Subgroups — C₇×#62860 #13240076

Order 1792.

6866 conjugacy classes of subgroups.

The subgroup lattice has 554 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×#3509	C₂	1	8	yes	maximal, complemented
3	C₇×#3507	C₂	1	8	yes	maximal, complemented
4	C₇×#3495	C₂	1	16	yes	maximal, complemented
5	C₇×#3491	C₂	1	8	yes	maximal, complemented
6	C₇×#3461	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
9	C₂×C₇×#536	C₂	1	2	yes	maximal, complemented
10	C₇×#3428	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×#41	C₂²	1	2	yes	—
13	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
14	C₇×#559	C₂²	1	16	yes	complemented
15	C₇×#557	C₂²	1	16	yes	complemented
16	C₇×#556	C₂²	1	16	yes	complemented
17	C₇×#556	C₂²	1	32	yes	complemented
18	C₇×#554	C₂²	1	16	yes	complemented
19	C₇×#552	C₂²	1	64	yes	complemented
20	C₇×#552	C₂²	1	32	yes	complemented
21	C₇×#551	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×#541	C₂²	1	32	yes	complemented
27	C₇×#539	C₂²	1	32	yes	complemented
28	C₇×#537	C₂²	1	4	yes	—
29	C₇×#536	C₂²	1	8	yes	—
30	C₇×#536	C₂²	1	8	yes	—
31	C₇×#536	C₂²	1	4	yes	—
32	C₇×#536	C₂²	1	8	yes	complemented
33	C₇×#536	C₂²	1	8	yes	complemented
34	C₇×#535	C₂²	1	4	yes	—
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×#533	C₂²	1	32	yes	complemented
39	C₇×#532	C₂²	1	4	yes	—
40	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	complemented
41	C₇×#529	C₂²	1	32	yes	complemented
42	C₇×#529	C₂²	1	32	yes	complemented
43	C₂×C₇×#124	C₂²	1	4	yes	complemented
44	C₇×#525	C₂²	1	8	yes	—
45	C₂×C₇×#123	C₂²	1	8	yes	—
46	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
47	C₇×#520	C₂²	1	8	yes	—
48	C₇×#520	C₂²	1	8	yes	complemented
49	C₇×#519	C₂²	1	8	yes	complemented
50	C₇×#519	C₂²	1	8	yes	complemented
51	C₇×#519	C₂²	1	4	yes	complemented
52	C₇×#518	C₂²	1	8	yes	—
53	C₇×#518	C₂²	1	4	yes	complemented
54	C₄×C₇×#41	C₂²	1	8	yes	—
55	C₄×C₇×#41	C₂²	1	8	yes	complemented
56	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
57	C₂×C₄×C₇×Q₈	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	4	yes	—
61	C₂×C₇×#117	C₂²	1	2	yes	—
62	C₂×C₇×#117	C₂²	1	8	yes	complemented
63	#62860	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂×C₇×#41	—	2	16	no	—
65	C₂×C₇×#41	C₂³	1	4	yes	—
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	C₂²×C₇×Q₈	—	2	8	no	—
70	C₂²×C₇×Q₈	C₂³	1	2	yes	—
71	C₂²×C₇×Q₈	C₂³	1	2	yes	—
72	C₂²×C₇×Q₈	C₂³	1	4	yes	—
73	C₂²×C₇×Q₈	C₂³	1	4	yes	—
74	C₂²×C₇×Q₈	C₂³	1	2	yes	—
75	C₂²×C₇×D₄	C₂³	1	4	yes	—
76	C₂²×C₇×D₄	C₂³	1	2	yes	—
77	C₂³×C₄×C₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₇	C₂³	1	4	yes	—
79	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
80	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
81	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
82	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
83	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
84	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
85	C₇×#127	C₂³	1	4	yes	—
86	C₇×#126	C₂³	1	64	yes	—
