Subgroups — C₇×#36601 #13213817

Order 1792.

1658 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2861	C₂	1	2	yes	maximal
2	C₇×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2596	C₂	1	4	yes	maximal, complemented
4	C₇×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2580	C₂	1	1	yes	maximal, characteristic
6	C₇×#2573	C₂	1	4	yes	maximal, complemented
7	C₇×#2512	C₂	1	2	yes	maximal
8	C₇×#2511	C₂	1	2	yes	maximal, complemented
9	C₇×#2469	C₂	1	4	yes	maximal, complemented
10	C₇×#2373	C₂	1	4	yes	maximal, complemented
11	C₇×#2357	C₂	1	1	yes	maximal, characteristic
12	C₇×#2356	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₇×#125	C₂	1	2	yes	maximal, complemented
14	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic
15	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#126	C₂²	1	4	yes	—
17	C₂×C₇×#125	C₂²	1	2	yes	—
18	C₂×C₇×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
20	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₇×#400	C₂²	1	4	yes	—
24	C₇×#400	C₂²	1	4	yes	—
25	C₇×#400	C₂²	1	2	yes	—
26	C₇×#399	C₂²	1	2	yes	—
27	C₇×#397	C₂²	1	4	yes	—
28	C₇×#396	C₂²	1	4	yes	—
29	C₇×#395	C₂²	1	2	yes	—
30	C₇×#393	C₂²	1	2	yes	—
31	C₇×#391	C₂²	1	1	yes	characteristic
32	C₇×#391	C₂²	1	2	yes	—
33	C₇×#391	C₂²	1	2	yes	—
34	C₇×#390	C₂²	1	1	yes	characteristic
35	C₇×#390	C₂²	1	2	yes	—
36	C₇×#390	C₂²	1	2	yes	—
37	C₇×#389	C₂²	1	4	yes	—
38	C₇×#389	C₂²	1	2	yes	—
39	C₇×#389	C₂²	1	2	yes	—
40	C₇×#389	C₂²	1	4	yes	—
41	C₇×#388	C₂²	1	4	yes	—
42	C₇×#388	C₂²	1	4	yes	—
43	C₇×#388	C₂²	1	4	yes	—
44	C₇×#388	C₂²	1	4	yes	—
45	C₇×#388	C₂²	1	4	yes	—
46	C₇×#388	C₂²	1	4	yes	—
47	C₇×#388	C₂²	1	4	yes	—
48	C₇×#387	C₂²	1	4	yes	—
49	C₇×#387	C₂²	1	4	yes	—
50	C₇×#387	C₂²	1	4	yes	—
51	C₇×#387	C₂²	1	4	yes	—
52	C₇×#387	C₂²	1	4	yes	—
53	C₇×#387	C₂²	1	4	yes	—
54	C₇×#385	C₂²	1	4	yes	—
55	C₇×#384	C₂²	1	2	yes	—
56	C₇×#383	C₂²	1	2	yes	—
57	C₇×#382	C₂²	1	1	yes	characteristic
58	C₇×#382	C₂²	1	1	yes	characteristic
59	C₇×#382	C₂²	1	1	yes	characteristic
60	C₇×#381	C₂²	1	2	yes	—
61	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
62	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
63	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
64	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
65	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
67	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
70	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₇×#376	C₂²	1	2	yes	—
73	C₄³×C₇	C₂²	1	1	yes	characteristic
74	C₄³×C₇	C₂²	1	2	yes	—
75	#36601	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₇	C₂³	1	2	yes	—
80	C₇×#126	—	2	16	no	—
81	C₇×#125	—	2	8	no	—
82	C₇×#124	—	2	4	no	—
83	C₄×C₇×Q₈	—	2	8	no	—
84	C₄×C₇×Q₈	—	2	4	no	—
85	C₄×C₇×Q₈	—	2	4	no	—
86	C₄×C₇×D₄	—	2	4	no	—
87	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
