Subgroups — C₇×#22699 #13199915

Order 1792.

904 conjugacy classes of subgroups.

The subgroup lattice has 696 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×#435	C₂	1	1	yes	maximal, characteristic
3	C₇×#2290	C₂	1	1	yes	maximal, characteristic
4	C₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1729	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₇×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
23	C₇×#436	—	2	4	no	—
24	C₇×#435	—	2	4	no	—
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₇×#388	C₄	1	1	yes	characteristic
40	C₇×#388	C₄	1	1	yes	characteristic
41	C₇×#387	C₄	1	1	yes	characteristic
42	C₇×#387	C₄	1	1	yes	characteristic
43	C₇×#386	C₄	1	1	yes	characteristic
44	C₇×#386	C₄	1	1	yes	characteristic
45	C₇×#385	C₄	1	1	yes	characteristic
46	C₇×#385	C₄	1	1	yes	characteristic
47	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₇×#376	C₂²	1	1	yes	characteristic
51	C₇×#336	C₂²	1	1	yes	characteristic
52	C₇×#336	C₂²	1	1	yes	characteristic
53	C₇×#336	C₂²	1	1	yes	characteristic
54	C₇×#336	C₂²	1	1	yes	characteristic
55	C₇×#336	C₂²	1	1	yes	characteristic
56	C₇×#336	C₂²	1	1	yes	characteristic
57	C₇×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	C₇×#336	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	#22699	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₂×C₇×M₁₆	—	2	2	no	—
68	C₂×C₇×M₁₆	—	2	2	no	—
69	C₂×C₇×M₁₆	—	2	2	no	—
70	C₂×C₇×M₁₆	—	2	2	no	—
71	C₂×C₇×M₁₆	—	2	2	no	—
72	C₂×C₇×M₁₆	—	2	2	no	—
73	C₂×C₇×M₁₆	—	4	1	no	—
74	C₂×C₇×M₁₆	—	4	1	no	—
75	C₂×C₇×M₁₆	—	4	1	no	—
76	C₂²×C₇×C₈	—	2	2	no	—
77	C₂²×C₇×C₈	—	2	2	no	—
78	C₂²×C₇×C₈	—	4	1	no	—
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₄×C₇×D₄	D₄	1	4	yes	—
88	C₄×C₇×D₄	Q₈	1	4	yes	—
89	C₇×#117	—	4	1	no	—
90	C₇×#117	—	4	1	no	—
91	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₇	—	4	1	no	—
105	C₂×C₄²×C₇	—	4	1	no	—
106	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊C₈	—	2	2	no	—
114	C₇×C₄⋊C₈	—	2	2	no	—
115	C₇×C₄⋊C₈	—	2	2	no	—
116	C₇×C₄⋊C₈	—	2	2	no	—
117	C₇×C₄⋊C₈	—	4	1	no	—
118	C₇×C₄⋊C₈	—	4	1	no	—
119	C₇×C₄⋊C₈	—	4	1	no	—
120	C₇×C₄⋊C₈	—	4	1	no	—
121	C₇×C₂²⋊C₈	—	2	2	no	—
122	C₇×C₂²⋊C₈	—	2	2	no	—
123	C₇×C₂²⋊C₈	—	2	2	no	—
124	C₇×C₂²⋊C₈	—	2	2	no	—
125	C₇×#97	—	2	2	no	—
126	C₄×C₇×C₈	—	2	2	no	—
127	C₇×#95	C₂×C₄	1	1	yes	characteristic
128	C₇×#95	C₂×C₄	1	1	yes	characteristic
129	C₇×#95	C₂×C₄	1	1	yes	characteristic
130	C₇×#95	C₂×C₄	1	1	yes	characteristic
131	C₇×#95	C₂×C₄	1	1	yes	characteristic
132	C₇×#95	C₂×C₄	1	1	yes	characteristic
133	C₇×#95	C₂×C₄	1	1	yes	characteristic
134	C₇×#95	C₂×C₄	1	1	yes	characteristic
135	C₇×#95	C₂×C₄	1	1	yes	characteristic
136	C₇×#95	C₂×C₄	1	1	yes	characteristic
137	C₂×#436	C₂×C₇	1	1	yes	characteristic
138	C₂×#435	C₂×C₇	1	1	yes	characteristic
139	#2290	C₂×C₇	1	1	yes	characteristic
140	#1940	C₂×C₇	1	1	yes	characteristic, complemented
141	#1939	C₂×C₇	1	1	yes	characteristic, complemented
142	#1851	C₂×C₇	1	1	yes	characteristic, complemented
143	#1851	C₂×C₇	1	1	yes	characteristic, complemented
144	#1851	C₂×C₇	1	1	yes	characteristic, complemented
145	#1850	C₂×C₇	1	1	yes	characteristic, complemented
146	#1832	C₂×C₇	1	1	yes	characteristic, complemented
147	#1798	C₂×C₇	1	1	yes	characteristic, complemented
148	#1797	C₂×C₇	1	1	yes	characteristic, complemented
149	#1768	C₂×C₇	1	1	yes	characteristic, complemented