87	C₇×#126	C₂³	1	64	yes	—
88	C₇×#125	C₂³	1	16	yes	—
89	C₇×#125	C₂³	1	32	yes	—
90	C₇×#125	C₂³	1	64	yes	—
91	C₇×#125	C₂³	1	8	yes	—
92	C₇×#124	C₂³	1	16	yes	—
93	C₇×#124	C₂³	1	16	yes	—
94	C₇×#124	C₂³	1	32	yes	—
95	C₇×#124	C₂³	1	8	yes	—
96	C₇×#123	C₂³	1	32	yes	—
97	C₇×#123	C₂³	1	32	yes	—
98	C₇×#123	C₂³	1	16	yes	—
99	C₇×#123	C₂³	1	64	yes	—
100	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
101	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
102	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
103	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
104	C₇×C₂²⋊Q₈	C₂³	1	64	yes	—
105	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
106	C₇×#121	C₂³	1	16	yes	—
107	C₇×#121	C₂³	1	16	yes	—
108	C₇×#120	C₂³	1	16	yes	—
109	C₄×C₇×Q₈	C₂³	1	32	yes	—
110	C₄×C₇×Q₈	C₂³	1	16	yes	—
111	C₄×C₇×Q₈	C₂³	1	16	yes	—
112	C₄×C₇×Q₈	C₂³	1	16	yes	—
113	C₄×C₇×Q₈	C₂³	1	16	yes	—
114	C₄×C₇×Q₈	C₂³	1	32	yes	—
115	C₄×C₇×Q₈	C₂³	1	16	yes	—
116	C₄×C₇×D₄	C₂³	1	32	yes	—
117	C₄×C₇×D₄	C₂³	1	16	yes	—
118	C₄×C₇×D₄	C₂³	1	32	yes	—
119	C₄×C₇×D₄	C₂³	1	16	yes	—
120	C₄×C₇×D₄	C₂³	1	16	yes	—
121	C₄×C₇×D₄	C₂³	1	32	yes	—
122	C₇×#117	C₂³	1	4	yes	—
123	C₇×#117	C₂³	1	4	yes	—
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	32	yes	—
130	C₇×#117	C₂³	1	4	yes	—
131	C₇×#117	C₂³	1	16	yes	—
132	C₇×#117	C₂³	1	16	yes	—
133	C₇×#117	C₂³	1	16	yes	—
134	C₇×#117	C₂³	1	64	yes	—
135	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
138	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
139	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
140	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
141	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
145	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
146	C₂×C₄²×C₇	C₂³	1	2	yes	—
147	C₂×C₄²×C₇	C₂³	1	8	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	—
151	#3510	C₂×C₇	1	8	yes	complemented
152	#3509	C₂×C₇	1	8	yes	complemented
153	#3507	C₂×C₇	1	8	yes	complemented
154	#3495	C₂×C₇	1	16	yes	complemented
155	#3491	C₂×C₇	1	8	yes	complemented
156	#3461	C₂×C₇	1	8	yes	complemented
157	#3458	C₂×C₇	1	1	yes	characteristic, complemented
158	#3449	C₂×C₇	1	1	yes	characteristic
159	C₂×#536	C₂×C₇	1	2	yes	complemented
160	#3428	C₂×C₇	1	2	yes	complemented
161	C₂×#519	C₂×C₇	1	1	yes	characteristic, complemented
162	C₂⁴×C₇	C₂⁴	1	4	yes	—
163	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
164	C₇×#41	—	2	16	no	—
165	C₇×#41	—	2	16	no	—
166	C₇×#41	—	2	16	no	—
167	C₇×#41	—	2	16	no	—
168	C₂×C₇×Q₈	—	2	16	no	—
169	C₂×C₇×Q₈	—	2	16	no	—
170	C₂×C₇×Q₈	—	2	8	no	—
171	C₂×C₇×Q₈	—	2	8	no	—
172	C₂×C₇×Q₈	—	2	8	no	—
173	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
174	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
175	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
176	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
177	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
178	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
179	C₂×C₇×D₄	—	2	16	no	—
