Subgroups — C₇×#22593 #13199809

Order 1792.

708 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2298	C₂	1	1	yes	maximal, characteristic
2	C₇×#1917	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1851	C₂	1	1	yes	maximal, characteristic
7	C₇×#1850	C₂	1	1	yes	maximal, characteristic
8	C₇×#1840	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1818	C₂	1	1	yes	maximal, characteristic
11	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1753	C₂	1	1	yes	maximal, characteristic
13	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₇×#1744	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1729	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×#117	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#97	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₇×#388	C₄	1	1	yes	characteristic
30	C₇×#388	C₄	1	1	yes	characteristic
31	C₇×#388	C₄	1	1	yes	characteristic
32	C₇×#388	C₄	1	1	yes	characteristic
33	C₇×#387	C₄	1	1	yes	characteristic
34	C₇×#387	C₄	1	1	yes	characteristic
35	C₇×#387	C₄	1	1	yes	characteristic
36	C₇×#387	C₄	1	1	yes	characteristic
37	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₇×#376	C₂²	1	1	yes	characteristic
42	C₄³×C₇	C₂²	1	1	yes	characteristic
43	C₇×#336	C₂²	1	1	yes	characteristic
44	C₇×#336	C₂²	1	1	yes	characteristic
45	C₇×#336	C₂²	1	1	yes	characteristic
46	C₇×#336	C₂²	1	1	yes	characteristic
47	C₇×#336	C₂²	1	1	yes	characteristic
48	C₇×#336	C₂²	1	1	yes	characteristic
49	C₇×#336	C₂²	1	1	yes	characteristic
50	C₇×#336	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	#22593	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂×C₇×M₁₆	—	2	2	no	—
62	C₂×C₇×M₁₆	—	2	2	no	—
63	C₂×C₇×M₁₆	—	4	1	no	—
64	C₂²×C₇×C₈	—	2	2	no	—
65	C₂²×C₇×C₈	—	2	2	no	—
66	C₂²×C₇×C₈	—	4	1	no	—
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₇×#117	—	2	2	no	—
76	C₇×#117	—	2	2	no	—
77	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
99	C₇×C₄⋊C₈	—	2	2	no	—
100	C₇×C₄⋊C₈	—	2	2	no	—
101	C₇×C₄⋊C₈	—	4	1	no	—
102	C₇×C₄⋊C₈	—	4	1	no	—
103	C₇×C₂²⋊C₈	—	2	2	no	—
104	C₇×C₂²⋊C₈	—	2	2	no	—
105	C₇×#97	—	4	1	no	—
106	C₄×C₇×C₈	—	2	2	no	—
107	C₄×C₇×C₈	—	2	2	no	—
108	C₄×C₇×C₈	—	4	1	no	—
109	C₇×#95	C₂×C₄	1	1	yes	characteristic
110	C₇×#95	C₂×C₄	1	1	yes	characteristic
111	C₇×#95	C₂×C₄	1	1	yes	characteristic
112	C₇×#95	C₂×C₄	1	1	yes	characteristic
113	C₇×#95	C₂×C₄	1	1	yes	characteristic
114	C₇×#95	C₂×C₄	1	1	yes	characteristic
115	C₇×#95	C₂×C₄	1	1	yes	characteristic
116	C₇×#95	C₂×C₄	1	1	yes	characteristic
117	C₇×#95	C₂×C₄	1	1	yes	characteristic
118	C₇×#95	C₂×C₄	1	1	yes	characteristic
119	C₇×#95	C₂×C₄	1	1	yes	characteristic
120	C₇×#95	C₂×C₄	1	1	yes	characteristic
121	#2298	C₂×C₇	1	1	yes	characteristic
122	#1917	C₂×C₇	1	1	yes	characteristic, complemented
