Subgroups — C₇×#19637 #13196853

Order 1792.

750 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3208	C₂	1	1	yes	maximal, characteristic
3	C₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3138	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic
7	C₇×#1720	C₂	1	2	yes	maximal, complemented
8	C₇×#1719	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×#533	C₂²	1	1	yes	characteristic
13	C₇×#533	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×#127	C₂²	1	1	yes	characteristic
16	C₇×#500	C₂²	1	1	yes	characteristic, complemented
17	C₇×#498	C₂²	1	2	yes	complemented
18	C₇×#494	C₂²	1	1	yes	characteristic, complemented
19	C₇×#492	C₂²	1	2	yes	—
20	C₇×#491	—	2	2	no	—
21	C₇×#490	—	2	2	no	—
22	C₇×#487	C₂²	1	1	yes	characteristic, complemented
23	C₇×#487	C₂²	1	2	yes	complemented
24	C₇×#487	C₂²	1	1	yes	characteristic, complemented
25	C₇×#487	C₂²	1	2	yes	complemented
26	C₇×#487	C₂²	1	2	yes	complemented
27	C₇×#486	—	2	2	no	—
28	C₇×#486	C₂²	1	2	yes	—
29	C₇×#486	C₂²	1	2	yes	—
30	C₇×#486	C₂²	1	2	yes	—
31	C₇×#486	C₂²	1	2	yes	—
32	C₇×#486	C₂²	1	2	yes	—
33	C₇×#483	—	2	2	no	—
34	C₇×#475	—	2	2	no	—
35	C₇×#467	—	2	2	no	—
36	C₇×#460	—	2	2	no	—
37	C₇×#450	—	2	2	no	—
38	C₄×C₇×Q₁₆	—	2	2	no	—
39	C₇×#431	C₂²	1	1	yes	characteristic
40	C₇×#419	—	2	2	no	—
41	C₇×#418	—	2	2	no	—
42	C₂×C₇×#102	—	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	complemented
46	C₇×C₈²	C₂²	1	2	yes	complemented
47	#19637	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₇×Q₈	—	2	1	no	—
49	C₂²×C₇×D₄	—	2	1	no	—
50	C₂²×C₇×D₄	—	2	1	no	—
51	C₂²×C₇×D₄	—	2	1	no	—
52	C₂×C₇×Q₁₆	—	2	2	no	—
53	C₂×C₇×SD₁₆	—	2	4	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	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	1	yes	characteristic
63	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₇×#127	—	2	1	no	—
65	C₇×#127	—	2	1	no	—
66	C₇×#127	—	2	1	no	—
67	C₇×#127	C₂³	1	2	yes	—
68	C₇×#125	—	2	1	no	—
69	C₇×#125	—	2	1	no	—
70	C₇×C₂²⋊Q₈	—	2	1	no	—
71	C₇×C₂²⋊Q₈	—	2	1	no	—
72	C₇×C₂²⋊Q₈	—	2	1	no	—
73	C₇×C₂²⋊Q₈	—	2	1	no	—
74	C₄×C₇×Q₈	—	2	1	no	—
75	C₄×C₇×Q₈	—	2	1	no	—
76	C₄×C₇×Q₈	—	2	1	no	—
77	C₄×C₇×Q₈	—	2	1	no	—
78	C₇×#117	—	2	1	no	—
79	C₇×#117	—	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	2	no	—
87	C₇×#103	—	2	2	no	—
88	C₇×#103	—	2	4	no	—
89	C₇×#103	—	2	4	no	—
90	C₇×#103	—	2	4	no	—
91	C₇×#102	—	2	4	no	—
92	C₇×#102	—	2	4	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	#3229	C₂×C₇	1	1	yes	characteristic, complemented
104	#3208	C₂×C₇	1	1	yes	characteristic
105	#3170	C₂×C₇	1	1	yes	characteristic, complemented
106	#3139	C₂×C₇	1	1	yes	characteristic, complemented
107	#3138	C₂×C₇	1	1	yes	characteristic
108	C₂×#486	C₂×C₇	1	1	yes	characteristic
109	#1720	C₂×C₇	1	2	yes	complemented
110	#1719	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	C₂⁴×C₇	—	4	1	no	—
115	C₂×C₇×Q₈	—	2	1	no	—
116	C₂×C₇×Q₈	—	2	2	no	—
117	C₂×C₇×Q₈	—	2	1	no	—
118	C₂×C₇×Q₈	—	2	1	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	4	1	no	—
121	C₂×C₇×Q₈	—	4	4	no	—
122	C₂×C₇×D₄	—	2	2	no	—
123	C₂×C₇×D₄	—	2	2	no	—
124	C₂×C₇×D₄	—	2	2	no	—
125	C₂×C₇×D₄	—	4	4	no	—
126	C₂×C₇×D₄	—	4	1	no	—
127	C₂×C₇×D₄	—	4	1	no	—
128	C₂×C₇×D₄	—	4	1	no	—
129	C₂×C₇×D₄	—	4	4	no	—
130	C₂×C₇×D₄	—	8	2	no	—
131	C₂²×C₄×C₇	—	4	1	no	—
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
135	C₇×Q₁₆	—	4	4	no	—
136	C₇×SD₁₆	—	8	4	no	—
137	C₇×M₁₆	—	2	4	no	—
138	C₂×C₇×C₈	—	4	2	no	—
139	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
140	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
141	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
142	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	2	1	no	—