180	C₂×C₇×D₄	—	2	8	no	—
181	C₂×C₇×D₄	C₂⁴	1	8	yes	—
182	C₂×C₇×D₄	C₂⁴	1	8	yes	—
183	C₂×C₇×D₄	C₂⁴	1	4	yes	—
184	C₂×C₇×D₄	C₂⁴	1	4	yes	—
185	C₂×C₇×D₄	C₂⁴	1	16	yes	—
186	C₂²×C₄×C₇	—	2	8	no	—
187	C₂²×C₄×C₇	—	2	16	no	—
188	C₂²×C₄×C₇	#41	1	8	yes	—
189	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
191	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
192	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
194	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
197	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
202	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
203	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
204	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
205	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
206	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
207	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
208	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
209	C₇×C₄⋊C₄	C₂⁴	1	64	yes	—
210	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
211	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
212	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
213	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
214	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
215	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
216	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
217	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
218	C₇×C₂²⋊C₄	C₂⁴	1	64	yes	—
219	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
220	C₄²×C₇	C₂⁴	1	8	yes	—
221	C₄²×C₇	C₂⁴	1	8	yes	—
222	C₄²×C₇	C₂⁴	1	32	yes	—
223	C₄²×C₇	C₂⁴	1	32	yes	—
224	C₄²×C₇	C₂⁴	1	4	yes	—
225	C₄²×C₇	C₂⁴	1	8	yes	—
226	C₄²×C₇	C₂⁴	1	4	yes	—
227	C₂²×#41	C₂²×C₇	1	2	yes	—
228	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
229	#559	C₂²×C₇	1	16	yes	complemented
230	#557	C₂²×C₇	1	16	yes	complemented
231	#556	C₂²×C₇	1	16	yes	complemented
232	#556	C₂²×C₇	1	32	yes	complemented
233	#554	C₂²×C₇	1	16	yes	complemented
234	#552	C₂²×C₇	1	64	yes	complemented
235	#552	C₂²×C₇	1	32	yes	complemented
236	#551	C₂²×C₇	1	64	yes	complemented
237	#544	C₂²×C₇	1	4	yes	complemented
238	#544	C₂²×C₇	1	8	yes	complemented
239	#543	C₂²×C₇	1	4	yes	—
240	#542	C₂²×C₇	1	32	yes	complemented
241	#541	C₂²×C₇	1	32	yes	complemented
242	#539	C₂²×C₇	1	32	yes	complemented
243	#537	C₂²×C₇	1	4	yes	—
244	#536	C₂²×C₇	1	8	yes	—
245	#536	C₂²×C₇	1	8	yes	—
246	#536	C₂²×C₇	1	4	yes	—
247	#536	C₂²×C₇	1	8	yes	complemented
248	#536	C₂²×C₇	1	8	yes	complemented
249	#535	C₂²×C₇	1	4	yes	—
250	#534	C₂²×C₇	1	4	yes	—
251	#533	C₂²×C₇	1	4	yes	complemented
252	#533	C₂²×C₇	1	8	yes	complemented
253	#533	C₂²×C₇	1	32	yes	complemented
254	#532	C₂²×C₇	1	4	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	complemented
256	#529	C₂²×C₇	1	32	yes	complemented
257	#529	C₂²×C₇	1	32	yes	complemented
258	C₂×#124	C₂²×C₇	1	4	yes	complemented
259	#525	C₂²×C₇	1	8	yes	—
260	C₂×#123	C₂²×C₇	1	8	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
