×C₃	semidirect
246. #6516	C₂²×C₃	semidirect
247. #6516	C₂²×C₃	semidirect
248. C₂×C₂²⋊Dic₇	C₂²×C₃	semidirect
249. #6503	C₂²×C₃	semidirect
250. #6503	C₂²×C₃	semidirect
251. #6503	C₂²×C₃	semidirect
252. #6502	C₂²×C₃	semidirect
253. #6502	C₂²×C₃	semidirect
254. #6502	C₂²×C₃	semidirect
255. #6501	C₂²×C₃	semidirect
256. #6501	C₂²×C₃	semidirect
257. #6501	C₂²×C₃	semidirect
258. #6501	C₂²×C₃	semidirect
261. #6500	C₂²×C₃	semidirect
262. #6500	C₂²×C₃	semidirect
263. #6500	C₂²×C₃	semidirect
264. #6500	C₂²×C₃	semidirect
265. #6500	C₂²×C₃	semidirect
266. #6500	C₂²×C₃	semidirect
267. #6500	C₂²×C₃	semidirect
268. #6500	C₂²×C₃	semidirect
269. #6499	C₂²×C₃	semidirect
270. #6499	C₂²×C₃	semidirect
271. #6499	C₂²×C₃	semidirect
272. #6498	C₂²×C₃	semidirect
273. D₄×Dic₇	C₂²×C₃	semidirect
274. #6493	C₂²×C₃	semidirect
275. #6493	C₂²×C₃	semidirect
276. #6492	C₂²×C₃	semidirect
277. C₄×C₂²⋊D₇	C₂²×C₃	semidirect
278. C₄×C₂²⋊D₇	C₂²×C₃	semidirect
279. C₂×(C₂×D₇)⋊C₄	C₂²×C₃	semidirect
280. #6489	C₂²×C₃	semidirect
281. #6461	C₂²×C₃	semidirect
282. #6461	C₂²×C₃	semidirect
283. #6460	C₂²×C₃	semidirect
284. #6459	C₂²×C₃	semidirect
285. #6458	C₂²×C₃	semidirect
286. #6457	C₂²×C₃	semidirect
287. #6456	C₂²×C₃	semidirect
288. #6455	C₂²×C₃	semidirect
289. #6449	C₂²×C₃	semidirect
290. #6448	C₂²×C₃	semidirect
291. #6448	C₂²×C₃	semidirect
292. #6448	C₂²×C₃	semidirect
293. #6448	C₂²×C₃	semidirect
294. #6447	C₂²×C₃	semidirect
295. #6447	C₂²×C₃	semidirect
296. #6447	C₂²×C₃	semidirect
297. #6446	C₂²×C₃	semidirect
298. #6446	C₂²×C₃	semidirect
299. #6446	C₂²×C₃	semidirect
300. #6445	C₂²×C₃	semidirect
301. #6445	C₂²×C₃	semidirect
302. #6445	C₂²×C₃	semidirect
303. #6445	C₂²×C₃	semidirect
304. (C₂²⋊D₇)⋊C₄	C₂²×C₃	semidirect
305. (C₂²⋊D₇)⋊C₄	C₂²×C₃	semidirect
306. D₇×C₂²⋊C₄	C₂²×C₃	semidirect
307. D₇×C₂²⋊C₄	C₂²×C₃	semidirect
308. D₇×C₂²⋊C₄	C₂²×C₃	semidirect
309. D₇×C₂²⋊C₄	C₂²×C₃	semidirect
310. #6442	C₂²×C₃	semidirect
311. #6442	C₂²×C₃	semidirect
312. #6441	C₂²×C₃	semidirect
411. C₂⁴×C₇	C₂³×C₃	semidirect
428. C₂×C₇×D₄	C₂³×C₃	semidirect
430. C₂²×C₄×C₇	C₂³×C₃	semidirect
431. C₂²×C₄×C₇	C₂³×C₃	semidirect
444. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
445. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
446. C₂×C₂²⋊D₇	C₂³×C₃	semidirect
448. C₂²×Dic₇	C₂³×C₃	semidirect