145	C₇×C₄⋊C₄	—	2	1	no	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	1	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	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×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	C₄²×C₇	—	4	1	no	—
162	C₄²×C₇	—	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	#533	C₂²×C₇	1	1	yes	characteristic
168	#533	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
170	C₂×#127	C₂²×C₇	1	1	yes	characteristic
171	#500	C₂²×C₇	1	1	yes	characteristic, complemented
172	#498	C₂²×C₇	1	2	yes	complemented
173	#494	C₂²×C₇	1	1	yes	characteristic, complemented
174	#492	C₂²×C₇	1	2	yes	—
175	#491	—	2	2	no	—
176	#490	—	2	2	no	—
177	#487	C₂²×C₇	1	2	yes	complemented
178	#487	C₂²×C₇	1	2	yes	complemented
179	#487	C₂²×C₇	1	1	yes	characteristic, complemented
180	#487	C₂²×C₇	1	1	yes	characteristic, complemented
181	#487	C₂²×C₇	1	2	yes	complemented
182	#486	—	2	2	no	—
183	#486	C₂²×C₇	1	2	yes	—
184	#486	C₂²×C₇	1	2	yes	—
185	#486	C₂²×C₇	1	2	yes	—
186	#486	C₂²×C₇	1	2	yes	—
187	#486	C₂²×C₇	1	2	yes	—
188	#483	—	2	2	no	—
189	#475	—	2	2	no	—
190	#467	—	2	2	no	—
191	#460	—	2	2	no	—
192	#450	—	2	2	no	—
193	C₄×Q₁₆	—	2	2	no	—
194	#431	C₂²×C₇	1	1	yes	characteristic
195	#419	—	2	2	no	—
196	#418	—	2	2	no	—
197	C₂×#102	—	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	complemented
201	C₈²	C₂²×C₇	1	2	yes	complemented
202	C₂³×C₇	—	4	2	no	—
203	C₂³×C₇	—	8	2	no	—
204	C₂³×C₇	—	8	2	no	—
205	C₂³×C₇	—	8	2	no	—
206	C₂³×C₇	#127	1	1	yes	characteristic
207	C₇×Q₈	—	4	4	no	—
208	C₇×Q₈	—	4	2	no	—
209	C₇×Q₈	—	4	2	no	—
210	C₇×Q₈	—	4	2	no	—
211	C₇×Q₈	—	4	2	no	—
212	C₇×Q₈	—	8	2	no	—
213	C₇×D₄	—	4	4	no	—
214	C₇×D₄	—	4	4	no	—
215	C₇×D₄	—	4	4	no	—
216	C₇×D₄	—	8	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	1	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	2	no	—
226	C₂×C₄×C₇	—	8	2	no	—
227	C₂×C₄×C₇	#127	1	1	yes	characteristic
228	C₂×C₄×C₇	#127	1	1	yes	characteristic
229	C₂×C₄×C₇	#127	1	1	yes	characteristic
230	C₂×C₄×C₇	#135	1	4	yes	—
231	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
234	C₇×C₈	—	2	4	no	—
235	C₇×C₈	—	2	2	no	—
236	C₇×C₈	—	2	2	no	—
237	C₇×C₈	—	2	4	no	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂×Q₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	2	4	no	—
244	C₂×M₁₆	C₇×D₄	1	2	yes	—
245	C₂²×C₈	C₇×D₄	1	2	yes	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
250	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
251	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
252	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
253	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
254	#127	—	2	1	no	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	C₂³×C₇	1	2	yes	—
258	#125	—	2	1	no	—
259	#125	—	2	1	no	—
260	C₂²⋊Q₈	—	2	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	—	2	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	#117	—	2	1	no	—
269	#117	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
273	#107	—	2	2	no	—
274	#106	—	2	4	no	—
275	C₄⋊C₈	C₇×D₄	1	2	yes	—
276	#103	—	2	4	no	—
277	#103	—	2	4	no	—
278	#103	—	2	2	no	—
279	#103	—	2	2	no	—
280	#103	—	2	4	no	—
281	#102	—	2	4	no	—
282	#102	—	2	4	no	—
283	#102	—	2	4	no	—
284	#102	—	2	4	no	—
285	#102	—	2	4	no	—
286	C₂²⋊C₈	C₇×D₄	1	2	yes	—
287	#97	C₇×D₄	1	2	yes	—
288	C₄×C₈	C₇×D₄	1	2	yes	—
289	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₇	1	2	yes	—
291	C₄×C₈	C₂³×C₇	1	2	yes	—
292	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
293	C₂²×C₇	—	2	1	no	—
294	C₂²×C₇	—	2	1	no	—
295	C₂²×C₇	—	8	2	no	—
296	C₂²×C₇	—	8	2	no	—
297	C₂²×C₇	—	8	2	no	—
298	C₂²×C₇	—	16	4	no	—