262	#520	C₂²×C₇	1	8	yes	—
263	#520	C₂²×C₇	1	8	yes	complemented
264	#519	C₂²×C₇	1	8	yes	complemented
265	#519	C₂²×C₇	1	8	yes	complemented
266	#519	C₂²×C₇	1	4	yes	complemented
267	#518	C₂²×C₇	1	8	yes	—
268	#518	C₂²×C₇	1	4	yes	complemented
269	C₄×#41	C₂²×C₇	1	8	yes	—
270	C₄×#41	C₂²×C₇	1	8	yes	complemented
271	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
272	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
273	C₂×#117	C₂²×C₇	1	1	yes	characteristic
274	C₂×#117	C₂²×C₇	1	1	yes	characteristic
275	C₂×#117	C₂²×C₇	1	4	yes	—
276	C₂×#117	C₂²×C₇	1	2	yes	—
277	C₂×#117	C₂²×C₇	1	8	yes	complemented
278	C₂³×C₇	—	2	8	no	—
279	C₂³×C₇	—	4	2	no	—
280	C₂³×C₇	—	4	8	no	—
281	C₂³×C₇	C₂×#41	1	4	yes	—
282	C₂³×C₇	C₂⁵	1	8	yes	—
283	C₂³×C₇	C₂⁵	1	2	yes	—
284	C₂³×C₇	C₂⁵	1	1	yes	characteristic
285	C₇×Q₈	—	2	8	no	—
286	C₇×Q₈	—	2	16	no	—
287	C₇×Q₈	—	2	8	no	—
288	C₇×Q₈	—	2	8	no	—
289	C₇×Q₈	—	2	8	no	—
290	C₇×Q₈	—	4	16	no	—
291	C₇×D₄	—	2	16	no	—
292	C₇×D₄	—	2	16	no	—
293	C₇×D₄	—	2	8	no	—
294	C₇×D₄	—	2	8	no	—
295	C₇×D₄	—	4	16	no	—
296	C₂×C₄×C₇	—	2	8	no	—
297	C₂×C₄×C₇	—	2	16	no	—
298	C₂×C₄×C₇	—	2	8	no	—
299	C₂×C₄×C₇	—	2	16	no	—
300	C₂×C₄×C₇	—	2	16	no	—
301	C₂×C₄×C₇	—	4	4	no	—
302	C₂×C₄×C₇	—	4	32	no	—
303	C₂×C₄×C₇	—	4	8	no	—
304	C₂×C₄×C₇	—	4	4	no	—
305	C₂×C₄×C₇	C₂×#41	1	8	yes	—
306	C₂×C₄×C₇	C₂×#41	1	8	yes	—
307	C₂×C₄×C₇	C₂×#41	1	4	yes	—
308	C₂×C₄×C₇	C₂×#41	1	4	yes	—
309	C₂×C₄×C₇	C₂⁵	1	8	yes	—
310	C₂×C₄×C₇	C₂⁵	1	8	yes	—
311	C₂×C₄×C₇	C₂⁵	1	16	yes	—
312	C₂×C₄×C₇	C₂⁵	1	8	yes	—
313	C₂×C₄×C₇	C₂⁵	1	8	yes	—
314	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
315	C₂×C₄×C₇	C₂⁵	1	2	yes	—
316	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
317	C₂×#41	—	2	16	no	—
318	C₂×#41	C₂³×C₇	1	4	yes	—
319	C₂×#41	C₂³×C₇	1	4	yes	—
320	C₂×#41	C₂³×C₇	1	4	yes	—
321	C₂×#41	C₂³×C₇	1	4	yes	—
322	C₂²×Q₈	—	2	8	no	—
323	C₂²×Q₈	C₂³×C₇	1	2	yes	—
324	C₂²×Q₈	C₂³×C₇	1	2	yes	—
325	C₂²×Q₈	C₂³×C₇	1	4	yes	—
326	C₂²×Q₈	C₂³×C₇	1	4	yes	—
327	C₂²×Q₈	C₂³×C₇	1	2	yes	—
328	C₂²×D₄	C₂³×C₇	1	4	yes	—
329	C₂²×D₄	C₂³×C₇	1	2	yes	—
330	C₂³×C₄	C₂³×C₇	1	2	yes	—
331	C₂³×C₄	C₂³×C₇	1	4	yes	—
332	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
333	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
334	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
335	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
336	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
337	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
338	#127	C₂³×C₇	1	4	yes	—
339	#126	C₂³×C₇	1	64	yes	—
340	#126	C₂³×C₇	1	64	yes	—
341	#125	C₂³×C₇	1	16	yes	—
342	#125	C₂³×C₇	1	32	yes	—
343	#125	C₂³×C₇	1	64	yes	—
344	#125	C₂³×C₇	1	8	yes	—
345	#124	C₂³×C₇	1	16	yes	—
346	#124	C₂³×C₇	1	16	yes	—
347	#124	C₂³×C₇	1	32	yes	—
348	#124	C₂³×C₇	1	8	yes	—
349	#123	C₂³×C₇	1	32	yes	—
350	#123	C₂³×C₇	1	32	yes	—
351	#123	C₂³×C₇	1	16	yes	—
352	#123	C₂³×C₇	1	64	yes	—
353	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
354	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