150	#1729	C₂×C₇	1	1	yes	characteristic, complemented
151	#1728	C₂×C₇	1	1	yes	characteristic, complemented
152	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
153	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₇×D₄	—	4	1	no	—
155	C₂×C₇×D₄	—	4	1	no	—
156	C₂×C₇×D₄	C₄⋊C₄	1	4	yes	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	1	no	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	2	no	—
166	C₂²×C₄×C₇	—	4	1	no	—
167	C₂²×C₄×C₇	—	4	1	no	—
168	C₂²×C₄×C₇	—	4	1	no	—
169	C₂²×C₄×C₇	—	4	1	no	—
170	C₂²×C₄×C₇	—	4	1	no	—
171	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
186	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
187	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
188	C₇×M₁₆	—	4	4	no	—
189	C₇×M₁₆	—	4	4	no	—
190	C₇×M₁₆	—	4	4	no	—
191	C₂×C₇×C₈	—	2	1	no	—
192	C₂×C₇×C₈	—	2	1	no	—
193	C₂×C₇×C₈	—	2	1	no	—
194	C₂×C₇×C₈	—	2	1	no	—
195	C₂×C₇×C₈	—	2	1	no	—
196	C₂×C₇×C₈	—	2	1	no	—
197	C₂×C₇×C₈	—	2	1	no	—
198	C₂×C₇×C₈	—	2	1	no	—
199	C₂×C₇×C₈	—	2	1	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	—	2	1	no	—
212	C₂×C₇×C₈	—	2	1	no	—
213	C₂×C₇×C₈	—	4	4	no	—
214	C₂×C₇×C₈	#41	1	2	yes	—
215	C₂×C₇×C₈	#41	1	2	yes	—
216	C₇×C₄⋊C₄	—	2	2	no	—
217	C₇×C₄⋊C₄	—	4	1	no	—
218	C₇×C₄⋊C₄	—	4	1	no	—
219	C₇×C₄⋊C₄	—	4	1	no	—
220	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
221	C₇×C₂²⋊C₄	—	2	2	no	—
222	C₇×C₂²⋊C₄	—	4	1	no	—
223	C₇×C₂²⋊C₄	—	4	1	no	—
224	C₇×C₂²⋊C₄	—	4	1	no	—
225	C₇×C₂²⋊C₄	—	4	1	no	—
226	C₇×C₂²⋊C₄	—	4	1	no	—
227	C₇×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
228	C₇×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
229	C₄²×C₇	—	2	1	no	—
230	C₄²×C₇	—	2	1	no	—
231	C₄²×C₇	—	2	1	no	—
232	C₄²×C₇	—	2	1	no	—
233	C₄²×C₇	—	2	1	no	—
234	C₄²×C₇	—	2	1	no	—
235	C₄²×C₇	—	2	1	no	—
236	C₄²×C₇	—	2	1	no	—
237	C₄²×C₇	—	4	1	no	—
238	C₄²×C₇	—	4	1	no	—
239	C₄²×C₇	C₂×D₄	1	2	yes	—
240	C₄²×C₇	C₂×Q₈	1	2	yes	—
241	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
242	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
243	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
244	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
246	C₂×#117	C₂²×C₇	1	1	yes	characteristic
247	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
248	#436	—	2	4	no	—
249	#435	—	2	4	no	—
250	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
259	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
260	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
262	C₂×#97	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
264	#388	C₄×C₇	1	1	yes	characteristic
265	#388	C₄×C₇	1	1	yes	characteristic
266	#387	C₄×C₇	1	1	yes	characteristic
267	#387	C₄×C₇	1	1	yes	characteristic
268	#386	C₄×C₇	1	1	yes	characteristic
269	#386	C₄×C₇	1	1	yes	characteristic
270	#385	C₄×C₇	1	1	yes	characteristic
271	#385	C₄×C₇	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
273	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
274	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
275	#376	C₂²×C₇	1	1	yes	characteristic
276	#336	C₂²×C₇	1	1	yes	characteristic
277	#336	C₂²×C₇	1	1	yes	characteristic
278	#336	C₂²×C₇	1	1	yes	characteristic
279	#336	C₂²×C₇	1	1	yes	characteristic
280	#336	C₂²×C₇	1	1	yes	characteristic
281	#336	C₂²×C₇	1	1	yes	characteristic
282	#336	C₂²×C₇	1	1	yes	characteristic
283	#336	C₂²×C₇	1	1	yes	characteristic
