Subgroups — C₇×#22700 #13199916

Order 1792.

1020 conjugacy classes of subgroups.

The subgroup lattice has 406 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	2	yes	maximal
2	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#1939	C₂	1	2	yes	maximal, complemented
4	C₇×#1851	C₂	1	4	yes	maximal, complemented
5	C₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1797	C₂	1	2	yes	maximal, complemented
7	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1728	C₂	1	2	yes	maximal, complemented
9	C₂²×C₇×M₁₆	C₂²	1	4	yes	—
10	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
11	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
12	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₇	C₂²	1	2	yes	—
14	C₇×#436	—	2	8	no	—
15	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	—
18	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	—
19	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
20	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
22	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₄×C₇×C₂²⋊C₄	C₄	1	2	yes	—
24	C₄×C₇×C₂²⋊C₄	C₄	1	2	yes	—
25	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₄³×C₇	C₂²	1	1	yes	characteristic
27	C₇×#336	C₂²	1	1	yes	characteristic
28	C₇×#336	C₂²	1	2	yes	—
29	C₇×#336	C₂²	1	4	yes	—
30	C₇×#336	C₂²	1	1	yes	characteristic
31	C₇×#336	C₂²	1	2	yes	—
32	#22700	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₇	C₂³	1	2	yes	—
37	C₂×C₇×M₁₆	—	2	8	no	—
38	C₂×C₇×M₁₆	—	2	8	no	—
39	C₂×C₇×M₁₆	—	4	4	no	—
40	C₂²×C₇×C₈	C₂³	1	4	yes	—
41	C₂²×C₇×C₈	C₂³	1	2	yes	—
42	C₂²×C₇×C₈	C₂³	1	2	yes	—
43	C₄×C₇×D₄	—	2	4	no	—
44	C₄×C₇×D₄	—	2	4	no	—
45	C₄×C₇×D₄	D₄	1	4	yes	—
46	C₄×C₇×D₄	Q₈	1	4	yes	—
47	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₇	—	4	4	no	—
54	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₇	C₂³	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	C₇×C₄⋊C₈	—	2	4	no	—
65	C₇×C₄⋊C₈	—	2	4	no	—
66	C₇×C₄⋊C₈	—	4	4	no	—
67	C₇×C₂²⋊C₈	—	2	8	no	—
68	C₄×C₇×C₈	—	2	4	no	—
69	C₇×#95	C₂×C₄	1	2	yes	—
70	C₇×#95	C₂×C₄	1	2	yes	—
71	C₇×#95	C₂×C₄	1	2	yes	—
72	C₂×#436	C₂×C₇	1	2	yes	—
73	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
74	#1939	C₂×C₇	1	2	yes	complemented
75	#1851	C₂×C₇	1	4	yes	complemented
76	#1831	C₂×C₇	1	1	yes	characteristic, complemented
77	#1797	C₂×C₇	1	2	yes	complemented
78	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
79	#1728	C₂×C₇	1	2	yes	complemented
80	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
81	C₂×C₇×D₄	—	2	2	no	—
82	C₂×C₇×D₄	—	2	2	no	—
83	C₂×C₇×D₄	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₇	—	2	4	no	—
85	C₂²×C₄×C₇	—	2	4	no	—
86	C₂²×C₄×C₇	—	2	4	no	—
87	C₂²×C₄×C₇	—	2	4	no	—
88	C₂²×C₄×C₇	—	2	4	no	—
89	C₂²×C₄×C₇	—	4	2	no	—
90	C₂²×C₄×C₇	—	4	2	no	—
91	C₂²×C₄×C₇	—	4	2	no	—
92	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
99	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
104	C₇×M₁₆	—	4	16	no	—
105	C₂×C₇×C₈	—	2	2	no	—
106	C₂×C₇×C₈	—	2	2	no	—
107	C₂×C₇×C₈	—	2	2	no	—
108	C₂×C₇×C₈	—	2	4	no	—
109	C₂×C₇×C₈	—	2	2	no	—
110	C₂×C₇×C₈	—	2	4	no	—
111	C₂×C₇×C₈	—	2	2	no	—
112	C₂×C₇×C₈	—	2	4	no	—
113	C₂×C₇×C₈	#41	1	4	yes	—
114	C₇×C₄⋊C₄	—	2	2	no	—
115	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
116	C₇×C₄⋊C₄	M₁₆	1	4	yes	complemented
117	C₇×C₂²⋊C₄	—	2	4	no	—
118	C₇×C₂²⋊C₄	—	2	4	no	—
119	C₇×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
120	C₄²×C₇	—	2	2	no	—
121	C₄²×C₇	—	2	2	no	—
122	C₄²×C₇	—	2	2	no	—
123	C₄²×C₇	—	2	4	no	—
124	C₄²×C₇	—	2	2	no	—
125	C₄²×C₇	—	4	2	no	—
126	C₄²×C₇	—	4	2	no	—
127	C₄²×C₇	—	4	1	no	—
128	C₄²×C₇	M₁₆	1	4	yes	complemented
129	C₄²×C₇	C₂×D₄	1	2	yes	—
130	C₄²×C₇	C₂×Q₈	1	2	yes	—
131	C₂²×M₁₆	C₂²×C₇	1	4	yes	—
132	C₂×C₄×D₄	C₄×C₇	1	1	yes	characteristic
133	C₂×C₄×D₄	C₄×C₇	1	1	yes	characteristic
134	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
