Subgroups — C₇×#62855 #13240071

Order 1792.

7370 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3510	C₂	1	8	yes	maximal, complemented
2	C₇×#3508	C₂	1	8	yes	maximal, complemented
3	C₇×#3506	C₂	1	8	yes	maximal, complemented
4	C₇×#3494	C₂	1	16	yes	maximal, complemented
5	C₇×#3490	C₂	1	8	yes	maximal, complemented
6	C₇×#3460	C₂	1	8	yes	maximal, complemented
7	C₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3449	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#535	C₂	1	2	yes	maximal, complemented
10	C₇×#3428	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×#41	C₂²	1	2	yes	—
13	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₇×#559	C₂²	1	32	yes	complemented
15	C₇×#556	C₂²	1	16	yes	complemented
16	C₇×#555	C₂²	1	16	yes	complemented
17	C₇×#553	C₂²	1	32	yes	complemented
18	C₇×#551	C₂²	1	64	yes	complemented
19	C₇×#550	C₂²	1	16	yes	complemented
20	C₇×#547	C₂²	1	16	yes	complemented
21	C₇×#546	C₂²	1	64	yes	complemented
22	C₇×#544	C₂²	1	4	yes	complemented
23	C₇×#544	C₂²	1	8	yes	complemented
24	C₇×#543	C₂²	1	4	yes	—
25	C₇×#542	C₂²	1	32	yes	complemented
26	C₇×#540	C₂²	1	32	yes	complemented
27	C₇×#538	C₂²	1	32	yes	complemented
28	C₇×#537	C₂²	1	4	yes	complemented
29	C₇×#536	C₂²	1	4	yes	complemented
30	C₇×#535	C₂²	1	8	yes	—
31	C₇×#535	C₂²	1	8	yes	—
32	C₇×#535	C₂²	1	8	yes	complemented
33	C₇×#535	C₂²	1	8	yes	complemented
34	C₇×#535	C₂²	1	4	yes	complemented
35	C₇×#534	C₂²	1	4	yes	—
36	C₇×#533	C₂²	1	4	yes	complemented
37	C₇×#533	C₂²	1	8	yes	complemented
38	C₇×#532	C₂²	1	4	yes	complemented
39	C₇×#532	C₂²	1	32	yes	complemented
40	C₂×C₇×#127	C₂²	1	4	yes	complemented
41	C₇×#529	C₂²	1	32	yes	complemented
42	C₂×C₇×#124	C₂²	1	4	yes	complemented
43	C₇×#525	C₂²	1	8	yes	complemented
44	C₇×#525	C₂²	1	32	yes	complemented
45	C₂×C₇×#121	C₂²	1	8	yes	complemented
46	C₂×C₇×#120	C₂²	1	8	yes	—
47	C₇×#520	C₂²	1	8	yes	complemented
48	C₇×#520	C₂²	1	8	yes	complemented
49	C₇×#519	C₂²	1	4	yes	complemented
50	C₇×#518	C₂²	1	8	yes	—
51	C₇×#518	C₂²	1	8	yes	complemented
52	C₇×#518	C₂²	1	8	yes	complemented
53	C₇×#518	C₂²	1	4	yes	complemented
54	C₄×C₇×#41	C₂²	1	8	yes	complemented
55	C₄×C₇×#41	C₂²	1	8	yes	complemented
56	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
57	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
58	C₂×C₇×#117	C₂²	1	1	yes	characteristic
59	C₂×C₇×#117	C₂²	1	1	yes	characteristic
60	C₂×C₇×#117	C₂²	1	2	yes	—
61	C₂×C₇×#117	C₂²	1	8	yes	complemented
62	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
63	#62855	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂⁵×C₇	C₂³	1	2	yes	—
65	C₂×C₇×#41	—	2	16	no	—
66	C₂×C₇×#41	C₂³	1	4	yes	—
67	C₂×C₇×#41	C₂³	1	4	yes	—
68	C₂×C₇×#41	C₂³	1	4	yes	—
69	C₂×C₇×#41	C₂³	1	4	yes	—
70	C₂×C₇×#41	C₂³	1	32	yes	complemented
71	C₂²×C₇×Q₈	C₂³	1	2	yes	—
72	C₂²×C₇×D₄	—	2	8	no	—
73	C₂²×C₇×D₄	C₂³	1	2	yes	—
74	C₂²×C₇×D₄	C₂³	1	2	yes	—
75	C₂²×C₇×D₄	C₂³	1	4	yes	—
76	C₂²×C₇×D₄	C₂³	1	4	yes	—
77	C₂²×C₇×D₄	C₂³	1	4	yes	—
78	C₂²×C₇×D₄	C₂³	1	2	yes	—
79	C₂²×C₇×D₄	C₂³	1	16	yes	—
80	C₂³×C₄×C₇	C₂³	1	4	yes	—
81	C₂³×C₄×C₇	C₂³	1	8	yes	—