107	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₄²×C₇	C₂³	1	2	yes	—
111	C₂×C₄²×C₇	C₂³	1	2	yes	—
112	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇	C₂³	1	2	yes	—
114	C₂×C₄²×C₇	C₂³	1	2	yes	—
115	C₂×C₄²×C₇	C₂³	1	2	yes	—
116	C₂×C₄²×C₇	C₂³	1	2	yes	—
117	C₂×C₄²×C₇	C₂³	1	4	yes	—
118	C₂×C₄²×C₇	C₂³	1	2	yes	—
119	C₂×C₄²×C₇	C₂³	1	2	yes	—
120	C₂×C₄²×C₇	C₂³	1	2	yes	—
121	C₂×C₄²×C₇	C₂³	1	4	yes	—
122	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
124	C₇×#95	C₂³	1	1	yes	characteristic
125	C₇×#95	C₂³	1	2	yes	—
126	C₇×#95	C₂³	1	4	yes	—
127	C₇×#95	C₂³	1	4	yes	—
128	C₇×#95	C₂³	1	2	yes	—
129	C₇×#95	C₂³	1	4	yes	—
130	C₇×#95	C₂³	1	1	yes	characteristic
131	C₇×#95	C₂³	1	2	yes	—
132	C₇×#95	C₂³	1	2	yes	—
133	C₇×#95	C₂³	1	4	yes	—
134	C₇×#95	C₂³	1	4	yes	—
135	C₇×#95	C₂³	1	4	yes	—
136	C₇×#95	C₂³	1	4	yes	—
137	C₇×#95	C₂³	1	2	yes	—
138	C₇×#95	C₂³	1	2	yes	—
139	C₇×#95	C₂³	1	4	yes	—
140	C₇×#95	C₂³	1	4	yes	—
141	C₇×#95	C₂³	1	4	yes	—
142	#2861	C₂×C₇	1	2	yes	—
143	#2859	C₂×C₇	1	1	yes	characteristic, complemented
144	#2596	C₂×C₇	1	4	yes	complemented
145	#2581	C₂×C₇	1	1	yes	characteristic, complemented
146	#2580	C₂×C₇	1	1	yes	characteristic
147	#2573	C₂×C₇	1	4	yes	complemented
148	#2512	C₂×C₇	1	2	yes	—
149	#2511	C₂×C₇	1	2	yes	complemented
150	#2469	C₂×C₇	1	4	yes	complemented
151	#2373	C₂×C₇	1	4	yes	complemented
152	#2357	C₂×C₇	1	1	yes	characteristic
153	#2356	C₂×C₇	1	1	yes	characteristic, complemented
154	C₄×#125	C₂×C₇	1	2	yes	complemented
155	C₄×#124	C₂×C₇	1	1	yes	characteristic
156	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂⁴×C₇	C₂⁴	1	2	yes	—
158	C₂×C₇×Q₈	—	2	4	no	—
159	C₂×C₇×Q₈	—	2	2	no	—
160	C₂×C₇×Q₈	—	2	2	no	—
161	C₂×C₇×Q₈	—	2	2	no	—
162	C₂×C₇×Q₈	—	2	2	no	—
163	C₂×C₇×D₄	—	2	2	no	—
164	C₂×C₇×D₄	—	2	2	no	—
165	C₂×C₇×D₄	—	2	2	no	—
166	C₂²×C₄×C₇	—	2	4	no	—
167	C₂²×C₄×C₇	—	4	4	no	—
168	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
182	C₇×C₄⋊C₄	—	2	2	no	—
183	C₇×C₄⋊C₄	—	2	4	no	—
184	C₇×C₄⋊C₄	—	2	4	no	—
185	C₇×C₄⋊C₄	—	2	4	no	—
186	C₇×C₄⋊C₄	—	2	2	no	—
187	C₇×C₄⋊C₄	—	2	2	no	—
188	C₇×C₄⋊C₄	—	2	4	no	—
189	C₇×C₄⋊C₄	—	2	8	no	—
190	C₇×C₄⋊C₄	—	2	8	no	—
191	C₇×C₄⋊C₄	—	2	4	no	—
192	C₇×C₄⋊C₄	—	2	4	no	—
193	C₇×C₄⋊C₄	—	2	8	no	—
194	C₇×C₄⋊C₄	—	2	8	no	—
195	C₇×C₄⋊C₄	—	4	4	no	—
196	C₇×C₄⋊C₄	—	4	4	no	—
197	C₇×C₄⋊C₄	#41	1	8	yes	—
198	C₇×C₂²⋊C₄	—	2	4	no	—
199	C₇×C₂²⋊C₄	—	2	8	no	—
200	C₇×C₂²⋊C₄	—	2	8	no	—
201	C₇×C₂²⋊C₄	—	2	8	no	—
202	C₇×C₂²⋊C₄	—	2	8	no	—
203	C₇×C₂²⋊C₄	—	4	4	no	—
204	C₇×C₂²⋊C₄	—	4	4	no	—
205	C₄²×C₇	—	2	4	no	—
206	C₄²×C₇	—	2	4	no	—
207	C₄²×C₇	—	2	4	no	—
208	C₄²×C₇	—	2	4	no	—
209	C₄²×C₇	—	2	4	no	—
210	C₄²×C₇	—	2	8	no	—
211	C₄²×C₇	—	2	2	no	—
212	C₄²×C₇	—	2	4	no	—
213	C₄²×C₇	—	4	2	no	—
214	C₄²×C₇	—	4	2	no	—
215	C₄²×C₇	—	4	2	no	—
216	C₄²×C₇	—	4	4	no	—
217	C₄²×C₇	#41	1	4	yes	—
218	C₄²×C₇	#41	1	4	yes	—