284	#336	C₂²×C₇	1	1	yes	characteristic
285	#336	C₂²×C₇	1	1	yes	characteristic
286	C₂³×C₇	—	2	1	no	—
287	C₂³×C₇	—	2	1	no	—
288	C₂³×C₇	—	2	1	no	—
289	C₂³×C₇	—	2	1	no	—
290	C₂³×C₇	—	2	1	no	—
291	C₂³×C₇	—	2	1	no	—
292	C₂³×C₇	—	2	1	no	—
293	C₂³×C₇	—	2	1	no	—
294	C₂³×C₇	—	2	1	no	—
295	C₂³×C₇	—	2	1	no	—
296	C₂³×C₇	—	2	1	no	—
297	C₂³×C₇	—	2	1	no	—
298	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
299	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
300	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
301	C₇×D₄	—	4	4	no	—
302	C₂×C₄×C₇	—	2	1	no	—
303	C₂×C₄×C₇	—	2	1	no	—
304	C₂×C₄×C₇	—	2	1	no	—
305	C₂×C₄×C₇	—	2	1	no	—
306	C₂×C₄×C₇	—	2	1	no	—
307	C₂×C₄×C₇	—	2	1	no	—
308	C₂×C₄×C₇	—	2	1	no	—
309	C₂×C₄×C₇	—	2	1	no	—
310	C₂×C₄×C₇	—	2	1	no	—
311	C₂×C₄×C₇	—	2	1	no	—
312	C₂×C₄×C₇	—	2	2	no	—
313	C₂×C₄×C₇	—	2	2	no	—
314	C₂×C₄×C₇	—	2	2	no	—
315	C₂×C₄×C₇	—	2	2	no	—
316	C₂×C₄×C₇	—	2	2	no	—
317	C₂×C₄×C₇	—	2	2	no	—
318	C₂×C₄×C₇	—	2	2	no	—
319	C₂×C₄×C₇	—	2	2	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	1	no	—
329	C₂×C₄×C₇	—	2	1	no	—
330	C₂×C₄×C₇	—	2	1	no	—
331	C₂×C₄×C₇	—	2	1	no	—
332	C₂×C₄×C₇	—	2	1	no	—
333	C₂×C₄×C₇	—	2	1	no	—
334	C₂×C₄×C₇	—	2	1	no	—
335	C₂×C₄×C₇	—	2	1	no	—
336	C₂×C₄×C₇	—	2	1	no	—
337	C₂×C₄×C₇	—	2	1	no	—
338	C₂×C₄×C₇	—	2	1	no	—
339	C₂×C₄×C₇	—	2	1	no	—
340	C₂×C₄×C₇	—	2	1	no	—
341	C₂×C₄×C₇	—	4	4	no	—
342	C₂×C₄×C₇	—	4	4	no	—
343	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
344	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
345	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
346	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
347	C₂×C₄×C₇	#131	1	2	yes	—
348	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
350	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
352	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
354	C₇×C₈	—	2	2	no	—
355	C₇×C₈	—	2	2	no	—
356	C₇×C₈	—	4	1	no	—
357	C₇×C₈	—	4	1	no	—
358	C₇×C₈	—	4	1	no	—
359	C₇×C₈	—	4	1	no	—
360	C₇×C₈	—	4	1	no	—
361	C₇×C₈	—	4	1	no	—
362	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
363	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
364	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
367	C₂×M₁₆	—	2	2	no	—
368	C₂×M₁₆	—	2	2	no	—
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	—	2	2	no	—
371	C₂×M₁₆	—	2	2	no	—
372	C₂×M₁₆	—	2	2	no	—
373	C₂×M₁₆	—	4	1	no	—
374	C₂×M₁₆	—	4	1	no	—
375	C₂×M₁₆	—	4	1	no	—
376	C₂²×C₈	—	2	2	no	—
377	C₂²×C₈	—	2	2	no	—
378	C₂²×C₈	—	4	1	no	—
379	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
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×D₄	C₇×D₄	1	4	yes	—
388	C₄×D₄	C₇×Q₈	1	4	yes	—
389	#117	—	4	1	no	—
390	#117	—	4	1	no	—
391	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
396	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
404	C₂×C₄²	—	4	1	no	—
405	C₂×C₄²	—	4	1	no	—
406	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
407	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
413	C₄⋊C₈	—	2	2	no	—
414	C₄⋊C₈	—	2	2	no	—
415	C₄⋊C₈	—	2	2	no	—
416	C₄⋊C₈	—	2	2	no	—
417	C₄⋊C₈	—	4	1	no	—
418	C₄⋊C₈	—	4	1	no	—
419	C₄⋊C₈	—	4	1	no	—
420	C₄⋊C₈	—	4	1	no	—
421	C₂²⋊C₈	—	2	2	no	—
422	C₂²⋊C₈	—	2	2	no	—
423	C₂²⋊C₈	—	2	2	no	—
424	C₂²⋊C₈	—	2	2	no	—
425	#97	—	2	2	no	—
426	C₄×C₈	—	2	2	no	—
427	#95	C₂×C₄×C₇	1	1	yes	characteristic