457. C₂×D₂₈	C₂³×C₃	semidirect
461. C₂×C₄×D₇	C₂³×C₃	semidirect
462. C₂×C₄×D₇	C₂³×C₃	semidirect
463. C₂×Dic₁₄	C₂³×C₃	semidirect
464. C₂×Dic₁₄	C₂³×C₃	semidirect
465. C₇×C₄⋊C₄	C₂³×C₃	semidirect
466. C₇×C₄⋊C₄	C₂³×C₃	semidirect
470. C₇×C₂²⋊C₄	C₂³×C₃	semidirect
471. C₇×C₂²⋊C₄	C₂³×C₃	semidirect
472. C₇×C₂²⋊C₄	C₂³×C₃	semidirect
473. C₇×C₂²⋊C₄	C₂³×C₃	semidirect
480. C₂²⋊Dic₇	C₂³×C₃	semidirect
481. C₂²⋊Dic₇	C₂³×C₃	semidirect
482. C₂²⋊Dic₇	C₂³×C₃	semidirect
483. C₂²⋊Dic₇	C₂³×C₃	semidirect
494. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
495. (C₂×D₇)⋊C₄	C₂³×C₃	semidirect
496. C₄⋊Dic₇	C₂³×C₃	semidirect
497. C₄⋊Dic₇	C₂³×C₃	semidirect
498. C₄⋊Dic₇	C₂³×C₃	semidirect
499. Dic₇⋊C₄	C₂³×C₃	semidirect
500. Dic₇⋊C₄	C₂³×C₃	semidirect
501. Dic₇⋊C₄	C₂³×C₃	semidirect
502. Dic₇⋊C₄	C₂³×C₃	semidirect
503. C₄×Dic₇	C₂³×C₃	semidirect
504. C₄×Dic₇	C₂³×C₃	semidirect
505. C₄×Dic₇	C₂³×C₃	semidirect
506. C₄×Dic₇	C₂³×C₃	semidirect
651. #534	AGL(1,𝔽₇)	semidirect
847. C₂²×D₄	C₂×AGL(1,𝔽₇)	semidirect
848. C₂²×D₄	C₂×AGL(1,𝔽₇)	semidirect
870. #123	C₂×AGL(1,𝔽₇)	semidirect
871. #123	C₂×AGL(1,𝔽₇)	semidirect
872. #123	C₂×AGL(1,𝔽₇)	semidirect
889. #121	C₂×AGL(1,𝔽₇)	semidirect
890. #121	C₂×AGL(1,𝔽₇)	semidirect
908. #120	C₂×AGL(1,𝔽₇)	semidirect
909. #120	C₂×AGL(1,𝔽₇)	semidirect
910. #120	C₂×AGL(1,𝔽₇)	semidirect
925. C₂×C₂²⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
1043. ΓL(1,𝔽₈)	#3532	semidirect
1053. C₂⁴	C₂²×AGL(1,𝔽₇)	semidirect
1089. C₂×D₄	C₂²×AGL(1,𝔽₇)	semidirect
1098. C₂²×C₄	C₂²×AGL(1,𝔽₇)	semidirect
1099. C₂²×C₄	C₂²×AGL(1,𝔽₇)	semidirect
1107. C₄⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1108. C₄⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1134. C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1135. C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1136. C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1137. C₂²⋊C₄	C₂²×AGL(1,𝔽₇)	semidirect
1270. C₇	C₃×#3532	semidirect

Maximal subgroups

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

subgroup	index
ΓL(1,𝔽₈)×#534	2
#90496⋊C₃	2
D₄×(C₂²⋊D₇)⋊C₃	2
C₂×#6500⋊C₃	2
#90357⋊C₃	2
#90350⋊C₃	2
#90349⋊C₃	2
#90348⋊C₃	2
#90345⋊C₃	2
#90311⋊C₃	2
#90304⋊C₃	2
#90303⋊C₃	2
#90298⋊C₃	2
#13057328	2
#90284⋊C₃	2
#90281⋊C₃	2
#90280⋊C₃	2
#120×AGL(1,𝔽₇)	2
#90181⋊C₃	2
#11743378	3
C₃×#3532	7