Subgroups — C₇×#22829 #13200045

Order 1792.

636 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2295	C₂	1	1	yes	maximal, characteristic
2	C₇×#1984	C₂	1	1	yes	maximal, characteristic
3	C₇×#1984	C₂	1	1	yes	maximal, characteristic
4	C₇×#1917	C₂	1	2	yes	maximal
5	C₇×#1916	C₂	1	2	yes	maximal
6	C₇×#1840	C₂	1	2	yes	maximal
7	C₇×#1831	C₂	1	1	yes	maximal, characteristic
8	C₇×#1770	C₂	1	1	yes	maximal, characteristic
9	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₇×#1746	C₂	1	2	yes	maximal
12	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×#97	C₂²	1	2	yes	—
18	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
21	C₇×#391	C₄	1	1	yes	characteristic
22	C₇×#391	C₄	1	1	yes	characteristic
23	C₇×#389	C₄	1	1	yes	characteristic
24	C₇×#389	C₄	1	1	yes	characteristic
25	C₇×#387	C₄	1	2	yes	—
26	C₇×#387	C₄	1	2	yes	—
27	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
29	C₇×#376	C₂²	1	2	yes	—
30	C₄³×C₇	C₂²	1	1	yes	characteristic
31	C₇×#336	C₂²	1	2	yes	—
32	C₇×#336	C₂²	1	2	yes	—
33	C₇×#336	C₂²	1	2	yes	—
34	C₇×#336	C₂²	1	2	yes	—
35	C₇×#336	C₂²	1	1	yes	characteristic
36	C₇×#336	C₂²	1	2	yes	—
37	C₇×#336	C₂²	1	1	yes	characteristic
38	C₇×#336	C₂²	1	2	yes	—
39	C₇×#336	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	#22829	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₇×C₈	C₂³	1	2	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	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₄×C₇×Q₈	—	2	2	no	—
50	C₄×C₇×Q₈	—	2	2	no	—
51	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₇	C₂³	1	2	yes	—
63	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₇	C₂³	1	2	yes	—
65	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
66	C₇×C₄⋊C₈	—	2	2	no	—
67	C₇×C₄⋊C₈	—	2	2	no	—
68	C₇×C₄⋊C₈	—	2	2	no	—
69	C₇×C₄⋊C₈	—	2	2	no	—
70	C₇×#97	—	2	4	no	—
71	C₄×C₇×C₈	—	2	4	no	—
72	C₄×C₇×C₈	—	2	2	no	—
73	C₄×C₇×C₈	—	2	2	no	—
74	C₇×#95	C₂×C₄	1	2	yes	—
75	C₇×#95	C₂×C₄	1	2	yes	—
76	C₇×#95	C₂×C₄	1	2	yes	—
77	C₇×#95	C₂×C₄	1	2	yes	—
78	C₇×#95	C₂×C₄	1	2	yes	—
79	C₇×#95	C₂×C₄	1	2	yes	—
80	C₇×#95	C₂×C₄	1	2	yes	—
81	#2295	C₂×C₇	1	1	yes	characteristic
82	#1984	C₂×C₇	1	1	yes	characteristic
83	#1984	C₂×C₇	1	1	yes	characteristic
84	#1917	C₂×C₇	1	2	yes	—
85	#1916	C₂×C₇	1	2	yes	—
86	#1840	C₂×C₇	1	2	yes	—
87	#1831	C₂×C₇	1	1	yes	characteristic
88	#1770	C₂×C₇	1	1	yes	characteristic
89	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
90	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic
91	#1746	C₂×C₇	1	2	yes	—
92	C₂×C₇×Q₈	—	2	2	no	—
93	C₂×C₇×Q₈	—	2	2	no	—
94	C₂×C₇×Q₈	—	2	2	no	—
95	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
106	C₂×C₇×C₈	—	2	1	no	—
107	C₂×C₇×C₈	—	2	1	no	—
108	C₂×C₇×C₈	—	2	1	no	—
109	C₂×C₇×C₈	—	2	1	no	—
110	C₂×C₇×C₈	—	2	1	no	—
111	C₂×C₇×C₈	—	2	1	no	—
112	C₂×C₇×C₈	—	2	2	no	—
113	C₂×C₇×C₈	—	2	2	no	—
114	C₂×C₇×C₈	—	2	1	no	—
115	C₂×C₇×C₈	—	2	1	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	—	2	1	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	#41	1	2	yes	—
123	C₂×C₇×C₈	#41	1	2	yes	—
124	C₇×C₄⋊C₄	—	2	2	no	—
125	C₇×C₄⋊C₄	—	2	4	no	—
126	C₇×C₄⋊C₄	—	2	4	no	—
127	C₇×C₄⋊C₄	—	2	2	no	—
128	C₇×C₄⋊C₄	—	2	2	no	—
129	C₇×C₄⋊C₄	—	4	2	no	—
130	C₄²×C₇	—	2	2	no	—
131	C₄²×C₇	—	2	2	no	—
132	C₄²×C₇	—	2	2	no	—
