Subgroups — C₇×#21264 #13198480

Order 1792.

1046 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#431	C₂	1	2	yes	maximal, complemented
2	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#1954	C₂	1	2	yes	maximal
4	C₇×#1939	C₂	1	2	yes	maximal, complemented
5	C₇×#1923	C₂	1	4	yes	maximal, complemented
6	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₇×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₄²×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
10	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
11	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₇	C₂²	1	2	yes	—
13	C₇×#431	—	2	8	no	—
14	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	—
15	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	—
17	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	—
18	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
24	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
25	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×C₇×C₂²⋊C₄	C₄	1	2	yes	—
27	C₄×C₇×C₂²⋊C₄	C₄	1	2	yes	—
28	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₄³×C₇	C₂²	1	1	yes	characteristic
30	C₇×#336	C₂²	1	4	yes	—
31	C₇×#336	C₂²	1	2	yes	—
32	#21264	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	C₂²×C₇×C₈	C₂³	1	4	yes	—
38	C₂²×C₇×C₈	C₂³	1	2	yes	—
39	C₂²×C₇×C₈	C₂³	1	2	yes	—
40	C₄×C₇×D₄	—	2	4	no	—
41	C₄×C₇×D₄	—	2	4	no	—
42	C₄×C₇×D₄	C₈	1	8	yes	complemented
43	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₇	—	2	4	no	—
50	C₂×C₄²×C₇	—	2	4	no	—
51	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₇	C₂³	1	2	yes	—
59	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
61	C₇×C₄⋊C₈	—	2	8	no	—
62	C₇×C₄⋊C₈	—	2	4	no	—
63	C₇×C₂²⋊C₈	—	2	8	no	—
64	C₇×C₂²⋊C₈	—	2	8	no	—
65	C₄×C₇×C₈	—	2	4	no	—
66	C₄×C₇×C₈	—	2	4	no	—
67	C₄×C₇×C₈	—	2	4	no	—
68	C₄×C₇×C₈	—	2	2	no	—
69	C₄×C₇×C₈	D₄	1	4	yes	complemented
70	C₇×#95	C₂×C₄	1	2	yes	—
71	C₇×#95	C₂×C₄	1	2	yes	—
72	C₇×#95	C₂×C₄	1	2	yes	—
73	C₂×#431	C₂×C₇	1	2	yes	complemented
74	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
75	#1954	C₂×C₇	1	2	yes	—
76	#1939	C₂×C₇	1	2	yes	complemented
77	#1923	C₂×C₇	1	4	yes	complemented
78	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊C₈	C₂×C₇	1	2	yes	complemented
80	C₄²×C₈	C₂×C₇	1	1	yes	characteristic, complemented
81	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
82	C₂×C₇×D₄	—	2	2	no	—
83	C₂×C₇×D₄	—	2	2	no	—
84	C₂×C₇×D₄	C₂×C₈	1	4	yes	—
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	—	2	4	no	—
90	C₂²×C₄×C₇	—	2	2	no	—
91	C₂²×C₄×C₇	—	2	4	no	—
92	C₂²×C₄×C₇	—	2	2	no	—
93	C₂²×C₄×C₇	—	2	4	no	—
94	C₂²×C₄×C₇	C₂×C₈	1	8	yes	—
95	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
102	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	2	no	—
109	C₂×C₇×C₈	—	2	4	no	—
110	C₂×C₇×C₈	—	2	4	no	—
111	C₂×C₇×C₈	—	2	4	no	—
112	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
113	C₂×C₇×C₈	#41	1	4	yes	—
114	C₇×C₄⋊C₄	—	2	2	no	—
115	C₇×C₄⋊C₄	—	2	2	no	—
116	C₇×C₄⋊C₄	C₂×C₈	1	4	yes	—
117	C₇×C₂²⋊C₄	—	2	4	no	—
118	C₇×C₂²⋊C₄	—	2	4	no	—
119	C₇×C₂²⋊C₄	C₂×C₈	1	8	yes	—
120	C₄²×C₇	—	2	4	no	—
121	C₄²×C₇	—	2	4	no	—
122	C₄²×C₇	—	2	2	no	—
123	C₄²×C₇	—	2	2	no	—
124	C₄²×C₇	—	2	2	no	—
125	C₄²×C₇	—	2	2	no	—
126	C₄²×C₇	—	2	2	no	—
127	C₄²×C₇	C₂×C₈	1	4	yes	—
128	C₄²×C₇	M₁₆	1	4	yes	—
129	C₄²×C₇	C₂×D₄	1	2	yes	—
130	C₄²×C₇	#41	1	4	yes	—
131	C₄²×C₇	#41	1	2	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	#431	—	2	8	no	—
137	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	—
138	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
139	C₂×C₂²⋊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	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
143	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