82	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
83	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
84	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
85	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
86	C₇×#127	C₂³	1	16	yes	—
87	C₇×#127	C₂³	1	16	yes	—
88	C₇×#127	C₂³	1	4	yes	complemented
89	C₇×#126	C₂³	1	64	yes	complemented
90	C₇×#125	C₂³	1	16	yes	complemented
91	C₇×#125	C₂³	1	8	yes	complemented
92	C₇×#124	C₂³	1	16	yes	—
93	C₇×#124	C₂³	1	16	yes	—
94	C₇×#124	C₂³	1	8	yes	complemented
95	C₇×#124	C₂³	1	64	yes	complemented
96	C₇×#123	C₂³	1	16	yes	—
97	C₇×#123	C₂³	1	64	yes	complemented
98	C₇×#123	C₂³	1	64	yes	complemented
99	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
100	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
101	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
102	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
103	C₇×#121	C₂³	1	32	yes	—
104	C₇×#121	C₂³	1	32	yes	—
105	C₇×#121	C₂³	1	16	yes	—
106	C₇×#121	C₂³	1	16	yes	complemented
107	C₇×#121	C₂³	1	32	yes	complemented
108	C₇×#121	C₂³	1	64	yes	complemented
109	C₇×#120	C₂³	1	32	yes	—
110	C₇×#120	C₂³	1	32	yes	—
111	C₇×#120	C₂³	1	16	yes	—
112	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
113	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
114	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
115	C₄×C₇×D₄	C₂³	1	32	yes	—
116	C₄×C₇×D₄	C₂³	1	16	yes	—
117	C₄×C₇×D₄	C₂³	1	16	yes	—
118	C₄×C₇×D₄	C₂³	1	32	yes	—
119	C₄×C₇×D₄	C₂³	1	32	yes	—
120	C₄×C₇×D₄	C₂³	1	16	yes	complemented
121	C₄×C₇×D₄	C₂³	1	16	yes	complemented
122	C₄×C₇×D₄	C₂³	1	16	yes	complemented
123	C₄×C₇×D₄	C₂³	1	64	yes	complemented
124	C₇×#117	C₂³	1	4	yes	—
125	C₇×#117	C₂³	1	4	yes	—
126	C₇×#117	C₂³	1	4	yes	—
127	C₇×#117	C₂³	1	4	yes	—
128	C₇×#117	C₂³	1	4	yes	—
129	C₇×#117	C₂³	1	4	yes	—
130	C₇×#117	C₂³	1	4	yes	—
131	C₇×#117	C₂³	1	4	yes	—
132	C₇×#117	C₂³	1	16	yes	—
133	C₇×#117	C₂³	1	16	yes	complemented
134	C₇×#117	C₂³	1	16	yes	complemented
135	C₇×#117	C₂³	1	32	yes	complemented
136	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
139	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
140	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
143	C₂×C₇×C₂²⋊C₄	C₂³	1	32	yes	—
144	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
146	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
147	C₂×C₄²×C₇	C₂³	1	2	yes	—
148	C₂×C₄²×C₇	C₂³	1	2	yes	—
149	C₂×C₄²×C₇	C₂³	1	4	yes	—
150	C₂×C₄²×C₇	C₂³	1	16	yes	complemented
151	#3510	C₂×C₇	1	8	yes	complemented
152	#3508	C₂×C₇	1	8	yes	complemented
153	#3506	C₂×C₇	1	8	yes	complemented
154	#3494	C₂×C₇	1	16	yes	complemented
155	#3490	C₂×C₇	1	8	yes	complemented
156	#3460	C₂×C₇	1	8	yes	complemented
157	#3458	C₂×C₇	1	1	yes	characteristic, complemented
158	#3449	C₂×C₇	1	1	yes	characteristic, complemented
159	C₂×#535	C₂×C₇	1	2	yes	complemented
160	#3428	C₂×C₇	1	2	yes	complemented
161	C₂×#518	C₂×C₇	1	1	yes	characteristic, complemented
162	C₂⁴×C₇	—	2	8	no	—
163	C₂⁴×C₇	—	8	4	no	—
164	C₂⁴×C₇	C₂⁴	1	8	yes	—
165	C₂⁴×C₇	C₂⁴	1	4	yes	—
166	C₂⁴×C₇	C₂⁴	1	4	yes	—
