Subgroups — C₇×#20487 #13197703

Order 1792.

1118 conjugacy classes of subgroups.

The subgroup lattice has 586 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	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2290	C₂	1	1	yes	maximal, characteristic
6	C₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1752	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1749	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1726	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	C₄	1	8	yes	complemented
24	C₇×#435	C₄	1	8	yes	complemented
25	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₇×#405	—	2	4	no	—
32	C₄×C₇×M₁₆	—	2	4	no	—
33	C₂×C₇×#97	C₂²	1	1	yes	characteristic
34	C₂×C₇×#97	C₂²	1	1	yes	characteristic
35	C₂×C₇×#97	C₂²	1	1	yes	characteristic
36	C₂×C₇×#97	C₂²	1	1	yes	characteristic
37	C₂×C₇×#97	C₂²	1	1	yes	characteristic
38	C₂×C₇×#97	C₂²	1	1	yes	characteristic
39	C₂×C₇×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
45	C₇×#388	C₄	1	2	yes	—
46	C₇×#387	C₄	1	2	yes	—
47	C₇×#386	C₄	1	2	yes	—
48	C₇×#385	C₄	1	2	yes	—
49	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₇×#376	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	#20487	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
62	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
64	C₂×C₇×M₁₆	—	2	2	no	—
65	C₂×C₇×M₁₆	—	2	2	no	—
66	C₂×C₇×M₁₆	—	2	2	no	—
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	C₂×C₄	1	4	yes	—
71	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
72	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	complemented
73	C₂²×C₇×C₈	—	2	2	no	—
74	C₂²×C₇×C₈	—	2	2	no	—
75	C₂²×C₇×C₈	C₂×C₄	1	4	yes	complemented
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	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	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
85	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
86	C₇×#117	—	2	2	no	—
87	C₇×#117	—	2	2	no	—
88	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
90	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
92	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
93	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
94	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₇	—	2	2	no	—
97	C₂×C₄²×C₇	—	2	2	no	—
98	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
99	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
104	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
105	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
106	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
107	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
108	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
109	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
110	C₇×#97	—	2	2	no	—
111	C₇×#97	—	2	2	no	—
112	C₇×#97	—	2	2	no	—
113	C₇×#97	—	2	2	no	—
114	C₇×#97	—	2	2	no	—
115	C₇×#97	—	2	2	no	—
116	C₇×#97	C₂×C₄	1	4	yes	complemented
117	C₄×C₇×C₈	—	2	2	no	—
118	C₄×C₇×C₈	—	2	2	no	—
119	C₄×C₇×C₈	—	2	2	no	—
120	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
121	C₄×C₇×C₈	D₄	1	4	yes	complemented
122	C₇×#95	C₂×C₄	1	2	yes	—
123	C₇×#95	C₂×C₄	1	2	yes	—
124	C₇×#95	C₂×C₄	1	2	yes	—
125	C₇×#95	C₂×C₄	1	2	yes	—
126	C₇×#95	C₂×C₄	1	2	yes	—
127	C₂×#436	C₂×C₇	1	1	yes	characteristic
128	C₂×#435	C₂×C₇	1	1	yes	characteristic
129	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
131	#2290	C₂×C₇	1	1	yes	characteristic
132	#1771	C₂×C₇	1	1	yes	characteristic, complemented
133	#1770	C₂×C₇	1	1	yes	characteristic, complemented
134	#1768	C₂×C₇	1	1	yes	characteristic, complemented
135	#1753	C₂×C₇	1	1	yes	characteristic, complemented
136	#1753	C₂×C₇	1	1	yes	characteristic, complemented
137	#1753	C₂×C₇	1	1	yes	characteristic, complemented
138	#1752	C₂×C₇	1	1	yes	characteristic, complemented
139	#1750	C₂×C₇	1	1	yes	characteristic, complemented
140	#1749	C₂×C₇	1	1	yes	characteristic, complemented
141	#1726	C₂×C₇	1	1	yes	characteristic, complemented
142	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
143	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₇×D₄	—	4	2	no	—
145	C₂×C₇×D₄	C₄²	1	4	yes	—
146	C₂²×C₄×C₇	—	2	1	no	—
147	C₂²×C₄×C₇	—	2	1	no	—
148	C₂²×C₄×C₇	—	2	1	no	—
149	C₂²×C₄×C₇	—	2	1	no	—
150	C₂²×C₄×C₇	—	2	1	no	—
151	C₂²×C₄×C₇	—	2	1	no	—
