Subgroups — C₇×#22717 #13199933

Order 1792.

822 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₄×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#1950	C₂	1	2	yes	maximal, complemented
4	C₇×#1855	C₂	1	4	yes	maximal, complemented
5	C₇×#1837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1810	C₂	1	2	yes	maximal, complemented
7	C₄×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#341	C₂	1	2	yes	maximal, complemented
9	C₂²×C₇×M₁₆	C₂²	1	4	yes	—
10	C₂³×C₇×C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
12	C₇×#436	—	2	2	no	—
13	C₇×#435	—	2	4	no	—
14	C₇×C₈×D₄	—	2	2	no	—
15	C₇×C₈×D₄	C₄	1	4	yes	—
16	C₇×C₈×D₄	C₄	1	2	yes	—
17	C₇×C₈×D₄	C₄	1	2	yes	—
18	C₂×C₇×#108	C₂²	1	2	yes	—
19	C₂×C₇×#108	C₂²	1	4	yes	—
20	C₇×#423	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₇×#407	C₂²	1	4	yes	—
23	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₄×C₇×M₁₆	C₂²	1	2	yes	—
25	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
26	C₇×#341	C₂²	1	1	yes	characteristic
27	C₇×#341	C₂²	1	2	yes	—
28	C₇×#341	C₂²	1	4	yes	—
29	C₇×#341	C₂²	1	1	yes	characteristic
30	C₇×#341	C₂²	1	2	yes	—
31	#22717	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₇×D₄	Q₈	1	1	yes	characteristic
33	C₂³×C₄×C₇	C₂³	1	2	yes	—
34	C₂×C₇×M₁₆	—	2	4	no	—
35	C₂×C₇×M₁₆	—	2	8	no	—
36	C₂×C₇×M₁₆	—	4	4	no	—
37	C₂×C₇×M₁₆	C₂³	1	4	yes	—
38	C₂×C₇×M₁₆	C₂³	1	2	yes	—
39	C₂×C₇×M₁₆	C₂³	1	2	yes	—
40	C₂²×C₇×C₈	—	2	4	no	—
41	C₂²×C₇×C₈	—	4	4	no	—
42	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
43	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
44	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇×C₈	C₂³	1	2	yes	—
47	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
48	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
49	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
50	C₄×C₇×D₄	D₄	1	1	yes	characteristic
51	C₄×C₇×D₄	D₄	1	2	yes	—
52	C₄×C₇×D₄	D₄	1	1	yes	characteristic
53	C₂×C₇×C₄⋊C₄	Q₈	1	1	yes	characteristic
54	C₂×C₇×C₂²⋊C₄	Q₈	1	2	yes	—
55	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
56	C₇×#108	—	2	4	no	—
57	C₇×#108	—	4	4	no	—
58	C₇×C₄⋊C₈	—	2	2	no	—
59	C₇×C₄⋊C₈	—	2	2	no	—
60	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₇×C₂²⋊C₈	—	2	4	no	—
63	C₇×C₂²⋊C₈	—	2	4	no	—
64	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
65	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
66	C₇×#97	—	2	2	no	—
67	C₄×C₇×C₈	—	2	2	no	—
68	C₄×C₇×C₈	C₂×C₄	1	2	yes	—
69	C₄×C₇×C₈	C₂×C₄	1	2	yes	—
70	D₄×M₁₆	C₂×C₇	1	2	yes	—
71	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic
72	#1950	C₂×C₇	1	2	yes	complemented
73	#1855	C₂×C₇	1	4	yes	complemented
74	#1837	C₂×C₇	1	1	yes	characteristic, complemented
75	#1810	C₂×C₇	1	2	yes	complemented
76	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
77	C₂×#341	C₂×C₇	1	2	yes	complemented
78	C₂⁴×C₇	C₂×Q₈	1	2	yes	—
79	C₂×C₇×D₄	—	2	4	no	—
80	C₂×C₇×D₄	C₄⋊C₄	1	2	yes	—
81	C₂×C₇×D₄	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₇×D₄	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇	—	2	4	no	—
84	C₂²×C₄×C₇	—	2	4	no	—
85	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
93	C₇×M₁₆	—	2	2	no	—
94	C₇×M₁₆	—	2	2	no	—
95	C₇×M₁₆	—	2	4	no	—
96	C₇×M₁₆	—	2	2	no	—
97	C₇×M₁₆	—	2	4	no	—
98	C₇×M₁₆	—	4	8	no	—
99	C₇×M₁₆	#41	1	4	yes	—
100	C₂×C₇×C₈	—	2	2	no	—
101	C₂×C₇×C₈	—	2	2	no	—
102	C₂×C₇×C₈	—	2	4	no	—
103	C₂×C₇×C₈	—	2	2	no	—
104	C₂×C₇×C₈	—	2	2	no	—
105	C₂×C₇×C₈	—	2	4	no	—
106	C₂×C₇×C₈	—	4	4	no	—
107	C₂×C₇×C₈	—	4	4	no	—
108	C₂×C₇×C₈	—	4	8	no	—
109	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
110	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
111	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
112	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
113	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
114	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
115	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
116	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
117	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