133	C₄²×C₇	—	2	2	no	—
134	C₄²×C₇	—	2	2	no	—
135	C₄²×C₇	—	2	1	no	—
136	C₄²×C₇	—	2	1	no	—
137	C₄²×C₇	—	2	2	no	—
138	C₄²×C₇	—	2	2	no	—
139	C₄²×C₇	—	2	1	no	—
140	C₄²×C₇	—	2	1	no	—
141	C₄²×C₇	—	4	1	no	—
142	C₄²×C₇	#41	1	2	yes	—
143	C₄²×C₇	#41	1	2	yes	—
144	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
145	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
146	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
147	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
148	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
149	C₂×#97	C₂²×C₇	1	2	yes	—
150	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
151	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
152	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
153	#391	C₄×C₇	1	1	yes	characteristic
154	#391	C₄×C₇	1	1	yes	characteristic
155	#389	C₄×C₇	1	1	yes	characteristic
156	#389	C₄×C₇	1	1	yes	characteristic
157	#387	C₄×C₇	1	2	yes	—
158	#387	C₄×C₇	1	2	yes	—
159	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
160	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
161	#376	C₂²×C₇	1	2	yes	—
162	C₄³	C₂²×C₇	1	1	yes	characteristic
163	#336	C₂²×C₇	1	2	yes	—
164	#336	C₂²×C₇	1	2	yes	—
165	#336	C₂²×C₇	1	1	yes	characteristic
166	#336	C₂²×C₇	1	2	yes	—
167	#336	C₂²×C₇	1	2	yes	—
168	#336	C₂²×C₇	1	2	yes	—
169	#336	C₂²×C₇	1	2	yes	—
170	#336	C₂²×C₇	1	2	yes	—
171	#336	C₂²×C₇	1	2	yes	—
172	#336	C₂²×C₇	1	1	yes	characteristic
173	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
174	C₇×Q₈	—	4	4	no	—
175	C₂×C₄×C₇	—	2	1	no	—
176	C₂×C₄×C₇	—	2	1	no	—
177	C₂×C₄×C₇	—	2	1	no	—
178	C₂×C₄×C₇	—	2	1	no	—
179	C₂×C₄×C₇	—	2	2	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	2	2	no	—
183	C₂×C₄×C₇	—	2	1	no	—
184	C₂×C₄×C₇	—	2	1	no	—
185	C₂×C₄×C₇	—	2	1	no	—
186	C₂×C₄×C₇	—	2	1	no	—
187	C₂×C₄×C₇	—	2	1	no	—
188	C₂×C₄×C₇	—	2	1	no	—
189	C₂×C₄×C₇	—	2	1	no	—
190	C₂×C₄×C₇	—	2	2	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	2	no	—
193	C₂×C₄×C₇	—	2	2	no	—
194	C₂×C₄×C₇	—	2	2	no	—
195	C₂×C₄×C₇	—	2	2	no	—
196	C₂×C₄×C₇	—	2	1	no	—
197	C₂×C₄×C₇	—	2	1	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	2	2	no	—
200	C₂×C₄×C₇	#117	1	2	yes	—
201	C₂×C₄×C₇	#117	1	2	yes	—
202	C₂×C₄×C₇	#131	1	2	yes	—
203	C₂×C₄×C₇	#131	1	2	yes	—
204	C₂×C₄×C₇	#131	1	2	yes	—
205	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
211	C₇×C₈	—	2	2	no	—
212	C₇×C₈	—	2	2	no	—
213	C₇×C₈	—	4	1	no	—
214	C₇×C₈	—	4	1	no	—
215	C₇×C₈	—	4	2	no	—
216	C₇×C₈	—	4	2	no	—
217	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₇	1	2	yes	—
219	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
220	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₇	1	2	yes	—
222	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
224	C₄×Q₈	—	2	2	no	—
225	C₄×Q₈	—	2	2	no	—
226	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
232	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₇	1	2	yes	—
237	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₇	1	2	yes	—
240	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	—	2	2	no	—
245	#97	—	2	4	no	—
246	C₄×C₈	—	2	4	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	#95	C₂×C₄×C₇	1	2	yes	—
250	#95	C₂×C₄×C₇	1	2	yes	—
251	#95	C₂×C₄×C₇	1	2	yes	—