299	C₂²×C₇	#495	1	2	yes	—
300	C₂²×C₇	C₂×#127	1	1	yes	characteristic
301	C₄×C₇	—	2	1	no	—
302	C₄×C₇	—	2	1	no	—
303	C₄×C₇	—	8	2	no	—
304	C₄×C₇	—	8	1	no	—
305	C₄×C₇	—	8	1	no	—
306	C₄×C₇	—	8	1	no	—
307	C₄×C₇	—	8	1	no	—
308	C₄×C₇	#495	1	2	yes	—
309	C₄×C₇	C₂×#135	1	2	yes	—
310	C₄×C₇	#575	1	2	yes	—
311	C₄×C₇	#577	1	2	yes	—
312	C₂⁴	—	4	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	4	1	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	—	8	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
333	Q₁₆	—	4	4	no	—
334	SD₁₆	—	8	4	no	—
335	M₁₆	—	2	4	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
338	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
339	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
340	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
362	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
363	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
364	C₄²	C₂⁴×C₇	1	1	yes	characteristic
365	C₂×C₇	—	2	2	no	—
366	C₂×C₇	—	16	2	no	—
367	C₂×C₇	C₂×#495	1	1	yes	characteristic
368	C₂×C₇	#3153	1	1	yes	characteristic
369	C₂×C₇	#3154	1	1	yes	characteristic
370	C₂³	—	4	2	no	—
371	C₂³	—	8	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	C₇×#127	1	1	yes	characteristic
375	Q₈	—	4	4	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	8	2	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	4	no	—
384	D₄	—	8	2	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	C₇×#127	1	1	yes	characteristic
396	C₂×C₄	C₇×#127	1	1	yes	characteristic
397	C₂×C₄	C₇×#127	1	1	yes	characteristic
398	C₂×C₄	C₇×#135	1	4	yes	—
399	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	2	2	no	—
404	C₈	—	2	2	no	—
405	C₈	—	2	4	no	—
406	C₇	#19637	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	16	4	no	—
413	C₂²	C₇×#495	1	2	yes	—
414	C₂²	C₂×C₇×#127	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	8	2	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	C₇×#495	1	2	yes	—
423	C₄	C₂×C₇×#135	1	2	yes	—
424	C₄	C₇×#575	1	2	yes	—
425	C₄	C₇×#577	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	16	2	no	—
428	C₂	C₂×C₇×#495	1	1	yes	characteristic
429	C₂	C₇×#3153	1	1	yes	characteristic
430	C₂	C₇×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₂×C₇×#127	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×#3229	C₂	semidirect
3. C₇×#3170	C₂	semidirect
4. C₇×#3139	C₂	semidirect
7. C₇×#1720	C₂	semidirect
8. C₇×#1719	C₂	semidirect
9. C₇×#1711	C₂	semidirect
10. C₇×#1708	C₂	semidirect
11. C₇×C₈×M₁₆	C₂	semidirect
16. C₇×#500	C₂²	semidirect
17. C₇×#498	C₂²	semidirect
18. C₇×#494	C₂²	semidirect
22. C₇×#487	C₂²	semidirect
23. C₇×#487	C₂²	semidirect
24. C₇×#487	C₂²	semidirect
25. C₇×#487	C₂²	semidirect
26. C₇×#487	C₂²	semidirect
45. C₇×#322	C₂²	semidirect
46. C₇×C₈²	C₂²	semidirect
47. #19637	C₇	direct (N × H)
103. #3229	C₂×C₇	semidirect
105. #3170	C₂×C₇	semidirect
106. #3139	C₂×C₇	semidirect
109. #1720	C₂×C₇	semidirect
110. #1719	C₂×C₇	semidirect
111. #1711	C₂×C₇	semidirect
112. #1708	C₂×C₇	semidirect
113. C₈×M₁₆	C₂×C₇	semidirect
171. #500	C₂²×C₇	semidirect
172. #498	C₂²×C₇	semidirect
173. #494	C₂²×C₇	semidirect
177. #487	C₂²×C₇	semidirect
178. #487	C₂²×C₇	semidirect
179. #487	C₂²×C₇	semidirect
180. #487	C₂²×C₇	semidirect
181. #487	C₂²×C₇	semidirect
200. #322	C₂²×C₇	semidirect
201. C₈²	C₂²×C₇	semidirect
406. C₇	#19637	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×#3229	2
C₇×#3208	2
C₇×#3170	2
C₇×#3139	2
C₇×#3138	2
C₂×C₇×#486	2
C₇×#1720	2
C₇×#1719	2
C₇×#1711	2
C₇×#1708	2
C₇×C₈×M₁₆	2
#19637	7

Subgroups — C7×#19637 #13196853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19637 #13196853