Subgroups — C₇×#20822 #13198038

Order 1792.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic
2	C₇×#2314	C₂	1	2	yes	maximal
3	C₇×#1847	C₂	1	2	yes	maximal, complemented
4	C₇×#1835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1809	C₂	1	2	yes	maximal
7	C₇×#1808	C₂	1	1	yes	maximal, characteristic
8	C₇×#1807	C₂	1	1	yes	maximal, characteristic
9	C₇×#1776	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#117	C₂²	1	1	yes	characteristic
15	C₂×C₇×#107	C₂²	1	2	yes	—
16	C₂×C₇×#107	C₂²	1	2	yes	—
17	C₂×C₇×#106	C₂²	1	2	yes	—
18	C₂×C₇×#106	C₂²	1	2	yes	—
19	C₇×#405	C₄	1	8	yes	complemented
20	C₂×C₇×#97	C₂²	1	1	yes	characteristic
21	C₂×C₇×#97	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₇×#388	—	2	2	no	—
25	C₇×#388	—	2	2	no	—
26	C₇×#387	—	2	2	no	—
27	C₇×#387	—	2	2	no	—
28	C₇×#384	C₂²	1	2	yes	—
29	C₇×#382	C₂²	1	2	yes	—
30	C₇×#380	C₂²	1	2	yes	—
31	C₇×#380	C₂²	1	2	yes	—
32	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₇×#340	C₂²	1	1	yes	characteristic
35	C₇×#340	C₂²	1	1	yes	characteristic
36	C₇×#340	C₂²	1	1	yes	characteristic
37	C₇×#340	C₂²	1	1	yes	characteristic
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	#20822	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
42	C₂×C₇×M₁₆	—	2	4	no	—
43	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
44	C₂²×C₇×C₈	—	2	4	no	—
45	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
46	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₇×#117	C₂×C₄	1	4	yes	—
51	C₇×#117	Q₈	1	4	yes	—
52	C₂×C₇×C₄⋊C₄	—	2	2	no	—
53	C₂×C₇×C₄⋊C₄	—	2	2	no	—
54	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
56	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₇	—	2	2	no	—
65	C₂×C₄²×C₇	—	2	2	no	—
66	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
68	C₇×#107	—	2	4	no	—
69	C₇×#107	—	2	4	no	—
70	C₇×#106	—	2	4	no	—
71	C₇×#106	—	2	4	no	—
72	C₇×#97	C₂×C₄	1	4	yes	—
73	C₇×#97	C₂×C₄	1	4	yes	—
74	C₄×C₇×C₈	C₂×C₄	1	4	yes	—
75	C₄×C₇×C₈	C₂×C₄	1	4	yes	—
76	C₇×#95	—	2	2	no	—
77	C₇×#95	—	2	2	no	—
78	C₇×#95	—	2	2	no	—
79	C₇×#95	—	2	2	no	—
80	C₇×#95	—	2	2	no	—
81	C₇×#95	—	2	2	no	—
82	C₂×#405	C₂×C₇	1	1	yes	characteristic
83	#2314	C₂×C₇	1	2	yes	—
84	#1847	C₂×C₇	1	2	yes	complemented
85	#1835	C₂×C₇	1	1	yes	characteristic, complemented
86	#1834	C₂×C₇	1	1	yes	characteristic, complemented
87	#1809	C₂×C₇	1	2	yes	—
88	#1808	C₂×C₇	1	1	yes	characteristic
89	#1807	C₂×C₇	1	1	yes	characteristic
90	#1776	C₂×C₇	1	2	yes	complemented
91	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
92	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
93	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇	—	2	2	no	—
95	C₂²×C₄×C₇	—	2	2	no	—
96	C₂²×C₄×C₇	—	2	2	no	—
97	C₂²×C₄×C₇	—	2	2	no	—
98	C₂²×C₄×C₇	—	2	2	no	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
108	C₇×M₁₆	—	2	8	no	—
109	C₂×C₇×C₈	—	2	2	no	—
110	C₂×C₇×C₈	—	2	2	no	—
111	C₂×C₇×C₈	—	2	8	no	—
112	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
113	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
114	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
115	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
116	C₂×C₇×C₈	#41	1	4	yes	—
117	C₂×C₇×C₈	#41	1	4	yes	—
118	C₇×C₄⋊C₄	—	2	2	no	—
119	C₇×C₄⋊C₄	—	2	2	no	—
120	C₇×C₄⋊C₄	—	2	2	no	—
121	C₇×C₄⋊C₄	—	2	2	no	—
122	C₇×C₄⋊C₄	—	2	2	no	—
123	C₇×C₄⋊C₄	—	2	2	no	—
124	C₇×C₄⋊C₄	—	2	2	no	—
125	C₇×C₄⋊C₄	—	2	2	no	—
126	C₇×C₄⋊C₄	—	8	2	no	—
127	C₇×C₄⋊C₄	—	8	2	no	—
128	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
129	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
130	C₇×C₂²⋊C₄	—	8	2	no	—
131	C₇×C₂²⋊C₄	—	8	2	no	—
