Subgroups — C₇×#3551 #11744503

Order 896.

1050 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#563	C₂	1	2	yes	maximal, complemented
2	C₇×#560	C₂	1	2	yes	maximal, complemented
3	C₇×#555	C₂	1	2	yes	maximal, complemented
4	C₇×#553	C₂	1	2	yes	maximal, complemented
5	C₇×#552	C₂	1	2	yes	maximal, complemented
6	C₇×#551	C₂	1	2	yes	maximal, complemented
7	C₇×#548	C₂	1	2	yes	maximal, complemented
8	C₇×#546	C₂	1	2	yes	maximal, complemented
9	C₇×#540	C₂	1	4	yes	maximal, complemented
10	C₇×#538	C₂	1	4	yes	maximal, complemented
11	C₇×#537	C₂	1	2	yes	maximal, complemented
12	C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#529	C₂	1	2	yes	maximal, complemented
16	C₂×C₇×#41	C₂²	1	1	yes	characteristic
17	C₂×C₇×#41	C₂²	1	2	yes	—
18	C₂×C₇×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₇×#127	C₂²	1	1	yes	characteristic
24	C₇×#127	C₂²	1	2	yes	—
25	C₇×#126	C₂²	1	4	yes	—
26	C₇×#126	C₂²	1	4	yes	complemented
27	C₇×#126	C₂²	1	4	yes	complemented
28	C₇×#125	C₂²	1	2	yes	complemented
29	C₇×#125	C₂²	1	4	yes	complemented
30	C₇×#124	C₂²	1	2	yes	—
31	C₇×#124	C₂²	1	1	yes	characteristic
32	C₇×#124	C₂²	1	2	yes	—
33	C₇×#124	C₂²	1	2	yes	—
34	C₇×#124	C₂²	1	1	yes	characteristic, complemented
35	C₇×#124	C₂²	1	4	yes	complemented
36	C₇×#123	C₂²	1	2	yes	—
37	C₇×#123	C₂²	1	4	yes	—
38	C₇×#123	C₂²	1	4	yes	—
39	C₇×#123	C₂²	1	4	yes	complemented
40	C₇×#123	C₂²	1	2	yes	complemented
41	C₇×#123	C₂²	1	4	yes	complemented
42	C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
44	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
47	C₇×#121	C₂²	1	2	yes	—
48	C₇×#121	C₂²	1	2	yes	—
49	C₇×#121	C₂²	1	2	yes	—
50	C₇×#121	C₂²	1	2	yes	—
51	C₇×#121	C₂²	1	4	yes	—
52	C₇×#121	C₂²	1	2	yes	complemented
53	C₇×#121	C₂²	1	4	yes	complemented
54	C₇×#121	C₂²	1	4	yes	complemented
55	C₇×#121	C₂²	1	4	yes	complemented
56	C₇×#121	C₂²	1	4	yes	complemented
57	C₇×#121	C₂²	1	4	yes	complemented
58	C₇×#120	C₂²	1	2	yes	—
59	C₇×#120	C₂²	1	2	yes	—
60	C₇×#120	C₂²	1	4	yes	—
61	C₄×C₇×Q₈	C₂²	1	2	yes	complemented
62	C₄×C₇×D₄	C₂²	1	2	yes	—
63	C₄×C₇×D₄	C₂²	1	2	yes	—
64	C₄×C₇×D₄	C₂²	1	4	yes	complemented
65	C₄×C₇×D₄	C₂²	1	2	yes	complemented
66	C₄×C₇×D₄	C₂²	1	4	yes	complemented
67	C₄×C₇×D₄	C₂²	1	4	yes	complemented
68	C₇×#117	C₂²	1	1	yes	characteristic
69	C₇×#117	C₂²	1	4	yes	complemented
70	C₇×#117	C₂²	1	1	yes	characteristic, complemented
71	C₇×#117	C₂²	1	4	yes	complemented
72	C₂×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
73	C₂×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
74	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
75	#3551	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₇	C₂³	1	2	yes	—