152	C₂²×C₄×C₇	—	2	1	no	—
153	C₂²×C₄×C₇	—	2	1	no	—
154	C₂²×C₄×C₇	—	2	4	no	—
155	C₂²×C₄×C₇	—	4	2	no	—
156	C₂²×C₄×C₇	—	4	2	no	—
157	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
170	C₇×M₁₆	—	2	8	no	—
171	C₇×M₁₆	—	2	8	no	—
172	C₇×M₁₆	—	2	8	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	—	2	1	no	—
181	C₂×C₇×C₈	—	2	1	no	—
182	C₂×C₇×C₈	—	2	1	no	—
183	C₂×C₇×C₈	—	2	1	no	—
184	C₂×C₇×C₈	—	2	1	no	—
185	C₂×C₇×C₈	—	2	8	no	—
186	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
187	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
188	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
189	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
190	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
191	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
192	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
193	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
194	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
195	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
196	C₂×C₇×C₈	#41	1	2	yes	—
197	C₂×C₇×C₈	#41	1	2	yes	—
198	C₇×C₄⋊C₄	—	2	4	no	—
199	C₇×C₄⋊C₄	—	4	2	no	—
200	C₇×C₄⋊C₄	C₄²	1	4	yes	—
201	C₇×C₂²⋊C₄	—	2	4	no	—
202	C₇×C₂²⋊C₄	—	4	2	no	—
203	C₇×C₂²⋊C₄	—	4	2	no	—
204	C₇×C₂²⋊C₄	C₄²	1	4	yes	—
205	C₇×C₂²⋊C₄	C₄²	1	4	yes	—
206	C₄²×C₇	—	2	4	no	—
207	C₄²×C₇	—	2	1	no	—
208	C₄²×C₇	—	2	1	no	—
209	C₄²×C₇	—	2	1	no	—
210	C₄²×C₇	—	2	1	no	—
211	C₄²×C₇	—	2	1	no	—
212	C₄²×C₇	—	2	1	no	—
213	C₄²×C₇	C₂²×C₄	1	2	yes	—
214	C₄²×C₇	C₂²×C₄	1	2	yes	—
215	C₄²×C₇	C₂×D₄	1	2	yes	—
216	C₄²×C₇	#41	1	2	yes	—
217	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
218	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
219	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
220	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
222	C₂×#117	C₂²×C₇	1	1	yes	characteristic
223	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
224	#436	C₄×C₇	1	8	yes	complemented
225	#435	C₄×C₇	1	8	yes	complemented
226	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
228	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
231	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
232	#405	—	2	4	no	—
233	C₄×M₁₆	—	2	4	no	—
234	C₂×#97	C₂²×C₇	1	1	yes	characteristic
235	C₂×#97	C₂²×C₇	1	1	yes	characteristic
236	C₂×#97	C₂²×C₇	1	1	yes	characteristic
237	C₂×#97	C₂²×C₇	1	1	yes	characteristic
238	C₂×#97	C₂²×C₇	1	1	yes	characteristic
239	C₂×#97	C₂²×C₇	1	1	yes	characteristic
240	C₂×#97	C₂²×C₇	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
242	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
246	#388	C₄×C₇	1	2	yes	—
247	#387	C₄×C₇	1	2	yes	—
248	#386	C₄×C₇	1	2	yes	—
249	#385	C₄×C₇	1	2	yes	—
250	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
251	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
252	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
253	#376	C₂²×C₇	1	1	yes	characteristic
254	#336	C₂²×C₇	1	1	yes	characteristic
255	#336	C₂²×C₇	1	1	yes	characteristic
256	#336	C₂²×C₇	1	1	yes	characteristic
257	#336	C₂²×C₇	1	1	yes	characteristic
258	#336	C₂²×C₇	1	1	yes	characteristic
259	#336	C₂²×C₇	1	1	yes	characteristic
260	C₂³×C₇	—	2	1	no	—
261	C₂³×C₇	—	2	1	no	—
262	C₂³×C₇	—	2	1	no	—
263	C₂³×C₇	—	2	1	no	—
264	C₂³×C₇	—	2	2	no	—
265	C₂³×C₇	—	2	2	no	—
266	C₂³×C₇	—	2	2	no	—
267	C₂³×C₇	—	2	2	no	—
268	C₂³×C₇	C₂×C₄²	1	2	yes	—
269	C₂³×C₇	C₂×C₄²	1	2	yes	—
270	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
271	C₇×D₄	—	4	4	no	—
272	C₂×C₄×C₇	—	2	1	no	—
273	C₂×C₄×C₇	—	2	1	no	—
274	C₂×C₄×C₇	—	2	1	no	—
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	2	no	—
277	C₂×C₄×C₇	—	2	2	no	—
278	C₂×C₄×C₇	—	2	2	no	—
279	C₂×C₄×C₇	—	2	2	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	2	2	no	—
284	C₂×C₄×C₇	—	2	2	no	—
285	C₂×C₄×C₇	—	2	2	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	2	no	—
290	C₂×C₄×C₇	—	2	2	no	—
291	C₂×C₄×C₇	—	2	2	no	—
292	C₂×C₄×C₇	—	2	2	no	—
293	C₂×C₄×C₇	—	2	2	no	—
294	C₂×C₄×C₇	—	2	2	no	—
295	C₂×C₄×C₇	—	2	2	no	—
296	C₂×C₄×C₇	—	2	2	no	—
297	C₂×C₄×C₇	—	4	8	no	—
298	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
299	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
300	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
301	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
