Subgroups — C₇×#22666 #13199882

Order 1792.

978 conjugacy classes of subgroups.

The subgroup lattice has 400 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×#1853	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×#106	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	2	yes	—
18	C₂×C₇×#106	C₂²	1	2	yes	—
19	C₂×C₇×#106	C₂²	1	1	yes	characteristic
20	C₂×C₇×#106	C₂²	1	1	yes	characteristic
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
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	#22666	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	4	no	—
67	C₇×#107	—	2	4	no	—
68	C₇×#106	—	2	2	no	—
69	C₇×#106	—	2	4	no	—
70	C₇×#106	—	4	1	no	—
71	C₇×#106	—	4	1	no	—
72	C₇×#106	D₄	1	4	yes	complemented
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	#1853	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×#106	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂⁴×C₇	C₂×D₄	1	2	yes	—
91	C₂×C₇×D₄	—	4	2	no	—
92	C₂×C₇×D₄	C₄⋊C₄	1	4	yes	—
93	C₂²×C₄×C₇	—	2	2	no	—
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	—	4	4	no	—
102	C₂²×C₄×C₇	—	4	4	no	—
103	C₂²×C₄×C₇	—	8	2	no	—
104	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
110	C₇×M₁₆	—	2	16	no	—
111	C₂×C₇×C₈	—	2	2	no	—
112	C₂×C₇×C₈	—	2	2	no	—
113	C₂×C₇×C₈	—	2	1	no	—
114	C₂×C₇×C₈	—	2	1	no	—
115	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
116	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
117	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
118	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
119	C₂×C₇×C₈	#41	1	2	yes	—
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	—	2	2	no	—
127	C₇×C₄⋊C₄	—	4	4	no	—
128	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
129	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
130	C₇×C₂²⋊C₄	—	4	4	no	—
131	C₇×C₂²⋊C₄	—	4	4	no	—
132	C₇×C₂²⋊C₄	—	8	2	no	—
133	C₇×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
134	C₄²×C₇	—	4	4	no	—
135	C₄²×C₇	—	8	2	no	—
136	C₄²×C₇	C₂²×C₄	1	2	yes	—
137	C₄²×C₇	C₂×Q₈	1	2	yes	—
138	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
139	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
140	C₂×#117	C₂²×C₇	1	2	yes	—
141	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
142	#436	C₄×C₇	1	8	yes	complemented
143	#428	—	2	8	no	—
144	C₂×#107	C₂²×C₇	1	2	yes	—
145	C₂×#107	C₂²×C₇	1	2	yes	—
146	C₂×#106	C₂²×C₇	1	1	yes	characteristic
147	C₂×#106	C₂²×C₇	1	2	yes	—
148	C₂×#106	C₂²×C₇	1	1	yes	characteristic
149	C₂×#106	C₂²×C₇	1	1	yes	characteristic
150	C₂×#106	C₂²×C₇	1	1	yes	characteristic
151	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
152	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
153	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
154	#388	—	2	2	no	—
155	#387	—	2	2	no	—
156	#386	—	2	2	no	—
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×C₂²⋊C₄	—	2	2	no	—
162	#340	C₂²×C₇	1	2	yes	—
163	#340	C₂²×C₇	1	2	yes	—
164	#340	C₂²×C₇	1	2	yes	—
165	C₂³×C₇	—	2	2	no	—
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	C₂×C₄⋊C₄	1	4	yes	—
172	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
173	C₇×D₄	—	4	4	no	—
174	C₂×C₄×C₇	—	2	2	no	—
175	C₂×C₄×C₇	—	2	2	no	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	2	2	no	—
178	C₂×C₄×C₇	—	2	4	no	—
179	C₂×C₄×C₇	—	2	4	no	—
180	C₂×C₄×C₇	—	2	4	no	—
181	C₂×C₄×C₇	—	2	4	no	—
182	C₂×C₄×C₇	—	2	4	no	—
183	C₂×C₄×C₇	—	4	2	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	—	8	8	no	—
195	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
196	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
197	C₂×C₄×C₇	C₂×C₄⋊C₄	1	4	yes	—
198	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
204	C₇×C₈	—	2	4	no	—
205	C₇×C₈	—	2	2	no	—
206	C₇×C₈	C₄×D₄	1	4	yes	—
207	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
208	C₂³×C₄	—	2	2	no	—
209	C₂³×C₄	C₂³×C₇	1	2	yes	—
210	C₂×M₁₆	—	2	4	no	—
211	C₂×M₁₆	—	2	4	no	—
212	C₂×M₁₆	C₂×C₄×C₇	1	8	yes	complemented
213	C₂²×C₈	C₂³×C₇	1	2	yes	—
214	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
216	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
217	C₄×D₄	C₇×Q₈	1	4	yes	—
218	#117	—	2	4	no	—
219	#117	—	4	2	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	4	2	no	—
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	—	2	2	no	—
231	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
235	#107	—	2	4	no	—
236	#107	—	2	4	no	—
237	#106	—	2	2	no	—
238	#106	—	2	4	no	—
239	#106	—	4	1	no	—
240	#106	—	4	1	no	—
241	#106	C₇×D₄	1	4	yes	complemented
242	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
243	C₂²⋊C₈	C₂×C₄×C₇	1	8	yes	complemented
