Subgroups — C₇×#3511 #11744463

Order 896.

1104 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#556	C₂	1	2	yes	maximal, complemented
2	C₇×#555	C₂	1	2	yes	maximal, complemented
3	C₇×#554	C₂	1	2	yes	maximal, complemented
4	C₇×#553	C₂	1	4	yes	maximal, complemented
5	C₇×#548	C₂	1	4	yes	maximal, complemented
6	C₇×#547	C₂	1	2	yes	maximal, complemented
7	C₇×#542	C₂	1	4	yes	maximal, complemented
8	C₇×#537	C₂	1	2	yes	maximal, complemented
9	C₇×#533	C₂	1	2	yes	maximal, complemented
10	C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#532	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#520	C₂	1	2	yes	maximal, complemented
14	C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#41	C₂²	1	1	yes	characteristic
16	C₂×C₇×#41	C₂²	1	2	yes	—
17	C₂×C₇×#41	C₂²	1	4	yes	—
18	C₂²×C₇×Q₈	C₂²	1	2	yes	—
19	C₇×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₇×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₇×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₇×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₇×#127	C₂²	1	1	yes	characteristic
25	C₇×#126	C₂²	1	8	yes	—
26	C₇×#125	C₂²	1	4	yes	—
27	C₇×#124	C₂²	1	2	yes	—
28	C₇×#124	C₂²	1	4	yes	—
29	C₇×#124	C₂²	1	8	yes	—
30	C₇×#123	C₂²	1	8	yes	—
31	C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
32	C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
33	C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
34	C₇×C₂²⋊Q₈	C₂²	1	8	yes	—
35	C₇×#121	C₂²	1	4	yes	—
36	C₇×#121	C₂²	1	2	yes	—
37	C₇×#121	C₂²	1	2	yes	—
38	C₇×#121	C₂²	1	4	yes	—
39	C₇×#121	C₂²	1	4	yes	—
40	C₇×#121	C₂²	1	8	yes	—
41	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
42	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
43	C₄×C₇×Q₈	C₂²	1	4	yes	—
44	C₄×C₇×Q₈	C₂²	1	4	yes	—
45	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₄×C₇×D₄	C₂²	1	2	yes	—
47	C₄×C₇×D₄	C₂²	1	2	yes	—
48	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×D₄	C₂²	1	4	yes	—
50	C₄×C₇×D₄	C₂²	1	8	yes	—
51	C₄×C₇×D₄	C₂²	1	2	yes	—
52	C₄×C₇×D₄	C₂²	1	4	yes	—
53	C₄×C₇×D₄	C₂²	1	2	yes	—
54	C₇×#117	C₂²	1	1	yes	characteristic
55	C₇×#117	C₂²	1	2	yes	—
56	C₇×#117	C₂²	1	4	yes	—
57	C₇×#117	C₂²	1	4	yes	—
58	C₂×C₇×C₄⋊C₄	C₂²	1	2	yes	—
59	C₂×C₇×C₄⋊C₄	C₂²	1	4	yes	—
60	C₂×C₇×C₄⋊C₄	C₂²	1	2	yes	—
61	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic
62	C₂×C₄²×C₇	C₂²	1	2	yes	—
63	#3511	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₇×#41	—	2	4	no	—
