Subgroups — C₇×#22175 #13199391

Order 1792.

912 conjugacy classes of subgroups.

The subgroup lattice has 746 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, complemented
2	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2392	C₂	1	1	yes	maximal, characteristic
4	C₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1729	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	C₂³×C₇×C₈	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×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₇×#117	C₂²	1	1	yes	characteristic
24	C₇×#436	—	2	4	no	—
25	C₇×#435	—	2	4	no	—
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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₂²⋊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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
40	C₇×#398	C₄	1	1	yes	characteristic
41	C₇×#397	C₄	1	1	yes	characteristic
42	C₇×#396	C₄	1	1	yes	characteristic
43	C₇×#396	C₄	1	1	yes	characteristic
44	C₇×#394	C₄	1	1	yes	characteristic
45	C₇×#394	C₄	1	1	yes	characteristic
46	C₇×#394	C₄	1	1	yes	characteristic
47	C₇×#392	C₄	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₂²⋊C₄	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	#22175	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₇×D₄	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	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₂×C₇×M₁₆	—	2	2	no	—
69	C₂×C₇×M₁₆	—	4	1	no	—
70	C₂×C₇×M₁₆	—	4	1	no	—
71	C₂×C₇×M₁₆	—	4	1	no	—
72	C₂×C₇×M₁₆	—	4	1	no	—
73	C₂×C₇×M₁₆	D₄	1	4	yes	complemented
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	—	4	1	no	—
78	C₂²×C₇×C₈	—	4	1	no	—
79	C₂²×C₇×C₈	—	4	1	no	—
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	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₄×C₇×D₄	—	2	2	no	—
89	C₄×C₇×D₄	—	2	2	no	—
90	C₄×C₇×D₄	—	2	2	no	—
91	C₄×C₇×D₄	—	2	2	no	—
92	C₄×C₇×D₄	—	4	1	no	—
93	C₄×C₇×D₄	—	4	1	no	—
94	C₇×#117	—	4	1	no	—
95	C₇×#117	—	4	1	no	—
96	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
119	C₇×C₄⋊C₈	—	2	2	no	—
120	C₇×C₄⋊C₈	—	2	2	no	—
121	C₇×C₄⋊C₈	—	4	1	no	—
122	C₇×C₄⋊C₈	—	4	1	no	—
123	C₇×C₂²⋊C₈	—	2	2	no	—
124	C₇×C₂²⋊C₈	—	2	2	no	—
125	C₇×C₂²⋊C₈	—	2	2	no	—
126	C₇×C₂²⋊C₈	—	2	2	no	—
127	C₇×C₂²⋊C₈	—	4	1	no	—
128	C₇×C₂²⋊C₈	—	4	1	no	—
129	C₇×C₂²⋊C₈	—	4	1	no	—
130	C₇×C₂²⋊C₈	—	4	1	no	—
131	C₇×#97	—	2	2	no	—
132	C₄×C₇×C₈	—	2	2	no	—
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	C₇×#95	C₂×C₄	1	1	yes	characteristic
138	C₇×#95	C₂×C₄	1	1	yes	characteristic
139	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
141	#2392	C₂×C₇	1	1	yes	characteristic
142	#1924	C₂×C₇	1	1	yes	characteristic, complemented
143	#1923	C₂×C₇	1	1	yes	characteristic, complemented
144	#1917	C₂×C₇	1	1	yes	characteristic, complemented
145	#1916	C₂×C₇	1	1	yes	characteristic, complemented
146	#1870	C₂×C₇	1	1	yes	characteristic, complemented
147	#1869	C₂×C₇	1	1	yes	characteristic, complemented
148	#1869	C₂×C₇	1	1	yes	characteristic, complemented
149	#1869	C₂×C₇	1	1	yes	characteristic, complemented
150	#1851	C₂×C₇	1	1	yes	characteristic, complemented
151	#1850	C₂×C₇	1	1	yes	characteristic, complemented
152	#1798	C₂×C₇	1	1	yes	characteristic, complemented
153	#1729	C₂×C₇	1	1	yes	characteristic, complemented
154	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
155	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
156	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₇×D₄	—	2	2	no	—
158	C₂×C₇×D₄	—	2	2	no	—
159	C₂×C₇×D₄	—	2	2	no	—
160	C₂×C₇×D₄	—	2	2	no	—
161	C₂×C₇×D₄	—	2	2	no	—
162	C₂×C₇×D₄	—	4	1	no	—
163	C₂×C₇×D₄	—	4	1	no	—
164	C₂×C₇×D₄	—	4	1	no	—
165	C₂×C₇×D₄	—	4	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₇	#41	1	2	yes	—