355	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
356	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
357	C₂²⋊Q₈	C₂³×C₇	1	64	yes	—
358	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
359	#121	C₂³×C₇	1	16	yes	—
360	#121	C₂³×C₇	1	16	yes	—
361	#120	C₂³×C₇	1	16	yes	—
362	C₄×Q₈	C₂³×C₇	1	32	yes	—
363	C₄×Q₈	C₂³×C₇	1	16	yes	—
364	C₄×Q₈	C₂³×C₇	1	16	yes	—
365	C₄×Q₈	C₂³×C₇	1	16	yes	—
366	C₄×Q₈	C₂³×C₇	1	16	yes	—
367	C₄×Q₈	C₂³×C₇	1	32	yes	—
368	C₄×Q₈	C₂³×C₇	1	16	yes	—
369	C₄×D₄	C₂³×C₇	1	32	yes	—
370	C₄×D₄	C₂³×C₇	1	16	yes	—
371	C₄×D₄	C₂³×C₇	1	32	yes	—
372	C₄×D₄	C₂³×C₇	1	16	yes	—
373	C₄×D₄	C₂³×C₇	1	16	yes	—
374	C₄×D₄	C₂³×C₇	1	32	yes	—
375	#117	C₂³×C₇	1	4	yes	—
376	#117	C₂³×C₇	1	4	yes	—
377	#117	C₂³×C₇	1	4	yes	—
378	#117	C₂³×C₇	1	4	yes	—
379	#117	C₂³×C₇	1	4	yes	—
380	#117	C₂³×C₇	1	4	yes	—
381	#117	C₂³×C₇	1	4	yes	—
382	#117	C₂³×C₇	1	32	yes	—
383	#117	C₂³×C₇	1	4	yes	—
384	#117	C₂³×C₇	1	16	yes	—
385	#117	C₂³×C₇	1	16	yes	—
386	#117	C₂³×C₇	1	16	yes	—
387	#117	C₂³×C₇	1	64	yes	—
388	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
391	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
393	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
399	C₂×C₄²	C₂³×C₇	1	2	yes	—
400	C₂×C₄²	C₂³×C₇	1	8	yes	—
401	C₂×C₄²	C₂³×C₇	1	2	yes	—
402	C₂×C₄²	C₂³×C₇	1	4	yes	—
403	C₂×C₄²	C₂³×C₇	1	16	yes	—
404	C₂²×C₇	—	2	2	no	—
405	C₂²×C₇	—	2	4	no	—
406	C₂²×C₇	—	2	8	no	—
407	C₂²×C₇	—	2	16	no	—
408	C₂²×C₇	—	4	4	no	—
409	C₂²×C₇	—	8	8	no	—
410	C₂²×C₇	C₂²×#41	1	4	yes	—
411	C₂²×C₇	C₂²×#41	1	2	yes	—
412	C₂²×C₇	C₂⁶	1	1	yes	characteristic
413	C₄×C₇	—	2	8	no	—
414	C₄×C₇	—	2	8	no	—
415	C₄×C₇	—	2	8	no	—
416	C₄×C₇	—	2	16	no	—
417	C₄×C₇	—	2	8	no	—
418	C₄×C₇	C₂²×#41	1	2	yes	—
419	C₄×C₇	C₂²×#41	1	4	yes	—
420	C₄×C₇	C₂²×#41	1	2	yes	—
421	C₂⁴	C₂⁴×C₇	1	4	yes	—
422	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
423	#41	—	2	16	no	—
424	#41	—	2	16	no	—
425	#41	—	2	16	no	—
426	#41	—	2	16	no	—
427	C₂×Q₈	—	2	16	no	—
428	C₂×Q₈	—	2	16	no	—
429	C₂×Q₈	—	2	8	no	—
430	C₂×Q₈	—	2	8	no	—
431	C₂×Q₈	—	2	8	no	—
432	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
433	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
434	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
435	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
436	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
437	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
438	C₂×D₄	—	2	16	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	C₂⁴×C₇	1	8	yes	—
441	C₂×D₄	C₂⁴×C₇	1	8	yes	—
442	C₂×D₄	C₂⁴×C₇	1	4	yes	—
443	C₂×D₄	C₂⁴×C₇	1	4	yes	—
444	C₂×D₄	C₂⁴×C₇	1	16	yes	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	16	no	—
447	C₂²×C₄	C₇×#41	1	8	yes	—
448	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
450	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
451	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
453	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
456	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