65	C₇×#41	—	2	8	no	—
66	C₇×#41	—	4	8	no	—
67	C₂×C₇×Q₈	—	4	4	no	—
68	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
69	C₂×C₇×Q₈	C₂³	1	2	yes	—
70	C₂×C₇×Q₈	C₂³	1	4	yes	—
71	C₂×C₇×Q₈	C₂³	1	4	yes	—
72	C₂×C₇×D₄	C₂³	1	2	yes	—
73	C₂×C₇×D₄	C₂³	1	2	yes	—
74	C₂×C₇×D₄	C₂³	1	4	yes	—
75	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
76	C₂×C₇×D₄	C₂³	1	2	yes	—
77	C₂×C₇×D₄	C₂³	1	2	yes	—
78	C₂×C₇×D₄	C₂³	1	8	yes	—
79	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₇	C₂³	1	2	yes	—
81	C₂²×C₄×C₇	C₂³	1	2	yes	—
82	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₇	C₂³	1	2	yes	—
84	C₂²×C₄×C₇	C₂³	1	4	yes	—
85	C₂²×C₄×C₇	C₂³	1	4	yes	—
86	C₂²×C₄×C₇	C₂³	1	8	yes	—
87	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₇×C₄⋊C₄	C₂³	1	4	yes	—
90	C₇×C₄⋊C₄	C₂³	1	4	yes	—
91	C₇×C₄⋊C₄	C₂³	1	4	yes	—
92	C₇×C₄⋊C₄	C₂³	1	8	yes	—
93	C₇×C₄⋊C₄	C₂³	1	4	yes	—
94	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₇×C₄⋊C₄	C₂³	1	2	yes	—
96	C₇×C₄⋊C₄	C₂³	1	2	yes	—
97	C₇×C₄⋊C₄	C₂³	1	2	yes	—
98	C₇×C₄⋊C₄	C₂³	1	2	yes	—
99	C₇×C₄⋊C₄	C₂³	1	8	yes	—
100	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
101	C₇×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
104	C₇×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₇×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₇×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₄²×C₇	C₂³	1	1	yes	characteristic
109	C₄²×C₇	C₂³	1	2	yes	—
110	C₄²×C₇	C₂³	1	1	yes	characteristic
111	C₄²×C₇	C₂³	1	2	yes	—
112	C₄²×C₇	C₂³	1	1	yes	characteristic
113	C₄²×C₇	C₂³	1	1	yes	characteristic
114	C₄²×C₇	C₂³	1	2	yes	—
115	C₄²×C₇	C₂³	1	8	yes	—
116	#556	C₂×C₇	1	2	yes	complemented
117	#555	C₂×C₇	1	2	yes	complemented
118	#554	C₂×C₇	1	2	yes	complemented
119	#553	C₂×C₇	1	4	yes	complemented
120	#548	C₂×C₇	1	4	yes	complemented
121	#547	C₂×C₇	1	2	yes	complemented
122	#542	C₂×C₇	1	4	yes	complemented
123	#537	C₂×C₇	1	2	yes	complemented
124	#533	C₂×C₇	1	2	yes	complemented
125	#532	C₂×C₇	1	1	yes	characteristic, complemented
126	#532	C₂×C₇	1	2	yes	complemented
127	C₂×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
128	#520	C₂×C₇	1	2	yes	complemented
129	C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂³×C₇	C₂⁴	1	2	yes	—
131	C₂³×C₇	C₂⁴	1	4	yes	—
132	C₂³×C₇	C₂⁴	1	1	yes	characteristic
133	C₇×Q₈	—	2	2	no	—
134	C₇×Q₈	—	2	4	no	—
135	C₇×Q₈	—	2	8	no	—
136	C₇×Q₈	—	4	4	no	—
137	C₇×D₄	—	2	4	no	—
138	C₇×D₄	—	2	8	no	—
139	C₇×D₄	—	2	2	no	—
140	C₇×D₄	—	2	4	no	—
141	C₇×D₄	—	2	4	no	—