167	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
168	C₇×#41	—	2	16	no	—
169	C₇×#41	—	2	16	no	—
170	C₇×#41	—	2	16	no	—
171	C₇×#41	—	2	16	no	—
172	C₇×#41	—	8	32	no	—
173	C₂×C₇×Q₈	—	2	8	no	—
174	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
175	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
176	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
177	C₂×C₇×D₄	—	2	16	no	—
178	C₂×C₇×D₄	—	2	16	no	—
179	C₂×C₇×D₄	—	2	16	no	—
180	C₂×C₇×D₄	—	2	8	no	—
181	C₂×C₇×D₄	—	2	8	no	—
182	C₂×C₇×D₄	—	2	8	no	—
183	C₂×C₇×D₄	—	8	16	no	—
184	C₂×C₇×D₄	C₂⁴	1	8	yes	—
185	C₂×C₇×D₄	C₂⁴	1	8	yes	—
186	C₂×C₇×D₄	C₂⁴	1	4	yes	—
187	C₂×C₇×D₄	C₂⁴	1	8	yes	—
188	C₂×C₇×D₄	C₂⁴	1	4	yes	—
189	C₂×C₇×D₄	C₂⁴	1	4	yes	—
190	C₂×C₇×D₄	C₂⁴	1	4	yes	—
191	C₂×C₇×D₄	C₂⁴	1	64	yes	—
192	C₂×C₇×D₄	C₂⁴	1	16	yes	—
193	C₂²×C₄×C₇	—	2	16	no	—
194	C₂²×C₄×C₇	—	8	8	no	—
195	C₂²×C₄×C₇	#41	1	8	yes	complemented
196	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
197	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
199	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
201	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
203	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
204	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
208	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
209	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
210	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
211	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
212	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
213	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
214	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
215	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
216	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
217	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
218	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
219	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
220	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
221	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
222	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
223	C₇×C₂²⋊C₄	C₂⁴	1	64	yes	—
224	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
225	C₄²×C₇	C₂⁴	1	8	yes	—
226	C₄²×C₇	C₂⁴	1	8	yes	—
227	C₄²×C₇	C₂⁴	1	4	yes	—
228	C₄²×C₇	C₂⁴	1	4	yes	—
229	C₄²×C₇	C₂⁴	1	8	yes	—
230	C₄²×C₇	C₂⁴	1	32	yes	—
231	C₂²×#41	C₂²×C₇	1	2	yes	—
232	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
233	#559	C₂²×C₇	1	32	yes	complemented
234	#556	C₂²×C₇	1	16	yes	complemented
235	#555	C₂²×C₇	1	16	yes	complemented
236	#553	C₂²×C₇	1	32	yes	complemented
237	#551	C₂²×C₇	1	64	yes	complemented
238	#550	C₂²×C₇	1	16	yes	complemented
239	#547	C₂²×C₇	1	16	yes	complemented
240	#546	C₂²×C₇	1	64	yes	complemented
241	#544	C₂²×C₇	1	4	yes	complemented
242	#544	C₂²×C₇	1	8	yes	complemented
243	#543	C₂²×C₇	1	4	yes	—
244	#542	C₂²×C₇	1	32	yes	complemented
245	#540	C₂²×C₇	1	32	yes	complemented
246	#538	C₂²×C₇	1	32	yes	complemented
247	#537	C₂²×C₇	1	4	yes	complemented
