Subgroups — C₇×#19657 #13196873

Order 1792.

700 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3226	C₂	1	1	yes	maximal, characteristic
4	C₇×#3206	C₂	1	1	yes	maximal, characteristic
5	C₇×#3131	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1719	C₂	1	2	yes	maximal, complemented
8	C₇×#1718	C₂	1	2	yes	maximal, complemented
9	C₇×#1710	C₂	1	2	yes	maximal, complemented
10	C₇×#1708	C₂	1	2	yes	maximal, complemented
11	C₇×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#533	C₂²	1	1	yes	characteristic
13	C₇×#532	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₇×#500	C₂²	1	2	yes	—
17	C₇×#500	C₂²	1	2	yes	—
18	C₇×#498	C₂²	1	2	yes	—
19	C₇×#492	C₂²	1	2	yes	—
20	C₇×#488	—	2	2	no	—
21	C₇×#487	—	2	2	no	—
22	C₇×#487	C₂²	1	2	yes	—
23	C₇×#487	C₂²	1	2	yes	—
24	C₇×#487	C₂²	1	1	yes	characteristic
25	C₇×#487	C₂²	1	2	yes	—
26	C₇×#487	C₂²	1	2	yes	—
27	C₇×#487	C₂²	1	1	yes	characteristic
28	C₇×#487	C₂²	1	2	yes	—
29	C₇×#486	C₂²	1	1	yes	characteristic
30	C₇×#486	C₂²	1	2	yes	—
31	C₇×#486	C₂²	1	1	yes	characteristic
32	C₇×#484	—	2	2	no	—
33	C₇×#483	—	2	2	no	—
34	C₇×#480	—	2	2	no	—
35	C₇×#477	—	2	2	no	—
36	C₇×#475	—	2	2	no	—
37	C₇×#474	—	2	2	no	—
38	C₇×#461	—	2	2	no	—
39	C₇×#448	—	2	2	no	—
40	C₇×#431	C₂²	1	1	yes	characteristic
41	C₇×#431	C₂²	1	1	yes	characteristic
42	C₇×#416	—	2	2	no	—
43	C₂×C₇×#103	—	2	2	no	—
44	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
45	C₇×#322	C₂²	1	2	yes	—
46	C₇×C₈²	C₂²	1	2	yes	—
47	#19657	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	1	no	—
49	C₂²×C₇×Q₈	—	2	1	no	—
50	C₂²×C₇×Q₈	—	2	1	no	—
51	C₂×C₇×SD₁₆	—	2	4	no	—
52	C₂²×C₇×C₈	D₄	1	2	yes	—
53	C₇×C₄⋊Q₈	—	2	1	no	—
54	C₇×C₄⋊Q₈	—	2	1	no	—
55	C₇×C₄⋊Q₈	—	2	1	no	—
56	C₇×C₄⋊Q₈	—	2	1	no	—
57	C₇×C₄⋊Q₈	—	2	1	no	—
58	C₇×C₄⋊Q₈	—	2	1	no	—
59	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₇×#127	C₂³	1	1	yes	characteristic
65	C₇×#125	—	2	1	no	—
66	C₇×#124	—	2	1	no	—
67	C₇×C₂²⋊Q₈	—	2	1	no	—
68	C₇×C₂²⋊Q₈	—	2	1	no	—
69	C₇×#121	—	2	1	no	—
70	C₇×#121	—	2	1	no	—
71	C₄×C₇×Q₈	—	2	1	no	—
72	C₄×C₇×Q₈	—	2	1	no	—
73	C₄×C₇×D₄	—	2	1	no	—
74	C₄×C₇×D₄	—	2	1	no	—
75	C₇×#117	—	2	1	no	—
76	C₂×C₇×C₄⋊C₄	—	2	1	no	—
77	C₂×C₇×C₄⋊C₄	—	2	1	no	—
78	C₂×C₇×C₄⋊C₄	—	2	1	no	—
79	C₂×C₇×C₄⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
81	C₇×#107	—	2	4	no	—
82	C₇×#107	—	2	4	no	—
83	C₇×#106	—	2	4	no	—
84	C₇×C₄⋊C₈	D₄	1	2	yes	—
85	C₇×C₄⋊C₈	D₄	1	2	yes	—
86	C₇×#103	—	2	4	no	—
87	C₇×#103	—	2	4	no	—
88	C₇×#103	—	2	4	no	—
89	C₇×#103	—	2	4	no	—
90	C₇×#103	—	2	2	no	—
91	C₇×#103	—	2	2	no	—
92	C₇×#103	—	2	4	no	—
93	C₇×#102	—	2	4	no	—
94	C₇×#102	—	2	2	no	—
95	C₇×#102	—	2	2	no	—
96	C₇×C₂²⋊C₈	D₄	1	2	yes	—
97	C₇×C₂²⋊C₈	D₄	1	2	yes	—
98	C₄×C₇×C₈	D₄	1	2	yes	—
99	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