77	C₇×#41	—	4	2	no	—
78	C₇×#41	—	4	2	no	—
79	C₇×#41	—	4	4	no	—
80	C₂×C₇×Q₈	—	4	2	no	—
81	C₂×C₇×Q₈	C₂³	1	2	yes	—
82	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
83	C₂×C₇×Q₈	C₂³	1	2	yes	—
84	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₇×D₄	—	4	2	no	—
86	C₂×C₇×D₄	C₂³	1	2	yes	—
87	C₂×C₇×D₄	C₂³	1	2	yes	—
88	C₂×C₇×D₄	C₂³	1	4	yes	—
89	C₂×C₇×D₄	C₂³	1	4	yes	—
90	C₂×C₇×D₄	C₂³	1	4	yes	—
91	C₂×C₇×D₄	C₂³	1	2	yes	—
92	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
93	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
94	C₂×C₇×D₄	C₂³	1	4	yes	—
95	C₂×C₇×D₄	C₂³	1	2	yes	—
96	C₂×C₇×D₄	C₂³	1	2	yes	—
97	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
98	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₇	C₂³	1	2	yes	—
101	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂³	1	2	yes	—
104	C₂²×C₄×C₇	C₂³	1	4	yes	—
105	C₂²×C₄×C₇	C₂³	1	4	yes	—
106	C₂²×C₄×C₇	C₂³	1	4	yes	—
107	C₂²×C₄×C₇	C₂³	1	2	yes	—
108	C₇×C₄⋊C₄	C₂³	1	2	yes	—
109	C₇×C₄⋊C₄	C₂³	1	2	yes	—
110	C₇×C₄⋊C₄	C₂³	1	4	yes	—
111	C₇×C₄⋊C₄	C₂³	1	4	yes	—
112	C₇×C₄⋊C₄	C₂³	1	4	yes	—
113	C₇×C₄⋊C₄	C₂³	1	4	yes	—
114	C₇×C₄⋊C₄	C₂³	1	2	yes	—
115	C₇×C₄⋊C₄	C₂³	1	2	yes	—
116	C₇×C₄⋊C₄	C₂³	1	4	yes	—
117	C₇×C₄⋊C₄	C₂³	1	4	yes	—
118	C₇×C₄⋊C₄	C₂³	1	4	yes	—
119	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₄²×C₇	C₂³	1	1	yes	characteristic
135	C₄²×C₇	C₂³	1	2	yes	—
136	C₄²×C₇	C₂³	1	1	yes	characteristic
137	C₄²×C₇	C₂³	1	2	yes	—
138	C₄²×C₇	C₂³	1	4	yes	—
139	C₄²×C₇	C₂³	1	2	yes	—
140	#563	C₂×C₇	1	2	yes	complemented
141	#560	C₂×C₇	1	2	yes	complemented
142	#555	C₂×C₇	1	2	yes	complemented
143	#553	C₂×C₇	1	2	yes	complemented
144	#552	C₂×C₇	1	2	yes	complemented
145	#551	C₂×C₇	1	2	yes	complemented
146	#548	C₂×C₇	1	2	yes	complemented
147	#546	C₂×C₇	1	2	yes	complemented
148	#540	C₂×C₇	1	4	yes	complemented
149	#538	C₂×C₇	1	4	yes	complemented
150	#537	C₂×C₇	1	2	yes	complemented
151	#536	C₂×C₇	1	1	yes	characteristic, complemented
152	#535	C₂×C₇	1	1	yes	characteristic, complemented
153	#532	C₂×C₇	1	1	yes	characteristic, complemented
154	#529	C₂×C₇	1	2	yes	complemented
155	C₂³×C₇	—	4	2	no	—
156	C₂³×C₇	—	4	4	no	—
157	C₂³×C₇	C₂⁴	1	1	yes	characteristic
158	C₂³×C₇	C₂⁴	1	4	yes	—
159	C₂³×C₇	C₂⁴	1	1	yes	characteristic
160	C₂³×C₇	C₂⁴	1	2	yes	—
161	C₂³×C₇	C₂⁴	1	1	yes	characteristic
162	C₇×Q₈	—	2	4	no	—
163	C₇×Q₈	—	4	2	no	—
164	C₇×Q₈	—	4	1	no	—
165	C₇×Q₈	—	4	1	no	—
166	C₇×D₄	—	2	4	no	—
167	C₇×D₄	—	4	2	no	—
168	C₇×D₄	—	4	4	no	—
169	C₇×D₄	—	4	2	no	—
170	C₇×D₄	—	4	4	no	—
171	C₇×D₄	—	4	4	no	—
172	C₇×D₄	—	4	2	no	—
173	C₇×D₄	—	4	2	no	—
174	C₇×D₄	—	4	1	no	—
175	C₇×D₄	—	4	1	no	—