244	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
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	4	no	—
251	C₂²×C₇	—	2	4	no	—
252	C₂²×C₇	—	2	4	no	—
253	C₂²×C₇	—	4	2	no	—
254	C₂²×C₇	—	4	2	no	—
255	C₂²×C₇	—	4	2	no	—
256	C₂²×C₇	—	4	2	no	—
257	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₇	D₄²	1	1	yes	characteristic
259	C₂²×C₇	#547	1	1	yes	characteristic
260	C₂²×C₇	#575	1	2	yes	—
261	C₂²×C₇	#577	1	2	yes	—
262	C₄×C₇	—	2	4	no	—
263	C₄×C₇	—	2	2	no	—
264	C₄×C₇	—	2	2	no	—
265	C₄×C₇	—	4	4	no	—
266	C₄×C₇	—	8	2	no	—
267	C₄×C₇	—	8	2	no	—
268	C₄×C₇	—	8	2	no	—
269	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₇	#520	1	1	yes	characteristic
271	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
272	C₄×C₇	#554	1	1	yes	characteristic
273	C₂⁴	C₂×C₇×D₄	1	2	yes	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	C₇×C₄⋊C₄	1	4	yes	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	4	4	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	8	2	no	—
287	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
288	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
291	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
292	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
293	M₁₆	—	2	16	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
299	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
300	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
301	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
302	C₂×C₈	C₇×#41	1	2	yes	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
312	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
313	C₂²⋊C₄	—	4	4	no	—
314	C₂²⋊C₄	—	4	4	no	—
315	C₂²⋊C₄	—	8	2	no	—
316	C₂²⋊C₄	C₇×C₄⋊C₄	1	8	yes	—
317	C₄²	—	4	4	no	—
318	C₄²	—	8	2	no	—
319	C₄²	C₂²×C₄×C₇	1	2	yes	—
320	C₄²	C₂×C₇×Q₈	1	2	yes	—
321	C₂×C₇	—	4	4	no	—
322	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₇	#2911	1	1	yes	characteristic
324	C₂×C₇	#2912	1	1	yes	characteristic
325	C₂×C₇	#3275	1	2	yes	—
326	C₂×C₇	#3351	1	2	yes	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	C₂×C₇×C₄⋊C₄	1	4	yes	—
334	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
335	D₄	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	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	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	8	8	no	—
357	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
358	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
359	C₂×C₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
360	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
361	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
362	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
363	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
364	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
366	C₈	—	2	4	no	—
367	C₈	—	2	2	no	—
368	C₈	C₄×C₇×D₄	1	4	yes	—
369	C₇	#22666	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²	—	2	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
378	C₂²	C₇×D₄²	1	1	yes	characteristic
379	C₂²	C₇×#547	1	1	yes	characteristic
380	C₂²	C₇×#575	1	2	yes	—
381	C₂²	C₇×#577	1	2	yes	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	4	no	—
385	C₄	—	4	4	no	—
386	C₄	—	8	2	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	2	no	—
389	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
390	C₄	C₇×#520	1	1	yes	characteristic
391	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
392	C₄	C₇×#554	1	1	yes	characteristic
393	C₂	—	4	4	no	—
394	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
395	C₂	C₇×#2911	1	1	yes	characteristic
396	C₂	C₇×#2912	1	1	yes	characteristic
397	C₂	C₇×#3275	1	2	yes	—
398	C₂	C₇×#3351	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	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×#1853	C₂	semidirect
7. C₇×#1846	C₂	semidirect
8. C₇×#1809	C₂	semidirect
9. C₄×C₇×#106	C₂	semidirect
14. C₇×#436	C₄	semidirect
37. #22666	C₇	direct (N × H)
43. C₂×C₇×M₁₆	C₂×C₄	semidirect
72. C₇×#106	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. #1853	C₂×C₇	semidirect
87. #1846	C₂×C₇	semidirect
88. #1809	C₂×C₇	semidirect
89. C₄×#106	C₂×C₇	semidirect
142. #436	C₄×C₇	semidirect
212. C₂×M₁₆	C₂×C₄×C₇	semidirect
241. #106	C₇×D₄	semidirect
242. C₄⋊C₈	C₂×C₄×C₇	semidirect
243. C₂²⋊C₈	C₂×C₄×C₇	semidirect
244. C₄×C₈	C₂×C₄×C₇	semidirect
369. C₇	#22666	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×#1853	2
C₇×#1846	2
C₇×#1809	2
C₄×C₇×#106	2
#22666	7

Subgroups — C7×#22666 #13199882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22666 #13199882