132	C₇×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
133	C₇×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
134	C₄²×C₇	—	8	2	no	—
135	C₄²×C₇	—	8	2	no	—
136	C₄²×C₇	C₂²×C₄	1	2	yes	—
137	C₄²×C₇	C₂²×C₄	1	2	yes	—
138	C₄²×C₇	C₂×Q₈	1	2	yes	—
139	C₄²×C₇	C₂×Q₈	1	2	yes	—
140	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
141	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
142	C₂×#117	C₂²×C₇	1	1	yes	characteristic
143	C₂×#107	C₂²×C₇	1	2	yes	—
144	C₂×#107	C₂²×C₇	1	2	yes	—
145	C₂×#106	C₂²×C₇	1	2	yes	—
146	C₂×#106	C₂²×C₇	1	2	yes	—
147	#405	C₄×C₇	1	8	yes	complemented
148	C₂×#97	C₂²×C₇	1	1	yes	characteristic
149	C₂×#97	C₂²×C₇	1	1	yes	characteristic
150	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
151	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
152	#388	—	2	2	no	—
153	#388	—	2	2	no	—
154	#387	—	2	2	no	—
155	#387	—	2	2	no	—
156	#384	C₂²×C₇	1	2	yes	—
157	#382	C₂²×C₇	1	2	yes	—
158	#380	C₂²×C₇	1	2	yes	—
159	#380	C₂²×C₇	1	2	yes	—
160	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
161	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
162	#340	C₂²×C₇	1	1	yes	characteristic
163	#340	C₂²×C₇	1	1	yes	characteristic
164	#340	C₂²×C₇	1	1	yes	characteristic
165	#340	C₂²×C₇	1	1	yes	characteristic
166	#340	C₂²×C₇	1	2	yes	—
167	#340	C₂²×C₇	1	2	yes	—
168	C₂³×C₇	—	2	2	no	—
169	C₂³×C₇	—	2	1	no	—
170	C₂³×C₇	—	2	2	no	—
171	C₂³×C₇	—	2	1	no	—
172	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
173	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇	—	2	2	no	—
175	C₂×C₄×C₇	—	2	1	no	—
176	C₂×C₄×C₇	—	2	1	no	—
177	C₂×C₄×C₇	—	2	2	no	—
178	C₂×C₄×C₇	—	2	2	no	—
179	C₂×C₄×C₇	—	2	1	no	—
180	C₂×C₄×C₇	—	2	1	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	2	2	no	—
183	C₂×C₄×C₇	—	2	4	no	—
184	C₂×C₄×C₇	—	4	2	no	—
185	C₂×C₄×C₇	—	4	2	no	—
186	C₂×C₄×C₇	—	4	2	no	—
187	C₂×C₄×C₇	—	4	2	no	—
188	C₂×C₄×C₇	—	4	2	no	—
189	C₂×C₄×C₇	—	4	2	no	—
190	C₂×C₄×C₇	—	4	2	no	—
191	C₂×C₄×C₇	—	4	2	no	—
192	C₂×C₄×C₇	—	4	2	no	—
193	C₂×C₄×C₇	—	4	2	no	—
194	C₂×C₄×C₇	—	4	2	no	—
195	C₂×C₄×C₇	—	4	2	no	—
196	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
197	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
198	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
199	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
200	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
201	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
203	C₂×C₄×C₇	C₂×#41	1	2	yes	—
204	C₂×C₄×C₇	C₂×#41	1	2	yes	—
205	C₇×C₈	—	2	2	no	—
206	C₇×C₈	—	2	2	no	—
207	C₇×C₈	#117	1	4	yes	—
208	C₇×C₈	#117	1	4	yes	—
209	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
210	C₂×M₁₆	—	2	4	no	—
211	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
212	C₂²×C₈	—	2	4	no	—
213	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
214	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
216	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
218	#117	C₂×C₄×C₇	1	4	yes	—
219	#117	C₇×Q₈	1	4	yes	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
225	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
228	C₂×C₂²⋊C₄	—	2	2	no	—
229	C₂×C₂²⋊C₄	—	2	2	no	—
230	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
236	#107	—	2	4	no	—
237	#107	—	2	4	no	—
238	#106	—	2	4	no	—
239	#106	—	2	4	no	—
240	#97	C₂×C₄×C₇	1	4	yes	—
241	#97	C₂×C₄×C₇	1	4	yes	—
242	C₄×C₈	C₂×C₄×C₇	1	4	yes	—
243	C₄×C₈	C₂×C₄×C₇	1	4	yes	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	C₂²×C₇	—	2	2	no	—
251	C₂²×C₇	—	2	2	no	—
252	C₂²×C₇	—	2	2	no	—
253	C₂²×C₇	—	4	2	no	—
254	C₂²×C₇	—	4	2	no	—
255	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
