Subgroups — C₇×#19640 #13196856

Order 1792.

742 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3169	C₂	1	1	yes	maximal, characteristic
4	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1718	C₂	1	2	yes	maximal, complemented
8	C₇×#1717	C₂	1	2	yes	maximal, complemented
9	C₇×#1711	C₂	1	2	yes	maximal, complemented
10	C₇×#1708	C₂	1	2	yes	maximal, complemented
11	C₇×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#532	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	1	yes	characteristic
17	C₇×#498	C₂²	1	2	yes	—
18	C₇×#493	C₂²	1	1	yes	characteristic
19	C₇×#492	C₂²	1	2	yes	—
20	C₇×#489	—	2	2	no	—
21	C₇×#489	—	2	2	no	—
22	C₇×#487	—	2	2	no	—
23	C₇×#487	C₂²	1	2	yes	—
24	C₇×#487	C₂²	1	2	yes	—
25	C₇×#487	C₂²	1	2	yes	—
26	C₇×#487	C₂²	1	2	yes	—
27	C₇×#487	C₂²	1	2	yes	—
28	C₇×#486	C₂²	1	1	yes	characteristic
29	C₇×#486	C₂²	1	2	yes	—
30	C₇×#486	C₂²	1	1	yes	characteristic
31	C₇×#486	C₂²	1	2	yes	—
32	C₇×#486	C₂²	1	2	yes	—
33	C₇×#481	—	2	2	no	—
34	C₇×#476	—	2	2	no	—
35	C₇×#466	—	2	2	no	—
36	C₇×#461	—	2	2	no	—
37	C₇×#448	—	2	2	no	—
38	C₄×C₇×D₈	—	2	2	no	—
39	C₇×#431	C₂²	1	1	yes	characteristic
40	C₇×#417	—	2	2	no	—
41	C₇×#417	—	2	2	no	—
42	C₂×C₇×#103	—	2	2	no	—
43	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
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	#19640	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	—	2	1	no	—
49	C₂×C₇×#41	—	2	1	no	—
50	C₂²×C₇×Q₈	—	2	1	no	—
51	C₂²×C₇×Q₈	—	2	1	no	—
52	C₂×C₇×SD₁₆	—	2	4	no	—
53	C₂×C₇×D₈	—	2	2	no	—
54	C₂×C₇×M₁₆	D₄	1	2	yes	—
55	C₂²×C₇×C₈	D₄	1	2	yes	—
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	—	2	1	no	—
60	C₇×C₄⋊Q₈	—	2	1	no	—
61	C₇×C₄⋊Q₈	—	2	1	no	—
62	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₇×#127	C₂³	1	1	yes	characteristic
67	C₇×#127	C₂³	1	1	yes	characteristic
68	C₇×#124	—	2	1	no	—
69	C₇×#124	—	2	1	no	—
70	C₇×#121	—	2	1	no	—
71	C₇×#121	—	2	1	no	—
72	C₇×#121	—	2	1	no	—
73	C₇×#121	—	2	1	no	—
74	C₄×C₇×D₄	—	2	1	no	—
75	C₄×C₇×D₄	—	2	1	no	—
76	C₄×C₇×D₄	—	2	1	no	—
77	C₄×C₇×D₄	—	2	1	no	—
78	C₂×C₇×C₄⋊C₄	—	2	1	no	—
79	C₂×C₇×C₄⋊C₄	—	2	1	no	—
80	C₂×C₇×C₄⋊C₄	—	2	1	no	—
81	C₂×C₇×C₄⋊C₄	—	2	1	no	—
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₇×#107	—	2	2	no	—
84	C₇×#106	—	2	4	no	—
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	4	no	—
91	C₇×#102	—	2	2	no	—
92	C₇×#102	—	2	2	no	—
93	C₇×#102	—	2	4	no	—
94	C₇×#102	—	2	4	no	—
95	C₇×#102	—	2	4	no	—
96	C₇×C₂²⋊C₈	D₄	1	2	yes	—
97	C₇×#97	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	#3227	C₂×C₇	1	1	yes	characteristic, complemented
104	#3206	C₂×C₇	1	1	yes	characteristic, complemented
105	#3169	C₂×C₇	1	1	yes	characteristic
106	#3141	C₂×C₇	1	1	yes	characteristic, complemented
107	#3141	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
109	#1718	C₂×C₇	1	2	yes	complemented
110	#1717	C₂×C₇	1	2	yes	complemented
111	#1711	C₂×C₇	1	2	yes	complemented
112	#1708	C₂×C₇	1	2	yes	complemented
113	C₈×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
114	C₇×#41	—	4	4	no	—
115	C₇×#41	—	4	4	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	4	no	—
121	C₂×C₇×Q₈	—	4	1	no	—
122	C₂×C₇×Q₈	—	4	1	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	—	2	1	no	—
128	C₂×C₇×D₄	—	2	1	no	—
129	C₂×C₇×D₄	—	2	1	no	—
130	C₂×C₇×D₄	—	4	1	no	—
131	C₂×C₇×D₄	—	4	1	no	—
132	C₂²×C₄×C₇	—	4	1	no	—
133	C₂²×C₄×C₇	—	4	1	no	—
134	C₂²×C₄×C₇	—	4	1	no	—
135	C₂²×C₄×C₇	—	4	1	no	—
136	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
139	C₇×SD₁₆	—	8	4	no	—
140	C₇×D₈	—	4	4	no	—
