Subgroups — C₇×#22494 #13199710

Order 1792.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic
3	C₇×#2352	C₂	1	1	yes	maximal, characteristic
4	C₇×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1825	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1825	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1736	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1735	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₇×#556	—	2	4	no	—
19	C₇×#556	C₄	1	8	yes	complemented
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#126	—	2	1	no	—
22	C₂×C₇×#126	—	2	1	no	—
23	C₂×C₇×#124	—	2	1	no	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×Q₈	—	2	1	no	—
27	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂×C₇×#117	C₂²	1	1	yes	characteristic
31	C₂×C₇×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₇×#435	—	2	4	no	—
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₇×#103	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₇×#97	C₂²	1	1	yes	characteristic
42	C₇×#388	—	2	1	no	—
43	C₇×#387	—	2	1	no	—
44	C₇×#386	—	2	1	no	—
45	C₇×#382	C₂²	1	1	yes	characteristic
46	C₇×#380	C₂²	1	1	yes	characteristic
47	C₇×#380	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
50	C₇×#340	C₂²	1	1	yes	characteristic
51	C₇×#340	C₂²	1	1	yes	characteristic
52	C₇×#340	C₂²	1	1	yes	characteristic
53	C₇×#340	C₂²	1	1	yes	characteristic
54	C₇×#340	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#340	C₂²	1	1	yes	characteristic
61	C₇×#340	C₂²	1	1	yes	characteristic
62	#22494	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×Q₈	—	2	1	no	—
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₇	—	2	1	no	—
67	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
69	C₂×C₇×M₁₆	—	2	2	no	—
70	C₂×C₇×M₁₆	—	2	2	no	—
71	C₂×C₇×M₁₆	—	4	1	no	—
72	C₂²×C₇×C₈	—	2	2	no	—
73	C₂²×C₇×C₈	—	2	2	no	—
74	C₂²×C₇×C₈	—	4	1	no	—
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
79	C₇×C₄⋊Q₈	—	2	2	no	—
80	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
81	C₇×#126	—	2	8	no	—
82	C₇×#126	—	2	8	no	—
83	C₇×#124	—	2	8	no	—
84	C₇×C₂²⋊Q₈	—	2	2	no	—
85	C₇×C₂²⋊Q₈	—	2	2	no	—
86	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
87	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
88	C₄×C₇×Q₈	—	2	8	no	—
89	C₄×C₇×Q₈	—	2	2	no	—
90	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
91	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
92	C₄×C₇×D₄	D₄	1	4	yes	—
93	C₇×#117	—	2	2	no	—
94	C₇×#117	—	2	2	no	—
95	C₇×#117	—	2	2	no	—
96	C₇×#117	—	4	1	no	—
97	C₇×#117	C₂×C₄	1	4	yes	—
98	C₇×#117	C₂×C₄	1	4	yes	complemented
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	—	2	2	no	—
104	C₂×C₇×C₄⋊C₄	—	2	1	no	—
105	C₂×C₇×C₄⋊C₄	—	4	1	no	—
106	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
122	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₇	—	2	1	no	—
124	C₂×C₄²×C₇	—	2	1	no	—
125	C₂×C₄²×C₇	—	2	1	no	—
126	C₂×C₄²×C₇	—	2	1	no	—
127	C₂×C₄²×C₇	—	2	1	no	—
128	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
129	C₇×C₄⋊C₈	—	2	2	no	—
130	C₇×#103	—	2	2	no	—
131	C₇×#103	—	2	2	no	—
132	C₇×#103	—	4	1	no	—
133	C₇×#103	—	4	1	no	—
134	C₇×C₂²⋊C₈	—	2	2	no	—
135	C₇×C₂²⋊C₈	—	2	2	no	—
136	C₇×#97	—	2	2	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₂×#556	C₂×C₇	1	1	yes	characteristic
143	C₂×#435	C₂×C₇	1	1	yes	characteristic
144	#2352	C₂×C₇	1	1	yes	characteristic
145	#1993	C₂×C₇	1	1	yes	characteristic, complemented