176	C₇×D₄	—	4	1	no	—
177	C₇×D₄	—	4	1	no	—
178	C₇×D₄	—	4	4	no	—
179	C₂×C₄×C₇	—	2	2	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	2	4	no	—
182	C₂×C₄×C₇	—	2	2	no	—
183	C₂×C₄×C₇	—	4	4	no	—
184	C₂×C₄×C₇	—	4	2	no	—
185	C₂×C₄×C₇	—	4	4	no	—
186	C₂×C₄×C₇	—	4	2	no	—
187	C₂×C₄×C₇	—	4	4	no	—
188	C₂×C₄×C₇	C₂⁴	1	2	yes	—
189	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₇	C₂⁴	1	2	yes	—
191	C₂×C₄×C₇	C₂⁴	1	4	yes	—
192	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₇	C₂⁴	1	4	yes	—
195	C₂×C₄×C₇	C₂⁴	1	4	yes	—
196	C₂×C₄×C₇	C₂⁴	1	2	yes	—
197	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
198	C₂×#41	C₂²×C₇	1	1	yes	characteristic
199	C₂×#41	C₂²×C₇	1	2	yes	—
200	C₂×#41	C₂²×C₇	1	1	yes	characteristic, complemented
201	C₂²×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
202	C₂²×D₄	C₂²×C₇	1	1	yes	characteristic
203	C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
204	C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
205	#127	C₂²×C₇	1	1	yes	characteristic
206	#127	C₂²×C₇	1	2	yes	—
207	#126	C₂²×C₇	1	4	yes	—
208	#126	C₂²×C₇	1	4	yes	complemented
209	#126	C₂²×C₇	1	4	yes	complemented
210	#125	C₂²×C₇	1	2	yes	complemented
211	#125	C₂²×C₇	1	4	yes	complemented
212	#124	C₂²×C₇	1	2	yes	—
213	#124	C₂²×C₇	1	1	yes	characteristic
214	#124	C₂²×C₇	1	2	yes	—
215	#124	C₂²×C₇	1	2	yes	—
216	#124	C₂²×C₇	1	1	yes	characteristic, complemented
217	#124	C₂²×C₇	1	4	yes	complemented
218	#123	C₂²×C₇	1	2	yes	—
219	#123	C₂²×C₇	1	4	yes	—
220	#123	C₂²×C₇	1	4	yes	—
221	#123	C₂²×C₇	1	4	yes	complemented
222	#123	C₂²×C₇	1	2	yes	complemented
223	#123	C₂²×C₇	1	4	yes	complemented
224	C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
225	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
226	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
227	C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
228	C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
229	#121	C₂²×C₇	1	2	yes	—
230	#121	C₂²×C₇	1	2	yes	—
231	#121	C₂²×C₇	1	2	yes	—
232	#121	C₂²×C₇	1	2	yes	—
233	#121	C₂²×C₇	1	4	yes	—
234	#121	C₂²×C₇	1	2	yes	complemented
235	#121	C₂²×C₇	1	4	yes	complemented
236	#121	C₂²×C₇	1	4	yes	complemented
237	#121	C₂²×C₇	1	4	yes	complemented
238	#121	C₂²×C₇	1	4	yes	complemented
239	#121	C₂²×C₇	1	4	yes	complemented
240	#120	C₂²×C₇	1	2	yes	—
241	#120	C₂²×C₇	1	2	yes	—
242	#120	C₂²×C₇	1	4	yes	—
243	C₄×Q₈	C₂²×C₇	1	2	yes	complemented
244	C₄×D₄	C₂²×C₇	1	2	yes	—
245	C₄×D₄	C₂²×C₇	1	2	yes	—
246	C₄×D₄	C₂²×C₇	1	4	yes	complemented
247	C₄×D₄	C₂²×C₇	1	2	yes	complemented
248	C₄×D₄	C₂²×C₇	1	4	yes	complemented
249	C₄×D₄	C₂²×C₇	1	4	yes	complemented
