Subgroups — C₇×#22497 #13199713

Order 1792.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#554	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×#1988	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×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1823	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	C₂×C₇×#340	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×#554	—	2	4	no	—
19	C₇×#554	C₄	1	8	yes	complemented
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#125	—	2	1	no	—
22	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₇×C₂²⋊Q₈	—	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	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×D₄	—	2	1	no	—
28	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₄⋊C₄	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	#22497	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	—	2	1	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
71	C₂×C₇×M₁₆	—	2	2	no	—
72	C₂×C₇×M₁₆	—	2	2	no	—
73	C₂×C₇×M₁₆	—	4	1	no	—
74	C₂²×C₇×C₈	—	2	2	no	—
75	C₂²×C₇×C₈	—	2	2	no	—
76	C₂²×C₇×C₈	—	4	1	no	—
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₇×C₄⋊Q₈	—	2	2	no	—
82	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
83	C₇×#125	—	2	8	no	—
84	C₇×C₂²⋊Q₈	—	2	2	no	—
85	C₇×C₂²⋊Q₈	—	2	2	no	—
86	C₇×C₂²⋊Q₈	—	2	8	no	—
87	C₇×C₂²⋊Q₈	—	2	8	no	—
88	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
89	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	complemented
90	C₄×C₇×Q₈	—	2	2	no	—
91	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
92	C₄×C₇×D₄	—	2	8	no	—
93	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
94	C₄×C₇×D₄	D₄	1	4	yes	—
95	C₇×#117	—	2	2	no	—
96	C₇×#117	—	4	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	2	no	—
100	C₂×C₇×C₄⋊C₄	—	2	2	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	—	2	1	no	—
104	C₂×C₇×C₄⋊C₄	—	2	1	no	—
105	C₂×C₇×C₄⋊C₄	—	2	2	no	—
106	C₂×C₇×C₄⋊C₄	—	2	1	no	—
107	C₂×C₇×C₄⋊C₄	—	4	1	no	—
108	C₂×C₇×C₄⋊C₄	C₂×C₄	1	4	yes	—
109	C₂×C₇×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
110	C₂×C₇×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
122	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
124	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
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×#554	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	#1988	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	#1824	C₂×C₇	1	1	yes	characteristic, complemented
152	#1823	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	C₂×#340	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	—	8	1	no	—
166	C₂×C₇×Q₈	—	8	1	no	—
167	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
168	C₂×C₇×D₄	—	2	2	no	—
169	C₂×C₇×D₄	—	2	2	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	4	no	—
185	C₂²×C₄×C₇	—	2	4	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	1	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	4	2	no	—
190	C₂²×C₄×C₇	—	4	2	no	—
191	C₂²×C₄×C₇	—	8	1	no	—
192	C₂²×C₄×C₇	—	8	1	no	—
193	C₂²×C₄×C₇	—	8	1	no	—
194	C₂²×C₄×C₇	—	8	1	no	—
195	C₂²×C₄×C₇	—	8	1	no	—
196	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
197	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
205	C₇×M₁₆	—	4	4	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	—	2	1	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₂×C₇×C₈	—	2	1	no	—
215	C₂×C₇×C₈	—	2	1	no	—
216	C₂×C₇×C₈	—	2	1	no	—
217	C₂×C₇×C₈	—	4	4	no	—
218	C₂×C₇×C₈	#41	1	2	yes	—
219	C₇×C₄⋊C₄	—	2	4	no	—
220	C₇×C₄⋊C₄	—	2	4	no	—
221	C₇×C₄⋊C₄	—	2	4	no	—
222	C₇×C₄⋊C₄	—	2	4	no	—
223	C₇×C₄⋊C₄	—	2	4	no	—
224	C₇×C₄⋊C₄	—	2	4	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	2	1	no	—
228	C₇×C₄⋊C₄	—	2	1	no	—
229	C₇×C₄⋊C₄	—	2	1	no	—