142	C₇×D₄	—	2	4	no	—
143	C₇×D₄	—	4	8	no	—
144	C₂×C₄×C₇	—	2	8	no	—
145	C₂×C₄×C₇	—	2	4	no	—
146	C₂×C₄×C₇	—	2	2	no	—
147	C₂×C₄×C₇	—	2	4	no	—
148	C₂×C₄×C₇	—	2	2	no	—
149	C₂×C₄×C₇	—	2	4	no	—
150	C₂×C₄×C₇	—	4	4	no	—
151	C₂×C₄×C₇	—	4	8	no	—
152	C₂×C₄×C₇	#41	1	4	yes	complemented
153	C₂×C₄×C₇	C₂⁴	1	2	yes	—
154	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
156	C₂×C₄×C₇	C₂⁴	1	2	yes	—
157	C₂×C₄×C₇	C₂⁴	1	4	yes	—
158	C₂×C₄×C₇	C₂⁴	1	2	yes	—
159	C₂×C₄×C₇	C₂⁴	1	8	yes	—
160	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
164	C₂×#41	C₂²×C₇	1	1	yes	characteristic
165	C₂×#41	C₂²×C₇	1	2	yes	—
166	C₂×#41	C₂²×C₇	1	4	yes	—
167	C₂²×Q₈	C₂²×C₇	1	2	yes	—
168	C₄⋊Q₈	C₂²×C₇	1	2	yes	—
169	C₄⋊Q₈	C₂²×C₇	1	2	yes	—
170	C₄⋊Q₈	C₂²×C₇	1	2	yes	—
171	C₄⋊Q₈	C₂²×C₇	1	2	yes	—
172	C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
173	#127	C₂²×C₇	1	1	yes	characteristic
174	#126	C₂²×C₇	1	8	yes	—
175	#125	C₂²×C₇	1	4	yes	—
176	#124	C₂²×C₇	1	2	yes	—
177	#124	C₂²×C₇	1	4	yes	—
178	#124	C₂²×C₇	1	8	yes	—
179	#123	C₂²×C₇	1	8	yes	—
180	C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
181	C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
182	C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
183	C₂²⋊Q₈	C₂²×C₇	1	8	yes	—
184	#121	C₂²×C₇	1	4	yes	—
185	#121	C₂²×C₇	1	2	yes	—
186	#121	C₂²×C₇	1	2	yes	—
187	#121	C₂²×C₇	1	4	yes	—
188	#121	C₂²×C₇	1	4	yes	—
189	#121	C₂²×C₇	1	8	yes	—
190	C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
191	C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
192	C₄×Q₈	C₂²×C₇	1	4	yes	—
193	C₄×Q₈	C₂²×C₇	1	4	yes	—
194	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
195	C₄×D₄	C₂²×C₇	1	2	yes	—
196	C₄×D₄	C₂²×C₇	1	2	yes	—
197	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
198	C₄×D₄	C₂²×C₇	1	4	yes	—
199	C₄×D₄	C₂²×C₇	1	8	yes	—
200	C₄×D₄	C₂²×C₇	1	2	yes	—
201	C₄×D₄	C₂²×C₇	1	4	yes	—
202	C₄×D₄	C₂²×C₇	1	2	yes	—
203	#117	C₂²×C₇	1	1	yes	characteristic
204	#117	C₂²×C₇	1	2	yes	—
205	#117	C₂²×C₇	1	4	yes	—
206	#117	C₂²×C₇	1	4	yes	—
207	C₂×C₄⋊C₄	C₂²×C₇	1	2	yes	—
208	C₂×C₄⋊C₄	C₂²×C₇	1	4	yes	—
209	C₂×C₄⋊C₄	C₂²×C₇	1	2	yes	—
210	C₂×C₄²	C₂²×C₇	1	1	yes	characteristic
211	C₂×C₄²	C₂²×C₇	1	2	yes	—
212	C₂²×C₇	—	2	1	no	—
213	C₂²×C₇	—	2	1	no	—
214	C₂²×C₇	—	2	2	no	—
215	C₂²×C₇	—	2	4	no	—
216	C₂²×C₇	—	2	2	no	—
217	C₂²×C₇	—	2	4	no	—
218	C₂²×C₇	—	2	2	no	—
219	C₂²×C₇	—	2	4	no	—
220	C₂²×C₇	C₂×#41	1	2	yes	—
221	C₂²×C₇	C₂⁵	1	1	yes	characteristic
222	C₄×C₇	—	2	4	no	—