146	#1987	C₂×C₇	1	1	yes	characteristic, complemented
147	#1894	C₂×C₇	1	1	yes	characteristic, complemented
148	#1892	C₂×C₇	1	1	yes	characteristic, complemented
149	#1873	C₂×C₇	1	1	yes	characteristic, complemented
150	#1872	C₂×C₇	1	1	yes	characteristic, complemented
151	#1825	C₂×C₇	1	1	yes	characteristic, complemented
152	#1825	C₂×C₇	1	1	yes	characteristic, complemented
153	#1805	C₂×C₇	1	1	yes	characteristic, complemented
154	#1763	C₂×C₇	1	1	yes	characteristic, complemented
155	#1736	C₂×C₇	1	1	yes	characteristic, complemented
156	#1735	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
159	C₂×C₇×Q₈	—	2	4	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	1	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
165	C₂×C₇×Q₈	—	4	2	no	—
166	C₂×C₇×Q₈	—	4	2	no	—
167	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
168	C₂×C₇×D₄	—	4	1	no	—
169	C₂×C₇×D₄	—	4	1	no	—
170	C₂×C₇×D₄	C₂²⋊C₄	1	4	yes	—
171	C₂²×C₄×C₇	—	2	1	no	—
172	C₂²×C₄×C₇	—	2	1	no	—
173	C₂²×C₄×C₇	—	2	1	no	—
174	C₂²×C₄×C₇	—	2	1	no	—
175	C₂²×C₄×C₇	—	2	1	no	—
176	C₂²×C₄×C₇	—	2	1	no	—
177	C₂²×C₄×C₇	—	2	1	no	—
178	C₂²×C₄×C₇	—	2	1	no	—
179	C₂²×C₄×C₇	—	2	1	no	—
180	C₂²×C₄×C₇	—	2	1	no	—
181	C₂²×C₄×C₇	—	2	1	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	4	2	no	—
188	C₂²×C₄×C₇	—	4	2	no	—
189	C₂²×C₄×C₇	—	8	1	no	—
190	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
192	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
199	C₇×M₁₆	—	4	4	no	—
200	C₂×C₇×C₈	—	2	1	no	—
201	C₂×C₇×C₈	—	2	1	no	—
202	C₂×C₇×C₈	—	2	1	no	—
203	C₂×C₇×C₈	—	2	1	no	—
204	C₂×C₇×C₈	—	2	1	no	—
205	C₂×C₇×C₈	—	2	1	no	—
206	C₂×C₇×C₈	—	2	1	no	—
207	C₂×C₇×C₈	—	2	1	no	—
208	C₂×C₇×C₈	—	2	1	no	—
209	C₂×C₇×C₈	—	2	1	no	—
210	C₂×C₇×C₈	—	2	1	no	—
211	C₂×C₇×C₈	—	4	4	no	—
212	C₂×C₇×C₈	#41	1	2	yes	—
213	C₇×C₄⋊C₄	—	2	4	no	—
214	C₇×C₄⋊C₄	—	2	4	no	—
215	C₇×C₄⋊C₄	—	2	4	no	—
216	C₇×C₄⋊C₄	—	2	4	no	—
217	C₇×C₄⋊C₄	—	2	1	no	—
218	C₇×C₄⋊C₄	—	2	1	no	—
219	C₇×C₄⋊C₄	—	2	1	no	—
220	C₇×C₄⋊C₄	—	2	1	no	—
221	C₇×C₄⋊C₄	—	2	1	no	—
222	C₇×C₄⋊C₄	—	2	1	no	—
223	C₇×C₄⋊C₄	—	2	1	no	—
224	C₇×C₄⋊C₄	—	2	1	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	4	2	no	—
228	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
229	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
230	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
231	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
232	C₇×C₄⋊C₄	#41	1	2	yes	—
233	C₇×C₂²⋊C₄	—	2	4	no	—
234	C₇×C₂²⋊C₄	—	2	4	no	—
235	C₇×C₂²⋊C₄	—	2	4	no	—
236	C₇×C₂²⋊C₄	—	2	4	no	—
237	C₇×C₂²⋊C₄	—	4	2	no	—
238	C₇×C₂²⋊C₄	—	4	2	no	—
239	C₇×C₂²⋊C₄	—	8	1	no	—
240	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
241	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
242	C₄²×C₇	—	2	4	no	—
243	C₄²×C₇	—	2	4	no	—
244	C₄²×C₇	—	2	4	no	—
245	C₄²×C₇	—	4	2	no	—
246	C₄²×C₇	—	8	1	no	—
247	C₄²×C₇	C₂²×C₄	1	2	yes	—
248	C₄²×C₇	C₂×D₄	1	2	yes	—
249	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
250	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
251	#556	—	2	4	no	—
252	#556	C₄×C₇	1	8	yes	complemented
253	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
254	C₂×#126	—	2	1	no	—
255	C₂×#126	—	2	1	no	—
256	C₂×#124	—	2	1	no	—
257	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
259	C₂×C₄×Q₈	—	2	1	no	—
260	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
262	C₂×#117	C₂²×C₇	1	1	yes	characteristic
263	C₂×#117	C₂²×C₇	1	1	yes	characteristic
264	C₂×#117	C₂²×C₇	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