457	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
461	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
462	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
463	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
464	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
465	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
466	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
467	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
468	C₄⋊C₄	C₂⁴×C₇	1	64	yes	—
469	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
470	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
471	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
472	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
473	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
474	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
475	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
476	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
477	C₂²⋊C₄	C₂⁴×C₇	1	64	yes	—
478	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
479	C₄²	C₂⁴×C₇	1	8	yes	—
480	C₄²	C₂⁴×C₇	1	8	yes	—
481	C₄²	C₂⁴×C₇	1	32	yes	—
482	C₄²	C₂⁴×C₇	1	32	yes	—
483	C₄²	C₂⁴×C₇	1	4	yes	—
484	C₄²	C₂⁴×C₇	1	8	yes	—
485	C₄²	C₂⁴×C₇	1	4	yes	—
486	C₂×C₇	—	2	4	no	—
487	C₂×C₇	—	2	2	no	—
488	C₂×C₇	—	4	8	no	—
489	C₂×C₇	C₂³×#41	1	1	yes	characteristic
490	C₂×C₇	2₋¹⁺⁶	1	2	yes	—
491	C₂³	—	2	8	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	8	no	—
494	C₂³	C₂×C₇×#41	1	4	yes	—
495	C₂³	C₂⁵×C₇	1	8	yes	—
496	C₂³	C₂⁵×C₇	1	2	yes	—
497	C₂³	C₂⁵×C₇	1	1	yes	characteristic
498	Q₈	—	2	8	no	—
499	Q₈	—	2	16	no	—
500	Q₈	—	2	8	no	—
501	Q₈	—	2	8	no	—
502	Q₈	—	2	8	no	—
503	Q₈	—	4	16	no	—
504	D₄	—	2	16	no	—
505	D₄	—	2	16	no	—
506	D₄	—	2	8	no	—
507	D₄	—	2	8	no	—
508	D₄	—	4	16	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	16	no	—
511	C₂×C₄	—	2	8	no	—
512	C₂×C₄	—	2	16	no	—
513	C₂×C₄	—	2	16	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	32	no	—
516	C₂×C₄	—	4	8	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	C₂×C₇×#41	1	8	yes	—
519	C₂×C₄	C₂×C₇×#41	1	8	yes	—
520	C₂×C₄	C₂×C₇×#41	1	4	yes	—
521	C₂×C₄	C₂×C₇×#41	1	4	yes	—
522	C₂×C₄	C₂⁵×C₇	1	8	yes	—
523	C₂×C₄	C₂⁵×C₇	1	8	yes	—
524	C₂×C₄	C₂⁵×C₇	1	16	yes	—
525	C₂×C₄	C₂⁵×C₇	1	8	yes	—
526	C₂×C₄	C₂⁵×C₇	1	8	yes	—
527	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
528	C₂×C₄	C₂⁵×C₇	1	2	yes	—
529	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
530	C₇	#62860	1	1	yes	characteristic, direct product factor, Sylow
531	C₂²	—	2	2	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	8	no	—
534	C₂²	—	2	16	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	8	8	no	—
537	C₂²	C₂²×C₇×#41	1	4	yes	—
538	C₂²	C₂²×C₇×#41	1	2	yes	—
539	C₂²	C₂⁶×C₇	1	1	yes	characteristic
540	C₄	—	2	8	no	—
541	C₄	—	2	8	no	—
542	C₄	—	2	8	no	—
543	C₄	—	2	16	no	—
544	C₄	—	2	8	no	—
545	C₄	C₂²×C₇×#41	1	2	yes	—
546	C₄	C₂²×C₇×#41	1	4	yes	—
547	C₄	C₂²×C₇×#41	1	2	yes	—
548	C₂	—	2	4	no	—
549	C₂	—	2	2	no	—
550	C₂	—	4	8	no	—