195	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
196	C₇×M₁₆	—	4	4	no	—
197	C₇×M₁₆	—	4	4	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	—	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	—	2	1	no	—
218	C₂×C₇×C₈	—	2	1	no	—
219	C₂×C₇×C₈	—	2	1	no	—
220	C₂×C₇×C₈	—	4	4	no	—
221	C₂×C₇×C₈	—	4	4	no	—
222	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
223	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
224	C₇×C₄⋊C₄	—	2	2	no	—
225	C₇×C₄⋊C₄	—	2	2	no	—
226	C₇×C₄⋊C₄	—	2	2	no	—
227	C₇×C₄⋊C₄	—	4	1	no	—
228	C₇×C₄⋊C₄	—	4	1	no	—
229	C₇×C₄⋊C₄	—	4	1	no	—
230	C₇×C₄⋊C₄	—	4	1	no	—
231	C₇×C₂²⋊C₄	—	2	2	no	—
232	C₇×C₂²⋊C₄	—	2	2	no	—
233	C₇×C₂²⋊C₄	—	2	2	no	—
234	C₇×C₂²⋊C₄	—	2	2	no	—
235	C₇×C₂²⋊C₄	—	2	2	no	—
236	C₇×C₂²⋊C₄	—	2	2	no	—
237	C₇×C₂²⋊C₄	—	4	1	no	—
238	C₇×C₂²⋊C₄	—	4	1	no	—
239	C₇×C₂²⋊C₄	—	4	1	no	—
240	C₇×C₂²⋊C₄	—	4	1	no	—
241	C₇×C₂²⋊C₄	—	4	1	no	—
242	C₇×C₂²⋊C₄	—	4	1	no	—
243	C₄²×C₇	—	2	1	no	—
244	C₄²×C₇	—	2	1	no	—
245	C₄²×C₇	—	2	1	no	—
246	C₄²×C₇	—	2	1	no	—
247	C₄²×C₇	—	2	1	no	—
248	C₄²×C₇	—	2	1	no	—
249	C₄²×C₇	—	2	1	no	—
250	C₄²×C₇	—	2	1	no	—
251	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
252	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
254	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
258	C₂×#117	C₂²×C₇	1	1	yes	characteristic
259	#436	—	2	4	no	—
260	#435	—	2	4	no	—
261	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
266	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
267	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
268	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
271	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
273	C₂×#97	C₂²×C₇	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
275	#398	C₄×C₇	1	1	yes	characteristic
276	#397	C₄×C₇	1	1	yes	characteristic
277	#396	C₄×C₇	1	1	yes	characteristic
278	#396	C₄×C₇	1	1	yes	characteristic
279	#394	C₄×C₇	1	1	yes	characteristic
280	#394	C₄×C₇	1	1	yes	characteristic
281	#394	C₄×C₇	1	1	yes	characteristic
282	#392	C₄×C₇	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
284	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
285	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
286	#336	C₂²×C₇	1	1	yes	characteristic
287	#336	C₂²×C₇	1	1	yes	characteristic
288	#336	C₂²×C₇	1	1	yes	characteristic
289	#336	C₂²×C₇	1	1	yes	characteristic
290	#336	C₂²×C₇	1	1	yes	characteristic
291	#336	C₂²×C₇	1	1	yes	characteristic
292	#336	C₂²×C₇	1	1	yes	characteristic
293	#336	C₂²×C₇	1	1	yes	characteristic
294	#336	C₂²×C₇	1	1	yes	characteristic
295	#336	C₂²×C₇	1	1	yes	characteristic
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	—	2	1	no	—
308	C₂³×C₇	—	2	1	no	—
309	C₂³×C₇	—	2	1	no	—
310	C₂³×C₇	—	2	1	no	—
311	C₂³×C₇	—	2	1	no	—
312	C₂³×C₇	—	2	1	no	—
313	C₂³×C₇	—	2	1	no	—
314	C₂³×C₇	—	2	1	no	—
315	C₂³×C₇	C₄×D₄	1	2	yes	—
316	C₂³×C₇	#131	1	2	yes	—
317	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
318	C₇×D₄	—	4	4	no	—
319	C₇×D₄	—	4	4	no	—
320	C₇×D₄	—	4	4	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	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	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	—	2	1	no	—
342	C₂×C₄×C₇	—	2	1	no	—
343	C₂×C₄×C₇	—	2	1	no	—
344	C₂×C₄×C₇	—	2	1	no	—
345	C₂×C₄×C₇	—	2	1	no	—
346	C₂×C₄×C₇	—	2	1	no	—
347	C₂×C₄×C₇	—	2	1	no	—
348	C₂×C₄×C₇	—	2	1	no	—
349	C₂×C₄×C₇	—	2	1	no	—
350	C₂×C₄×C₇	—	2	1	no	—
351	C₂×C₄×C₇	—	2	1	no	—
352	C₂×C₄×C₇	—	2	1	no	—
353	C₂×C₄×C₇	—	2	1	no	—
354	C₂×C₄×C₇	—	2	1	no	—
355	C₂×C₄×C₇	—	2	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	—	4	1	no	—
361	C₂×C₄×C₇	—	4	1	no	—
362	C₂×C₄×C₇	—	4	1	no	—
363	C₂×C₄×C₇	—	4	1	no	—