266	#435	—	2	4	no	—
267	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
268	C₂×#103	C₂²×C₇	1	1	yes	characteristic
269	C₂×#103	C₂²×C₇	1	1	yes	characteristic
270	C₂×#103	C₂²×C₇	1	1	yes	characteristic
271	C₂×#103	C₂²×C₇	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
274	C₂×#97	C₂²×C₇	1	1	yes	characteristic
275	#388	—	2	1	no	—
276	#387	—	2	1	no	—
277	#386	—	2	1	no	—
278	#382	C₂²×C₇	1	1	yes	characteristic
279	#380	C₂²×C₇	1	1	yes	characteristic
280	#380	C₂²×C₇	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
282	C₄×C₂²⋊C₄	—	2	1	no	—
283	#340	C₂²×C₇	1	1	yes	characteristic
284	#340	C₂²×C₇	1	1	yes	characteristic
285	#340	C₂²×C₇	1	1	yes	characteristic
286	#340	C₂²×C₇	1	1	yes	characteristic
287	#340	C₂²×C₇	1	1	yes	characteristic
288	#340	C₂²×C₇	1	1	yes	characteristic
289	#340	C₂²×C₇	1	1	yes	characteristic
290	#340	C₂²×C₇	1	1	yes	characteristic
291	#340	C₂²×C₇	1	1	yes	characteristic
292	#340	C₂²×C₇	1	1	yes	characteristic
293	#340	C₂²×C₇	1	1	yes	characteristic
294	#340	C₂²×C₇	1	1	yes	characteristic
295	C₂³×C₇	—	2	1	no	—
296	C₂³×C₇	—	2	1	no	—
297	C₂³×C₇	—	2	1	no	—
298	C₂³×C₇	—	2	1	no	—
299	C₂³×C₇	—	2	1	no	—
300	C₂³×C₇	—	2	1	no	—
301	C₂³×C₇	—	2	1	no	—
302	C₂³×C₇	—	2	1	no	—
303	C₂³×C₇	—	2	1	no	—
304	C₂³×C₇	—	2	1	no	—
305	C₂³×C₇	—	2	1	no	—
306	C₂³×C₇	—	2	1	no	—
307	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
309	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
310	C₇×Q₈	—	2	2	no	—
311	C₇×Q₈	—	2	2	no	—
312	C₇×Q₈	—	4	8	no	—
313	C₇×Q₈	—	4	1	no	—
314	C₇×Q₈	—	4	1	no	—
315	C₇×D₄	—	4	4	no	—
316	C₂×C₄×C₇	—	2	1	no	—
317	C₂×C₄×C₇	—	2	1	no	—
318	C₂×C₄×C₇	—	2	1	no	—
319	C₂×C₄×C₇	—	2	1	no	—
320	C₂×C₄×C₇	—	2	1	no	—
321	C₂×C₄×C₇	—	2	1	no	—
322	C₂×C₄×C₇	—	2	1	no	—
323	C₂×C₄×C₇	—	2	1	no	—
324	C₂×C₄×C₇	—	2	2	no	—
325	C₂×C₄×C₇	—	2	2	no	—
326	C₂×C₄×C₇	—	2	2	no	—
327	C₂×C₄×C₇	—	2	2	no	—
328	C₂×C₄×C₇	—	2	2	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	2	no	—
331	C₂×C₄×C₇	—	2	2	no	—
332	C₂×C₄×C₇	—	2	2	no	—
333	C₂×C₄×C₇	—	2	2	no	—
334	C₂×C₄×C₇	—	2	2	no	—
335	C₂×C₄×C₇	—	2	2	no	—
336	C₂×C₄×C₇	—	2	2	no	—
337	C₂×C₄×C₇	—	4	1	no	—
338	C₂×C₄×C₇	—	4	1	no	—
339	C₂×C₄×C₇	—	4	1	no	—
340	C₂×C₄×C₇	—	4	1	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	4	1	no	—
354	C₂×C₄×C₇	—	4	1	no	—
355	C₂×C₄×C₇	—	4	1	no	—
356	C₂×C₄×C₇	—	8	4	no	—
357	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
358	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
359	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
360	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
361	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
362	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
364	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
365	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
367	C₇×C₈	—	2	2	no	—
368	C₇×C₈	—	4	1	no	—
369	C₇×C₈	—	4	1	no	—
370	C₇×C₈	—	4	1	no	—
371	C₂²×Q₈	—	2	1	no	—
372	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
373	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
377	C₂×M₁₆	—	2	2	no	—
378	C₂×M₁₆	—	2	2	no	—
379	C₂×M₁₆	—	4	1	no	—
380	C₂²×C₈	—	2	2	no	—
381	C₂²×C₈	—	2	2	no	—
382	C₂²×C₈	—	4	1	no	—
383	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
387	C₄⋊Q₈	—	2	2	no	—
388	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
389	#126	—	2	8	no	—
390	#126	—	2	8	no	—
391	#124	—	2	8	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