223	C₄×C₇	—	2	2	no	—
224	C₄×C₇	—	2	2	no	—
225	C₄×C₇	—	2	1	no	—
226	C₄×C₇	—	2	8	no	—
227	C₄×C₇	—	2	2	no	—
228	C₄×C₇	—	2	1	no	—
229	C₄×C₇	C₂×#41	1	2	yes	—
230	C₄×C₇	C₂×#41	1	2	yes	—
231	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
232	C₄×C₇	2₋¹⁺⁴	1	2	yes	—
233	#41	—	2	4	no	—
234	#41	—	2	8	no	—
235	#41	—	4	8	no	—
236	C₂×Q₈	—	4	4	no	—
237	C₂×Q₈	C₂³×C₇	1	1	yes	characteristic
238	C₂×Q₈	C₂³×C₇	1	2	yes	—
239	C₂×Q₈	C₂³×C₇	1	4	yes	—
240	C₂×Q₈	C₂³×C₇	1	4	yes	—
241	C₂×D₄	C₂³×C₇	1	2	yes	—
242	C₂×D₄	C₂³×C₇	1	2	yes	—
243	C₂×D₄	C₂³×C₇	1	4	yes	—
244	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
245	C₂×D₄	C₂³×C₇	1	2	yes	—
246	C₂×D₄	C₂³×C₇	1	2	yes	—
247	C₂×D₄	C₂³×C₇	1	8	yes	—
248	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₇	1	2	yes	—
250	C₂²×C₄	C₂³×C₇	1	2	yes	—
251	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
252	C₂²×C₄	C₂³×C₇	1	2	yes	—
253	C₂²×C₄	C₂³×C₇	1	4	yes	—
254	C₂²×C₄	C₂³×C₇	1	4	yes	—
255	C₂²×C₄	C₂³×C₇	1	8	yes	—
256	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
257	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
258	C₄⋊C₄	C₂³×C₇	1	4	yes	—
259	C₄⋊C₄	C₂³×C₇	1	4	yes	—
260	C₄⋊C₄	C₂³×C₇	1	4	yes	—
261	C₄⋊C₄	C₂³×C₇	1	8	yes	—
262	C₄⋊C₄	C₂³×C₇	1	4	yes	—
263	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
264	C₄⋊C₄	C₂³×C₇	1	2	yes	—
265	C₄⋊C₄	C₂³×C₇	1	2	yes	—
266	C₄⋊C₄	C₂³×C₇	1	2	yes	—
267	C₄⋊C₄	C₂³×C₇	1	2	yes	—
268	C₄⋊C₄	C₂³×C₇	1	8	yes	—
269	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
270	C₂²⋊C₄	C₂³×C₇	1	8	yes	—
271	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
272	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
273	C₂²⋊C₄	C₂³×C₇	1	8	yes	—
274	C₂²⋊C₄	C₂³×C₇	1	8	yes	—
275	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
276	C₂²⋊C₄	C₂³×C₇	1	4	yes	—
277	C₄²	C₂³×C₇	1	1	yes	characteristic
278	C₄²	C₂³×C₇	1	2	yes	—
279	C₄²	C₂³×C₇	1	1	yes	characteristic
280	C₄²	C₂³×C₇	1	2	yes	—
281	C₄²	C₂³×C₇	1	1	yes	characteristic
282	C₄²	C₂³×C₇	1	1	yes	characteristic
283	C₄²	C₂³×C₇	1	2	yes	—
284	C₄²	C₂³×C₇	1	8	yes	—
285	C₂×C₇	—	2	2	no	—
286	C₂×C₇	—	4	2	no	—
287	C₂×C₇	—	4	4	no	—
288	C₂×C₇	C₂²×#41	1	1	yes	characteristic
289	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
291	C₂³	C₂⁴×C₇	1	2	yes	—
292	C₂³	C₂⁴×C₇	1	4	yes	—
293	C₂³	C₂⁴×C₇	1	1	yes	characteristic
294	Q₈	—	2	2	no	—
295	Q₈	—	2	4	no	—
296	Q₈	—	2	8	no	—
297	Q₈	—	4	4	no	—
298	D₄	—	2	4	no	—
299	D₄	—	2	8	no	—
300	D₄	—	2	2	no	—
301	D₄	—	2	4	no	—