252	#95	C₂×C₄×C₇	1	2	yes	—
253	#95	C₂×C₄×C₇	1	2	yes	—
254	#95	C₂×C₄×C₇	1	2	yes	—
255	#95	C₂×C₄×C₇	1	2	yes	—
256	C₂²×C₇	C₂×#117	1	1	yes	characteristic
257	C₂²×C₇	C₄×#41	1	1	yes	characteristic
258	C₂²×C₇	#519	1	1	yes	characteristic
259	C₂²×C₇	C₂×#131	1	1	yes	characteristic
260	C₂²×C₇	C₂×#131	1	1	yes	characteristic
261	C₂²×C₇	C₂×#131	1	1	yes	characteristic
262	C₂²×C₇	#568	1	1	yes	characteristic
263	C₄×C₇	—	2	2	no	—
264	C₄×C₇	—	2	2	no	—
265	C₄×C₇	—	4	2	no	—
266	C₄×C₇	—	4	2	no	—
267	C₄×C₇	—	4	2	no	—
268	C₄×C₇	—	4	1	no	—
269	C₄×C₇	—	4	2	no	—
270	C₄×C₇	—	4	1	no	—
271	C₄×C₇	—	4	1	no	—
272	C₄×C₇	#433	1	4	yes	—
273	C₄×C₇	#552	1	1	yes	characteristic
274	C₄×C₇	#552	1	1	yes	characteristic
275	C₄×C₇	#556	1	1	yes	characteristic
276	C₄×C₇	#556	1	1	yes	characteristic
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
290	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	C₇×#41	1	2	yes	—
308	C₂×C₈	C₇×#41	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	4	1	no	—
327	C₄²	C₇×#41	1	2	yes	—
328	C₄²	C₇×#41	1	2	yes	—
329	C₂×C₇	#2356	1	1	yes	characteristic
330	C₂×C₇	C₂×#433	1	1	yes	characteristic
331	C₂×C₇	#2925	1	1	yes	characteristic
332	C₂×C₇	#2966	1	1	yes	characteristic
333	C₂×C₇	#2969	1	1	yes	characteristic
334	C₂×C₇	#2985	1	1	yes	characteristic
335	C₂×C₇	#2986	1	1	yes	characteristic
336	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
337	Q₈	—	4	4	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	C₇×#117	1	2	yes	—
364	C₂×C₄	C₇×#117	1	2	yes	—
365	C₂×C₄	C₇×#131	1	2	yes	—
366	C₂×C₄	C₇×#131	1	2	yes	—
367	C₂×C₄	C₇×#131	1	2	yes	—
368	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
369	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
370	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
371	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
372	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
373	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
374	C₈	—	2	2	no	—
375	C₈	—	2	2	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₇	#22829	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²	C₂×C₇×#117	1	1	yes	characteristic
382	C₂²	C₄×C₇×#41	1	1	yes	characteristic
383	C₂²	C₇×#519	1	1	yes	characteristic
384	C₂²	C₂×C₇×#131	1	1	yes	characteristic
385	C₂²	C₂×C₇×#131	1	1	yes	characteristic
386	C₂²	C₂×C₇×#131	1	1	yes	characteristic
387	C₂²	C₇×#568	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	C₇×#433	1	4	yes	—
398	C₄	C₇×#552	1	1	yes	characteristic
399	C₄	C₇×#552	1	1	yes	characteristic
400	C₄	C₇×#556	1	1	yes	characteristic
401	C₄	C₇×#556	1	1	yes	characteristic
402	C₂	C₇×#2356	1	1	yes	characteristic
403	C₂	C₂×C₇×#433	1	1	yes	characteristic
404	C₂	C₇×#2925	1	1	yes	characteristic
405	C₂	C₇×#2966	1	1	yes	characteristic
406	C₂	C₇×#2969	1	1	yes	characteristic
407	C₂	C₇×#2985	1	1	yes	characteristic
408	C₂	C₇×#2986	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
41. #22829	C₇	direct (N × H)
380. C₇	#22829	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×#2295	2
C₇×#1984	2
C₇×#1917	2
C₇×#1916	2
C₇×#1840	2
C₇×#1831	2
C₇×#1770	2
C₇×C₈×C₄⋊C₄	2
C₄×C₇×C₄⋊C₈	2
C₇×#1746	2
#22829	7

Subgroups — C7×#22829 #13200045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22829 #13200045