100	C₄×C₇×C₈	C₂³	1	2	yes	—
101	C₄×C₇×C₈	C₂³	1	2	yes	—
102	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
103	#3230	C₂×C₇	1	1	yes	characteristic, complemented
104	#3229	C₂×C₇	1	1	yes	characteristic, complemented
105	#3226	C₂×C₇	1	1	yes	characteristic
106	#3206	C₂×C₇	1	1	yes	characteristic
107	#3131	C₂×C₇	1	1	yes	characteristic
108	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
109	#1719	C₂×C₇	1	2	yes	complemented
110	#1718	C₂×C₇	1	2	yes	complemented
111	#1710	C₂×C₇	1	2	yes	complemented
112	#1708	C₂×C₇	1	2	yes	complemented
113	#1450	C₂×C₇	1	1	yes	characteristic, complemented
114	C₇×#41	—	4	4	no	—
115	C₂×C₇×Q₈	—	2	1	no	—
116	C₂×C₇×Q₈	—	2	1	no	—
117	C₂×C₇×Q₈	—	2	1	no	—
118	C₂×C₇×Q₈	—	2	2	no	—
119	C₂×C₇×Q₈	—	2	2	no	—
120	C₂×C₇×Q₈	—	4	1	no	—
121	C₂×C₇×Q₈	—	4	1	no	—
122	C₂×C₇×Q₈	—	4	4	no	—
123	C₂×C₇×Q₈	—	8	2	no	—
124	C₂×C₇×D₄	—	2	1	no	—
125	C₂×C₇×D₄	—	2	1	no	—
126	C₂×C₇×D₄	—	2	1	no	—
127	C₂×C₇×D₄	—	4	1	no	—
128	C₂²×C₄×C₇	—	4	1	no	—
129	C₂²×C₄×C₇	—	4	1	no	—
130	C₂²×C₄×C₇	—	4	1	no	—
131	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
134	C₇×SD₁₆	—	8	4	no	—
135	C₂×C₇×C₈	—	2	4	no	—
136	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
137	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
139	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
140	C₇×C₄⋊C₄	—	2	1	no	—
141	C₇×C₄⋊C₄	—	2	1	no	—
142	C₇×C₄⋊C₄	—	2	2	no	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	2	1	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	2	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	4	1	no	—
151	C₇×C₄⋊C₄	—	4	1	no	—
152	C₇×C₄⋊C₄	—	4	1	no	—
153	C₇×C₄⋊C₄	—	4	1	no	—
154	C₇×C₄⋊C₄	—	4	1	no	—
155	C₇×C₄⋊C₄	—	4	1	no	—
156	C₇×C₂²⋊C₄	—	4	1	no	—
157	C₇×C₂²⋊C₄	—	4	1	no	—
158	C₇×C₂²⋊C₄	—	4	1	no	—
159	C₄²×C₇	—	4	1	no	—
160	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₇	C₂⁴	1	1	yes	characteristic
164	#533	C₂²×C₇	1	1	yes	characteristic
165	#532	C₂²×C₇	1	1	yes	characteristic
166	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
168	#500	C₂²×C₇	1	2	yes	—
169	#500	C₂²×C₇	1	2	yes	—
170	#498	C₂²×C₇	1	2	yes	—
171	#492	C₂²×C₇	1	2	yes	—
172	#488	—	2	2	no	—
173	#487	—	2	2	no	—
174	#487	C₂²×C₇	1	2	yes	—
175	#487	C₂²×C₇	1	2	yes	—
176	#487	C₂²×C₇	1	1	yes	characteristic
177	#487	C₂²×C₇	1	1	yes	characteristic
178	#487	C₂²×C₇	1	2	yes	—
179	#487	C₂²×C₇	1	2	yes	—
180	#487	C₂²×C₇	1	2	yes	—
181	#486	C₂²×C₇	1	1	yes	characteristic
182	#486	C₂²×C₇	1	1	yes	characteristic
183	#486	C₂²×C₇	1	2	yes	—
184	#484	—	2	2	no	—
185	#483	—	2	2	no	—
186	#480	—	2	2	no	—
187	#477	—	2	2	no	—
188	#475	—	2	2	no	—
189	#474	—	2	2	no	—
190	#461	—	2	2	no	—
191	#448	—	2	2	no	—
192	#431	C₂²×C₇	1	1	yes	characteristic
193	#431	C₂²×C₇	1	1	yes	characteristic