248	#536	C₂²×C₇	1	4	yes	complemented
249	#535	C₂²×C₇	1	8	yes	—
250	#535	C₂²×C₇	1	8	yes	—
251	#535	C₂²×C₇	1	8	yes	complemented
252	#535	C₂²×C₇	1	8	yes	complemented
253	#535	C₂²×C₇	1	4	yes	complemented
254	#534	C₂²×C₇	1	4	yes	—
255	#533	C₂²×C₇	1	4	yes	complemented
256	#533	C₂²×C₇	1	8	yes	complemented
257	#532	C₂²×C₇	1	4	yes	complemented
258	#532	C₂²×C₇	1	32	yes	complemented
259	C₂×#127	C₂²×C₇	1	4	yes	complemented
260	#529	C₂²×C₇	1	32	yes	complemented
261	C₂×#124	C₂²×C₇	1	4	yes	complemented
262	#525	C₂²×C₇	1	8	yes	complemented
263	#525	C₂²×C₇	1	32	yes	complemented
264	C₂×#121	C₂²×C₇	1	8	yes	complemented
265	C₂×#120	C₂²×C₇	1	8	yes	—
266	#520	C₂²×C₇	1	8	yes	complemented
267	#520	C₂²×C₇	1	8	yes	complemented
268	#519	C₂²×C₇	1	4	yes	complemented
269	#518	C₂²×C₇	1	8	yes	—
270	#518	C₂²×C₇	1	8	yes	complemented
271	#518	C₂²×C₇	1	8	yes	complemented
272	#518	C₂²×C₇	1	4	yes	complemented
273	C₄×#41	C₂²×C₇	1	8	yes	complemented
274	C₄×#41	C₂²×C₇	1	8	yes	complemented
275	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
276	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
277	C₂×#117	C₂²×C₇	1	1	yes	characteristic
278	C₂×#117	C₂²×C₇	1	1	yes	characteristic
279	C₂×#117	C₂²×C₇	1	2	yes	—
280	C₂×#117	C₂²×C₇	1	8	yes	complemented
281	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
282	C₂³×C₇	—	2	8	no	—
283	C₂³×C₇	—	2	8	no	—
284	C₂³×C₇	—	2	16	no	—
285	C₂³×C₇	—	4	8	no	—
286	C₂³×C₇	—	4	2	no	—
287	C₂³×C₇	—	4	8	no	—
288	C₂³×C₇	—	4	16	no	—
289	C₂³×C₇	—	8	16	no	—
290	C₂³×C₇	C₂×#41	1	4	yes	—
291	C₂³×C₇	C₂⁵	1	8	yes	—
292	C₂³×C₇	C₂⁵	1	8	yes	—
293	C₂³×C₇	C₂⁵	1	2	yes	—
294	C₂³×C₇	C₂⁵	1	1	yes	characteristic
295	C₇×Q₈	—	2	8	no	—
296	C₇×Q₈	—	2	8	no	—
297	C₇×Q₈	—	4	16	no	—
298	C₇×D₄	—	2	16	no	—
299	C₇×D₄	—	2	16	no	—
300	C₇×D₄	—	2	8	no	—
301	C₇×D₄	—	2	16	no	—
302	C₇×D₄	—	2	8	no	—
303	C₇×D₄	—	2	8	no	—
304	C₇×D₄	—	2	8	no	—
305	C₇×D₄	—	4	64	no	—
306	C₇×D₄	—	4	16	no	—
307	C₂×C₄×C₇	—	2	8	no	—
308	C₂×C₄×C₇	—	2	16	no	—
309	C₂×C₄×C₇	—	2	16	no	—
310	C₂×C₄×C₇	—	4	4	no	—
311	C₂×C₄×C₇	—	4	4	no	—
312	C₂×C₄×C₇	—	4	32	no	—
313	C₂×C₄×C₇	—	4	8	no	—
314	C₂×C₄×C₇	—	4	32	no	—
315	C₂×C₄×C₇	C₂×#41	1	8	yes	—
316	C₂×C₄×C₇	C₂×#41	1	8	yes	—
317	C₂×C₄×C₇	C₂×#41	1	4	yes	—
318	C₂×C₄×C₇	C₂×#41	1	4	yes	—
319	C₂×C₄×C₇	C₂⁵	1	8	yes	—
320	C₂×C₄×C₇	C₂⁵	1	8	yes	—
321	C₂×C₄×C₇	C₂⁵	1	16	yes	—
322	C₂×C₄×C₇	C₂⁵	1	8	yes	—
323	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
324	C₂×C₄×C₇	C₂⁵	1	2	yes	—
325	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
326	C₂⁵	C₂³×C₇	1	2	yes	—
327	C₂×#41	—	2	16	no	—
328	C₂×#41	C₂³×C₇	1	4	yes	—
329	C₂×#41	C₂³×C₇	1	4	yes	—
330	C₂×#41	C₂³×C₇	1	4	yes	—
331	C₂×#41	C₂³×C₇	1	4	yes	—
332	C₂×#41	C₂³×C₇	1	32	yes	complemented
333	C₂²×Q₈	C₂³×C₇	1	2	yes	—
334	C₂²×D₄	—	2	8	no	—
335	C₂²×D₄	C₂³×C₇	1	2	yes	—
336	C₂²×D₄	C₂³×C₇	1	2	yes	—
337	C₂²×D₄	C₂³×C₇	1	4	yes	—
338	C₂²×D₄	C₂³×C₇	1	4	yes	—
339	C₂²×D₄	C₂³×C₇	1	4	yes	—
340	C₂²×D₄	C₂³×C₇	1	2	yes	—
341	C₂²×D₄	C₂³×C₇	1	16	yes	—
342	C₂³×C₄	C₂³×C₇	1	4	yes	—
343	C₂³×C₄	C₂³×C₇	1	8	yes	—
344	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