141	C₇×M₁₆	—	2	4	no	—
142	C₂×C₇×C₈	—	4	2	no	—
143	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
144	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
145	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
146	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	2	2	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	1	no	—
151	C₇×C₄⋊C₄	—	2	1	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	1	no	—
154	C₇×C₄⋊C₄	—	2	1	no	—
155	C₇×C₄⋊C₄	—	4	1	no	—
156	C₇×C₄⋊C₄	—	4	1	no	—
157	C₇×C₄⋊C₄	—	4	1	no	—
158	C₇×C₄⋊C₄	—	4	1	no	—
159	C₇×C₂²⋊C₄	—	4	1	no	—
160	C₇×C₂²⋊C₄	—	4	1	no	—
161	C₇×C₂²⋊C₄	—	4	1	no	—
162	C₇×C₂²⋊C₄	—	4	1	no	—
163	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₇	C₂⁴	1	1	yes	characteristic
167	#532	C₂²×C₇	1	1	yes	characteristic
168	#532	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
170	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
171	#500	C₂²×C₇	1	1	yes	characteristic
172	#498	C₂²×C₇	1	2	yes	—
173	#493	C₂²×C₇	1	1	yes	characteristic
174	#492	C₂²×C₇	1	2	yes	—
175	#489	—	2	2	no	—
176	#489	—	2	2	no	—
177	#487	—	2	2	no	—
178	#487	C₂²×C₇	1	2	yes	—
179	#487	C₂²×C₇	1	2	yes	—
180	#487	C₂²×C₇	1	2	yes	—
181	#487	C₂²×C₇	1	2	yes	—
182	#487	C₂²×C₇	1	2	yes	—
183	#486	C₂²×C₇	1	2	yes	—
184	#486	C₂²×C₇	1	2	yes	—
185	#486	C₂²×C₇	1	1	yes	characteristic
186	#486	C₂²×C₇	1	1	yes	characteristic
187	#486	C₂²×C₇	1	2	yes	—
188	#481	—	2	2	no	—
189	#476	—	2	2	no	—
190	#466	—	2	2	no	—
191	#461	—	2	2	no	—
192	#448	—	2	2	no	—
193	C₄×D₈	—	2	2	no	—
194	#431	C₂²×C₇	1	1	yes	characteristic
195	#417	—	2	2	no	—
196	#417	—	2	2	no	—
197	C₂×#103	—	2	2	no	—
198	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
200	#322	C₂²×C₇	1	2	yes	—
201	C₈²	C₂²×C₇	1	2	yes	—
202	C₂³×C₇	—	4	1	no	—
203	C₂³×C₇	—	4	1	no	—
204	C₂³×C₇	#127	1	1	yes	characteristic
205	C₇×Q₈	—	4	2	no	—
206	C₇×Q₈	—	4	2	no	—
207	C₇×Q₈	—	4	4	no	—
208	C₇×Q₈	—	4	4	no	—
209	C₇×Q₈	—	8	2	no	—
210	C₇×Q₈	—	8	2	no	—
211	C₇×D₄	—	4	2	no	—
212	C₇×D₄	—	4	2	no	—
213	C₇×D₄	—	4	2	no	—
214	C₇×D₄	—	4	2	no	—
215	C₇×D₄	—	4	2	no	—
216	C₇×D₄	—	4	2	no	—
217	C₇×D₄	—	8	2	no	—
218	C₇×D₄	—	8	2	no	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	4	1	no	—
222	C₂×C₄×C₇	—	4	1	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	8	2	no	—
226	C₂×C₄×C₇	—	8	2	no	—
227	C₂×C₄×C₇	—	8	2	no	—
228	C₂×C₄×C₇	—	8	2	no	—
229	C₂×C₄×C₇	#127	1	1	yes	characteristic
230	C₂×C₄×C₇	#127	1	1	yes	characteristic
231	C₂×C₄×C₇	#127	1	1	yes	characteristic
232	C₂×C₄×C₇	#135	1	4	yes	—
233	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
236	C₇×C₈	—	2	4	no	—
237	C₇×C₈	—	2	2	no	—
238	C₇×C₈	—	2	2	no	—
239	C₇×C₈	—	2	4	no	—
240	C₂×#41	—	2	1	no	—
241	C₂×#41	—	2	1	no	—
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×D₈	—	2	2	no	—
246	C₂×M₁₆	C₇×D₄	1	2	yes	—
247	C₂²×C₈	C₇×D₄	1	2	yes	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
255	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
256	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
257	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
258	#127	C₂³×C₇	1	1	yes	characteristic
259	#127	C₂³×C₇	1	1	yes	characteristic
260	#124	—	2	1	no	—
261	#124	—	2	1	no	—
262	#121	—	2	1	no	—
263	#121	—	2	1	no	—
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
275	#107	—	2	2	no	—
276	#106	—	2	4	no	—
277	C₄⋊C₈	C₇×D₄	1	2	yes	—
278	#103	—	2	4	no	—
279	#103	—	2	4	no	—
280	#103	—	2	4	no	—
281	#103	—	2	4	no	—
282	#103	—	2	4	no	—
283	#102	—	2	4	no	—
284	#102	—	2	4	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	4	no	—