302	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
303	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂²×D₄	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	C₇×C₈	—	2	2	no	—
310	C₇×C₈	—	2	2	no	—
311	C₇×C₈	—	2	2	no	—
312	C₇×C₈	—	2	2	no	—
313	C₇×C₈	—	2	2	no	—
314	C₇×C₈	—	2	2	no	—
315	C₇×C₈	C₄×D₄	1	4	yes	—
316	C₇×C₈	C₄×D₄	1	4	yes	—
317	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
318	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
319	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	—	2	2	no	—
323	C₂×M₁₆	—	2	2	no	—
324	C₂×M₁₆	—	2	2	no	—
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
328	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	—
329	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	complemented
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	C₂×C₄×C₇	1	4	yes	complemented
333	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
341	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
342	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
343	#117	—	2	2	no	—
344	#117	—	2	2	no	—
345	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
346	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
347	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
356	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
361	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
362	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
363	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
364	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	—
365	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
366	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
367	#97	—	2	2	no	—
368	#97	—	2	2	no	—
369	#97	—	2	2	no	—
370	#97	—	2	2	no	—
371	#97	—	2	2	no	—
372	#97	—	2	2	no	—
373	#97	C₂×C₄×C₇	1	4	yes	complemented
374	C₄×C₈	—	2	2	no	—
375	C₄×C₈	—	2	2	no	—
376	C₄×C₈	—	2	2	no	—
377	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
378	C₄×C₈	C₇×D₄	1	4	yes	complemented
379	#95	C₂×C₄×C₇	1	2	yes	—
380	#95	C₂×C₄×C₇	1	2	yes	—
381	#95	C₂×C₄×C₇	1	2	yes	—
382	#95	C₂×C₄×C₇	1	2	yes	—
383	#95	C₂×C₄×C₇	1	2	yes	—
384	C₂²×C₇	—	2	2	no	—
385	C₂²×C₇	—	2	2	no	—
386	C₂²×C₇	—	2	2	no	—
387	C₂²×C₇	—	2	2	no	—
388	C₂²×C₇	—	2	2	no	—
389	C₂²×C₇	—	2	2	no	—
390	C₂²×C₇	—	4	2	no	—
391	C₂²×C₇	—	4	2	no	—
392	C₂²×C₇	—	4	2	no	—
393	C₂²×C₇	—	4	2	no	—
394	C₂²×C₇	C₂²×C₄²	1	1	yes	characteristic
395	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
396	C₂²×C₇	C₄×#41	1	1	yes	characteristic
397	C₂²×C₇	#568	1	2	yes	—
398	C₂²×C₇	#568	1	2	yes	—
399	C₄×C₇	—	2	2	no	—
400	C₄×C₇	—	2	2	no	—
401	C₄×C₇	—	2	4	no	—
402	C₄×C₇	—	2	2	no	—
403	C₄×C₇	—	2	2	no	—
404	C₄×C₇	—	4	2	no	—
405	C₄×C₇	—	4	2	no	—
406	C₄×C₇	—	4	2	no	—
407	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
408	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
409	C₄×C₇	C₄×#41	1	1	yes	characteristic
410	C₄×C₇	C₄×#41	1	1	yes	characteristic
411	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
412	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	C₄²×C₇	1	4	yes	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
427	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
428	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
429	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
430	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
432	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
433	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
434	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
435	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
436	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
437	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
439	M₁₆	—	2	8	no	—
440	M₁₆	—	2	8	no	—
441	M₁₆	—	2	8	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	8	no	—
455	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
456	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
457	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
458	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
459	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
460	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
461	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
462	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