395	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
396	C₄×Q₈	—	2	8	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
399	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
400	C₄×D₄	C₇×D₄	1	4	yes	—
401	#117	—	2	2	no	—
402	#117	—	2	2	no	—
403	#117	—	2	2	no	—
404	#117	—	4	1	no	—
405	#117	C₂×C₄×C₇	1	4	yes	—
406	#117	C₂×C₄×C₇	1	4	yes	complemented
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	2	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	4	1	no	—
414	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
437	C₄⋊C₈	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	—	4	1	no	—
441	#103	—	4	1	no	—
442	C₂²⋊C₈	—	2	2	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	#97	—	2	2	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	C₂²×C₇	—	2	2	no	—
451	C₂²×C₇	—	2	2	no	—
452	C₂²×C₇	—	2	2	no	—
453	C₂²×C₇	—	2	2	no	—
454	C₂²×C₇	—	2	2	no	—
455	C₂²×C₇	—	2	2	no	—
456	C₂²×C₇	—	4	1	no	—
457	C₂²×C₇	—	4	1	no	—
458	C₂²×C₇	—	4	1	no	—
459	C₂²×C₇	—	4	1	no	—
460	C₂²×C₇	—	4	1	no	—
461	C₂²×C₇	—	4	1	no	—
462	C₂²×C₇	—	4	1	no	—
463	C₂²×C₇	—	4	1	no	—
464	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
465	C₂²×C₇	#546	1	1	yes	characteristic
466	C₂²×C₇	#547	1	1	yes	characteristic
467	C₂²×C₇	#575	1	1	yes	characteristic
468	C₂²×C₇	#575	1	1	yes	characteristic
469	C₂²×C₇	#577	1	1	yes	characteristic
470	C₂²×C₇	#578	1	1	yes	characteristic
471	C₄×C₇	—	2	2	no	—
472	C₄×C₇	—	2	2	no	—
473	C₄×C₇	—	2	2	no	—
474	C₄×C₇	—	2	2	no	—
475	C₄×C₇	—	4	2	no	—
476	C₄×C₇	—	4	2	no	—
477	C₄×C₇	—	4	2	no	—
478	C₄×C₇	—	4	2	no	—
479	C₄×C₇	—	4	2	no	—
480	C₄×C₇	—	8	1	no	—
481	C₄×C₇	—	8	1	no	—
482	C₄×C₇	—	8	1	no	—
483	C₄×C₇	C₄×#41	1	1	yes	characteristic
484	C₄×C₇	#520	1	1	yes	characteristic
485	C₄×C₇	#546	1	1	yes	characteristic
486	C₄×C₇	#547	1	1	yes	characteristic
487	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
488	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
489	C₂×Q₈	—	2	4	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	4	2	no	—
496	C₂×Q₈	—	4	2	no	—
497	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
498	C₂×D₄	—	4	1	no	—
499	C₂×D₄	—	4	1	no	—
500	C₂×D₄	C₇×C₂²⋊C₄	1	4	yes	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	8	1	no	—
520	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
521	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
522	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
526	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
527	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
529	M₁₆	—	4	4	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	4	4	no	—
542	C₂×C₈	C₇×#41	1	2	yes	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
559	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
560	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
561	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
562	C₄⋊C₄	C₇×#41	1	2	yes	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	4	no	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	8	1	no	—
570	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
571	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	4	no	—
574	C₄²	—	2	4	no	—
575	C₄²	—	4	2	no	—
576	C₄²	—	8	1	no	—
577	C₄²	C₂²×C₄×C₇	1	2	yes	—
578	C₄²	C₂×C₇×D₄	1	2	yes	—
579	C₂×C₇	—	4	2	no	—
580	C₂×C₇	—	4	2	no	—
581	C₂×C₇	#2339	1	1	yes	characteristic
582	C₂×C₇	#2896	1	1	yes	characteristic
583	C₂×C₇	#2898	1	1	yes	characteristic
584	C₂×C₇	#3311	1	1	yes	characteristic