144	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
145	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
146	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
147	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
149	C₄×C₂²⋊C₄	C₄×C₇	1	2	yes	—
150	C₄×C₂²⋊C₄	C₄×C₇	1	2	yes	—
151	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
152	C₄³	C₂²×C₇	1	1	yes	characteristic
153	#336	C₂²×C₇	1	2	yes	—
154	#336	C₂²×C₇	1	4	yes	—
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	—	2	2	no	—
161	C₂³×C₇	C₂²×C₈	1	4	yes	—
162	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
163	C₇×D₄	—	2	8	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	1	no	—
168	C₂×C₄×C₇	—	2	1	no	—
169	C₂×C₄×C₇	—	2	1	no	—
170	C₂×C₄×C₇	—	2	1	no	—
171	C₂×C₄×C₇	—	2	2	no	—
172	C₂×C₄×C₇	—	2	16	no	—
173	C₂×C₄×C₇	—	2	2	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	2	no	—
179	C₂×C₄×C₇	—	4	4	no	—
180	C₂×C₄×C₇	—	4	4	no	—
181	C₂×C₄×C₇	—	4	8	no	—
182	C₂×C₄×C₇	#117	1	2	yes	—
183	C₂×C₄×C₇	#117	1	2	yes	—
184	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
187	C₂×C₄×C₇	C₂²×C₈	1	4	yes	—
188	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
189	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
190	C₂×C₄×C₇	C₂×M₁₆	1	2	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	#131	1	2	yes	—
195	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₇	C₂×#41	1	2	yes	—
198	C₂×C₄×C₇	C₂×#41	1	2	yes	—
199	C₇×C₈	—	2	4	no	—
200	C₇×C₈	—	2	4	no	—
201	C₇×C₈	—	4	4	no	—
202	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
203	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
204	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
205	C₂³×C₄	C₂³×C₇	1	2	yes	—
206	C₂²×C₈	C₂³×C₇	1	4	yes	—
207	C₂²×C₈	C₂³×C₇	1	2	yes	—
208	C₂²×C₈	C₂³×C₇	1	2	yes	—
209	C₄×D₄	—	2	4	no	—
210	C₄×D₄	—	2	4	no	—
211	C₄×D₄	C₇×C₈	1	8	yes	complemented
212	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
213	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
216	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
217	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
218	C₂×C₄²	—	2	4	no	—
219	C₂×C₄²	—	2	4	no	—
220	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
224	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₇	1	2	yes	—
228	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
230	C₄⋊C₈	—	2	8	no	—
231	C₄⋊C₈	—	2	4	no	—
232	C₂²⋊C₈	—	2	8	no	—
233	C₂²⋊C₈	—	2	8	no	—
234	C₄×C₈	—	2	4	no	—
235	C₄×C₈	—	2	4	no	—
236	C₄×C₈	—	2	4	no	—
237	C₄×C₈	—	2	2	no	—
238	C₄×C₈	C₇×D₄	1	4	yes	complemented
239	#95	C₂×C₄×C₇	1	2	yes	—
240	#95	C₂×C₄×C₇	1	2	yes	—
241	#95	C₂×C₄×C₇	1	2	yes	—
242	C₂²×C₇	—	2	4	no	—
243	C₂²×C₇	—	2	4	no	—
244	C₂²×C₇	—	2	4	no	—
245	C₂²×C₇	—	4	2	no	—
246	C₂²×C₇	—	4	2	no	—
247	C₂²×C₇	—	4	2	no	—
248	C₂²×C₇	—	4	2	no	—
249	C₂²×C₇	C₂×#117	1	1	yes	characteristic
250	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₇	C₄×#41	1	1	yes	characteristic
252	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
253	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
254	C₂²×C₇	C₂×#131	1	1	yes	characteristic
255	C₂²×C₇	C₂×#131	1	1	yes	characteristic
256	C₄×C₇	—	2	2	no	—
257	C₄×C₇	—	2	4	no	—
258	C₄×C₇	—	2	2	no	—
259	C₄×C₇	—	2	2	no	—
260	C₄×C₇	—	4	2	no	—
261	C₄×C₇	—	4	2	no	—
262	C₄×C₇	#431	1	4	yes	complemented
263	C₄×C₇	C₈×D₄	1	4	yes	—
264	C₄×C₇	#436	1	4	yes	—
265	C₄×C₇	#529	1	2	yes	—
266	C₄×C₇	#532	1	2	yes	—
267	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	C₂×C₇×C₈	1	4	yes	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	C₂×C₇×C₈	1	8	yes	—
281	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
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	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