463	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
464	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
465	C₂×C₈	C₇×#41	1	2	yes	—
466	C₂×C₈	C₇×#41	1	2	yes	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	C₄²×C₇	1	4	yes	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	C₄²×C₇	1	4	yes	—
474	C₂²⋊C₄	C₄²×C₇	1	4	yes	—
475	C₄²	—	2	4	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	C₂²×C₄×C₇	1	2	yes	—
483	C₄²	C₂²×C₄×C₇	1	2	yes	—
484	C₄²	C₂×C₇×D₄	1	2	yes	—
485	C₄²	C₇×#41	1	2	yes	—
486	C₂×C₇	—	4	2	no	—
487	C₂×C₇	—	4	2	no	—
488	C₂×C₇	C₄²×D₄	1	1	yes	characteristic
489	C₂×C₇	#2873	1	1	yes	characteristic
490	C₂×C₇	#2875	1	1	yes	characteristic
491	C₂×C₇	#2930	1	2	yes	—
492	C₂×C₇	#2967	1	2	yes	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	C₂×C₄²×C₇	1	2	yes	—
502	C₂³	C₂×C₄²×C₇	1	2	yes	—
503	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
504	D₄	—	4	4	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	2	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	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
532	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
533	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
534	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
535	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
536	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
537	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
538	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
539	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
540	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
541	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	2	2	no	—
547	C₈	—	2	2	no	—
548	C₈	C₄×C₇×D₄	1	4	yes	—
549	C₈	C₄×C₇×D₄	1	4	yes	—
550	C₇	#20487	1	1	yes	characteristic, direct product factor, Sylow
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	C₂²×C₄²×C₇	1	1	yes	characteristic
562	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
563	C₂²	C₄×C₇×#41	1	1	yes	characteristic
564	C₂²	C₇×#568	1	2	yes	—
565	C₂²	C₇×#568	1	2	yes	—
566	C₄	—	2	4	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
575	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
576	C₄	C₄×C₇×#41	1	1	yes	characteristic
577	C₄	C₄×C₇×#41	1	1	yes	characteristic
578	C₂	—	4	2	no	—
579	C₂	—	4	2	no	—
580	C₂	C₄²×C₇×D₄	1	1	yes	characteristic
581	C₂	C₇×#2873	1	1	yes	characteristic
582	C₂	C₇×#2875	1	1	yes	characteristic
583	C₂	C₇×#2930	1	2	yes	—
584	C₂	C₇×#2967	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂²×C₇×D₄	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂×C₇×#405	C₂	semidirect
4. C₂×C₄×C₇×M₁₆	C₂	semidirect
6. C₇×#1771	C₂	semidirect
7. C₇×#1770	C₂	semidirect
8. C₇×#1768	C₂	semidirect
9. C₇×#1753	C₂	semidirect
10. C₇×#1753	C₂	semidirect
11. C₇×#1753	C₂	semidirect
12. C₇×#1752	C₂	semidirect
13. C₇×#1750	C₂	semidirect
14. C₇×#1749	C₂	semidirect
15. C₇×#1726	C₂	semidirect
23. C₇×#436	C₄	semidirect
24. C₇×#435	C₄	semidirect
59. #20487	C₇	direct (N × H)
72. C₂×C₇×M₁₆	C₂×C₄	semidirect
75. C₂²×C₇×C₈	C₂×C₄	semidirect
104. C₇×C₄⋊C₈	C₂×C₄	semidirect
105. C₇×C₄⋊C₈	C₂×C₄	semidirect
108. C₇×C₂²⋊C₈	C₂×C₄	semidirect
109. C₇×C₂²⋊C₈	C₂×C₄	semidirect
116. C₇×#97	C₂×C₄	semidirect
120. C₄×C₇×C₈	C₂×C₄	semidirect
121. C₄×C₇×C₈	D₄	semidirect
129. C₂×#405	C₂×C₇	semidirect
130. C₂×C₄×M₁₆	C₂×C₇	semidirect
132. #1771	C₂×C₇	semidirect
133. #1770	C₂×C₇	semidirect
134. #1768	C₂×C₇	semidirect
135. #1753	C₂×C₇	semidirect
136. #1753	C₂×C₇	semidirect
137. #1753	C₂×C₇	semidirect
138. #1752	C₂×C₇	semidirect
139. #1750	C₂×C₇	semidirect
140. #1749	C₂×C₇	semidirect
141. #1726	C₂×C₇	semidirect
224. #436	C₄×C₇	semidirect
225. #435	C₄×C₇	semidirect
329. C₂×M₁₆	C₂×C₄×C₇	semidirect
332. C₂²×C₈	C₂×C₄×C₇	semidirect
361. C₄⋊C₈	C₂×C₄×C₇	semidirect
362. C₄⋊C₈	C₂×C₄×C₇	semidirect
365. C₂²⋊C₈	C₂×C₄×C₇	semidirect
366. C₂²⋊C₈	C₂×C₄×C₇	semidirect
373. #97	C₂×C₄×C₇	semidirect
377. C₄×C₈	C₂×C₄×C₇	semidirect
378. C₄×C₈	C₇×D₄	semidirect
550. C₇	#20487	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
C₂×C₇×#405	2
C₂×C₄×C₇×M₁₆	2
C₇×#2290	2
C₇×#1771	2
C₇×#1770	2
C₇×#1768	2
C₇×#1753	2
C₇×#1752	2
C₇×#1750	2
C₇×#1749	2
C₇×#1726	2
#20487	7

Subgroups — C7×#20487 #13197703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#20487 #13197703