345	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
346	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
347	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
348	#127	C₂³×C₇	1	16	yes	—
349	#127	C₂³×C₇	1	16	yes	—
350	#127	C₂³×C₇	1	4	yes	complemented
351	#126	C₂³×C₇	1	64	yes	complemented
352	#125	C₂³×C₇	1	16	yes	complemented
353	#125	C₂³×C₇	1	8	yes	complemented
354	#124	C₂³×C₇	1	16	yes	—
355	#124	C₂³×C₇	1	16	yes	—
356	#124	C₂³×C₇	1	8	yes	complemented
357	#124	C₂³×C₇	1	64	yes	complemented
358	#123	C₂³×C₇	1	16	yes	—
359	#123	C₂³×C₇	1	64	yes	complemented
360	#123	C₂³×C₇	1	64	yes	complemented
361	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
362	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
363	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
364	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
365	#121	C₂³×C₇	1	32	yes	—
366	#121	C₂³×C₇	1	32	yes	—
367	#121	C₂³×C₇	1	16	yes	—
368	#121	C₂³×C₇	1	16	yes	complemented
369	#121	C₂³×C₇	1	32	yes	complemented
370	#121	C₂³×C₇	1	64	yes	complemented
371	#120	C₂³×C₇	1	32	yes	—
372	#120	C₂³×C₇	1	32	yes	—
373	#120	C₂³×C₇	1	16	yes	—
374	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
375	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
376	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
377	C₄×D₄	C₂³×C₇	1	32	yes	—
378	C₄×D₄	C₂³×C₇	1	16	yes	—
379	C₄×D₄	C₂³×C₇	1	16	yes	—
380	C₄×D₄	C₂³×C₇	1	32	yes	—
381	C₄×D₄	C₂³×C₇	1	32	yes	—
382	C₄×D₄	C₂³×C₇	1	16	yes	complemented
383	C₄×D₄	C₂³×C₇	1	16	yes	complemented
384	C₄×D₄	C₂³×C₇	1	16	yes	complemented
385	C₄×D₄	C₂³×C₇	1	64	yes	complemented
386	#117	C₂³×C₇	1	4	yes	—
387	#117	C₂³×C₇	1	4	yes	—
388	#117	C₂³×C₇	1	4	yes	—
389	#117	C₂³×C₇	1	4	yes	—
390	#117	C₂³×C₇	1	4	yes	—
391	#117	C₂³×C₇	1	4	yes	—
392	#117	C₂³×C₇	1	4	yes	—
393	#117	C₂³×C₇	1	4	yes	—
394	#117	C₂³×C₇	1	16	yes	—
395	#117	C₂³×C₇	1	16	yes	complemented
396	#117	C₂³×C₇	1	16	yes	complemented
397	#117	C₂³×C₇	1	32	yes	complemented
398	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
402	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₇	1	32	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
409	C₂×C₄²	C₂³×C₇	1	2	yes	—
410	C₂×C₄²	C₂³×C₇	1	2	yes	—
411	C₂×C₄²	C₂³×C₇	1	4	yes	—
412	C₂×C₄²	C₂³×C₇	1	16	yes	complemented
413	C₂²×C₇	—	2	2	no	—
414	C₂²×C₇	—	2	4	no	—
415	C₂²×C₇	—	2	8	no	—
416	C₂²×C₇	—	2	8	no	—
417	C₂²×C₇	—	2	16	no	—
418	C₂²×C₇	—	2	16	no	—
419	C₂²×C₇	—	4	4	no	—
420	C₂²×C₇	—	4	16	no	—
421	C₂²×C₇	—	8	8	no	—
422	C₂²×C₇	—	8	16	no	—
423	C₂²×C₇	C₂²×#41	1	4	yes	—
424	C₂²×C₇	C₂²×#41	1	2	yes	—
425	C₂²×C₇	C₂⁶	1	1	yes	characteristic
426	C₄×C₇	—	2	8	no	—
427	C₄×C₇	—	2	8	no	—
428	C₄×C₇	—	2	8	no	—
429	C₄×C₇	—	2	16	no	—
430	C₄×C₇	C₂²×#41	1	2	yes	—
431	C₄×C₇	C₂²×#41	1	4	yes	—
432	C₄×C₇	C₂²×#41	1	2	yes	—
433	C₂⁴	—	2	8	no	—
434	C₂⁴	—	8	4	no	—
435	C₂⁴	C₂⁴×C₇	1	8	yes	—
436	C₂⁴	C₂⁴×C₇	1	4	yes	—
437	C₂⁴	C₂⁴×C₇	1	4	yes	—
438	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
439	#41	—	2	16	no	—
440	#41	—	2	16	no	—
441	#41	—	2	16	no	—
442	#41	—	2	16	no	—
443	#41	—	8	32	no	—
444	C₂×Q₈	—	2	8	no	—