219	C₂×#126	C₂²×C₇	1	4	yes	—
220	C₂×#125	C₂²×C₇	1	2	yes	—
221	C₂×#124	C₂²×C₇	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
225	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
226	#400	C₂²×C₇	1	4	yes	—
227	#400	C₂²×C₇	1	4	yes	—
228	#400	C₂²×C₇	1	2	yes	—
229	#399	C₂²×C₇	1	2	yes	—
230	#397	C₂²×C₇	1	4	yes	—
231	#396	C₂²×C₇	1	4	yes	—
232	#395	C₂²×C₇	1	2	yes	—
233	#393	C₂²×C₇	1	2	yes	—
234	#391	C₂²×C₇	1	2	yes	—
235	#391	C₂²×C₇	1	2	yes	—
236	#391	C₂²×C₇	1	1	yes	characteristic
237	#390	C₂²×C₇	1	2	yes	—
238	#390	C₂²×C₇	1	2	yes	—
239	#390	C₂²×C₇	1	1	yes	characteristic
240	#389	C₂²×C₇	1	2	yes	—
241	#389	C₂²×C₇	1	2	yes	—
242	#389	C₂²×C₇	1	4	yes	—
243	#389	C₂²×C₇	1	4	yes	—
244	#388	C₂²×C₇	1	4	yes	—
245	#388	C₂²×C₇	1	4	yes	—
246	#388	C₂²×C₇	1	4	yes	—
247	#388	C₂²×C₇	1	4	yes	—
248	#388	C₂²×C₇	1	4	yes	—
249	#388	C₂²×C₇	1	4	yes	—
250	#388	C₂²×C₇	1	4	yes	—
251	#387	C₂²×C₇	1	4	yes	—
252	#387	C₂²×C₇	1	4	yes	—
253	#387	C₂²×C₇	1	4	yes	—
254	#387	C₂²×C₇	1	4	yes	—
255	#387	C₂²×C₇	1	4	yes	—
256	#387	C₂²×C₇	1	4	yes	—
257	#385	C₂²×C₇	1	4	yes	—
258	#384	C₂²×C₇	1	2	yes	—
259	#383	C₂²×C₇	1	2	yes	—
260	#382	C₂²×C₇	1	1	yes	characteristic
261	#382	C₂²×C₇	1	1	yes	characteristic
262	#382	C₂²×C₇	1	1	yes	characteristic
263	#381	C₂²×C₇	1	2	yes	—
264	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
265	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
266	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
267	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
268	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
269	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
270	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
271	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
272	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
273	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
274	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
275	#376	C₂²×C₇	1	2	yes	—
276	C₄³	C₂²×C₇	1	2	yes	—
277	C₄³	C₂²×C₇	1	1	yes	characteristic
278	C₂³×C₇	—	2	4	no	—
279	C₂³×C₇	—	2	2	no	—
280	C₂³×C₇	—	2	2	no	—
281	C₂³×C₇	—	2	2	no	—
282	C₂³×C₇	—	2	4	no	—
283	C₂³×C₇	C₂⁵	1	1	yes	characteristic
284	C₇×Q₈	—	2	8	no	—
285	C₇×Q₈	—	4	4	no	—
286	C₇×D₄	—	4	4	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	2	no	—
290	C₂×C₄×C₇	—	2	2	no	—
291	C₂×C₄×C₇	—	2	2	no	—
292	C₂×C₄×C₇	—	2	2	no	—
293	C₂×C₄×C₇	—	2	2	no	—
294	C₂×C₄×C₇	—	2	2	no	—
295	C₂×C₄×C₇	—	2	2	no	—
296	C₂×C₄×C₇	—	2	2	no	—
297	C₂×C₄×C₇	—	2	4	no	—
298	C₂×C₄×C₇	—	2	4	no	—
299	C₂×C₄×C₇	—	2	2	no	—
300	C₂×C₄×C₇	—	2	2	no	—
301	C₂×C₄×C₇	—	2	2	no	—
302	C₂×C₄×C₇	—	2	2	no	—
303	C₂×C₄×C₇	—	2	2	no	—
304	C₂×C₄×C₇	—	2	4	no	—
305	C₂×C₄×C₇	—	2	2	no	—
306	C₂×C₄×C₇	—	2	4	no	—
307	C₂×C₄×C₇	—	2	4	no	—
308	C₂×C₄×C₇	—	2	2	no	—
309	C₂×C₄×C₇	—	2	2	no	—
310	C₂×C₄×C₇	—	2	2	no	—