428	#95	C₂×C₄×C₇	1	1	yes	characteristic
429	#95	C₂×C₄×C₇	1	1	yes	characteristic
430	#95	C₂×C₄×C₇	1	1	yes	characteristic
431	#95	C₂×C₄×C₇	1	1	yes	characteristic
432	#95	C₂×C₄×C₇	1	1	yes	characteristic
433	#95	C₂×C₄×C₇	1	1	yes	characteristic
434	#95	C₂×C₄×C₇	1	1	yes	characteristic
435	#95	C₂×C₄×C₇	1	1	yes	characteristic
436	#95	C₂×C₄×C₇	1	1	yes	characteristic
437	C₂²×C₇	—	2	2	no	—
438	C₂²×C₇	—	2	2	no	—
439	C₂²×C₇	—	2	2	no	—
440	C₂²×C₇	—	2	2	no	—
441	C₂²×C₇	—	2	2	no	—
442	C₂²×C₇	—	2	2	no	—
443	C₂²×C₇	—	4	1	no	—
444	C₂²×C₇	—	4	1	no	—
445	C₂²×C₇	—	4	1	no	—
446	C₂²×C₇	—	4	1	no	—
447	C₂²×C₇	—	4	1	no	—
448	C₂²×C₇	—	4	1	no	—
449	C₂²×C₇	—	4	1	no	—
450	C₂²×C₇	—	4	1	no	—
451	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
452	C₂²×C₇	C₄×#41	1	1	yes	characteristic
453	C₂²×C₇	#518	1	1	yes	characteristic
454	C₂²×C₇	C₂×#131	1	1	yes	characteristic
455	C₂²×C₇	#568	1	1	yes	characteristic
456	C₂²×C₇	#568	1	1	yes	characteristic
457	C₂²×C₇	#568	1	1	yes	characteristic
458	C₄×C₇	—	2	2	no	—
459	C₄×C₇	—	2	2	no	—
460	C₄×C₇	—	2	2	no	—
461	C₄×C₇	—	2	2	no	—
462	C₄×C₇	—	2	2	no	—
463	C₄×C₇	—	4	1	no	—
464	C₄×C₇	—	4	1	no	—
465	C₄×C₇	—	4	1	no	—
466	C₄×C₇	—	4	1	no	—
467	C₄×C₇	—	4	1	no	—
468	C₄×C₇	—	4	1	no	—
469	C₄×C₇	—	4	1	no	—
470	C₄×C₇	#546	1	1	yes	characteristic
471	C₄×C₇	#546	1	1	yes	characteristic
472	C₄×C₇	#554	1	1	yes	characteristic
473	C₄×C₇	#554	1	1	yes	characteristic
474	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
475	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
476	C₂×D₄	—	4	1	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	C₇×C₄⋊C₄	1	4	yes	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	—	4	1	no	—
491	C₂²×C₄	—	4	1	no	—
492	C₂²×C₄	—	4	1	no	—
493	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
494	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
495	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
496	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
497	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
498	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
499	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
500	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
501	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
502	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
503	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
506	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
507	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
508	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
510	M₁₆	—	4	4	no	—
511	M₁₆	—	4	4	no	—
512	M₁₆	—	4	4	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	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	—	4	4	no	—
536	C₂×C₈	C₇×#41	1	2	yes	—
537	C₂×C₈	C₇×#41	1	2	yes	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	—	4	1	no	—
541	C₄⋊C₄	—	4	1	no	—
542	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	4	1	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₂²⋊C₄	—	4	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₂²⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
550	C₂²⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	4	1	no	—
560	C₄²	—	4	1	no	—
561	C₄²	C₂×C₇×D₄	1	2	yes	—
562	C₄²	C₂×C₇×Q₈	1	2	yes	—
563	C₂×C₇	—	4	2	no	—
564	C₂×C₇	—	4	2	no	—
565	C₂×C₇	#2349	1	1	yes	characteristic