256	C₂²×C₇	#532	1	2	yes	—
257	C₂²×C₇	#576	1	1	yes	characteristic
258	C₂²×C₇	#577	1	2	yes	—
259	C₂²×C₇	#578	1	1	yes	characteristic
260	C₄×C₇	—	2	2	no	—
261	C₄×C₇	—	2	2	no	—
262	C₄×C₇	—	2	2	no	—
263	C₄×C₇	—	2	2	no	—
264	C₄×C₇	—	2	2	no	—
265	C₄×C₇	—	8	2	no	—
266	C₄×C₇	—	8	2	no	—
267	C₄×C₇	—	8	2	no	—
268	C₄×C₇	—	8	2	no	—
269	C₄×C₇	C₂×#117	1	1	yes	characteristic
270	C₄×C₇	C₂×#117	1	1	yes	characteristic
271	C₄×C₇	#533	1	2	yes	—
272	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
280	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
287	M₁₆	—	2	8	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	8	no	—
291	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
292	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
293	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
294	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
295	C₂×C₈	C₇×#41	1	4	yes	—
296	C₂×C₈	C₇×#41	1	4	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	8	2	no	—
306	C₄⋊C₄	—	8	2	no	—
307	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
308	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
309	C₂²⋊C₄	—	8	2	no	—
310	C₂²⋊C₄	—	8	2	no	—
311	C₂²⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
312	C₂²⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
313	C₄²	—	8	2	no	—
314	C₄²	—	8	2	no	—
315	C₄²	C₂²×C₄×C₇	1	2	yes	—
316	C₄²	C₂²×C₄×C₇	1	2	yes	—
317	C₄²	C₂×C₇×Q₈	1	2	yes	—
318	C₄²	C₂×C₇×Q₈	1	2	yes	—
319	C₂×C₇	—	4	2	no	—
320	C₂×C₇	#2285	1	1	yes	characteristic
321	C₂×C₇	#2912	1	1	yes	characteristic
322	C₂×C₇	#2913	1	1	yes	characteristic
323	C₂×C₇	#3178	1	2	yes	—
324	C₂×C₇	#3179	1	2	yes	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	1	no	—
329	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
330	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
354	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
355	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
356	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
357	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
358	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
359	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
360	C₂×C₄	C₂×C₇×#41	1	2	yes	—
361	C₂×C₄	C₂×C₇×#41	1	2	yes	—
362	C₈	—	2	2	no	—
363	C₈	—	2	2	no	—
364	C₈	C₇×#117	1	4	yes	—
365	C₈	C₇×#117	1	4	yes	—
366	C₇	#20822	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
373	C₂²	C₇×#532	1	2	yes	—
374	C₂²	C₇×#576	1	1	yes	characteristic
375	C₂²	C₇×#577	1	2	yes	—
376	C₂²	C₇×#578	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₂×C₇×#117	1	1	yes	characteristic
387	C₄	C₂×C₇×#117	1	1	yes	characteristic
388	C₄	C₇×#533	1	2	yes	—
389	C₂	—	4	2	no	—
390	C₂	C₇×#2285	1	1	yes	characteristic
391	C₂	C₇×#2912	1	1	yes	characteristic
392	C₂	C₇×#2913	1	1	yes	characteristic
393	C₂	C₇×#3178	1	2	yes	—
394	C₂	C₇×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#1847	C₂	semidirect
4. C₇×#1835	C₂	semidirect
5. C₇×#1834	C₂	semidirect
9. C₇×#1776	C₂	semidirect
10. C₄×C₇×#107	C₂	semidirect
11. C₄×C₇×#106	C₂	semidirect
19. C₇×#405	C₄	semidirect
40. #20822	C₇	direct (N × H)
84. #1847	C₂×C₇	semidirect
85. #1835	C₂×C₇	semidirect
86. #1834	C₂×C₇	semidirect
90. #1776	C₂×C₇	semidirect
91. C₄×#107	C₂×C₇	semidirect
92. C₄×#106	C₂×C₇	semidirect
147. #405	C₄×C₇	semidirect
366. C₇	#20822	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#405	2
C₇×#2314	2
C₇×#1847	2
C₇×#1835	2
C₇×#1834	2
C₇×#1809	2
C₇×#1808	2
C₇×#1807	2
C₇×#1776	2
C₄×C₇×#107	2
C₄×C₇×#106	2
#20822	7

Subgroups — C7×#20822 #13198038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#20822 #13198038