311	C₂×C₄×C₇	—	2	2	no	—
312	C₂×C₄×C₇	—	2	4	no	—
313	C₂×C₄×C₇	—	2	2	no	—
314	C₂×C₄×C₇	—	2	4	no	—
315	C₂×C₄×C₇	—	2	4	no	—
316	C₂×C₄×C₇	—	8	4	no	—
317	C₂×C₄×C₇	C₂×#41	1	4	yes	—
318	C₂×C₄×C₇	C₂×#41	1	2	yes	—
319	C₂×C₄×C₇	C₂×#41	1	4	yes	—
320	C₂×C₄×C₇	C₂×#41	1	4	yes	—
321	C₂×C₄×C₇	C₂×#41	1	4	yes	—
322	C₂×C₄×C₇	C₂×#41	1	2	yes	—
323	C₂×C₄×C₇	C₂×#41	1	2	yes	—
324	C₂×C₄×C₇	C₂×#41	1	2	yes	—
325	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
326	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
328	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₇	1	2	yes	—
330	#126	—	2	16	no	—
331	#125	—	2	8	no	—
332	#124	—	2	4	no	—
333	C₄×Q₈	—	2	8	no	—
334	C₄×Q₈	—	2	4	no	—
335	C₄×Q₈	—	2	4	no	—
336	C₄×D₄	—	2	4	no	—
337	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
349	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
351	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
352	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
360	C₂×C₄²	C₂³×C₇	1	2	yes	—
361	C₂×C₄²	C₂³×C₇	1	2	yes	—
362	C₂×C₄²	C₂³×C₇	1	2	yes	—
363	C₂×C₄²	C₂³×C₇	1	2	yes	—
364	C₂×C₄²	C₂³×C₇	1	2	yes	—
365	C₂×C₄²	C₂³×C₇	1	4	yes	—
366	C₂×C₄²	C₂³×C₇	1	2	yes	—
367	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₇	1	2	yes	—
369	C₂×C₄²	C₂³×C₇	1	2	yes	—
370	C₂×C₄²	C₂³×C₇	1	2	yes	—
371	C₂×C₄²	C₂³×C₇	1	4	yes	—
372	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
374	#95	C₂³×C₇	1	1	yes	characteristic
375	#95	C₂³×C₇	1	2	yes	—
376	#95	C₂³×C₇	1	4	yes	—
377	#95	C₂³×C₇	1	4	yes	—
378	#95	C₂³×C₇	1	2	yes	—
379	#95	C₂³×C₇	1	4	yes	—
380	#95	C₂³×C₇	1	1	yes	characteristic
381	#95	C₂³×C₇	1	2	yes	—
382	#95	C₂³×C₇	1	2	yes	—
383	#95	C₂³×C₇	1	4	yes	—
384	#95	C₂³×C₇	1	4	yes	—
385	#95	C₂³×C₇	1	4	yes	—
386	#95	C₂³×C₇	1	4	yes	—
387	#95	C₂³×C₇	1	2	yes	—
388	#95	C₂³×C₇	1	2	yes	—
389	#95	C₂³×C₇	1	4	yes	—
390	#95	C₂³×C₇	1	4	yes	—
391	#95	C₂³×C₇	1	4	yes	—
392	C₂²×C₇	—	4	2	no	—
393	C₂²×C₇	—	4	2	no	—
394	C₂²×C₇	—	4	4	no	—
395	C₂²×C₇	—	4	2	no	—
396	C₂²×C₇	—	4	4	no	—
397	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
398	C₂²×C₇	C₂²×#41	1	2	yes	—
399	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
401	C₂²×C₇	#585	1	2	yes	—
402	C₄×C₇	—	2	4	no	—
403	C₄×C₇	—	2	2	no	—
404	C₄×C₇	—	2	4	no	—
405	C₄×C₇	—	2	2	no	—
406	C₄×C₇	—	2	4	no	—
407	C₄×C₇	—	2	4	no	—
408	C₄×C₇	—	4	2	no	—
409	C₄×C₇	—	4	2	no	—
410	C₄×C₇	—	4	4	no	—
411	C₄×C₇	—	4	4	no	—
412	C₄×C₇	—	4	2	no	—
413	C₄×C₇	—	4	2	no	—
414	C₄×C₇	—	4	2	no	—
415	C₄×C₇	#556	1	4	yes	—
416	C₂⁴	C₂⁴×C₇	1	2	yes	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
429	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
434	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
440	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₄⋊C₄	—	4	4	no	—
456	C₄⋊C₄	C₇×#41	1	8	yes	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₂²⋊C₄	—	2	8	no	—
