Subgroups — #90238⋊C₃ #13057284

Order 1344.

660 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1157⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#6502⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#6500⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×(C₂²⋊D₇)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×(C₂²⋊D₇)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#6459⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#6457⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#6447⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#6446⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#6445⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#6441⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₄⋊AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
15	#6435⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#90238	C₃	1	1	yes	maximal, characteristic, complemented, Hall
17	C₂³×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
18	C₂×D₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
19	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
20	C₂²×C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
21	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic
22	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic
23	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic
24	C₂×(C₂²⋊D₇)⋊C₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic
26	#1157⋊C₃	—	2	4	no	—
27	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
29	C₂×C₄×AGL(1,𝔽₇)	—	2	4	no	—
30	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
31	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
32	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
33	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic
34	C₂×C₄×AGL(1,𝔽₇)	C₂²	1	1	yes	characteristic, complemented
35	C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
37	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
39	C₄²×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented
40	(C₂²⋊Dic₇)⋊C₃	C₂²	1	1	yes	characteristic
41	(C₂²⋊Dic₇)⋊C₃	C₂²	1	1	yes	characteristic, complemented
42	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic
43	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic
44	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic
45	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic
46	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	(C₂×AGL(1,𝔽₇))⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	1	1	yes	characteristic, complemented
49	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	(ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₂×#1157	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂²×C₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
57	#6502	C₂×C₃	1	1	yes	characteristic, complemented
58	#6500	C₂×C₃	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
60	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
61	#6459	C₂×C₃	1	1	yes	characteristic, complemented
62	#6457	C₂×C₃	1	1	yes	characteristic, complemented