302	D₄	—	2	4	no	—
303	D₄	—	2	4	no	—
304	D₄	—	4	8	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	C₇×#41	1	4	yes	complemented
314	C₂×C₄	C₂⁴×C₇	1	2	yes	—
315	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
316	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
317	C₂×C₄	C₂⁴×C₇	1	2	yes	—
318	C₂×C₄	C₂⁴×C₇	1	4	yes	—
319	C₂×C₄	C₂⁴×C₇	1	2	yes	—
320	C₂×C₄	C₂⁴×C₇	1	8	yes	—
321	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
322	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
323	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
324	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
325	C₇	#3511	1	1	yes	characteristic, direct product factor, Sylow
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	C₂×C₇×#41	1	2	yes	—
335	C₂²	C₂⁵×C₇	1	1	yes	characteristic
336	C₄	—	2	4	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	1	no	—
340	C₄	—	2	8	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	C₂×C₇×#41	1	2	yes	—
344	C₄	C₂×C₇×#41	1	2	yes	—
345	C₄	C₇×H(5,𝔽₂)	1	2	yes	—
346	C₄	C₇×2₋¹⁺⁴	1	2	yes	—
347	C₂	—	2	2	no	—
348	C₂	—	4	2	no	—
349	C₂	—	4	4	no	—
350	C₂	C₂²×C₇×#41	1	1	yes	characteristic
351	C₂	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic

	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×#556	C₂	semidirect
2. C₇×#555	C₂	semidirect
3. C₇×#554	C₂	semidirect
4. C₇×#553	C₂	semidirect
5. C₇×#548	C₂	semidirect
6. C₇×#547	C₂	semidirect
7. C₇×#542	C₂	semidirect
8. C₇×#537	C₂	semidirect
9. C₇×#533	C₂	semidirect
10. C₇×#532	C₂	semidirect
11. C₇×#532	C₂	semidirect
12. C₂×C₇×C₄⋊Q₈	C₂	semidirect
13. C₇×#520	C₂	semidirect
14. C₄×C₇×#41	C₂	semidirect
63. #3511	C₇	direct (N × H)
116. #556	C₂×C₇	semidirect
117. #555	C₂×C₇	semidirect
118. #554	C₂×C₇	semidirect
119. #553	C₂×C₇	semidirect
120. #548	C₂×C₇	semidirect
121. #547	C₂×C₇	semidirect
122. #542	C₂×C₇	semidirect
123. #537	C₂×C₇	semidirect
124. #533	C₂×C₇	semidirect
125. #532	C₂×C₇	semidirect
126. #532	C₂×C₇	semidirect
127. C₂×C₄⋊Q₈	C₂×C₇	semidirect
128. #520	C₂×C₇	semidirect
129. C₄×#41	C₂×C₇	semidirect
152. C₂×C₄×C₇	#41	semidirect
313. C₂×C₄	C₇×#41	semidirect
325. C₇	#3511	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×#556	2
C₇×#555	2
C₇×#554	2
C₇×#553	2
C₇×#548	2
C₇×#547	2
C₇×#542	2
C₇×#537	2
C₇×#533	2
C₇×#532	2
C₂×C₇×C₄⋊Q₈	2
C₇×#520	2
C₄×C₇×#41	2
#3511	7

Subgroups — C7×#3511 #11744463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#3511 #11744463