250	#117	C₂²×C₇	1	1	yes	characteristic
251	#117	C₂²×C₇	1	4	yes	complemented
252	#117	C₂²×C₇	1	1	yes	characteristic, complemented
253	#117	C₂²×C₇	1	4	yes	complemented
254	C₂×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
255	C₂×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
256	C₂×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
257	C₂²×C₇	—	2	1	no	—
258	C₂²×C₇	—	2	2	no	—
259	C₂²×C₇	—	2	1	no	—
260	C₂²×C₇	—	2	1	no	—
261	C₂²×C₇	—	2	4	no	—
262	C₂²×C₇	—	2	2	no	—
263	C₂²×C₇	—	2	2	no	—
264	C₂²×C₇	—	2	4	no	—
265	C₂²×C₇	—	2	2	no	—
266	C₂²×C₇	—	2	2	no	—
267	C₂²×C₇	—	2	4	no	—
268	C₂²×C₇	—	2	2	no	—
269	C₂²×C₇	—	8	4	no	—
270	C₂²×C₇	C₂⁵	1	1	yes	characteristic
271	C₄×C₇	—	2	2	no	—
272	C₄×C₇	—	2	1	no	—
273	C₄×C₇	—	2	1	no	—
274	C₄×C₇	—	2	1	no	—
275	C₄×C₇	—	2	4	no	—
276	C₄×C₇	—	2	2	no	—
277	C₄×C₇	—	2	4	no	—
278	C₄×C₇	—	2	2	no	—
279	C₄×C₇	—	2	4	no	—
280	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
281	C₂⁴	C₂³×C₇	1	2	yes	—
282	#41	—	4	2	no	—
283	#41	—	4	2	no	—
284	#41	—	4	4	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	C₂³×C₇	1	2	yes	—
287	C₂×Q₈	C₂³×C₇	1	1	yes	characteristic
288	C₂×Q₈	C₂³×C₇	1	2	yes	—
289	C₂×Q₈	C₂³×C₇	1	1	yes	characteristic
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	C₂³×C₇	1	2	yes	—
292	C₂×D₄	C₂³×C₇	1	2	yes	—
293	C₂×D₄	C₂³×C₇	1	4	yes	—
294	C₂×D₄	C₂³×C₇	1	4	yes	—
295	C₂×D₄	C₂³×C₇	1	4	yes	—
296	C₂×D₄	C₂³×C₇	1	2	yes	—
297	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
298	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
299	C₂×D₄	C₂³×C₇	1	4	yes	—
300	C₂×D₄	C₂³×C₇	1	2	yes	—
301	C₂×D₄	C₂³×C₇	1	2	yes	—
302	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
303	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
304	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
305	C₂²×C₄	C₂³×C₇	1	2	yes	—
306	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
308	C₂²×C₄	C₂³×C₇	1	2	yes	—
309	C₂²×C₄	C₂³×C₇	1	4	yes	—
310	C₂²×C₄	C₂³×C₇	1	4	yes	—
311	C₂²×C₄	C₂³×C₇	1	4	yes	—
312	C₂²×C₄	C₂³×C₇	1	2	yes	—
313	C₄⋊C₄	C₂³×C₇	1	2	yes	—
314	C₄⋊C₄	C₂³×C₇	1	2	yes	—
315	C₄⋊C₄	C₂³×C₇	1	4	yes	—
316	C₄⋊C₄	C₂³×C₇	1	4	yes	—
317	C₄⋊C₄	C₂³×C₇	1	4	yes	—
318	C₄⋊C₄	C₂³×C₇	1	4	yes	—
319	C₄⋊C₄	C₂³×C₇	1	2	yes	—
320	C₄⋊C₄	C₂³×C₇	1	2	yes	—
321	C₄⋊C₄	C₂³×C₇	1	4	yes	—
322	C₄⋊C₄	C₂³×C₇	1	4	yes	—
323	C₄⋊C₄	C₂³×C₇	1	4	yes	—
324	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
325	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
326	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
327	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
328	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