63	#6447	C₂×C₃	1	1	yes	characteristic, complemented
64	#6446	C₂×C₃	1	1	yes	characteristic, complemented
65	#6445	C₂×C₃	1	1	yes	characteristic, complemented
66	#6441	C₂×C₃	1	1	yes	characteristic, complemented
67	C₄×D₂₈	C₂×C₃	1	1	yes	characteristic, complemented
68	#6435	C₂×C₃	1	1	yes	characteristic, complemented
69	C₃×#525	—	7	1	no	maximal, Hall
70	C₂³×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
71	C₂³×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
72	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
73	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
74	C₂²×AGL(1,𝔽₇)	—	2	2	no	—
75	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
76	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
77	C₂²×AGL(1,𝔽₇)	C₂³	1	1	yes	characteristic
78	D₄×ΓL(1,𝔽₈)	—	2	2	no	—
79	C₂×C₄×ΓL(1,𝔽₈)	—	2	2	no	—
80	C₂×C₄×ΓL(1,𝔽₈)	—	2	2	no	—
81	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
82	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
83	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
84	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
85	C₂×C₄×ΓL(1,𝔽₈)	C₂³	1	1	yes	characteristic
86	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
87	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
88	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
89	(C₂²⋊D₇)⋊C₃	—	2	2	no	—
90	C₂×ΓL(1,𝔽₈)⋊C₄	—	2	2	no	—
91	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×ΓL(1,𝔽₈)⋊C₄	C₂³	1	1	yes	characteristic
96	C₄⋊AGL(1,𝔽₇)	—	2	2	no	—
97	C₄⋊AGL(1,𝔽₇)	—	2	2	no	—
98	C₄×AGL(1,𝔽₇)	—	2	2	no	—
99	C₄×AGL(1,𝔽₇)	—	2	2	no	—
100	C₄×AGL(1,𝔽₇)	—	2	2	no	—
101	C₄×AGL(1,𝔽₇)	—	2	2	no	—
102	C₄×AGL(1,𝔽₇)	D₄	1	4	yes	complemented
103	ΓL(1,𝔽₈)⋊Q₈	—	2	2	no	—
104	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic
113	#1157	—	2	4	no	—
114	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
115	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₄×D₇	—	2	4	no	—
117	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic
128	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
129	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
134	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
135	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
136	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
137	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
138	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
139	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
141	C₂×C₃×#41	—	7	1	no	—
142	C₂³×C₃×C₄	—	7	1	no	—
143	C₃×#123	—	7	1	no	—
144	C₃×#123	—	7	1	no	—
145	C₃×C₂²⋊Q₈	—	7	1	no	—
146	C₃×C₂²⋊Q₈	—	7	1	no	—
147	C₃×#121	—	7	1	no	—
148	C₃×#121	—	7	1	no	—
149	C₃×#120	—	7	1	no	—
150	C₃×#120	—	7	1	no	—
151	C₃×C₄×D₄	—	7	1	no	—
152	C₃×C₄×D₄	—	7	1	no	—
153	C₃×C₄×D₄	—	7	1	no	—
154	C₃×C₄×D₄	—	7	1	no	—
155	C₃×#117	—	7	1	no	—
156	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
157	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
158	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
159	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
160	C₂²×ΓL(1,𝔽₈)	—	2	1	no	—
161	C₂²×ΓL(1,𝔽₈)	#41	1	2	yes	complemented