118	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
119	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×M₁₆	C₂²×C₇	1	4	yes	—
124	C₂³×C₈	C₂²×C₇	1	2	yes	—
125	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
126	#436	—	2	2	no	—
127	#435	—	2	4	no	—
128	C₈×D₄	—	2	2	no	—
129	C₈×D₄	C₄×C₇	1	4	yes	—
130	C₈×D₄	C₄×C₇	1	2	yes	—
131	C₈×D₄	C₄×C₇	1	2	yes	—
132	C₂×#108	C₂²×C₇	1	2	yes	—
133	C₂×#108	C₂²×C₇	1	4	yes	—
134	#423	C₂²×C₇	1	2	yes	—
135	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
136	#407	C₂²×C₇	1	4	yes	—
137	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
138	C₄×M₁₆	C₂²×C₇	1	2	yes	—
139	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
140	#341	C₂²×C₇	1	1	yes	characteristic
141	#341	C₂²×C₇	1	2	yes	—
142	#341	C₂²×C₇	1	2	yes	—
143	#341	C₂²×C₇	1	4	yes	—
144	#341	C₂²×C₇	1	1	yes	characteristic
145	C₂³×C₇	—	2	4	no	—
146	C₂³×C₇	—	2	4	no	—
147	C₂³×C₇	—	4	2	no	—
148	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
149	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
150	C₂³×C₇	C₂²×Q₈	1	1	yes	characteristic
151	C₇×D₄	—	2	4	no	—
152	C₇×D₄	—	2	2	no	—
153	C₇×D₄	#108	1	4	yes	complemented
154	C₂×C₄×C₇	—	2	4	no	—
155	C₂×C₄×C₇	—	2	2	no	—
156	C₂×C₄×C₇	—	2	2	no	—
157	C₂×C₄×C₇	—	2	2	no	—
158	C₂×C₄×C₇	—	2	2	no	—
159	C₂×C₄×C₇	—	2	4	no	—
160	C₂×C₄×C₇	—	2	4	no	—
161	C₂×C₄×C₇	—	2	2	no	—
162	C₂×C₄×C₇	—	4	1	no	—
163	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
167	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇	C₂×#41	1	2	yes	—
172	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
173	C₇×C₈	—	2	2	no	—
174	C₇×C₈	—	2	2	no	—
175	C₇×C₈	—	2	4	no	—
176	C₇×C₈	—	2	4	no	—
177	C₇×C₈	—	4	4	no	—
178	C₇×C₈	—	4	2	no	—
179	C₂²×D₄	C₇×Q₈	1	1	yes	characteristic
180	C₂³×C₄	C₂³×C₇	1	2	yes	—
181	C₂×M₁₆	—	2	4	no	—
182	C₂×M₁₆	—	2	8	no	—
183	C₂×M₁₆	—	4	4	no	—
184	C₂×M₁₆	C₂³×C₇	1	4	yes	—
185	C₂×M₁₆	C₂³×C₇	1	2	yes	—
186	C₂×M₁₆	C₂³×C₇	1	2	yes	—
187	C₂²×C₈	—	2	4	no	—
188	C₂²×C₈	—	4	4	no	—
189	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
190	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
191	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
192	C₂²×C₈	C₂³×C₇	1	2	yes	—
193	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
194	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
195	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
196	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
197	C₄×D₄	C₇×D₄	1	1	yes	characteristic
198	C₄×D₄	C₇×D₄	1	2	yes	—
199	C₄×D₄	C₇×D₄	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₇×Q₈	1	1	yes	characteristic
201	C₂×C₂²⋊C₄	C₇×Q₈	1	2	yes	—
202	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
203	#108	—	2	4	no	—
204	#108	—	4	4	no	—
205	C₄⋊C₈	—	2	2	no	—
206	C₄⋊C₈	—	2	2	no	—
207	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
208	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
209	C₂²⋊C₈	—	2	4	no	—
210	C₂²⋊C₈	—	2	4	no	—
211	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
212	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
213	#97	—	2	2	no	—
214	C₄×C₈	—	2	2	no	—
215	C₄×C₈	C₂×C₄×C₇	1	2	yes	—
216	C₄×C₈	C₂×C₄×C₇	1	2	yes	—
217	C₂²×C₇	—	2	2	no	—
218	C₂²×C₇	—	2	1	no	—
219	C₂²×C₇	—	2	1	no	—
220	C₂²×C₇	—	2	2	no	—
221	C₂²×C₇	—	2	2	no	—
222	C₂²×C₇	—	2	2	no	—
223	C₂²×C₇	—	2	2	no	—
224	C₂²×C₇	—	4	8	no	—
225	C₂²×C₇	C₂×#108	1	4	yes	—
226	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
227	C₂²×C₇	#554	1	2	yes	—
228	C₄×C₇	—	2	2	no	—
229	C₄×C₇	—	2	2	no	—
230	C₄×C₇	—	2	1	no	—
231	C₄×C₇	—	2	1	no	—
232	C₄×C₇	—	2	1	no	—
233	C₄×C₇	C₂×#108	1	2	yes	—
234	C₄×C₇	C₄×#41	1	1	yes	characteristic
235	C₄×C₇	#518	1	1	yes	characteristic
236	C₄×C₇	#546	1	2	yes	—
237	C₂⁴	C₂×C₇×Q₈	1	2	yes	—
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	C₇×C₄⋊C₄	1	2	yes	—
240	C₂×D₄	C₇×C₄⋊C₄	1	1	yes	characteristic
241	C₂×D₄	C₇×C₄⋊C₄	1	1	yes	characteristic
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
245	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