329	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
330	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
331	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
332	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
333	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
334	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
335	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
336	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
337	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
338	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
339	C₄²	C₂³×C₇	1	1	yes	characteristic
340	C₄²	C₂³×C₇	1	2	yes	—
341	C₄²	C₂³×C₇	1	1	yes	characteristic
342	C₄²	C₂³×C₇	1	2	yes	—
343	C₄²	C₂³×C₇	1	4	yes	—
344	C₄²	C₂³×C₇	1	2	yes	—
345	C₂×C₇	—	4	1	no	—
346	C₂×C₇	—	4	2	no	—
347	C₂×C₇	—	4	1	no	—
348	C₂×C₇	—	4	4	no	—
349	C₂×C₇	—	4	1	no	—
350	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₇	#585	1	2	yes	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	4	no	—
354	C₂³	C₂⁴×C₇	1	1	yes	characteristic
355	C₂³	C₂⁴×C₇	1	4	yes	—
356	C₂³	C₂⁴×C₇	1	1	yes	characteristic
357	C₂³	C₂⁴×C₇	1	2	yes	—
358	C₂³	C₂⁴×C₇	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	4	1	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	C₂⁴×C₇	1	2	yes	—
386	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
387	C₂×C₄	C₂⁴×C₇	1	2	yes	—
388	C₂×C₄	C₂⁴×C₇	1	4	yes	—
389	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
390	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
391	C₂×C₄	C₂⁴×C₇	1	4	yes	—
392	C₂×C₄	C₂⁴×C₇	1	4	yes	—
393	C₂×C₄	C₂⁴×C₇	1	2	yes	—
394	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
395	C₇	#3551	1	1	yes	characteristic, direct product factor, Sylow
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	8	4	no	—
409	C₂²	C₂⁵×C₇	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	4	no	—
419	C₄	C₇×H(5,𝔽₂)	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	4	4	no	—
422	C₂	—	4	1	no	—
423	C₂	—	4	2	no	—
424	C₂	—	4	1	no	—
425	C₂	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂	C₇×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×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×#563	C₂	semidirect
2. C₇×#560	C₂	semidirect
3. C₇×#555	C₂	semidirect
4. C₇×#553	C₂	semidirect
5. C₇×#552	C₂	semidirect
6. C₇×#551	C₂	semidirect
7. C₇×#548	C₂	semidirect
8. C₇×#546	C₂	semidirect
9. C₇×#540	C₂	semidirect
10. C₇×#538	C₂	semidirect
11. C₇×#537	C₂	semidirect
12. C₇×#536	C₂	semidirect
13. C₇×#535	C₂	semidirect
14. C₇×#532	C₂	semidirect
15. C₇×#529	C₂	semidirect
18. C₂×C₇×#41	C₂²	semidirect
19. C₂²×C₇×Q₈	C₂²	semidirect