162	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	1	yes	characteristic
163	C₂×AGL(1,𝔽₇)	—	2	8	no	—
164	C₂×AGL(1,𝔽₇)	—	2	1	no	—
165	C₂×AGL(1,𝔽₇)	—	2	1	no	—
166	C₂×AGL(1,𝔽₇)	—	2	1	no	—
167	C₂×AGL(1,𝔽₇)	—	2	1	no	—
168	C₂×AGL(1,𝔽₇)	—	2	1	no	—
169	C₂×AGL(1,𝔽₇)	—	2	1	no	—
170	C₂×AGL(1,𝔽₇)	—	2	1	no	—
171	C₂×AGL(1,𝔽₇)	C₂×D₄	1	2	yes	—
172	C₂×AGL(1,𝔽₇)	#41	1	2	yes	complemented
173	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
174	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
175	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
176	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
177	C₄×ΓL(1,𝔽₈)	C₂×D₄	1	2	yes	—
178	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
179	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
180	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
181	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
182	ΓL(1,𝔽₈)⋊C₄	C₂×D₄	1	2	yes	—
183	#525	—	7	1	no	Sylow
184	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
185	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
186	C₂²×D₇	—	2	2	no	—
187	C₂²×D₇	—	2	2	no	—
188	C₂²×D₇	—	2	2	no	—
189	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
190	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
191	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
192	C₇×D₄	—	2	2	no	—
193	C₂×C₄×C₇	—	2	2	no	—
194	C₂×C₄×C₇	—	2	2	no	—
195	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
200	C₂²⋊D₇	—	2	2	no	—
201	C₂²⋊D₇	—	2	2	no	—
202	C₂²⋊D₇	—	2	2	no	—
203	C₂²⋊D₇	—	2	2	no	—
204	C₂×Dic₇	—	2	2	no	—
205	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
206	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
207	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
208	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
209	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
210	D₂₈	—	2	2	no	—
211	D₂₈	—	2	2	no	—
212	C₄×D₇	—	2	2	no	—
213	C₄×D₇	—	2	2	no	—
214	C₄×D₇	—	2	2	no	—
215	C₄×D₇	—	2	2	no	—
216	C₄×D₇	C₃×D₄	1	4	yes	complemented
217	Dic₁₄	—	2	2	no	—
218	C₂⁴×C₃	—	7	1	no	—
219	C₃×#41	—	14	4	no	—
220	C₂×C₃×Q₈	—	7	1	no	—
221	C₂×C₃×D₄	—	7	1	no	—
222	C₂×C₃×D₄	—	7	1	no	—
223	C₂×C₃×D₄	—	7	1	no	—
224	C₂×C₃×D₄	—	7	1	no	—
225	C₂×C₃×D₄	—	7	1	no	—
226	C₂×C₃×D₄	—	7	1	no	—
227	C₂×C₃×D₄	—	7	1	no	—
228	C₂²×C₃×C₄	—	7	1	no	—
229	C₂²×C₃×C₄	—	7	1	no	—
230	C₂²×C₃×C₄	—	7	1	no	—
231	C₂²×C₃×C₄	—	7	1	no	—
232	C₂²×C₃×C₄	—	7	1	no	—
233	C₂²×C₃×C₄	—	7	1	no	—
234	C₂²×C₃×C₄	—	7	1	no	—
235	C₂²×C₃×C₄	—	7	1	no	—
236	C₂²×C₃×C₄	—	14	4	no	—
237	C₃×C₄⋊C₄	—	7	1	no	—
238	C₃×C₄⋊C₄	—	7	1	no	—
239	C₃×C₄⋊C₄	—	7	1	no	—
240	C₃×C₄⋊C₄	—	7	1	no	—
241	C₃×C₄⋊C₄	—	7	1	no	—
242	C₃×C₄⋊C₄	—	7	1	no	—
243	C₃×C₂²⋊C₄	—	7	1	no	—
244	C₃×C₂²⋊C₄	—	7	1	no	—
245	C₃×C₂²⋊C₄	—	7	1	no	—
246	C₃×C₂²⋊C₄	—	7	1	no	—
247	C₃×C₂²⋊C₄	—	7	1	no	—
248	C₃×C₂²⋊C₄	—	7	1	no	—
249	C₃×C₂²⋊C₄	—	7	1	no	—
250	C₃×C₂²⋊C₄	—	7	1	no	—
251	C₃×C₂²⋊C₄	—	7	1	no	—
252	C₃×C₂²⋊C₄	—	7	1	no	—
253	C₃×C₄²	—	7	1	no	—
254	C₃×C₄²	—	7	1	no	—
255	C₂×ΓL(1,𝔽₈)	—	2	2	no	—
256	C₂×ΓL(1,𝔽₈)	—	4	1	no	—
257	C₂×ΓL(1,𝔽₈)	C₂²×D₄	1	1	yes	characteristic
258	C₂×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