445	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
446	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
447	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
448	C₂×D₄	—	2	16	no	—
449	C₂×D₄	—	2	16	no	—
450	C₂×D₄	—	2	16	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	8	16	no	—
455	C₂×D₄	C₂⁴×C₇	1	8	yes	—
456	C₂×D₄	C₂⁴×C₇	1	8	yes	—
457	C₂×D₄	C₂⁴×C₇	1	4	yes	—
458	C₂×D₄	C₂⁴×C₇	1	8	yes	—
459	C₂×D₄	C₂⁴×C₇	1	4	yes	—
460	C₂×D₄	C₂⁴×C₇	1	4	yes	—
461	C₂×D₄	C₂⁴×C₇	1	4	yes	—
462	C₂×D₄	C₂⁴×C₇	1	64	yes	—
463	C₂×D₄	C₂⁴×C₇	1	16	yes	—
464	C₂²×C₄	—	2	16	no	—
465	C₂²×C₄	—	8	8	no	—
466	C₂²×C₄	C₇×#41	1	8	yes	complemented
467	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
468	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
469	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
470	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
471	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
472	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
474	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
475	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
479	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
480	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
481	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
482	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
483	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
484	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
485	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
486	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
487	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
488	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
489	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
490	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
491	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
492	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
493	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
494	C₂²⋊C₄	C₂⁴×C₇	1	64	yes	—
495	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
496	C₄²	C₂⁴×C₇	1	8	yes	—
497	C₄²	C₂⁴×C₇	1	8	yes	—
498	C₄²	C₂⁴×C₇	1	4	yes	—
499	C₄²	C₂⁴×C₇	1	4	yes	—
500	C₄²	C₂⁴×C₇	1	8	yes	—
501	C₄²	C₂⁴×C₇	1	32	yes	—
502	C₂×C₇	—	2	2	no	—
503	C₂×C₇	—	2	4	no	—
504	C₂×C₇	—	4	8	no	—
505	C₂×C₇	—	4	8	no	—
506	C₂×C₇	C₂³×#41	1	1	yes	characteristic
507	C₂×C₇	H(7,𝔽₂)	1	2	yes	—
508	C₂³	—	2	8	no	—
509	C₂³	—	2	8	no	—
510	C₂³	—	2	16	no	—
511	C₂³	—	4	8	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	4	16	no	—
515	C₂³	—	8	16	no	—
516	C₂³	C₂×C₇×#41	1	4	yes	—
517	C₂³	C₂⁵×C₇	1	8	yes	—
518	C₂³	C₂⁵×C₇	1	8	yes	—
519	C₂³	C₂⁵×C₇	1	2	yes	—
520	C₂³	C₂⁵×C₇	1	1	yes	characteristic
521	Q₈	—	2	8	no	—
522	Q₈	—	2	8	no	—
523	Q₈	—	4	16	no	—
524	D₄	—	2	16	no	—
525	D₄	—	2	16	no	—
526	D₄	—	2	8	no	—
527	D₄	—	2	16	no	—
528	D₄	—	2	8	no	—
529	D₄	—	2	8	no	—
530	D₄	—	2	8	no	—
531	D₄	—	4	64	no	—
532	D₄	—	4	16	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	16	no	—
535	C₂×C₄	—	2	16	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	32	no	—