21. C₇×C₄⋊Q₈	C₂²	semidirect
22. C₇×C₄⋊Q₈	C₂²	semidirect
26. C₇×#126	C₂²	semidirect
27. C₇×#126	C₂²	semidirect
28. C₇×#125	C₂²	semidirect
29. C₇×#125	C₂²	semidirect
34. C₇×#124	C₂²	semidirect
35. C₇×#124	C₂²	semidirect
39. C₇×#123	C₂²	semidirect
40. C₇×#123	C₂²	semidirect
41. C₇×#123	C₂²	semidirect
43. C₇×C₂²⋊Q₈	C₂²	semidirect
44. C₇×C₂²⋊Q₈	C₂²	semidirect
45. C₇×C₂²⋊Q₈	C₂²	semidirect
46. C₇×C₂²⋊Q₈	C₂²	semidirect
52. C₇×#121	C₂²	semidirect
53. C₇×#121	C₂²	semidirect
54. C₇×#121	C₂²	semidirect
55. C₇×#121	C₂²	semidirect
56. C₇×#121	C₂²	semidirect
57. C₇×#121	C₂²	semidirect
61. C₄×C₇×Q₈	C₂²	semidirect
64. C₄×C₇×D₄	C₂²	semidirect
65. C₄×C₇×D₄	C₂²	semidirect
66. C₄×C₇×D₄	C₂²	semidirect
67. C₄×C₇×D₄	C₂²	semidirect
69. C₇×#117	C₂²	semidirect
70. C₇×#117	C₂²	semidirect
71. C₇×#117	C₂²	semidirect
72. C₂×C₇×C₄⋊C₄	C₂²	semidirect
74. C₂×C₄²×C₇	C₂²	semidirect
75. #3551	C₇	direct (N × H)
140. #563	C₂×C₇	semidirect
141. #560	C₂×C₇	semidirect
142. #555	C₂×C₇	semidirect
143. #553	C₂×C₇	semidirect
144. #552	C₂×C₇	semidirect
145. #551	C₂×C₇	semidirect
146. #548	C₂×C₇	semidirect
147. #546	C₂×C₇	semidirect
148. #540	C₂×C₇	semidirect
149. #538	C₂×C₇	semidirect
150. #537	C₂×C₇	semidirect
151. #536	C₂×C₇	semidirect
152. #535	C₂×C₇	semidirect
153. #532	C₂×C₇	semidirect
154. #529	C₂×C₇	semidirect
200. C₂×#41	C₂²×C₇	semidirect
201. C₂²×Q₈	C₂²×C₇	semidirect
203. C₄⋊Q₈	C₂²×C₇	semidirect
204. C₄⋊Q₈	C₂²×C₇	semidirect
208. #126	C₂²×C₇	semidirect
209. #126	C₂²×C₇	semidirect
210. #125	C₂²×C₇	semidirect
211. #125	C₂²×C₇	semidirect
216. #124	C₂²×C₇	semidirect
217. #124	C₂²×C₇	semidirect
221. #123	C₂²×C₇	semidirect
222. #123	C₂²×C₇	semidirect
223. #123	C₂²×C₇	semidirect
225. C₂²⋊Q₈	C₂²×C₇	semidirect
226. C₂²⋊Q₈	C₂²×C₇	semidirect
227. C₂²⋊Q₈	C₂²×C₇	semidirect
228. C₂²⋊Q₈	C₂²×C₇	semidirect
234. #121	C₂²×C₇	semidirect
235. #121	C₂²×C₇	semidirect
236. #121	C₂²×C₇	semidirect
237. #121	C₂²×C₇	semidirect
238. #121	C₂²×C₇	semidirect
239. #121	C₂²×C₇	semidirect
243. C₄×Q₈	C₂²×C₇	semidirect
246. C₄×D₄	C₂²×C₇	semidirect
247. C₄×D₄	C₂²×C₇	semidirect
248. C₄×D₄	C₂²×C₇	semidirect
249. C₄×D₄	C₂²×C₇	semidirect
251. #117	C₂²×C₇	semidirect
252. #117	C₂²×C₇	semidirect
253. #117	C₂²×C₇	semidirect
254. C₂×C₄⋊C₄	C₂²×C₇	semidirect
256. C₂×C₄²	C₂²×C₇	semidirect
395. C₇	#3551	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×#563	2
C₇×#560	2
C₇×#555	2
C₇×#553	2
C₇×#552	2
C₇×#551	2
C₇×#548	2
C₇×#546	2
C₇×#540	2
C₇×#538	2
C₇×#537	2
C₇×#536	2
C₇×#535	2
C₇×#532	2
C₇×#529	2
#3551	7

Subgroups — C7×#3551 #11744503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#3551 #11744503