259	C₂×ΓL(1,𝔽₈)	C₂×#41	1	1	yes	characteristic
260	AGL(1,𝔽₇)	—	2	2	no	—
261	AGL(1,𝔽₇)	—	2	2	no	—
262	AGL(1,𝔽₇)	—	4	1	no	—
263	C₂×#41	—	7	1	no	—
264	C₂³×C₄	—	7	1	no	—
265	#123	—	7	1	no	—
266	#123	—	7	1	no	—
267	C₂²⋊Q₈	—	7	1	no	—
268	C₂²⋊Q₈	—	7	1	no	—
269	#121	—	7	1	no	—
270	#121	—	7	1	no	—
271	#120	—	7	1	no	—
272	#120	—	7	1	no	—
273	C₄×D₄	—	7	1	no	—
274	C₄×D₄	—	7	1	no	—
275	C₄×D₄	—	7	1	no	—
276	C₄×D₄	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
277	#117	—	7	1	no	—
278	C₂²×C₇	—	2	1	no	—
279	C₂²×C₇	—	2	1	no	—
280	C₂²×C₇	—	2	1	no	—
281	C₂²×C₇	—	2	1	no	—
282	C₂²×C₇	—	2	1	no	—
283	C₂²×C₇	C₃×#41	1	2	yes	complemented
284	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
285	C₂×D₇	—	2	8	no	—
286	C₂×D₇	—	2	1	no	—
287	C₂×D₇	—	2	1	no	—
288	C₂×D₇	—	2	1	no	—
289	C₂×D₇	—	2	1	no	—
290	C₂×D₇	—	2	1	no	—
291	C₂×D₇	—	2	1	no	—
292	C₂×D₇	—	2	1	no	—
293	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
294	C₂×D₇	C₃×#41	1	2	yes	complemented
295	C₄×C₇	—	2	1	no	—
296	C₄×C₇	—	2	1	no	—
297	C₄×C₇	—	2	1	no	—
298	C₄×C₇	—	2	1	no	—
299	C₄×C₇	C₂×C₃×D₄	1	2	yes	—
300	Dic₇	—	2	1	no	—
301	Dic₇	—	2	1	no	—
302	Dic₇	—	2	1	no	—
303	Dic₇	—	2	1	no	—
304	Dic₇	C₂×C₃×D₄	1	2	yes	—
305	C₂³×C₃	—	7	1	no	—
306	C₂³×C₃	—	7	1	no	—
307	C₂³×C₃	—	7	1	no	—
308	C₂³×C₃	—	7	1	no	—
309	C₂³×C₃	—	7	1	no	—
310	C₂³×C₃	—	14	2	no	—
311	C₂³×C₃	—	14	2	no	—
312	C₂³×C₃	—	14	2	no	—
313	C₃×Q₈	—	14	2	no	—
314	C₃×D₄	—	14	2	no	—
315	C₃×D₄	—	14	2	no	—
316	C₃×D₄	—	14	2	no	—
317	C₃×D₄	—	14	2	no	—
318	C₃×D₄	—	14	2	no	—
319	C₃×D₄	—	14	2	no	—
320	C₃×D₄	—	14	2	no	—
321	C₂×C₃×C₄	—	7	4	no	—
322	C₂×C₃×C₄	—	7	1	no	—
323	C₂×C₃×C₄	—	7	1	no	—
324	C₂×C₃×C₄	—	7	1	no	—
325	C₂×C₃×C₄	—	7	1	no	—
326	C₂×C₃×C₄	—	7	1	no	—
327	C₂×C₃×C₄	—	7	1	no	—
328	C₂×C₃×C₄	—	7	1	no	—
329	C₂×C₃×C₄	—	7	1	no	—
330	C₂×C₃×C₄	—	7	1	no	—
331	C₂×C₃×C₄	—	7	1	no	—
332	C₂×C₃×C₄	—	14	2	no	—
333	C₂×C₃×C₄	—	14	2	no	—
334	C₂×C₃×C₄	—	14	2	no	—
335	C₂×C₃×C₄	—	14	2	no	—
336	C₂×C₃×C₄	—	14	2	no	—
337	C₂×C₃×C₄	—	14	2	no	—
338	C₂×C₃×C₄	—	14	2	no	—
339	ΓL(1,𝔽₈)	#525	1	1	yes	characteristic, complemented, Hall
340	C₂⁴	—	7	1	no	—
341	#41	—	14	4	no	—
342	C₂×Q₈	—	7	1	no	—
343	C₂×D₄	—	7	1	no	—
344	C₂×D₄	—	7	1	no	—
345	C₂×D₄	—	7	1	no	—
346	C₂×D₄	—	7	1	no	—
347	C₂×D₄	—	7	1	no	—
348	C₂×D₄	—	7	1	no	—
349	C₂×D₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
350	C₂²×C₄	—	7	1	no	—
351	C₂²×C₄	—	7	1	no	—
352	C₂²×C₄	—	7	1	no	—
353	C₂²×C₄	—	7	1	no	—
354	C₂²×C₄	—	7	1	no	—
355	C₂²×C₄	—	7	1	no	—
356	C₂²×C₄	—	14	4	no	—
357	C₂²×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
358	C₂²×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
359	C₄⋊C₄	—	7	1	no	—
360	C₄⋊C₄	—	7	1	no	—
361	C₄⋊C₄	—	7	1	no	—
362	C₄⋊C₄	—	7	1	no	—
363	C₄⋊C₄	—	7	1	no	—
364	C₄⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
365	C₂²⋊C₄	—	7	1	no	—
366	C₂²⋊C₄	—	7	1	no	—
367	C₂²⋊C₄	—	7	1	no	—
368	C₂²⋊C₄	—	7	1	no	—
369	C₂²⋊C₄	—	7	1	no	—
370	C₂²⋊C₄	—	7	1	no	—
371	C₂²⋊C₄	—	7	1	no	—
372	C₂²⋊C₄	—	7	1	no	—
373	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
374	C₂²⋊C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