539	C₂×C₄	—	4	8	no	—
540	C₂×C₄	—	4	32	no	—
541	C₂×C₄	C₂×C₇×#41	1	8	yes	—
542	C₂×C₄	C₂×C₇×#41	1	8	yes	—
543	C₂×C₄	C₂×C₇×#41	1	4	yes	—
544	C₂×C₄	C₂×C₇×#41	1	4	yes	—
545	C₂×C₄	C₂⁵×C₇	1	8	yes	—
546	C₂×C₄	C₂⁵×C₇	1	8	yes	—
547	C₂×C₄	C₂⁵×C₇	1	16	yes	—
548	C₂×C₄	C₂⁵×C₇	1	8	yes	—
549	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
550	C₂×C₄	C₂⁵×C₇	1	2	yes	—
551	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
552	C₇	#62855	1	1	yes	characteristic, direct product factor, Sylow
553	C₂²	—	2	2	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	8	no	—
556	C₂²	—	2	8	no	—
557	C₂²	—	2	16	no	—
558	C₂²	—	2	16	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	16	no	—
561	C₂²	—	8	16	no	—
562	C₂²	—	8	8	no	—
563	C₂²	C₂²×C₇×#41	1	4	yes	—
564	C₂²	C₂²×C₇×#41	1	2	yes	—
565	C₂²	C₂⁶×C₇	1	1	yes	characteristic
566	C₄	—	2	8	no	—
567	C₄	—	2	8	no	—
568	C₄	—	2	8	no	—
569	C₄	—	2	16	no	—
570	C₄	C₂²×C₇×#41	1	2	yes	—
571	C₄	C₂²×C₇×#41	1	4	yes	—
572	C₄	C₂²×C₇×#41	1	2	yes	—
573	C₂	—	2	2	no	—
574	C₂	—	2	4	no	—
575	C₂	—	4	8	no	—
576	C₂	—	4	8	no	—
577	C₂	C₂³×C₇×#41	1	1	yes	characteristic
578	C₂	C₇×H(7,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3510	C₂	semidirect
2. C₇×#3508	C₂	semidirect
3. C₇×#3506	C₂	semidirect
4. C₇×#3494	C₂	semidirect
5. C₇×#3490	C₂	semidirect
6. C₇×#3460	C₂	semidirect
7. C₇×#3458	C₂	semidirect
8. C₇×#3449	C₂	semidirect
9. C₂×C₇×#535	C₂	semidirect
10. C₇×#3428	C₂	semidirect
11. C₂×C₇×#518	C₂	semidirect
14. C₇×#559	C₂²	semidirect
15. C₇×#556	C₂²	semidirect
16. C₇×#555	C₂²	semidirect
17. C₇×#553	C₂²	semidirect
18. C₇×#551	C₂²	semidirect
19. C₇×#550	C₂²	semidirect
20. C₇×#547	C₂²	semidirect
21. C₇×#546	C₂²	semidirect
22. C₇×#544	C₂²	semidirect
23. C₇×#544	C₂²	semidirect
25. C₇×#542	C₂²	semidirect
26. C₇×#540	C₂²	semidirect
27. C₇×#538	C₂²	semidirect
28. C₇×#537	C₂²	semidirect
29. C₇×#536	C₂²	semidirect
32. C₇×#535	C₂²	semidirect
33. C₇×#535	C₂²	semidirect
34. C₇×#535	C₂²	semidirect
36. C₇×#533	C₂²	semidirect
37. C₇×#533	C₂²	semidirect
38. C₇×#532	C₂²	semidirect
39. C₇×#532	C₂²	semidirect
40. C₂×C₇×#127	C₂²	semidirect
41. C₇×#529	C₂²	semidirect
42. C₂×C₇×#124	C₂²	semidirect
43. C₇×#525	C₂²	semidirect
44. C₇×#525	C₂²	semidirect
45. C₂×C₇×#121	C₂²	semidirect
47. C₇×#520	C₂²	semidirect
48. C₇×#520	C₂²	semidirect
49. C₇×#519	C₂²	semidirect
51. C₇×#518	C₂²	semidirect
52. C₇×#518	C₂²	semidirect
53. C₇×#518	C₂²	semidirect
54. C₄×C₇×#41	C₂²	semidirect
55. C₄×C₇×#41	C₂²	semidirect
56. C₂×C₄×C₇×D₄	C₂²	semidirect
57. C₂×C₄×C₇×D₄	C₂²	semidirect
61. C₂×C₇×#117	C₂²	semidirect
63. #62855	C₇	direct (N × H)
70. C₂×C₇×#41	C₂³	semidirect
83. C₇×C₄⋊Q₈	C₂³	semidirect
84. C₇×C₄⋊Q₈	C₂³	semidirect
85. C₇×C₄⋊Q₈	C₂³	semidirect
88. C₇×#127	C₂³	semidirect
89. C₇×#126	C₂³	semidirect
90. C₇×#125	C₂³	semidirect
91. C₇×#125	C₂³	semidirect
94. C₇×#124	C₂³	semidirect
95. C₇×#124	C₂³	semidirect
97. C₇×#123	C₂³	semidirect
98. C₇×#123	C₂³	semidirect
101. C₇×C₂²⋊Q₈	C₂³	semidirect
102. C₇×C₂²⋊Q₈	C₂³	semidirect
106. C₇×#121	C₂³	semidirect
107. C₇×#121	C₂³	semidirect