230	C₇×C₄⋊C₄	—	2	1	no	—
231	C₇×C₄⋊C₄	—	2	1	no	—
232	C₇×C₄⋊C₄	—	2	1	no	—
233	C₇×C₄⋊C₄	—	2	1	no	—
234	C₇×C₄⋊C₄	—	2	1	no	—
235	C₇×C₄⋊C₄	—	4	2	no	—
236	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
237	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
238	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
239	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
240	C₇×C₄⋊C₄	#41	1	2	yes	—
241	C₇×C₂²⋊C₄	—	2	4	no	—
242	C₇×C₂²⋊C₄	—	2	4	no	—
243	C₇×C₂²⋊C₄	—	4	2	no	—
244	C₇×C₂²⋊C₄	—	4	2	no	—
245	C₇×C₂²⋊C₄	—	8	1	no	—
246	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
247	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
248	C₄²×C₇	—	2	4	no	—
249	C₄²×C₇	—	4	2	no	—
250	C₄²×C₇	—	8	1	no	—
251	C₄²×C₇	C₂²×C₄	1	2	yes	—
252	C₄²×C₇	C₂×D₄	1	2	yes	—
253	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
254	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
255	#554	—	2	4	no	—
256	#554	C₄×C₇	1	8	yes	complemented
257	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×#125	—	2	1	no	—
259	C₂×C₂²⋊Q₈	—	2	1	no	—
260	C₂×C₂²⋊Q₈	—	2	1	no	—
261	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
262	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×C₄×D₄	—	2	1	no	—
265	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
266	C₂×#117	C₂²×C₇	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
270	#435	—	2	4	no	—
271	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
272	C₂×#103	C₂²×C₇	1	1	yes	characteristic
273	C₂×#103	C₂²×C₇	1	1	yes	characteristic
274	C₂×#103	C₂²×C₇	1	1	yes	characteristic
275	C₂×#103	C₂²×C₇	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
278	C₂×#97	C₂²×C₇	1	1	yes	characteristic
279	#388	—	2	1	no	—
280	#387	—	2	1	no	—
281	#386	—	2	1	no	—
282	#382	C₂²×C₇	1	1	yes	characteristic
283	#380	C₂²×C₇	1	1	yes	characteristic
284	#380	C₂²×C₇	1	1	yes	characteristic
285	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
286	C₄×C₂²⋊C₄	—	2	1	no	—
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	#340	C₂²×C₇	1	1	yes	characteristic
296	#340	C₂²×C₇	1	1	yes	characteristic
297	#340	C₂²×C₇	1	1	yes	characteristic
298	#340	C₂²×C₇	1	1	yes	characteristic
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	—	2	1	no	—
308	C₂³×C₇	—	2	1	no	—
309	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
311	C₂³×C₇	#137	1	2	yes	—
312	C₂³×C₇	#137	1	2	yes	—
313	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
314	C₇×Q₈	—	2	2	no	—
315	C₇×Q₈	—	2	2	no	—
316	C₇×Q₈	—	4	1	no	—
317	C₇×Q₈	—	4	1	no	—
318	C₇×Q₈	—	8	4	no	—
319	C₇×D₄	—	2	8	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	1	no	—
325	C₂×C₄×C₇	—	2	1	no	—
326	C₂×C₄×C₇	—	2	1	no	—
327	C₂×C₄×C₇	—	2	1	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	—	2	2	no	—
338	C₂×C₄×C₇	—	2	2	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	2	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	—	4	1	no	—
357	C₂×C₄×C₇	—	4	1	no	—
358	C₂×C₄×C₇	—	4	1	no	—
359	C₂×C₄×C₇	—	4	1	no	—
360	C₂×C₄×C₇	—	8	4	no	—
361	C₂×C₄×C₇	—	8	4	no	—
362	C₂×C₄×C₇	—	8	4	no	—
363	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
364	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
365	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
366	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
367	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
370	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
372	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
373	C₇×C₈	—	2	2	no	—
374	C₇×C₈	—	4	1	no	—
375	C₇×C₈	—	4	1	no	—
376	C₇×C₈	—	4	1	no	—
377	C₂²×Q₈	—	2	1	no	—
378	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
379	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
385	C₂×M₁₆	—	2	2	no	—
386	C₂×M₁₆	—	2	2	no	—
387	C₂×M₁₆	—	4	1	no	—
