Subgroups — C₇×#22664 #13199880

Order 1792.

978 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
3	C₇×#2352	C₂	1	2	yes	maximal
4	C₇×#1949	C₂	1	2	yes	maximal, complemented
5	C₇×#1854	C₂	1	2	yes	maximal, complemented
6	C₇×#1852	C₂	1	2	yes	maximal, complemented
7	C₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1809	C₂	1	2	yes	maximal, complemented
9	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
11	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₇×#117	C₂²	1	2	yes	—
13	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
14	C₇×#436	C₄	1	8	yes	complemented
15	C₇×#428	—	2	8	no	—
16	C₂×C₇×#107	C₂²	1	2	yes	—
17	C₂×C₇×#107	C₂²	1	1	yes	characteristic
18	C₂×C₇×#107	C₂²	1	1	yes	characteristic
19	C₂×C₇×#107	C₂²	1	1	yes	characteristic
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#106	C₂²	1	2	yes	—
22	C₂×C₇×#106	C₂²	1	2	yes	—
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
26	C₇×#388	—	2	2	no	—
27	C₇×#387	—	2	2	no	—
28	C₇×#386	—	2	2	no	—
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×C₂²⋊C₄	—	2	2	no	—
34	C₇×#340	C₂²	1	2	yes	—
35	C₇×#340	C₂²	1	2	yes	—
36	C₇×#340	C₂²	1	2	yes	—
37	#22664	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇	—	2	2	no	—
40	C₂³×C₄×C₇	C₂³	1	2	yes	—
41	C₂×C₇×M₁₆	—	2	4	no	—
42	C₂×C₇×M₁₆	—	2	4	no	—
43	C₂×C₇×M₁₆	C₂×C₄	1	8	yes	complemented
44	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇×C₈	C₂³	1	2	yes	—
46	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
47	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
48	C₄×C₇×D₄	Q₈	1	4	yes	—
49	C₇×#117	—	2	4	no	—
50	C₇×#117	—	4	2	no	—
51	C₂×C₇×C₄⋊C₄	—	2	4	no	—
52	C₂×C₇×C₄⋊C₄	—	2	2	no	—
53	C₂×C₇×C₄⋊C₄	—	4	2	no	—
54	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
63	C₂×C₄²×C₇	—	2	2	no	—
64	C₂×C₄²×C₇	—	2	2	no	—
65	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
66	C₇×#107	—	2	2	no	—
67	C₇×#107	—	2	4	no	—
68	C₇×#107	—	4	1	no	—
69	C₇×#107	—	4	1	no	—
70	C₇×#107	D₄	1	4	yes	complemented
71	C₇×#106	—	2	4	no	—
72	C₇×#106	—	2	4	no	—
73	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
74	C₇×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
75	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
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	C₂×#436	C₂×C₇	1	1	yes	characteristic
82	C₂×#428	C₂×C₇	1	2	yes	complemented
83	#2352	C₂×C₇	1	2	yes	—
84	#1949	C₂×C₇	1	2	yes	complemented
85	#1854	C₂×C₇	1	2	yes	complemented
86	#1852	C₂×C₇	1	2	yes	complemented
87	#1846	C₂×C₇	1	1	yes	characteristic, complemented
88	#1809	C₂×C₇	1	2	yes	complemented
89	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂⁴×C₇	C₂×D₄	1	2	yes	—
91	C₂×C₇×D₄	—	4	1	no	—
92	C₂×C₇×D₄	—	4	1	no	—
93	C₂×C₇×D₄	C₄⋊C₄	1	4	yes	—
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	—	2	2	no	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	—	4	4	no	—
103	C₂²×C₄×C₇	—	4	4	no	—
104	C₂²×C₄×C₇	—	8	2	no	—
105	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
111	C₇×M₁₆	—	2	16	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	C₂²×C₄	1	2	yes	—
117	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
118	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
119	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
120	C₂×C₇×C₈	#41	1	2	yes	—
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	—	2	2	no	—
127	C₇×C₄⋊C₄	—	2	2	no	—
128	C₇×C₄⋊C₄	—	4	4	no	—
129	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
130	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
131	C₇×C₂²⋊C₄	—	4	4	no	—
132	C₇×C₂²⋊C₄	—	4	4	no	—
133	C₇×C₂²⋊C₄	—	8	2	no	—
134	C₇×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
135	C₄²×C₇	—	4	4	no	—
136	C₄²×C₇	—	8	2	no	—
137	C₄²×C₇	C₂²×C₄	1	2	yes	—
138	C₄²×C₇	C₂×Q₈	1	2	yes	—
139	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