299	C₂×C₈	C₇×#41	1	4	yes	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	C₂×C₇×C₈	1	4	yes	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	C₂×C₇×C₈	1	8	yes	—
306	C₄²	—	2	4	no	—
307	C₄²	—	2	4	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂×C₇×C₈	1	4	yes	—
314	C₄²	C₇×M₁₆	1	4	yes	—
315	C₄²	C₂×C₇×D₄	1	2	yes	—
316	C₄²	C₇×#41	1	4	yes	—
317	C₄²	C₇×#41	1	2	yes	—
318	C₂×C₇	—	4	4	no	—
319	C₂×C₇	#2293	1	1	yes	characteristic
320	C₂×C₇	C₂×#431	1	1	yes	characteristic
321	C₂×C₇	#2922	1	1	yes	characteristic
322	C₂×C₇	C₂×C₈×D₄	1	1	yes	characteristic
323	C₂×C₇	C₂×#436	1	1	yes	characteristic
324	C₂×C₇	C₈×#41	1	1	yes	characteristic
325	C₂×C₇	#2965	1	1	yes	characteristic
326	C₂³	—	2	2	no	—
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	C₂²×C₇×C₈	1	4	yes	—
333	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
334	D₄	—	2	8	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	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	16	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	C₇×#117	1	2	yes	—
354	C₂×C₄	C₇×#117	1	2	yes	—
355	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
356	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
357	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
358	C₂×C₄	C₂²×C₇×C₈	1	4	yes	—
359	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
360	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
361	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
362	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
363	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
364	C₂×C₄	C₇×#131	1	2	yes	—
365	C₂×C₄	C₇×#131	1	2	yes	—
366	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
367	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
368	C₂×C₄	C₂×C₇×#41	1	2	yes	—
369	C₂×C₄	C₂×C₇×#41	1	2	yes	—
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₈	—	4	4	no	—
373	C₇	#21264	1	1	yes	characteristic, direct product factor, Sylow
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	C₂×C₇×#117	1	1	yes	characteristic
382	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
383	C₂²	C₄×C₇×#41	1	1	yes	characteristic
384	C₂²	C₂³×C₇×C₈	1	1	yes	characteristic
385	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
386	C₂²	C₂×C₇×#131	1	1	yes	characteristic
387	C₂²	C₂×C₇×#131	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	C₇×#431	1	4	yes	complemented
395	C₄	C₇×C₈×D₄	1	4	yes	—
396	C₄	C₇×#436	1	4	yes	—
397	C₄	C₇×#529	1	2	yes	—
398	C₄	C₇×#532	1	2	yes	—
399	C₂	—	4	4	no	—
400	C₂	C₇×#2293	1	1	yes	characteristic
401	C₂	C₂×C₇×#431	1	1	yes	characteristic
402	C₂	C₇×#2922	1	1	yes	characteristic
403	C₂	C₂×C₇×C₈×D₄	1	1	yes	characteristic
404	C₂	C₂×C₇×#436	1	1	yes	characteristic
405	C₂	C₇×C₈×#41	1	1	yes	characteristic
406	C₂	C₇×#2965	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₇	C₂³
commutator	C₂²	C₂³×C₇×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂²×C₇×D₄	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#431	C₂	semidirect
4. C₇×#1939	C₂	semidirect
5. C₇×#1923	C₂	semidirect
6. C₄×C₇×C₄⋊C₈	C₂	semidirect
7. C₄×C₇×C₂²⋊C₈	C₂	semidirect
8. C₄²×C₇×C₈	C₂	semidirect
32. #21264	C₇	direct (N × H)
42. C₄×C₇×D₄	C₈	semidirect
69. C₄×C₇×C₈	D₄	semidirect
73. C₂×#431	C₂×C₇	semidirect
76. #1939	C₂×C₇	semidirect
77. #1923	C₂×C₇	semidirect
78. C₄×C₄⋊C₈	C₂×C₇	semidirect
79. C₄×C₂²⋊C₈	C₂×C₇	semidirect
80. C₄²×C₈	C₂×C₇	semidirect
211. C₄×D₄	C₇×C₈	semidirect
238. C₄×C₈	C₇×D₄	semidirect
262. C₄×C₇	#431	semidirect
373. C₇	#21264	direct (N × H)
394. C₄	C₇×#431	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#431	2
C₄²×C₇×D₄	2
C₇×#1954	2
C₇×#1939	2
C₇×#1923	2
C₄×C₇×C₄⋊C₈	2
C₄×C₇×C₂²⋊C₈	2
C₄²×C₇×C₈	2
#21264	7

Subgroups — C7×#21264 #13198480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21264 #13198480