388	C₂²×C₈	—	2	2	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	—	4	1	no	—
391	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
395	C₄⋊Q₈	—	2	2	no	—
396	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
397	#125	—	2	8	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	8	no	—
401	C₂²⋊Q₈	—	2	8	no	—
402	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
403	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
404	C₄×Q₈	—	2	2	no	—
405	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
406	C₄×D₄	—	2	8	no	—
407	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
408	C₄×D₄	C₇×D₄	1	4	yes	—
409	#117	—	2	2	no	—
410	#117	—	4	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	2	no	—
414	C₂×C₄⋊C₄	—	2	2	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	2	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	4	1	no	—
422	C₂×C₄⋊C₄	C₂×C₄×C₇	1	4	yes	—
423	C₂×C₄⋊C₄	C₂×C₄×C₇	1	4	yes	complemented
424	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
443	C₄⋊C₈	—	2	2	no	—
444	#103	—	2	2	no	—
445	#103	—	2	2	no	—
446	#103	—	4	1	no	—
447	#103	—	4	1	no	—
448	C₂²⋊C₈	—	2	2	no	—
449	C₂²⋊C₈	—	2	2	no	—
450	#97	—	2	2	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	C₂²×C₇	—	2	2	no	—
457	C₂²×C₇	—	2	2	no	—
458	C₂²×C₇	—	2	2	no	—
459	C₂²×C₇	—	2	2	no	—
460	C₂²×C₇	—	2	2	no	—
461	C₂²×C₇	—	2	2	no	—
462	C₂²×C₇	—	2	2	no	—
463	C₂²×C₇	—	2	2	no	—
464	C₂²×C₇	—	2	2	no	—
465	C₂²×C₇	—	4	1	no	—
466	C₂²×C₇	—	4	1	no	—
467	C₂²×C₇	—	4	1	no	—
468	C₂²×C₇	—	4	1	no	—
469	C₂²×C₇	#419	1	4	yes	—
470	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
471	C₂²×C₇	#546	1	1	yes	characteristic
472	C₂²×C₇	#547	1	1	yes	characteristic
473	C₂²×C₇	C₂×#137	1	1	yes	characteristic
474	C₂²×C₇	C₂×#137	1	1	yes	characteristic
475	C₂²×C₇	#576	1	1	yes	characteristic
476	C₂²×C₇	#577	1	1	yes	characteristic
477	C₄×C₇	—	2	2	no	—
478	C₄×C₇	—	2	2	no	—
479	C₄×C₇	—	2	2	no	—
480	C₄×C₇	—	2	2	no	—
481	C₄×C₇	—	4	2	no	—
482	C₄×C₇	—	4	2	no	—
483	C₄×C₇	—	4	2	no	—
484	C₄×C₇	—	4	2	no	—
485	C₄×C₇	—	4	2	no	—
486	C₄×C₇	—	8	1	no	—
487	C₄×C₇	—	8	1	no	—
488	C₄×C₇	—	8	1	no	—
489	C₄×C₇	C₄×#41	1	1	yes	characteristic
490	C₄×C₇	#520	1	1	yes	characteristic
491	C₄×C₇	#546	1	1	yes	characteristic
492	C₄×C₇	#547	1	1	yes	characteristic
493	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
494	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	8	1	no	—
502	C₂×Q₈	—	8	1	no	—
503	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	C₇×C₂²⋊C₄	1	4	yes	—
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	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	8	1	no	—
528	C₂²×C₄	—	8	1	no	—
529	C₂²×C₄	—	8	1	no	—
530	C₂²×C₄	—	8	1	no	—
531	C₂²×C₄	—	8	1	no	—
532	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
533	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
534	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
535	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
539	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
541	M₁₆	—	4	4	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	4	4	no	—
554	C₂×C₈	C₇×#41	1	2	yes	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
573	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
574	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
575	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
576	C₄⋊C₄	C₇×#41	1	2	yes	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	8	1	no	—
582	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
583	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
584	C₄²	—	2	4	no	—
585	C₄²	—	4	2	no	—
586	C₄²	—	8	1	no	—
587	C₄²	C₂²×C₄×C₇	1	2	yes	—
588	C₄²	C₂×C₇×D₄	1	2	yes	—
589	C₂×C₇	—	2	4	no	—
590	C₂×C₇	—	4	2	no	—
591	C₂×C₇	#2339	1	1	yes	characteristic