375	C₄²	—	7	1	no	—
376	C₄²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
377	C₂×C₇	—	2	2	no	—
378	C₂×C₇	—	4	1	no	—
379	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
380	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
381	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
382	D₇	—	2	2	no	—
383	D₇	—	2	2	no	—
384	D₇	—	4	1	no	—
385	C₂²×C₃	—	7	2	no	—
386	C₂²×C₃	—	7	2	no	—
387	C₂²×C₃	—	7	2	no	—
388	C₂²×C₃	—	7	1	no	—
389	C₂²×C₃	—	14	1	no	—
390	C₂²×C₃	—	14	1	no	—
391	C₂²×C₃	—	14	1	no	—
392	C₂²×C₃	—	14	1	no	—
393	C₂²×C₃	—	14	1	no	—
394	C₂²×C₃	—	14	1	no	—
395	C₂²×C₃	—	14	1	no	—
396	C₂²×C₃	—	14	1	no	—
397	C₂²×C₃	—	14	1	no	—
398	C₂²×C₃	—	14	1	no	—
399	C₂²×C₃	—	14	1	no	—
400	C₂²×C₃	—	14	1	no	—
401	C₂²×C₃	—	14	8	no	—
402	C₃×C₄	—	7	2	no	—
403	C₃×C₄	—	7	2	no	—
404	C₃×C₄	—	14	1	no	—
405	C₃×C₄	—	14	1	no	—
406	C₃×C₄	—	14	1	no	—
407	C₃×C₄	—	14	1	no	—
408	C₃×C₄	—	14	1	no	—
409	C₃×C₄	—	14	1	no	—
410	C₃×C₄	—	14	1	no	—
411	C₃×C₄	—	14	1	no	—
412	C₂³	—	7	1	no	—
413	C₂³	—	7	1	no	—
414	C₂³	—	7	1	no	—
415	C₂³	—	14	2	no	—
416	C₂³	—	14	2	no	—
417	C₂³	—	14	2	no	—
418	C₂³	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
419	C₂³	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
420	Q₈	—	14	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	14	2	no	—
423	D₄	—	14	2	no	—
424	D₄	—	14	2	no	—
425	D₄	—	14	2	no	—
426	D₄	—	14	2	no	—
427	D₄	—	14	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	7	1	no	—
431	C₂×C₄	—	7	4	no	—
432	C₂×C₄	—	7	1	no	—
433	C₂×C₄	—	7	1	no	—
434	C₂×C₄	—	7	1	no	—
435	C₂×C₄	—	7	1	no	—
436	C₂×C₄	—	14	2	no	—
437	C₂×C₄	—	14	2	no	—
438	C₂×C₄	—	14	2	no	—
439	C₂×C₄	—	14	2	no	—
440	C₂×C₄	—	14	2	no	—
441	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
442	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
443	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
444	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
445	C₂×C₄	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
446	C₇	C₃×#525	1	1	yes	characteristic, complemented, Sylow
447	C₂×C₃	—	7	1	no	—
448	C₂×C₃	—	7	1	no	—
449	C₂×C₃	—	7	1	no	—
450	C₂×C₃	—	14	2	no	—
451	C₂×C₃	—	14	2	no	—
452	C₂×C₃	—	14	2	no	—
453	C₂×C₃	—	28	1	no	—
454	C₂×C₃	—	28	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	7	2	no	—
461	C₂²	—	7	2	no	—
462	C₂²	—	14	8	no	—
463	C₂²	—	14	1	no	—
464	C₂²	—	14	1	no	—
465	C₂²	—	14	1	no	—
466	C₂²	—	14	1	no	—
467	C₂²	—	14	1	no	—
468	C₂²	—	14	1	no	—
469	C₂²	—	14	1	no	—
470	C₂²	#1157⋊C₃	1	2	yes	complemented
471	C₂²	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	7	2	no	—
477	C₄	—	14	1	no	—
478	C₄	—	14	1	no	—
479	C₄	—	14	1	no	—
480	C₄	—	14	1	no	—
481	C₄	D₄×AGL(1,𝔽₇)	1	2	yes	—
482	C₃	—	7	1	no	Sylow
483	C₂	—	2	2	no	—
484	C₂	—	4	1	no	—
485	C₂	—	14	2	no	—
486	C₂	—	14	2	no	—
487	C₂	—	28	1	no	—
488	C₂	C₂×#1157⋊C₃	1	1	yes	characteristic
489	C₂	C₂×D₄×AGL(1,𝔽₇)	1	1	yes	characteristic
490	C₂	#41×AGL(1,𝔽₇)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×AGL(1,𝔽₇)
commutator, socle, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×AGL(1,𝔽₇)
Fitting	C₄×C₇×D₄	C₂×C₃
hypercenter	C₄×D₄	AGL(1,𝔽₇)
hypocenter	C₇	C₃×#525