585	C₂×C₇	#3313	1	1	yes	characteristic
586	C₂×C₇	#3349	1	1	yes	characteristic
587	C₂×C₇	#3350	1	1	yes	characteristic
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
601	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
602	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
603	Q₈	—	2	2	no	—
604	Q₈	—	2	2	no	—
605	Q₈	—	4	8	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	4	1	no	—
608	D₄	—	4	4	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	8	4	no	—
650	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
651	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
652	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
653	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
654	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
655	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
656	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
657	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
658	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
660	C₈	—	2	2	no	—
661	C₈	—	4	1	no	—
662	C₈	—	4	1	no	—
663	C₈	—	4	1	no	—
664	C₇	#22494	1	1	yes	characteristic, direct product factor, Sylow
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
680	C₂²	C₇×#546	1	1	yes	characteristic
681	C₂²	C₇×#547	1	1	yes	characteristic
682	C₂²	C₇×#575	1	1	yes	characteristic
683	C₂²	C₇×#575	1	1	yes	characteristic
684	C₂²	C₇×#577	1	1	yes	characteristic
685	C₂²	C₇×#578	1	1	yes	characteristic
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	8	1	no	—
696	C₄	—	8	1	no	—
697	C₄	—	8	1	no	—
698	C₄	C₄×C₇×#41	1	1	yes	characteristic
699	C₄	C₇×#520	1	1	yes	characteristic
700	C₄	C₇×#546	1	1	yes	characteristic
701	C₄	C₇×#547	1	1	yes	characteristic
702	C₂	—	4	2	no	—
703	C₂	—	4	2	no	—
704	C₂	C₇×#2339	1	1	yes	characteristic
705	C₂	C₇×#2896	1	1	yes	characteristic
706	C₂	C₇×#2898	1	1	yes	characteristic
707	C₂	C₇×#3311	1	1	yes	characteristic
708	C₂	C₇×#3313	1	1	yes	characteristic
709	C₂	C₇×#3349	1	1	yes	characteristic
710	C₂	C₇×#3350	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
4. C₇×#1993	C₂	semidirect
5. C₇×#1987	C₂	semidirect
6. C₇×#1894	C₂	semidirect
7. C₇×#1892	C₂	semidirect
8. C₇×#1873	C₂	semidirect
9. C₇×#1872	C₂	semidirect
10. C₇×#1825	C₂	semidirect
11. C₇×#1825	C₂	semidirect
12. C₇×#1805	C₂	semidirect
13. C₇×#1763	C₂	semidirect
14. C₇×#1736	C₂	semidirect
15. C₇×#1735	C₂	semidirect
19. C₇×#556	C₄	semidirect
62. #22494	C₇	direct (N × H)
80. C₇×C₄⋊Q₈	C₂×C₄	semidirect
87. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
90. C₄×C₇×Q₈	C₂×C₄	semidirect
98. C₇×#117	C₂×C₄	semidirect
145. #1993	C₂×C₇	semidirect
146. #1987	C₂×C₇	semidirect
147. #1894	C₂×C₇	semidirect
148. #1892	C₂×C₇	semidirect
149. #1873	C₂×C₇	semidirect
150. #1872	C₂×C₇	semidirect
151. #1825	C₂×C₇	semidirect
152. #1825	C₂×C₇	semidirect
153. #1805	C₂×C₇	semidirect
154. #1763	C₂×C₇	semidirect
155. #1736	C₂×C₇	semidirect
156. #1735	C₂×C₇	semidirect
252. #556	C₄×C₇	semidirect
388. C₄⋊Q₈	C₂×C₄×C₇	semidirect
395. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
398. C₄×Q₈	C₂×C₄×C₇	semidirect
406. #117	C₂×C₄×C₇	semidirect
664. C₇	#22494	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×#556	2
C₂×C₇×#435	2
C₇×#2352	2
C₇×#1993	2
C₇×#1987	2
C₇×#1894	2
C₇×#1892	2
C₇×#1873	2
C₇×#1872	2
C₇×#1825	2
C₇×#1805	2
C₇×#1763	2
C₇×#1736	2
C₇×#1735	2
#22494	7

Subgroups — C7×#22494 #13199710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22494 #13199710