592	C₂×C₇	C₂×#419	1	1	yes	characteristic
593	C₂×C₇	#2897	1	1	yes	characteristic
594	C₂×C₇	#3314	1	1	yes	characteristic
595	C₂×C₇	#3316	1	1	yes	characteristic
596	C₂×C₇	#3344	1	1	yes	characteristic
597	C₂×C₇	#3346	1	1	yes	characteristic
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
609	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
610	C₂³	C₇×#137	1	2	yes	—
611	C₂³	C₇×#137	1	2	yes	—
612	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
613	Q₈	—	2	2	no	—
614	Q₈	—	2	2	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	8	4	no	—
618	D₄	—	2	8	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	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	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	8	4	no	—
660	C₂×C₄	—	8	4	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
663	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
664	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
665	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
666	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
667	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
668	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
669	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
670	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
672	C₈	—	2	2	no	—
673	C₈	—	4	1	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₇	#22497	1	1	yes	characteristic, direct product factor, Sylow
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	C₇×#419	1	4	yes	—
691	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
692	C₂²	C₇×#546	1	1	yes	characteristic
693	C₂²	C₇×#547	1	1	yes	characteristic
694	C₂²	C₂×C₇×#137	1	1	yes	characteristic
695	C₂²	C₂×C₇×#137	1	1	yes	characteristic
696	C₂²	C₇×#576	1	1	yes	characteristic
697	C₂²	C₇×#577	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	—	8	1	no	—
710	C₄	C₄×C₇×#41	1	1	yes	characteristic
711	C₄	C₇×#520	1	1	yes	characteristic
712	C₄	C₇×#546	1	1	yes	characteristic
713	C₄	C₇×#547	1	1	yes	characteristic
714	C₂	—	2	4	no	—
715	C₂	—	4	2	no	—
716	C₂	C₇×#2339	1	1	yes	characteristic
717	C₂	C₂×C₇×#419	1	1	yes	characteristic
718	C₂	C₇×#2897	1	1	yes	characteristic
719	C₂	C₇×#3314	1	1	yes	characteristic
720	C₂	C₇×#3316	1	1	yes	characteristic
721	C₂	C₇×#3344	1	1	yes	characteristic
722	C₂	C₇×#3346	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×#1988	C₂	semidirect
6. C₇×#1894	C₂	semidirect
7. C₇×#1892	C₂	semidirect
8. C₇×#1873	C₂	semidirect
9. C₇×#1872	C₂	semidirect
10. C₇×#1824	C₂	semidirect
11. C₇×#1823	C₂	semidirect
12. C₇×#1805	C₂	semidirect
13. C₇×#1763	C₂	semidirect
14. C₇×#1736	C₂	semidirect
15. C₂×C₇×#340	C₂	semidirect
19. C₇×#554	C₄	semidirect
62. #22497	C₇	direct (N × H)
82. C₇×C₄⋊Q₈	C₂×C₄	semidirect
89. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
91. C₄×C₇×Q₈	C₂×C₄	semidirect
109. C₂×C₇×C₄⋊C₄	C₂×C₄	semidirect
145. #1993	C₂×C₇	semidirect
146. #1988	C₂×C₇	semidirect
147. #1894	C₂×C₇	semidirect
148. #1892	C₂×C₇	semidirect
149. #1873	C₂×C₇	semidirect
150. #1872	C₂×C₇	semidirect
151. #1824	C₂×C₇	semidirect
152. #1823	C₂×C₇	semidirect
153. #1805	C₂×C₇	semidirect
154. #1763	C₂×C₇	semidirect
155. #1736	C₂×C₇	semidirect
156. C₂×#340	C₂×C₇	semidirect
256. #554	C₄×C₇	semidirect
396. C₄⋊Q₈	C₂×C₄×C₇	semidirect
403. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
405. C₄×Q₈	C₂×C₄×C₇	semidirect
423. C₂×C₄⋊C₄	C₂×C₄×C₇	semidirect
676. C₇	#22497	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×#554	2
C₂×C₇×#435	2
C₇×#2352	2
C₇×#1993	2
C₇×#1988	2
C₇×#1894	2
C₇×#1892	2
C₇×#1873	2
C₇×#1872	2
C₇×#1824	2
C₇×#1823	2
C₇×#1805	2
C₇×#1763	2
C₇×#1736	2
C₂×C₇×#340	2
#22497	7

Subgroups — C7×#22497 #13199713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22497 #13199713