566	C₂×C₇	#2905	1	1	yes	characteristic
567	C₂×C₇	#2906	1	1	yes	characteristic
568	C₂×C₇	#2967	1	1	yes	characteristic
569	C₂×C₇	#2969	1	1	yes	characteristic
570	C₂×C₇	#2976	1	1	yes	characteristic
571	C₂×C₇	#2978	1	1	yes	characteristic
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
585	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
586	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
587	D₄	—	4	4	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	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	1	no	—
618	C₂×C₄	—	2	1	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	—	4	4	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
630	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
631	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
632	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
633	C₂×C₄	C₇×#131	1	2	yes	—
634	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
635	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
636	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
637	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
638	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
640	C₈	—	2	2	no	—
641	C₈	—	2	2	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	1	no	—
645	C₈	—	4	1	no	—
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₇	#22699	1	1	yes	characteristic, direct product factor, Sylow
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
664	C₂²	C₄×C₇×#41	1	1	yes	characteristic
665	C₂²	C₇×#518	1	1	yes	characteristic
666	C₂²	C₂×C₇×#131	1	1	yes	characteristic
667	C₂²	C₇×#568	1	1	yes	characteristic
668	C₂²	C₇×#568	1	1	yes	characteristic
669	C₂²	C₇×#568	1	1	yes	characteristic
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	2	2	no	—
674	C₄	—	2	2	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	C₇×#546	1	1	yes	characteristic
683	C₄	C₇×#546	1	1	yes	characteristic
684	C₄	C₇×#554	1	1	yes	characteristic
685	C₄	C₇×#554	1	1	yes	characteristic
686	C₂	—	4	2	no	—
687	C₂	—	4	2	no	—
688	C₂	C₇×#2349	1	1	yes	characteristic
689	C₂	C₇×#2905	1	1	yes	characteristic
690	C₂	C₇×#2906	1	1	yes	characteristic
691	C₂	C₇×#2967	1	1	yes	characteristic
692	C₂	C₇×#2969	1	1	yes	characteristic
693	C₂	C₇×#2976	1	1	yes	characteristic
694	C₂	C₇×#2978	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
4. C₇×#1940	C₂	semidirect
5. C₇×#1939	C₂	semidirect
6. C₇×#1851	C₂	semidirect
7. C₇×#1851	C₂	semidirect
8. C₇×#1851	C₂	semidirect
9. C₇×#1850	C₂	semidirect
10. C₇×#1832	C₂	semidirect
11. C₇×#1798	C₂	semidirect
12. C₇×#1797	C₂	semidirect
13. C₇×#1768	C₂	semidirect
14. C₇×#1729	C₂	semidirect
15. C₇×#1728	C₂	semidirect
61. #22699	C₇	direct (N × H)
140. #1940	C₂×C₇	semidirect
141. #1939	C₂×C₇	semidirect
142. #1851	C₂×C₇	semidirect
143. #1851	C₂×C₇	semidirect
144. #1851	C₂×C₇	semidirect
145. #1850	C₂×C₇	semidirect
146. #1832	C₂×C₇	semidirect
147. #1798	C₂×C₇	semidirect
148. #1797	C₂×C₇	semidirect
149. #1768	C₂×C₇	semidirect
150. #1729	C₂×C₇	semidirect
151. #1728	C₂×C₇	semidirect
648. C₇	#22699	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×#435	2
C₇×#2290	2
C₇×#1940	2
C₇×#1939	2
C₇×#1851	2
C₇×#1850	2
C₇×#1832	2
C₇×#1798	2
C₇×#1797	2
C₇×#1768	2
C₇×#1729	2
C₇×#1728	2
#22699	7

Subgroups — C7×#22699 #13199915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22699 #13199915