123	#1916	C₂×C₇	1	1	yes	characteristic, complemented
124	#1916	C₂×C₇	1	1	yes	characteristic, complemented
125	#1916	C₂×C₇	1	1	yes	characteristic, complemented
126	#1851	C₂×C₇	1	1	yes	characteristic
127	#1850	C₂×C₇	1	1	yes	characteristic
128	#1840	C₂×C₇	1	1	yes	characteristic, complemented
129	#1831	C₂×C₇	1	1	yes	characteristic, complemented
130	#1818	C₂×C₇	1	1	yes	characteristic
131	#1768	C₂×C₇	1	1	yes	characteristic, complemented
132	#1753	C₂×C₇	1	1	yes	characteristic
133	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
134	#1744	C₂×C₇	1	1	yes	characteristic, complemented
135	#1729	C₂×C₇	1	1	yes	characteristic
136	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	—	2	1	no	—
138	C₂²×C₄×C₇	—	2	1	no	—
139	C₂²×C₄×C₇	—	2	1	no	—
140	C₂²×C₄×C₇	—	2	1	no	—
141	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇	#41	1	2	yes	—
155	C₂²×C₄×C₇	#41	1	2	yes	—
156	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
157	C₇×M₁₆	—	4	4	no	—
158	C₂×C₇×C₈	—	2	1	no	—
159	C₂×C₇×C₈	—	2	1	no	—
160	C₂×C₇×C₈	—	2	1	no	—
161	C₂×C₇×C₈	—	2	1	no	—
162	C₂×C₇×C₈	—	2	1	no	—
163	C₂×C₇×C₈	—	2	1	no	—
164	C₂×C₇×C₈	—	2	1	no	—
165	C₂×C₇×C₈	—	2	1	no	—
166	C₂×C₇×C₈	—	2	1	no	—
167	C₂×C₇×C₈	—	2	1	no	—
168	C₂×C₇×C₈	—	2	1	no	—
169	C₂×C₇×C₈	—	2	1	no	—
170	C₂×C₇×C₈	—	2	1	no	—
171	C₂×C₇×C₈	—	2	1	no	—
172	C₂×C₇×C₈	—	2	1	no	—
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	—	2	1	no	—
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	—	2	1	no	—
180	C₂×C₇×C₈	—	4	4	no	—
181	C₂×C₇×C₈	#41	1	2	yes	—
182	C₂×C₇×C₈	#41	1	2	yes	—
183	C₇×C₄⋊C₄	—	2	2	no	—
184	C₇×C₄⋊C₄	—	2	2	no	—
185	C₇×C₄⋊C₄	—	2	2	no	—
186	C₇×C₄⋊C₄	—	2	2	no	—
187	C₇×C₄⋊C₄	—	2	2	no	—
188	C₇×C₄⋊C₄	—	4	1	no	—
189	C₇×C₂²⋊C₄	—	2	2	no	—
190	C₇×C₂²⋊C₄	—	2	2	no	—
191	C₇×C₂²⋊C₄	—	2	2	no	—
192	C₇×C₂²⋊C₄	—	2	2	no	—
193	C₇×C₂²⋊C₄	—	2	2	no	—
194	C₇×C₂²⋊C₄	—	4	1	no	—
195	C₄²×C₇	—	2	2	no	—
196	C₄²×C₇	—	2	2	no	—
197	C₄²×C₇	—	2	2	no	—
198	C₄²×C₇	—	2	1	no	—
199	C₄²×C₇	—	2	1	no	—
200	C₄²×C₇	—	2	1	no	—
201	C₄²×C₇	—	2	1	no	—
202	C₄²×C₇	—	2	1	no	—
203	C₄²×C₇	—	2	1	no	—
204	C₄²×C₇	—	2	1	no	—
205	C₄²×C₇	—	2	1	no	—
206	C₄²×C₇	—	2	1	no	—
207	C₄²×C₇	—	2	1	no	—
208	C₄²×C₇	—	2	1	no	—
209	C₄²×C₇	—	2	1	no	—
210	C₄²×C₇	—	4	1	no	—
211	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
212	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
213	C₂×#117	C₂²×C₇	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
220	C₂×#97	C₂²×C₇	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
224	#388	C₄×C₇	1	1	yes	characteristic
225	#388	C₄×C₇	1	1	yes	characteristic
226	#388	C₄×C₇	1	1	yes	characteristic
227	#388	C₄×C₇	1	1	yes	characteristic
228	#387	C₄×C₇	1	1	yes	characteristic
229	#387	C₄×C₇	1	1	yes	characteristic
230	#387	C₄×C₇	1	1	yes	characteristic
231	#387	C₄×C₇	1	1	yes	characteristic