108. C₇×#121	C₂³	semidirect
112. C₄×C₇×Q₈	C₂³	semidirect
113. C₄×C₇×Q₈	C₂³	semidirect
114. C₄×C₇×Q₈	C₂³	semidirect
120. C₄×C₇×D₄	C₂³	semidirect
121. C₄×C₇×D₄	C₂³	semidirect
122. C₄×C₇×D₄	C₂³	semidirect
123. C₄×C₇×D₄	C₂³	semidirect
133. C₇×#117	C₂³	semidirect
134. C₇×#117	C₂³	semidirect
135. C₇×#117	C₂³	semidirect
139. C₂×C₇×C₄⋊C₄	C₂³	semidirect
150. C₂×C₄²×C₇	C₂³	semidirect
151. #3510	C₂×C₇	semidirect
152. #3508	C₂×C₇	semidirect
153. #3506	C₂×C₇	semidirect
154. #3494	C₂×C₇	semidirect
155. #3490	C₂×C₇	semidirect
156. #3460	C₂×C₇	semidirect
157. #3458	C₂×C₇	semidirect
158. #3449	C₂×C₇	semidirect
159. C₂×#535	C₂×C₇	semidirect
160. #3428	C₂×C₇	semidirect
161. C₂×#518	C₂×C₇	semidirect
195. C₂²×C₄×C₇	#41	semidirect
233. #559	C₂²×C₇	semidirect
234. #556	C₂²×C₇	semidirect
235. #555	C₂²×C₇	semidirect
236. #553	C₂²×C₇	semidirect
237. #551	C₂²×C₇	semidirect
238. #550	C₂²×C₇	semidirect
239. #547	C₂²×C₇	semidirect
240. #546	C₂²×C₇	semidirect
241. #544	C₂²×C₇	semidirect
242. #544	C₂²×C₇	semidirect
244. #542	C₂²×C₇	semidirect
245. #540	C₂²×C₇	semidirect
246. #538	C₂²×C₇	semidirect
247. #537	C₂²×C₇	semidirect
248. #536	C₂²×C₇	semidirect
251. #535	C₂²×C₇	semidirect
252. #535	C₂²×C₇	semidirect
253. #535	C₂²×C₇	semidirect
255. #533	C₂²×C₇	semidirect
256. #533	C₂²×C₇	semidirect
257. #532	C₂²×C₇	semidirect
258. #532	C₂²×C₇	semidirect
259. C₂×#127	C₂²×C₇	semidirect
260. #529	C₂²×C₇	semidirect
261. C₂×#124	C₂²×C₇	semidirect
262. #525	C₂²×C₇	semidirect
263. #525	C₂²×C₇	semidirect
264. C₂×#121	C₂²×C₇	semidirect
266. #520	C₂²×C₇	semidirect
267. #520	C₂²×C₇	semidirect
268. #519	C₂²×C₇	semidirect
270. #518	C₂²×C₇	semidirect
271. #518	C₂²×C₇	semidirect
272. #518	C₂²×C₇	semidirect
273. C₄×#41	C₂²×C₇	semidirect
274. C₄×#41	C₂²×C₇	semidirect
275. C₂×C₄×D₄	C₂²×C₇	semidirect
276. C₂×C₄×D₄	C₂²×C₇	semidirect
280. C₂×#117	C₂²×C₇	semidirect
332. C₂×#41	C₂³×C₇	semidirect
345. C₄⋊Q₈	C₂³×C₇	semidirect
346. C₄⋊Q₈	C₂³×C₇	semidirect
347. C₄⋊Q₈	C₂³×C₇	semidirect
350. #127	C₂³×C₇	semidirect
351. #126	C₂³×C₇	semidirect
352. #125	C₂³×C₇	semidirect
353. #125	C₂³×C₇	semidirect
356. #124	C₂³×C₇	semidirect
357. #124	C₂³×C₇	semidirect
359. #123	C₂³×C₇	semidirect
360. #123	C₂³×C₇	semidirect
363. C₂²⋊Q₈	C₂³×C₇	semidirect
364. C₂²⋊Q₈	C₂³×C₇	semidirect
368. #121	C₂³×C₇	semidirect
369. #121	C₂³×C₇	semidirect
370. #121	C₂³×C₇	semidirect
374. C₄×Q₈	C₂³×C₇	semidirect
375. C₄×Q₈	C₂³×C₇	semidirect
376. C₄×Q₈	C₂³×C₇	semidirect
382. C₄×D₄	C₂³×C₇	semidirect
383. C₄×D₄	C₂³×C₇	semidirect
384. C₄×D₄	C₂³×C₇	semidirect
385. C₄×D₄	C₂³×C₇	semidirect
395. #117	C₂³×C₇	semidirect
396. #117	C₂³×C₇	semidirect
397. #117	C₂³×C₇	semidirect
401. C₂×C₄⋊C₄	C₂³×C₇	semidirect
412. C₂×C₄²	C₂³×C₇	semidirect
466. C₂²×C₄	C₇×#41	semidirect
552. C₇	#62855	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3510	2
C₇×#3508	2
C₇×#3506	2
C₇×#3494	2
C₇×#3490	2
C₇×#3460	2
C₇×#3458	2
C₇×#3449	2
C₂×C₇×#535	2
C₇×#3428	2
C₂×C₇×#518	2
#62855	7

Subgroups — C7×#62855 #13240071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62855 #13240071