551	C₂	C₂³×C₇×#41	1	1	yes	characteristic
552	C₂	C₇×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
prime radical	C₇×#3449	C₂
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×#3509	C₂	semidirect
3. C₇×#3507	C₂	semidirect
4. C₇×#3495	C₂	semidirect
5. C₇×#3491	C₂	semidirect
6. C₇×#3461	C₂	semidirect
7. C₇×#3458	C₂	semidirect
9. C₂×C₇×#536	C₂	semidirect
10. C₇×#3428	C₂	semidirect
11. C₂×C₇×#519	C₂	semidirect
14. C₇×#559	C₂²	semidirect
15. C₇×#557	C₂²	semidirect
16. C₇×#556	C₂²	semidirect
17. C₇×#556	C₂²	semidirect
18. C₇×#554	C₂²	semidirect
19. C₇×#552	C₂²	semidirect
20. C₇×#552	C₂²	semidirect
21. C₇×#551	C₂²	semidirect
22. C₇×#544	C₂²	semidirect
23. C₇×#544	C₂²	semidirect
25. C₇×#542	C₂²	semidirect
26. C₇×#541	C₂²	semidirect
27. C₇×#539	C₂²	semidirect
32. C₇×#536	C₂²	semidirect
33. C₇×#536	C₂²	semidirect
36. C₇×#533	C₂²	semidirect
37. C₇×#533	C₂²	semidirect
38. C₇×#533	C₂²	semidirect
40. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
41. C₇×#529	C₂²	semidirect
42. C₇×#529	C₂²	semidirect
43. C₂×C₇×#124	C₂²	semidirect
46. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
48. C₇×#520	C₂²	semidirect
49. C₇×#519	C₂²	semidirect
50. C₇×#519	C₂²	semidirect
51. C₇×#519	C₂²	semidirect
53. C₇×#518	C₂²	semidirect
55. C₄×C₇×#41	C₂²	semidirect
56. C₂×C₄×C₇×Q₈	C₂²	semidirect
57. C₂×C₄×C₇×Q₈	C₂²	semidirect
62. C₂×C₇×#117	C₂²	semidirect
63. #62860	C₇	direct (N × H)
151. #3510	C₂×C₇	semidirect
152. #3509	C₂×C₇	semidirect
153. #3507	C₂×C₇	semidirect
154. #3495	C₂×C₇	semidirect
155. #3491	C₂×C₇	semidirect
156. #3461	C₂×C₇	semidirect
157. #3458	C₂×C₇	semidirect
159. C₂×#536	C₂×C₇	semidirect
160. #3428	C₂×C₇	semidirect
161. C₂×#519	C₂×C₇	semidirect
229. #559	C₂²×C₇	semidirect
230. #557	C₂²×C₇	semidirect
231. #556	C₂²×C₇	semidirect
232. #556	C₂²×C₇	semidirect
233. #554	C₂²×C₇	semidirect
234. #552	C₂²×C₇	semidirect
235. #552	C₂²×C₇	semidirect
236. #551	C₂²×C₇	semidirect
237. #544	C₂²×C₇	semidirect
238. #544	C₂²×C₇	semidirect
240. #542	C₂²×C₇	semidirect
241. #541	C₂²×C₇	semidirect
242. #539	C₂²×C₇	semidirect
247. #536	C₂²×C₇	semidirect
248. #536	C₂²×C₇	semidirect
251. #533	C₂²×C₇	semidirect
252. #533	C₂²×C₇	semidirect
253. #533	C₂²×C₇	semidirect
255. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
256. #529	C₂²×C₇	semidirect
257. #529	C₂²×C₇	semidirect
258. C₂×#124	C₂²×C₇	semidirect
261. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
263. #520	C₂²×C₇	semidirect
264. #519	C₂²×C₇	semidirect
265. #519	C₂²×C₇	semidirect
266. #519	C₂²×C₇	semidirect
268. #518	C₂²×C₇	semidirect
270. C₄×#41	C₂²×C₇	semidirect
271. C₂×C₄×Q₈	C₂²×C₇	semidirect
272. C₂×C₄×Q₈	C₂²×C₇	semidirect
277. C₂×#117	C₂²×C₇	semidirect
530. C₇	#62860	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×#3509	2
C₇×#3507	2
C₇×#3495	2
C₇×#3491	2
C₇×#3461	2
C₇×#3458	2
C₇×#3449	2
C₂×C₇×#536	2
C₇×#3428	2
C₂×C₇×#519	2
#62860	7

Subgroups — C7×#62860 #13240076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62860 #13240076