288	C₂²⋊C₈	C₇×D₄	1	2	yes	—
289	#97	C₇×D₄	1	2	yes	—
290	C₄×C₈	C₇×D₄	1	2	yes	—
291	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₇	1	2	yes	—
293	C₄×C₈	C₂³×C₇	1	2	yes	—
294	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
295	C₂²×C₇	—	2	1	no	—
296	C₂²×C₇	—	2	1	no	—
297	C₂²×C₇	—	8	1	no	—
298	C₂²×C₇	—	8	1	no	—
299	C₂²×C₇	—	8	1	no	—
300	C₂²×C₇	—	8	1	no	—
301	C₂²×C₇	—	8	1	no	—
302	C₂²×C₇	—	8	1	no	—
303	C₂²×C₇	#495	1	2	yes	—
304	C₂²×C₇	C₂×#127	1	1	yes	characteristic
305	C₄×C₇	—	2	1	no	—
306	C₄×C₇	—	2	1	no	—
307	C₄×C₇	—	8	1	no	—
308	C₄×C₇	—	8	1	no	—
309	C₄×C₇	—	8	2	no	—
310	C₄×C₇	—	8	2	no	—
311	C₄×C₇	#495	1	2	yes	—
312	C₄×C₇	C₂×#135	1	2	yes	—
313	C₄×C₇	#575	1	2	yes	—
314	C₄×C₇	#577	1	2	yes	—
315	#41	—	4	4	no	—
316	#41	—	4	4	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	4	1	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
340	SD₁₆	—	8	4	no	—
341	D₈	—	4	4	no	—
342	M₁₆	—	2	4	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
345	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
346	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
347	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
365	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
366	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
367	C₄²	C₂⁴×C₇	1	1	yes	characteristic
368	C₂×C₇	—	2	2	no	—
369	C₂×C₇	—	16	1	no	—
370	C₂×C₇	—	16	1	no	—
371	C₂×C₇	C₂×#495	1	1	yes	characteristic
372	C₂×C₇	#3153	1	1	yes	characteristic
373	C₂×C₇	#3154	1	1	yes	characteristic
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	C₇×#127	1	1	yes	characteristic
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	4	no	—
380	Q₈	—	4	4	no	—
381	Q₈	—	8	2	no	—
382	Q₈	—	8	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	C₇×#127	1	1	yes	characteristic
402	C₂×C₄	C₇×#127	1	1	yes	characteristic
403	C₂×C₄	C₇×#127	1	1	yes	characteristic
404	C₂×C₄	C₇×#135	1	4	yes	—
405	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
408	C₈	—	2	4	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	4	no	—
412	C₇	#19640	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	C₇×#495	1	2	yes	—
422	C₂²	C₂×C₇×#127	1	1	yes	characteristic
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	C₇×#495	1	2	yes	—
430	C₄	C₂×C₇×#135	1	2	yes	—
431	C₄	C₇×#575	1	2	yes	—
432	C₄	C₇×#577	1	2	yes	—
433	C₂	—	2	2	no	—
434	C₂	—	16	1	no	—
435	C₂	—	16	1	no	—
436	C₂	C₂×C₇×#495	1	1	yes	characteristic
437	C₂	C₇×#3153	1	1	yes	characteristic
438	C₂	C₇×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3169	C₂
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×#3227	C₂	semidirect
2. C₇×#3206	C₂	semidirect
4. C₇×#3141	C₂	semidirect
5. C₇×#3141	C₂	semidirect
6. C₂×C₇×#487	C₂	semidirect
7. C₇×#1718	C₂	semidirect
8. C₇×#1717	C₂	semidirect
9. C₇×#1711	C₂	semidirect
10. C₇×#1708	C₂	semidirect
11. C₇×C₈×M₁₆	C₂	semidirect
47. #19640	C₇	direct (N × H)
103. #3227	C₂×C₇	semidirect
104. #3206	C₂×C₇	semidirect
106. #3141	C₂×C₇	semidirect
107. #3141	C₂×C₇	semidirect
108. C₂×#487	C₂×C₇	semidirect
109. #1718	C₂×C₇	semidirect
110. #1717	C₂×C₇	semidirect
111. #1711	C₂×C₇	semidirect
112. #1708	C₂×C₇	semidirect
113. C₈×M₁₆	C₂×C₇	semidirect
412. C₇	#19640	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×#3227	2
C₇×#3206	2
C₇×#3169	2
C₇×#3141	2
C₂×C₇×#487	2
C₇×#1718	2
C₇×#1717	2
C₇×#1711	2
C₇×#1708	2
C₇×C₈×M₁₆	2
#19640	7

Subgroups — C7×#19640 #13196856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19640 #13196856