140	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
141	C₂×#117	C₂²×C₇	1	2	yes	—
142	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
143	#436	C₄×C₇	1	8	yes	complemented
144	#428	—	2	8	no	—
145	C₂×#107	C₂²×C₇	1	1	yes	characteristic
146	C₂×#107	C₂²×C₇	1	2	yes	—
147	C₂×#107	C₂²×C₇	1	1	yes	characteristic
148	C₂×#107	C₂²×C₇	1	1	yes	characteristic
149	C₂×#107	C₂²×C₇	1	1	yes	characteristic
150	C₂×#106	C₂²×C₇	1	2	yes	—
151	C₂×#106	C₂²×C₇	1	2	yes	—
152	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
153	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
154	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
155	#388	—	2	2	no	—
156	#387	—	2	2	no	—
157	#386	—	2	2	no	—
158	#382	C₂²×C₇	1	2	yes	—
159	#380	C₂²×C₇	1	2	yes	—
160	#380	C₂²×C₇	1	2	yes	—
161	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
162	C₄×C₂²⋊C₄	—	2	2	no	—
163	#340	C₂²×C₇	1	2	yes	—
164	#340	C₂²×C₇	1	2	yes	—
165	#340	C₂²×C₇	1	2	yes	—
166	C₂³×C₇	—	2	2	no	—
167	C₂³×C₇	—	2	2	no	—
168	C₂³×C₇	—	2	2	no	—
169	C₂³×C₇	—	2	2	no	—
170	C₂³×C₇	—	2	2	no	—
171	C₂³×C₇	—	2	2	no	—
172	C₂³×C₇	C₂×C₄⋊C₄	1	4	yes	—
173	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
174	C₇×D₄	—	4	4	no	—
175	C₂×C₄×C₇	—	2	2	no	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	2	1	no	—
178	C₂×C₄×C₇	—	2	1	no	—
179	C₂×C₄×C₇	—	2	1	no	—
180	C₂×C₄×C₇	—	2	1	no	—
181	C₂×C₄×C₇	—	2	4	no	—
182	C₂×C₄×C₇	—	2	4	no	—
183	C₂×C₄×C₇	—	2	4	no	—
184	C₂×C₄×C₇	—	2	4	no	—
185	C₂×C₄×C₇	—	2	4	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	—	4	2	no	—
197	C₂×C₄×C₇	—	8	8	no	—
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	4	yes	—
201	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
207	C₇×C₈	—	2	4	no	—
208	C₇×C₈	—	2	2	no	—
209	C₇×C₈	C₄×D₄	1	4	yes	—
210	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
211	C₂³×C₄	—	2	2	no	—
212	C₂³×C₄	C₂³×C₇	1	2	yes	—
213	C₂×M₁₆	—	2	4	no	—
214	C₂×M₁₆	—	2	4	no	—
215	C₂×M₁₆	C₂×C₄×C₇	1	8	yes	complemented
216	C₂²×C₈	C₂³×C₇	1	2	yes	—
217	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
219	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
220	C₄×D₄	C₇×Q₈	1	4	yes	—
221	#117	—	2	4	no	—
222	#117	—	4	2	no	—
223	C₂×C₄⋊C₄	—	2	4	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	4	2	no	—
226	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
229	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
230	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
231	C₂×C₂²⋊C₄	—	2	2	no	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
238	#107	—	2	2	no	—
239	#107	—	2	4	no	—
240	#107	—	4	1	no	—
241	#107	—	4	1	no	—
242	#107	C₇×D₄	1	4	yes	complemented
243	#106	—	2	4	no	—
244	#106	—	2	4	no	—
245	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
246	C₂²⋊C₈	C₂×C₄×C₇	1	8	yes	complemented
247	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	—	2	2	no	—
253	C₂²×C₇	—	2	4	no	—
254	C₂²×C₇	—	2	4	no	—
255	C₂²×C₇	—	2	4	no	—
256	C₂²×C₇	—	4	2	no	—
257	C₂²×C₇	—	4	2	no	—
258	C₂²×C₇	—	4	2	no	—
259	C₂²×C₇	—	4	2	no	—
260	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
261	C₂²×C₇	D₄²	1	1	yes	characteristic
262	C₂²×C₇	#547	1	1	yes	characteristic
263	C₂²×C₇	#575	1	1	yes	characteristic
264	C₂²×C₇	#575	1	1	yes	characteristic
265	C₂²×C₇	#576	1	1	yes	characteristic
266	C₂²×C₇	#578	1	1	yes	characteristic
267	C₄×C₇	—	2	4	no	—
268	C₄×C₇	—	2	2	no	—
269	C₄×C₇	—	2	2	no	—
270	C₄×C₇	—	4	4	no	—
271	C₄×C₇	—	8	2	no	—
272	C₄×C₇	—	8	2	no	—
273	C₄×C₇	—	8	2	no	—
274	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
275	C₄×C₇	#520	1	1	yes	characteristic
276	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
277	C₄×C₇	#554	1	1	yes	characteristic
278	C₂⁴	C₂×C₇×D₄	1	2	yes	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	C₇×C₄⋊C₄	1	4	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	8	2	no	—