232	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
233	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
234	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
235	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
236	#376	C₂²×C₇	1	1	yes	characteristic
237	C₄³	C₂²×C₇	1	1	yes	characteristic
238	#336	C₂²×C₇	1	1	yes	characteristic
239	#336	C₂²×C₇	1	1	yes	characteristic
240	#336	C₂²×C₇	1	1	yes	characteristic
241	#336	C₂²×C₇	1	1	yes	characteristic
242	#336	C₂²×C₇	1	1	yes	characteristic
243	#336	C₂²×C₇	1	1	yes	characteristic
244	#336	C₂²×C₇	1	1	yes	characteristic
245	#336	C₂²×C₇	1	1	yes	characteristic
246	#336	C₂²×C₇	1	1	yes	characteristic
247	#336	C₂²×C₇	1	1	yes	characteristic
248	#336	C₂²×C₇	1	1	yes	characteristic
249	#336	C₂²×C₇	1	1	yes	characteristic
250	#336	C₂²×C₇	1	1	yes	characteristic
251	#336	C₂²×C₇	1	1	yes	characteristic
252	#336	C₂²×C₇	1	1	yes	characteristic
253	#336	C₂²×C₇	1	1	yes	characteristic
254	C₂³×C₇	—	2	1	no	—
255	C₂³×C₇	—	2	1	no	—
256	C₂³×C₇	—	2	1	no	—
257	C₂³×C₇	—	2	1	no	—
258	C₂³×C₇	—	2	1	no	—
259	C₂³×C₇	—	2	1	no	—
260	C₂³×C₇	#117	1	2	yes	—
261	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₇	—	2	1	no	—
263	C₂×C₄×C₇	—	2	1	no	—
264	C₂×C₄×C₇	—	2	1	no	—
265	C₂×C₄×C₇	—	2	1	no	—
266	C₂×C₄×C₇	—	2	1	no	—
267	C₂×C₄×C₇	—	2	1	no	—
268	C₂×C₄×C₇	—	2	1	no	—
269	C₂×C₄×C₇	—	2	1	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	1	no	—
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	1	no	—
277	C₂×C₄×C₇	—	2	1	no	—
278	C₂×C₄×C₇	—	2	1	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	2	1	no	—
281	C₂×C₄×C₇	—	2	1	no	—
282	C₂×C₄×C₇	—	2	1	no	—
283	C₂×C₄×C₇	—	2	1	no	—
284	C₂×C₄×C₇	—	2	1	no	—
285	C₂×C₄×C₇	—	2	1	no	—
286	C₂×C₄×C₇	—	2	1	no	—
287	C₂×C₄×C₇	—	2	1	no	—
288	C₂×C₄×C₇	—	2	1	no	—
289	C₂×C₄×C₇	—	2	1	no	—
290	C₂×C₄×C₇	—	2	1	no	—
291	C₂×C₄×C₇	—	2	1	no	—
292	C₂×C₄×C₇	—	2	1	no	—
293	C₂×C₄×C₇	—	2	1	no	—
294	C₂×C₄×C₇	—	2	1	no	—
295	C₂×C₄×C₇	—	2	1	no	—
296	C₂×C₄×C₇	—	2	1	no	—
297	C₂×C₄×C₇	—	2	1	no	—
298	C₂×C₄×C₇	—	2	1	no	—
299	C₂×C₄×C₇	—	2	1	no	—
300	C₂×C₄×C₇	—	2	1	no	—
301	C₂×C₄×C₇	#117	1	2	yes	—
302	C₂×C₄×C₇	#131	1	2	yes	—
303	C₂×C₄×C₇	#131	1	2	yes	—
304	C₂×C₄×C₇	#131	1	2	yes	—
305	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
311	C₇×C₈	—	2	2	no	—
312	C₇×C₈	—	2	2	no	—
313	C₇×C₈	—	4	1	no	—
314	C₇×C₈	—	4	1	no	—
315	C₇×C₈	—	4	1	no	—
316	C₇×C₈	—	4	1	no	—
317	C₇×C₈	—	4	1	no	—
318	C₇×C₈	—	4	1	no	—
319	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
320	C₂×M₁₆	—	2	2	no	—
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	4	1	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	—	2	2	no	—
325	C₂²×C₈	—	4	1	no	—
326	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
334	#117	—	2	2	no	—
335	#117	—	2	2	no	—
336	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