246	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
247	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
248	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
249	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
250	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
251	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
252	M₁₆	—	2	2	no	—
253	M₁₆	—	2	2	no	—
254	M₁₆	—	2	4	no	—
255	M₁₆	—	2	2	no	—
256	M₁₆	—	2	4	no	—
257	M₁₆	—	4	8	no	—
258	M₁₆	C₇×#41	1	4	yes	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	4	4	no	—
266	C₂×C₈	—	4	4	no	—
267	C₂×C₈	—	4	8	no	—
268	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
269	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
270	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
271	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
272	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
273	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
274	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
275	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
276	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
277	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
278	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
279	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
280	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
281	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
282	C₂×C₇	—	2	2	no	—
283	C₂×C₇	—	2	4	no	—
284	C₂×C₇	—	4	2	no	—
285	C₂×C₇	#2349	1	1	yes	characteristic
286	C₂×C₇	C₂²×#108	1	1	yes	characteristic
287	C₂×C₇	#2916	1	1	yes	characteristic
288	C₂³	—	2	4	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	4	2	no	—
291	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
292	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
293	C₂³	C₂²×C₇×Q₈	1	1	yes	characteristic
294	D₄	—	2	4	no	—
295	D₄	—	2	2	no	—
296	D₄	C₇×#108	1	4	yes	complemented
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	4	1	no	—
306	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
307	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
308	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
309	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
310	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
311	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
312	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
313	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
314	C₂×C₄	C₂×C₇×#41	1	2	yes	—
315	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
316	C₈	—	2	2	no	—
317	C₈	—	2	2	no	—
318	C₈	—	2	4	no	—
319	C₈	—	2	4	no	—
320	C₈	—	4	4	no	—
321	C₈	—	4	2	no	—
322	C₇	#22717	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	4	8	no	—
331	C₂²	C₂×C₇×#108	1	4	yes	—
332	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
333	C₂²	C₇×#554	1	2	yes	—
334	C₄	—	2	1	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	C₂×C₇×#108	1	2	yes	—
340	C₄	C₄×C₇×#41	1	1	yes	characteristic
341	C₄	C₇×#518	1	1	yes	characteristic
342	C₄	C₇×#546	1	2	yes	—
343	C₂	—	2	2	no	—
344	C₂	—	2	4	no	—
345	C₂	—	4	2	no	—
346	C₂	C₇×#2349	1	1	yes	characteristic
347	C₂	C₂²×C₇×#108	1	1	yes	characteristic
348	C₂	C₇×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂²×C₄⋊C₄
prime radical	C₂²×C₇×D₄	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#1950	C₂	semidirect
4. C₇×#1855	C₂	semidirect
5. C₇×#1837	C₂	semidirect
6. C₇×#1810	C₂	semidirect
7. C₄×C₇×#108	C₂	semidirect
8. C₂×C₇×#341	C₂	semidirect
31. #22717	C₇	direct (N × H)
72. #1950	C₂×C₇	semidirect
73. #1855	C₂×C₇	semidirect
74. #1837	C₂×C₇	semidirect
75. #1810	C₂×C₇	semidirect
76. C₄×#108	C₂×C₇	semidirect
77. C₂×#341	C₂×C₇	semidirect
153. C₇×D₄	#108	semidirect
296. D₄	C₇×#108	semidirect
322. C₇	#22717	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×D₄×M₁₆	2
C₂×C₇×C₈×D₄	2
C₇×#1950	2
C₇×#1855	2
C₇×#1837	2
C₇×#1810	2
C₄×C₇×#108	2
C₂×C₇×#341	2
#22717	7

Subgroups — C7×#22717 #13199933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22717 #13199933