135	C₂²×C₄²	C₂²×C₇	1	2	yes	—
136	#436	—	2	8	no	—
137	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
138	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
139	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	—
140	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	—
141	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
142	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
143	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
144	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
145	C₄×C₂²⋊C₄	C₄×C₇	1	2	yes	—
146	C₄×C₂²⋊C₄	C₄×C₇	1	2	yes	—
147	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
148	C₄³	C₂²×C₇	1	1	yes	characteristic
149	#336	C₂²×C₇	1	1	yes	characteristic
150	#336	C₂²×C₇	1	2	yes	—
151	#336	C₂²×C₇	1	2	yes	—
152	#336	C₂²×C₇	1	4	yes	—
153	#336	C₂²×C₇	1	1	yes	characteristic
154	C₂³×C₇	—	2	2	no	—
155	C₂³×C₇	—	2	2	no	—
156	C₂³×C₇	—	2	2	no	—
157	C₂³×C₇	—	2	2	no	—
158	C₂³×C₇	—	2	2	no	—
159	C₂³×C₇	—	2	2	no	—
160	C₂³×C₇	C₂×C₄⋊C₄	1	4	yes	—
161	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
162	C₇×D₄	—	2	8	no	—
163	C₂×C₄×C₇	—	2	1	no	—
164	C₂×C₄×C₇	—	2	2	no	—
165	C₂×C₄×C₇	—	2	1	no	—
166	C₂×C₄×C₇	—	2	1	no	—
167	C₂×C₄×C₇	—	2	2	no	—
168	C₂×C₄×C₇	—	2	2	no	—
169	C₂×C₄×C₇	—	2	1	no	—
170	C₂×C₄×C₇	—	2	1	no	—
171	C₂×C₄×C₇	—	2	1	no	—
172	C₂×C₄×C₇	—	2	2	no	—
173	C₂×C₄×C₇	—	2	1	no	—
174	C₂×C₄×C₇	—	2	1	no	—
175	C₂×C₄×C₇	—	2	8	no	—
176	C₂×C₄×C₇	—	2	8	no	—
177	C₂×C₄×C₇	—	2	1	no	—
178	C₂×C₄×C₇	—	2	2	no	—
179	C₂×C₄×C₇	—	2	1	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	2	1	no	—
182	C₂×C₄×C₇	—	2	2	no	—
183	C₂×C₄×C₇	—	4	8	no	—
184	C₂×C₄×C₇	—	4	8	no	—
185	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
186	C₂×C₄×C₇	C₂×C₄⋊C₄	1	4	yes	—
187	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
189	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
190	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
191	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
193	C₂×C₄×C₇	#131	1	2	yes	—
194	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₇	C₂×#41	1	2	yes	—
197	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
198	C₇×C₈	—	2	4	no	—
199	C₇×C₈	—	4	2	no	—
200	C₇×C₈	—	4	4	no	—
201	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
202	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
203	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
204	C₂³×C₄	C₂³×C₇	1	2	yes	—
205	C₂×M₁₆	—	2	8	no	—
206	C₂×M₁₆	—	2	8	no	—
207	C₂×M₁₆	—	4	4	no	—
208	C₂²×C₈	C₂³×C₇	1	4	yes	—
209	C₂²×C₈	C₂³×C₇	1	2	yes	—
210	C₂²×C₈	C₂³×C₇	1	2	yes	—
211	C₄×D₄	—	2	4	no	—
212	C₄×D₄	—	2	4	no	—
213	C₄×D₄	C₇×D₄	1	4	yes	—
214	C₄×D₄	C₇×Q₈	1	4	yes	—
215	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
218	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
221	C₂×C₄²	—	4	4	no	—
222	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
227	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₇	1	2	yes	—
231	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
232	C₄⋊C₈	—	2	4	no	—
233	C₄⋊C₈	—	2	4	no	—
234	C₄⋊C₈	—	4	4	no	—
235	C₂²⋊C₈	—	2	8	no	—
236	C₄×C₈	—	2	4	no	—
237	#95	C₂×C₄×C₇	1	2	yes	—
238	#95	C₂×C₄×C₇	1	2	yes	—
239	#95	C₂×C₄×C₇	1	2	yes	—
240	C₂²×C₇	—	2	4	no	—
241	C₂²×C₇	—	2	4	no	—
242	C₂²×C₇	—	2	4	no	—
243	C₂²×C₇	—	4	2	no	—
244	C₂²×C₇	—	4	2	no	—
245	C₂²×C₇	—	4	2	no	—
246	C₂²×C₇	—	4	2	no	—
247	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
248	C₂²×C₇	C₄×#41	1	1	yes	characteristic
249	C₂²×C₇	#518	1	1	yes	characteristic
250	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
251	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
252	C₂²×C₇	C₂×#131	1	1	yes	characteristic
253	C₂²×C₇	#568	1	1	yes	characteristic
254	C₄×C₇	—	2	4	no	—
255	C₄×C₇	—	2	2	no	—
256	C₄×C₇	—	2	2	no	—
257	C₄×C₇	—	2	2	no	—
258	C₄×C₇	—	2	4	no	—
259	C₄×C₇	—	2	2	no	—
260	C₄×C₇	—	4	1	no	—