364	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
365	C₂×C₄×C₇	#131	1	2	yes	—
366	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
368	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
370	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
372	C₇×C₈	—	2	2	no	—
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	C₇×C₈	—	4	1	no	—
378	C₇×C₈	—	4	1	no	—
379	C₇×C₈	—	4	1	no	—
380	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
381	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
382	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
386	C₂×M₁₆	—	2	2	no	—
387	C₂×M₁₆	—	4	1	no	—
388	C₂×M₁₆	—	4	1	no	—
389	C₂×M₁₆	—	4	1	no	—
390	C₂×M₁₆	—	4	1	no	—
391	C₂×M₁₆	C₇×D₄	1	4	yes	complemented
392	C₂²×C₈	—	2	2	no	—
393	C₂²×C₈	—	2	2	no	—
394	C₂²×C₈	—	4	1	no	—
395	C₂²×C₈	—	4	1	no	—
396	C₂²×C₈	—	4	1	no	—
397	C₂²×C₈	—	4	1	no	—
398	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	4	1	no	—
411	C₄×D₄	—	4	1	no	—
412	#117	—	4	1	no	—
413	#117	—	4	1	no	—
414	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
437	C₄⋊C₈	—	2	2	no	—
438	C₄⋊C₈	—	2	2	no	—
439	C₄⋊C₈	—	4	1	no	—
440	C₄⋊C₈	—	4	1	no	—
441	C₂²⋊C₈	—	2	2	no	—
442	C₂²⋊C₈	—	2	2	no	—
443	C₂²⋊C₈	—	2	2	no	—
444	C₂²⋊C₈	—	2	2	no	—
445	C₂²⋊C₈	—	4	1	no	—
446	C₂²⋊C₈	—	4	1	no	—
447	C₂²⋊C₈	—	4	1	no	—
448	C₂²⋊C₈	—	4	1	no	—
449	#97	—	2	2	no	—
450	C₄×C₈	—	2	2	no	—
451	#95	C₂×C₄×C₇	1	1	yes	characteristic
452	#95	C₂×C₄×C₇	1	1	yes	characteristic
453	#95	C₂×C₄×C₇	1	1	yes	characteristic
454	#95	C₂×C₄×C₇	1	1	yes	characteristic
455	#95	C₂×C₄×C₇	1	1	yes	characteristic
456	#95	C₂×C₄×C₇	1	1	yes	characteristic
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	—	4	1	no	—
464	C₂²×C₇	—	4	1	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	—	4	1	no	—
470	C₂²×C₇	—	4	1	no	—
471	C₂²×C₇	—	4	1	no	—
472	C₂²×C₇	—	4	1	no	—
473	C₂²×C₇	—	4	1	no	—
474	C₂²×C₇	—	4	1	no	—
475	C₂²×C₇	—	4	1	no	—
476	C₂²×C₇	—	4	1	no	—
477	C₂²×C₇	—	4	1	no	—
478	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
479	C₂²×C₇	#518	1	1	yes	characteristic
480	C₂²×C₇	#520	1	1	yes	characteristic
481	C₂²×C₇	C₂×#131	1	1	yes	characteristic
482	C₂²×C₇	C₂×#131	1	1	yes	characteristic
483	C₂²×C₇	#568	1	1	yes	characteristic
484	C₂²×C₇	#568	1	1	yes	characteristic
485	C₄×C₇	—	2	2	no	—
486	C₄×C₇	—	2	2	no	—
487	C₄×C₇	—	4	1	no	—
488	C₄×C₇	—	4	1	no	—
489	C₄×C₇	—	4	1	no	—
490	C₄×C₇	—	4	1	no	—
491	C₄×C₇	—	4	1	no	—
492	C₄×C₇	—	4	1	no	—
493	C₄×C₇	—	4	1	no	—
494	C₄×C₇	—	4	1	no	—
495	C₄×C₇	—	4	1	no	—
496	C₄×C₇	#534	1	1	yes	characteristic
497	C₄×C₇	#537	1	1	yes	characteristic
498	C₄×C₇	#538	1	1	yes	characteristic
499	C₄×C₇	#539	1	1	yes	characteristic
500	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
501	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
502	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	4	1	no	—
509	C₂×D₄	—	4	1	no	—
510	C₂×D₄	—	4	1	no	—
511	C₂×D₄	—	4	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	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
529	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
530	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
531	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
532	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
533	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
539	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
540	C₂²×C₄	C₇×#41	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
542	M₁₆	—	4	4	no	—
543	M₁₆	—	4	4	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	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	4	4	no	—
567	C₂×C₈	—	4	4	no	—
568	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