194	#416	—	2	2	no	—
195	C₂×#103	—	2	2	no	—
196	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
197	#322	C₂²×C₇	1	2	yes	—
198	C₈²	C₂²×C₇	1	2	yes	—
199	C₂³×C₇	—	4	1	no	—
200	C₂³×C₇	#127	1	1	yes	characteristic
201	C₇×Q₈	—	4	4	no	—
202	C₇×Q₈	—	4	2	no	—
203	C₇×Q₈	—	4	4	no	—
204	C₇×Q₈	—	4	2	no	—
205	C₇×Q₈	—	4	2	no	—
206	C₇×Q₈	—	8	2	no	—
207	C₇×Q₈	—	8	2	no	—
208	C₇×D₄	—	4	2	no	—
209	C₇×D₄	—	4	2	no	—
210	C₇×D₄	—	4	2	no	—
211	C₇×D₄	—	8	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	4	1	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	no	—
217	C₂×C₄×C₇	—	4	2	no	—
218	C₂×C₄×C₇	—	4	2	no	—
219	C₂×C₄×C₇	—	8	2	no	—
220	C₂×C₄×C₇	—	8	2	no	—
221	C₂×C₄×C₇	—	8	2	no	—
222	C₂×C₄×C₇	#127	1	1	yes	characteristic
223	C₂×C₄×C₇	#127	1	1	yes	characteristic
224	C₂×C₄×C₇	#127	1	1	yes	characteristic
225	C₂×C₄×C₇	#135	1	4	yes	—
226	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
229	C₇×C₈	—	2	2	no	—
230	C₇×C₈	—	2	2	no	—
231	C₇×C₈	—	2	4	no	—
232	C₇×C₈	—	2	4	no	—
233	C₂×#41	—	2	1	no	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂×SD₁₆	—	2	4	no	—
237	C₂²×C₈	C₇×D₄	1	2	yes	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
245	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
246	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
247	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
248	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
249	#127	C₂³×C₇	1	1	yes	characteristic
250	#125	—	2	1	no	—
251	#124	—	2	1	no	—
252	C₂²⋊Q₈	—	2	1	no	—
253	C₂²⋊Q₈	—	2	1	no	—
254	#121	—	2	1	no	—
255	#121	—	2	1	no	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	#117	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
266	#107	—	2	4	no	—
267	#107	—	2	4	no	—
268	#106	—	2	4	no	—
269	C₄⋊C₈	C₇×D₄	1	2	yes	—
270	C₄⋊C₈	C₇×D₄	1	2	yes	—
271	#103	—	2	4	no	—
272	#103	—	2	4	no	—
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	2	4	no	—
276	#103	—	2	4	no	—
277	#103	—	2	4	no	—
278	#102	—	2	2	no	—
279	#102	—	2	2	no	—
280	#102	—	2	4	no	—
281	C₂²⋊C₈	C₇×D₄	1	2	yes	—
282	C₂²⋊C₈	C₇×D₄	1	2	yes	—
283	C₄×C₈	C₇×D₄	1	2	yes	—
284	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₇	1	2	yes	—
286	C₄×C₈	C₂³×C₇	1	2	yes	—
287	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
288	C₂²×C₇	—	2	1	no	—
289	C₂²×C₇	—	2	1	no	—
290	C₂²×C₇	—	8	1	no	—
291	C₂²×C₇	—	8	1	no	—
292	C₂²×C₇	—	8	1	no	—
293	C₂²×C₇	#495	1	2	yes	—
294	C₂²×C₇	C₂×#127	1	1	yes	characteristic
295	C₄×C₇	—	2	1	no	—
296	C₄×C₇	—	2	1	no	—
297	C₄×C₇	—	8	1	no	—
298	C₄×C₇	—	8	2	no	—
299	C₄×C₇	—	8	2	no	—
300	C₄×C₇	—	8	1	no	—
301	C₄×C₇	—	8	1	no	—
302	C₄×C₇	#495	1	2	yes	—
303	C₄×C₇	C₂×#135	1	2	yes	—
304	C₄×C₇	#577	1	2	yes	—
305	C₄×C₇	#578	1	2	yes	—
306	#41	—	4	4	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×Q₈	—	4	4	no	—