293	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
294	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
297	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
298	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
299	M₁₆	—	2	16	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
305	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
306	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
307	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
308	C₂×C₈	C₇×#41	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
318	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₂²⋊C₄	C₇×C₄⋊C₄	1	8	yes	—
323	C₄²	—	4	4	no	—
324	C₄²	—	8	2	no	—
325	C₄²	C₂²×C₄×C₇	1	2	yes	—
326	C₄²	C₂×C₇×Q₈	1	2	yes	—
327	C₂×C₇	—	4	4	no	—
328	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
329	C₂×C₇	#2911	1	1	yes	characteristic
330	C₂×C₇	#2913	1	1	yes	characteristic
331	C₂×C₇	#3273	1	1	yes	characteristic
332	C₂×C₇	#3277	1	1	yes	characteristic
333	C₂×C₇	#3352	1	1	yes	characteristic
334	C₂×C₇	#3355	1	1	yes	characteristic
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	C₂×C₇×C₄⋊C₄	1	4	yes	—
342	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
343	D₄	—	4	4	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	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	8	8	no	—
367	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
368	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
369	C₂×C₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
370	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
373	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
374	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
376	C₈	—	2	4	no	—
377	C₈	—	2	2	no	—
378	C₈	C₄×C₇×D₄	1	4	yes	—
379	C₇	#22664	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
388	C₂²	C₇×D₄²	1	1	yes	characteristic
389	C₂²	C₇×#547	1	1	yes	characteristic
390	C₂²	C₇×#575	1	1	yes	characteristic
391	C₂²	C₇×#575	1	1	yes	characteristic
392	C₂²	C₇×#576	1	1	yes	characteristic
393	C₂²	C₇×#578	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	4	no	—
397	C₄	—	4	4	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	2	no	—
401	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
402	C₄	C₇×#520	1	1	yes	characteristic
403	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
404	C₄	C₇×#554	1	1	yes	characteristic
405	C₂	—	4	4	no	—
406	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
407	C₂	C₇×#2911	1	1	yes	characteristic
408	C₂	C₇×#2913	1	1	yes	characteristic
409	C₂	C₇×#3273	1	1	yes	characteristic
410	C₂	C₇×#3277	1	1	yes	characteristic
411	C₂	C₇×#3352	1	1	yes	characteristic
412	C₂	C₇×#3355	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#428	C₂	semidirect
4. C₇×#1949	C₂	semidirect
5. C₇×#1854	C₂	semidirect
6. C₇×#1852	C₂	semidirect
7. C₇×#1846	C₂	semidirect
8. C₇×#1809	C₂	semidirect
9. C₄×C₇×#107	C₂	semidirect
14. C₇×#436	C₄	semidirect
37. #22664	C₇	direct (N × H)
43. C₂×C₇×M₁₆	C₂×C₄	semidirect
70. C₇×#107	D₄	semidirect
73. C₇×C₄⋊C₈	C₂×C₄	semidirect
74. C₇×C₂²⋊C₈	C₂×C₄	semidirect
75. C₄×C₇×C₈	C₂×C₄	semidirect
82. C₂×#428	C₂×C₇	semidirect
84. #1949	C₂×C₇	semidirect
85. #1854	C₂×C₇	semidirect
86. #1852	C₂×C₇	semidirect
87. #1846	C₂×C₇	semidirect
88. #1809	C₂×C₇	semidirect
89. C₄×#107	C₂×C₇	semidirect
143. #436	C₄×C₇	semidirect
215. C₂×M₁₆	C₂×C₄×C₇	semidirect
242. #107	C₇×D₄	semidirect
245. C₄⋊C₈	C₂×C₄×C₇	semidirect
246. C₂²⋊C₈	C₂×C₄×C₇	semidirect
247. C₄×C₈	C₂×C₄×C₇	semidirect
379. C₇	#22664	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×#436	2
C₂×C₇×#428	2
C₇×#2352	2
C₇×#1949	2
C₇×#1854	2
C₇×#1852	2
C₇×#1846	2
C₇×#1809	2
C₄×C₇×#107	2
#22664	7

Subgroups — C7×#22664 #13199880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22664 #13199880