460	C₂²⋊C₄	—	2	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	2	4	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	4	no	—
469	C₄²	—	2	8	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	4	2	no	—
473	C₄²	—	4	2	no	—
474	C₄²	—	4	2	no	—
475	C₄²	—	4	4	no	—
476	C₄²	C₇×#41	1	4	yes	—
477	C₄²	C₇×#41	1	4	yes	—
478	C₂×C₇	—	8	2	no	—
479	C₂×C₇	#3444	1	1	yes	characteristic
480	C₂×C₇	C₂×#556	1	1	yes	characteristic
481	C₂×C₇	#3480	1	2	yes	—
482	C₂×C₇	#3510	1	1	yes	characteristic
483	C₂×C₇	#3515	1	2	yes	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	4	no	—
489	C₂³	C₂⁵×C₇	1	1	yes	characteristic
490	Q₈	—	2	8	no	—
491	Q₈	—	4	4	no	—
492	D₄	—	4	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	C₂×C₇×#41	1	4	yes	—
524	C₂×C₄	C₂×C₇×#41	1	2	yes	—
525	C₂×C₄	C₂×C₇×#41	1	4	yes	—
526	C₂×C₄	C₂×C₇×#41	1	4	yes	—
527	C₂×C₄	C₂×C₇×#41	1	4	yes	—
528	C₂×C₄	C₂×C₇×#41	1	2	yes	—
529	C₂×C₄	C₂×C₇×#41	1	2	yes	—
530	C₂×C₄	C₂×C₇×#41	1	2	yes	—
531	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
532	C₇	#36601	1	1	yes	characteristic, direct product factor, Sylow
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	4	no	—
538	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
539	C₂²	C₂²×C₇×#41	1	2	yes	—
540	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
541	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
542	C₂²	C₇×#585	1	2	yes	—
543	C₄	—	2	4	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	4	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	4	no	—
548	C₄	—	2	4	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	2	no	—
556	C₄	C₇×#556	1	4	yes	—
557	C₂	—	8	2	no	—
558	C₂	C₇×#3444	1	1	yes	characteristic
559	C₂	C₂×C₇×#556	1	1	yes	characteristic
560	C₂	C₇×#3480	1	2	yes	—
561	C₂	C₇×#3510	1	1	yes	characteristic
562	C₂	C₇×#3515	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2859	C₂	semidirect
3. C₇×#2596	C₂	semidirect
4. C₇×#2581	C₂	semidirect
6. C₇×#2573	C₂	semidirect
8. C₇×#2511	C₂	semidirect
9. C₇×#2469	C₂	semidirect
10. C₇×#2373	C₂	semidirect
12. C₇×#2356	C₂	semidirect
13. C₄×C₇×#125	C₂	semidirect
15. C₄²×C₇×Q₈	C₂	semidirect
75. #36601	C₇	direct (N × H)
143. #2859	C₂×C₇	semidirect
144. #2596	C₂×C₇	semidirect
145. #2581	C₂×C₇	semidirect
147. #2573	C₂×C₇	semidirect
149. #2511	C₂×C₇	semidirect
150. #2469	C₂×C₇	semidirect
151. #2373	C₂×C₇	semidirect
153. #2356	C₂×C₇	semidirect
154. C₄×#125	C₂×C₇	semidirect
156. C₄²×Q₈	C₂×C₇	semidirect
532. C₇	#36601	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×#2861	2
C₇×#2859	2
C₇×#2596	2
C₇×#2581	2
C₇×#2580	2
C₇×#2573	2
C₇×#2512	2
C₇×#2511	2
C₇×#2469	2
C₇×#2373	2
C₇×#2357	2
C₇×#2356	2
C₄×C₇×#125	2
C₄×C₇×#124	2
C₄²×C₇×Q₈	2
#36601	7

Subgroups — C7×#36601 #13213817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36601 #13213817