315	C₂×Q₈	—	8	2	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
326	SD₁₆	—	8	4	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
329	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
330	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
331	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₄²	—	4	1	no	—
352	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
353	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
354	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
355	C₄²	C₂⁴×C₇	1	1	yes	characteristic
356	C₂×C₇	—	2	2	no	—
357	C₂×C₇	—	16	1	no	—
358	C₂×C₇	C₂×#495	1	1	yes	characteristic
359	C₂×C₇	#3154	1	1	yes	characteristic
360	C₂×C₇	#3156	1	1	yes	characteristic
361	C₂³	—	4	1	no	—
362	C₂³	C₇×#127	1	1	yes	characteristic
363	Q₈	—	4	4	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	4	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	8	2	no	—
369	Q₈	—	8	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	8	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	C₇×#127	1	1	yes	characteristic
385	C₂×C₄	C₇×#127	1	1	yes	characteristic
386	C₂×C₄	C₇×#127	1	1	yes	characteristic
387	C₂×C₄	C₇×#135	1	4	yes	—
388	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
389	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₈	—	2	4	no	—
394	C₈	—	2	4	no	—
395	C₇	#19657	1	1	yes	characteristic, direct product factor, Sylow
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₇×#495	1	2	yes	—
402	C₂²	C₂×C₇×#127	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	1	no	—
407	C₄	—	8	2	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	1	no	—
410	C₄	C₇×#495	1	2	yes	—
411	C₄	C₂×C₇×#135	1	2	yes	—
412	C₄	C₇×#577	1	2	yes	—
413	C₄	C₇×#578	1	2	yes	—
414	C₂	—	2	2	no	—
415	C₂	—	16	1	no	—
416	C₂	C₂×C₇×#495	1	1	yes	characteristic
417	C₂	C₇×#3154	1	1	yes	characteristic
418	C₂	C₇×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3230	C₂	semidirect
2. C₇×#3229	C₂	semidirect
6. C₂×C₇×#487	C₂	semidirect
7. C₇×#1719	C₂	semidirect
8. C₇×#1718	C₂	semidirect
9. C₇×#1710	C₂	semidirect
10. C₇×#1708	C₂	semidirect
11. C₇×#1450	C₂	semidirect
47. #19657	C₇	direct (N × H)
103. #3230	C₂×C₇	semidirect
104. #3229	C₂×C₇	semidirect
108. C₂×#487	C₂×C₇	semidirect
109. #1719	C₂×C₇	semidirect
110. #1718	C₂×C₇	semidirect
111. #1710	C₂×C₇	semidirect
112. #1708	C₂×C₇	semidirect
113. #1450	C₂×C₇	semidirect
395. C₇	#19657	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×#3230	2
C₇×#3229	2
C₇×#3226	2
C₇×#3206	2
C₇×#3131	2
C₂×C₇×#487	2
C₇×#1719	2
C₇×#1718	2
C₇×#1710	2
C₇×#1708	2
C₇×#1450	2
#19657	7

Subgroups — C7×#19657 #13196873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19657 #13196873