343	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
346	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
348	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
349	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
350	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
351	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
358	C₄⋊C₈	—	2	2	no	—
359	C₄⋊C₈	—	2	2	no	—
360	C₄⋊C₈	—	4	1	no	—
361	C₄⋊C₈	—	4	1	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	#97	—	4	1	no	—
365	C₄×C₈	—	2	2	no	—
366	C₄×C₈	—	2	2	no	—
367	C₄×C₈	—	4	1	no	—
368	#95	C₂×C₄×C₇	1	1	yes	characteristic
369	#95	C₂×C₄×C₇	1	1	yes	characteristic
370	#95	C₂×C₄×C₇	1	1	yes	characteristic
371	#95	C₂×C₄×C₇	1	1	yes	characteristic
372	#95	C₂×C₄×C₇	1	1	yes	characteristic
373	#95	C₂×C₄×C₇	1	1	yes	characteristic
374	#95	C₂×C₄×C₇	1	1	yes	characteristic
375	#95	C₂×C₄×C₇	1	1	yes	characteristic
376	#95	C₂×C₄×C₇	1	1	yes	characteristic
377	#95	C₂×C₄×C₇	1	1	yes	characteristic
378	#95	C₂×C₄×C₇	1	1	yes	characteristic
379	#95	C₂×C₄×C₇	1	1	yes	characteristic
380	C₂²×C₇	—	2	2	no	—
381	C₂²×C₇	—	2	2	no	—
382	C₂²×C₇	—	2	2	no	—
383	C₂²×C₇	—	4	1	no	—
384	C₂²×C₇	—	4	1	no	—
385	C₂²×C₇	—	4	1	no	—
386	C₂²×C₇	—	4	1	no	—
387	C₂²×C₇	C₂×#117	1	1	yes	characteristic
388	C₂²×C₇	C₄×#41	1	1	yes	characteristic
389	C₂²×C₇	#520	1	1	yes	characteristic
390	C₂²×C₇	C₂×#131	1	1	yes	characteristic
391	C₂²×C₇	C₂×#131	1	1	yes	characteristic
392	C₂²×C₇	C₂×#131	1	1	yes	characteristic
393	C₂²×C₇	#568	1	1	yes	characteristic
394	C₄×C₇	—	2	2	no	—
395	C₄×C₇	—	2	2	no	—
396	C₄×C₇	—	2	2	no	—
397	C₄×C₇	—	2	2	no	—
398	C₄×C₇	—	4	1	no	—
399	C₄×C₇	—	4	1	no	—
400	C₄×C₇	—	4	1	no	—
401	C₄×C₇	—	4	1	no	—
402	C₄×C₇	—	4	1	no	—
403	C₄×C₇	—	4	1	no	—
404	C₄×C₇	—	4	1	no	—
405	C₄×C₇	—	4	1	no	—
406	C₄×C₇	—	4	1	no	—
407	C₄×C₇	#551	1	1	yes	characteristic
408	C₄×C₇	#551	1	1	yes	characteristic
409	C₄×C₇	#552	1	1	yes	characteristic
410	C₄×C₇	#552	1	1	yes	characteristic
411	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
417	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
418	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
419	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
420	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
421	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
422	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
423	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
425	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
426	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
427	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
429	C₂²×C₄	C₇×#41	1	2	yes	—
430	C₂²×C₄	C₇×#41	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
432	M₁₆	—	4	4	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	4	4	no	—