569	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	4	1	no	—
574	C₄⋊C₄	—	4	1	no	—
575	C₄⋊C₄	—	4	1	no	—
576	C₄⋊C₄	—	4	1	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	4	1	no	—
584	C₂²⋊C₄	—	4	1	no	—
585	C₂²⋊C₄	—	4	1	no	—
586	C₂²⋊C₄	—	4	1	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₂²⋊C₄	—	4	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₂×C₇	—	4	2	no	—
598	C₂×C₇	—	4	2	no	—
599	C₂×C₇	—	8	1	no	—
600	C₂×C₇	#2325	1	1	yes	characteristic
601	C₂×C₇	#2933	1	1	yes	characteristic
602	C₂×C₇	#2933	1	1	yes	characteristic
603	C₂×C₇	#2976	1	1	yes	characteristic
604	C₂×C₇	#2981	1	1	yes	characteristic
605	C₂×C₇	#2994	1	1	yes	characteristic
606	C₂×C₇	#2995	1	1	yes	characteristic
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	C₄×C₇×D₄	1	2	yes	—
627	C₂³	C₇×#131	1	2	yes	—
628	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
629	D₄	—	4	4	no	—
630	D₄	—	4	4	no	—
631	D₄	—	4	4	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	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	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
676	C₂×C₄	C₇×#131	1	2	yes	—
677	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
678	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
679	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
681	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
682	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
683	C₈	—	2	2	no	—
684	C₈	—	2	2	no	—
685	C₈	—	4	1	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₇	#22175	1	1	yes	characteristic, direct product factor, Sylow
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
714	C₂²	C₇×#518	1	1	yes	characteristic
715	C₂²	C₇×#520	1	1	yes	characteristic
716	C₂²	C₂×C₇×#131	1	1	yes	characteristic
717	C₂²	C₂×C₇×#131	1	1	yes	characteristic
718	C₂²	C₇×#568	1	1	yes	characteristic
719	C₂²	C₇×#568	1	1	yes	characteristic
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	C₇×#534	1	1	yes	characteristic
732	C₄	C₇×#537	1	1	yes	characteristic
733	C₄	C₇×#538	1	1	yes	characteristic
734	C₄	C₇×#539	1	1	yes	characteristic
735	C₂	—	4	2	no	—
736	C₂	—	4	2	no	—
737	C₂	—	8	1	no	—
738	C₂	C₇×#2325	1	1	yes	characteristic
739	C₂	C₇×#2933	1	1	yes	characteristic
740	C₂	C₇×#2933	1	1	yes	characteristic
741	C₂	C₇×#2976	1	1	yes	characteristic
742	C₂	C₇×#2981	1	1	yes	characteristic
743	C₂	C₇×#2994	1	1	yes	characteristic
744	C₂	C₇×#2995	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	C₇×#392	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
1. C₂×C₇×#436	C₂	semidirect
2. C₂×C₇×#435	C₂	semidirect
4. C₇×#1924	C₂	semidirect
5. C₇×#1923	C₂	semidirect
6. C₇×#1917	C₂	semidirect
7. C₇×#1916	C₂	semidirect
8. C₇×#1870	C₂	semidirect
9. C₇×#1869	C₂	semidirect
10. C₇×#1869	C₂	semidirect
11. C₇×#1869	C₂	semidirect
12. C₇×#1851	C₂	semidirect
13. C₇×#1850	C₂	semidirect
14. C₇×#1798	C₂	semidirect
15. C₇×#1729	C₂	semidirect
61. #22175	C₇	direct (N × H)
73. C₂×C₇×M₁₆	D₄	semidirect
139. C₂×#436	C₂×C₇	semidirect
140. C₂×#435	C₂×C₇	semidirect
142. #1924	C₂×C₇	semidirect
143. #1923	C₂×C₇	semidirect
144. #1917	C₂×C₇	semidirect
145. #1916	C₂×C₇	semidirect
146. #1870	C₂×C₇	semidirect
147. #1869	C₂×C₇	semidirect
148. #1869	C₂×C₇	semidirect
149. #1869	C₂×C₇	semidirect
150. #1851	C₂×C₇	semidirect
151. #1850	C₂×C₇	semidirect
152. #1798	C₂×C₇	semidirect
153. #1729	C₂×C₇	semidirect
391. C₂×M₁₆	C₇×D₄	semidirect
691. C₇	#22175	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×#2392	2
C₇×#1924	2
C₇×#1923	2
C₇×#1917	2
C₇×#1916	2
C₇×#1870	2
C₇×#1869	2
C₇×#1851	2
C₇×#1850	2
C₇×#1798	2
C₇×#1729	2
#22175	7

Subgroups — C7×#22175 #13199391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22175 #13199391