261	C₄×C₇	—	4	2	no	—
262	C₄×C₇	#423	1	4	yes	—
263	C₄×C₇	#546	1	2	yes	—
264	C₄×C₇	#554	1	2	yes	—
265	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	C₇×C₄⋊C₄	1	4	yes	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
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	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
287	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
288	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
289	M₁₆	—	4	16	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	C₇×#41	1	4	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
301	C₄⋊C₄	C₇×M₁₆	1	4	yes	complemented
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	C₇×C₄⋊C₄	1	8	yes	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	4	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	4	2	no	—
311	C₄²	—	4	2	no	—
312	C₄²	—	4	1	no	—
313	C₄²	C₇×M₁₆	1	4	yes	complemented
314	C₄²	C₂×C₇×D₄	1	2	yes	—
315	C₄²	C₂×C₇×Q₈	1	2	yes	—
316	C₂×C₇	—	4	4	no	—
317	C₂×C₇	#2349	1	1	yes	characteristic
318	C₂×C₇	C₂×#423	1	1	yes	characteristic
319	C₂×C₇	#2906	1	1	yes	characteristic
320	C₂×C₇	#2965	1	1	yes	characteristic
321	C₂×C₇	#2971	1	1	yes	characteristic
322	C₂×C₇	#2974	1	1	yes	characteristic
323	C₂×C₇	#2975	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	C₂×C₇×C₄⋊C₄	1	4	yes	—
331	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
332	D₄	—	2	8	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	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	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
356	C₂×C₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
357	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
358	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
359	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
360	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
361	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
362	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
363	C₂×C₄	C₇×#131	1	2	yes	—
364	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
366	C₂×C₄	C₂×C₇×#41	1	2	yes	—
367	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
368	C₈	—	2	4	no	—
369	C₈	—	4	2	no	—
370	C₈	—	4	4	no	—
371	C₇	#22700	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
380	C₂²	C₄×C₇×#41	1	1	yes	characteristic
381	C₂²	C₇×#518	1	1	yes	characteristic
382	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
383	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
384	C₂²	C₂×C₇×#131	1	1	yes	characteristic
385	C₂²	C₇×#568	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	2	no	—
394	C₄	C₇×#423	1	4	yes	—
395	C₄	C₇×#546	1	2	yes	—
396	C₄	C₇×#554	1	2	yes	—
397	C₂	—	4	4	no	—
398	C₂	C₇×#2349	1	1	yes	characteristic
399	C₂	C₂×C₇×#423	1	1	yes	characteristic
400	C₂	C₇×#2906	1	1	yes	characteristic
401	C₂	C₇×#2965	1	1	yes	characteristic
402	C₂	C₇×#2971	1	1	yes	characteristic
403	C₂	C₇×#2974	1	1	yes	characteristic
404	C₂	C₇×#2975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂²×C₇×D₄	C₂×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
3. C₇×#1939	C₂	semidirect
4. C₇×#1851	C₂	semidirect
5. C₇×#1831	C₂	semidirect
6. C₇×#1797	C₂	semidirect
7. C₄×C₇×C₄⋊C₈	C₂	semidirect
8. C₇×#1728	C₂	semidirect
32. #22700	C₇	direct (N × H)
74. #1939	C₂×C₇	semidirect
75. #1851	C₂×C₇	semidirect
76. #1831	C₂×C₇	semidirect
77. #1797	C₂×C₇	semidirect
78. C₄×C₄⋊C₈	C₂×C₇	semidirect
79. #1728	C₂×C₇	semidirect
116. C₇×C₄⋊C₄	M₁₆	semidirect
128. C₄²×C₇	M₁₆	semidirect
301. C₄⋊C₄	C₇×M₁₆	semidirect
313. C₄²	C₇×M₁₆	semidirect
371. C₇	#22700	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
C₄²×C₇×D₄	2
C₇×#1939	2
C₇×#1851	2
C₇×#1831	2
C₇×#1797	2
C₄×C₇×C₄⋊C₈	2
C₇×#1728	2
#22700	7

Subgroups — C7×#22700 #13199916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22700 #13199916