456	C₂×C₈	C₇×#41	1	2	yes	—
457	C₂×C₈	C₇×#41	1	2	yes	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	4	1	no	—
486	C₂×C₇	—	4	2	no	—
487	C₂×C₇	#2343	1	1	yes	characteristic
488	C₂×C₇	#2922	1	1	yes	characteristic
489	C₂×C₇	#2925	1	1	yes	characteristic
490	C₂×C₇	#2966	1	1	yes	characteristic
491	C₂×C₇	#2968	1	1	yes	characteristic
492	C₂×C₇	#2993	1	1	yes	characteristic
493	C₂×C₇	#2994	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	C₇×#117	1	2	yes	—
501	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	C₇×#117	1	2	yes	—
542	C₂×C₄	C₇×#131	1	2	yes	—
543	C₂×C₄	C₇×#131	1	2	yes	—
544	C₂×C₄	C₇×#131	1	2	yes	—
545	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
546	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
547	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
548	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
549	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	2	2	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₇	#22593	1	1	yes	characteristic, direct product factor, Sylow
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	C₂×C₇×#117	1	1	yes	characteristic
568	C₂²	C₄×C₇×#41	1	1	yes	characteristic
569	C₂²	C₇×#520	1	1	yes	characteristic
570	C₂²	C₂×C₇×#131	1	1	yes	characteristic
571	C₂²	C₂×C₇×#131	1	1	yes	characteristic
572	C₂²	C₂×C₇×#131	1	1	yes	characteristic
573	C₂²	C₇×#568	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	C₇×#551	1	1	yes	characteristic
588	C₄	C₇×#551	1	1	yes	characteristic
589	C₄	C₇×#552	1	1	yes	characteristic
590	C₄	C₇×#552	1	1	yes	characteristic
591	C₂	—	4	2	no	—
592	C₂	C₇×#2343	1	1	yes	characteristic
593	C₂	C₇×#2922	1	1	yes	characteristic
594	C₂	C₇×#2925	1	1	yes	characteristic
595	C₂	C₇×#2966	1	1	yes	characteristic
596	C₂	C₇×#2968	1	1	yes	characteristic
597	C₂	C₇×#2993	1	1	yes	characteristic
598	C₂	C₇×#2994	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	C₂⁴×C₇	C₂²×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
2. C₇×#1917	C₂	semidirect
3. C₇×#1916	C₂	semidirect
4. C₇×#1916	C₂	semidirect
5. C₇×#1916	C₂	semidirect
8. C₇×#1840	C₂	semidirect
9. C₇×#1831	C₂	semidirect
11. C₇×#1768	C₂	semidirect
14. C₇×#1744	C₂	semidirect
59. #22593	C₇	direct (N × H)
122. #1917	C₂×C₇	semidirect
123. #1916	C₂×C₇	semidirect
124. #1916	C₂×C₇	semidirect
125. #1916	C₂×C₇	semidirect
128. #1840	C₂×C₇	semidirect
129. #1831	C₂×C₇	semidirect
131. #1768	C₂×C₇	semidirect
134. #1744	C₂×C₇	semidirect
559. C₇	#22593	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2298	2
C₇×#1917	2
C₇×#1916	2
C₇×#1851	2
C₇×#1850	2
C₇×#1840	2
C₇×#1831	2
C₇×#1818	2
C₇×#1768	2
C₇×#1753	2
C₇×C₈×C₂²⋊C₄	2
C₇×#1744	2
C₇×#1729	2
#22593	7

Subgroups — C7×#22593 #13199809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22593 #13199809