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#1157⋊C₃	C₂	semidirect
2. C₂²×C₄×AGL(1,𝔽₇)	C₂	semidirect
3. C₄×D₄×ΓL(1,𝔽₈)	C₂	semidirect
4. #6502⋊C₃	C₂	semidirect
5. #6500⋊C₃	C₂	semidirect
6. C₄×(C₂²⋊D₇)⋊C₃	C₂	semidirect
7. C₄×(C₂²⋊D₇)⋊C₃	C₂	semidirect
8. #6459⋊C₃	C₂	semidirect
9. #6457⋊C₃	C₂	semidirect
10. #6447⋊C₃	C₂	semidirect
11. #6446⋊C₃	C₂	semidirect
12. #6445⋊C₃	C₂	semidirect
13. #6441⋊C₃	C₂	semidirect
14. C₄×C₄⋊AGL(1,𝔽₇)	C₂	semidirect
15. #6435⋊C₃	C₂	semidirect
16. #90238	C₃	semidirect
20. C₂²×C₄×ΓL(1,𝔽₈)	C₂²	semidirect
24. C₂×(C₂²⋊D₇)⋊C₃	C₂²	semidirect
34. C₂×C₄×AGL(1,𝔽₇)	C₂²	semidirect
35. C₂×ΓL(1,𝔽₈)⋊Q₈	C₂²	semidirect
36. C₄⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
38. C₂²⋊C₄×ΓL(1,𝔽₈)	C₂²	semidirect
39. C₄²×ΓL(1,𝔽₈)	C₂²	semidirect
41. (C₂²⋊Dic₇)⋊C₃	C₂²	semidirect
46. (C₂×AGL(1,𝔽₇))⋊C₄	C₂²	semidirect
47. (C₂×AGL(1,𝔽₇))⋊C₄	C₂²	semidirect
48. C₄⋊(ΓL(1,𝔽₈)⋊C₄)	C₂²	semidirect
49. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	semidirect
50. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	semidirect
51. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	semidirect
52. (ΓL(1,𝔽₈)⋊C₄)⋊C₄	C₂²	semidirect
53. C₄×ΓL(1,𝔽₈)⋊C₄	C₂²	semidirect
54. C₂×#1157	C₂×C₃	semidirect
55. C₂²×C₄×D₇	C₂×C₃	semidirect
56. C₄×C₇×D₄	C₂×C₃	semidirect
57. #6502	C₂×C₃	semidirect
58. #6500	C₂×C₃	semidirect
59. C₄×C₂²⋊D₇	C₂×C₃	semidirect
60. C₄×C₂²⋊D₇	C₂×C₃	semidirect
61. #6459	C₂×C₃	semidirect
62. #6457	C₂×C₃	semidirect
63. #6447	C₂×C₃	semidirect
64. #6446	C₂×C₃	semidirect
65. #6445	C₂×C₃	semidirect
66. #6441	C₂×C₃	semidirect
67. C₄×D₂₈	C₂×C₃	semidirect
68. #6435	C₂×C₃	semidirect
102. C₄×AGL(1,𝔽₇)	D₄	semidirect
107. C₂²×C₄×C₇	C₂²×C₃	semidirect
111. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
121. C₂×C₄×D₇	C₂²×C₃	semidirect
122. C₂×Dic₁₄	C₂²×C₃	semidirect
123. C₇×C₄⋊C₄	C₂²×C₃	semidirect
125. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
126. C₄²×C₇	C₂²×C₃	semidirect
128. C₂²⋊Dic₇	C₂²×C₃	semidirect
133. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
134. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
135. C₄⋊Dic₇	C₂²×C₃	semidirect
136. Dic₇⋊C₄	C₂²×C₃	semidirect
137. Dic₇⋊C₄	C₂²×C₃	semidirect
138. Dic₇⋊C₄	C₂²×C₃	semidirect
139. Dic₇⋊C₄	C₂²×C₃	semidirect
140. C₄×Dic₇	C₂²×C₃	semidirect
161. C₂²×ΓL(1,𝔽₈)	#41	semidirect
172. C₂×AGL(1,𝔽₇)	#41	semidirect
216. C₄×D₇	C₃×D₄	semidirect
276. C₄×D₄	AGL(1,𝔽₇)	semidirect
283. C₂²×C₇	C₃×#41	semidirect
294. C₂×D₇	C₃×#41	semidirect
339. ΓL(1,𝔽₈)	#525	semidirect
358. C₂²×C₄	C₂×AGL(1,𝔽₇)	semidirect
364. C₄⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
374. C₂²⋊C₄	C₂×AGL(1,𝔽₇)	semidirect
376. C₄²	C₂×AGL(1,𝔽₇)	semidirect
446. C₇	C₃×#525	semidirect
470. C₂²	#1157⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#1157⋊C₃	2
C₂²×C₄×AGL(1,𝔽₇)	2
C₄×D₄×ΓL(1,𝔽₈)	2
#6502⋊C₃	2
#6500⋊C₃	2
C₄×(C₂²⋊D₇)⋊C₃	2
#6459⋊C₃	2
#6457⋊C₃	2
#6447⋊C₃	2
#6446⋊C₃	2
#6445⋊C₃	2
#6441⋊C₃	2
C₄×C₄⋊AGL(1,𝔽₇)	2
#6435⋊C₃	2
#90238	3
C₃×#525	7

Subgroups — #90238⋊C3 #13057284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #90238⋊C₃ #13057284