Subgroups — C₇×#22601 #13199817

Order 1792.

932 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#1940	C₂	1	2	yes	maximal, complemented
5	C₇×#1917	C₂	1	2	yes	maximal, complemented
6	C₇×#1916	C₂	1	2	yes	maximal, complemented
7	C₇×#1817	C₂	1	1	yes	maximal, characteristic
8	C₇×#1817	C₂	1	1	yes	maximal, characteristic
9	C₇×#1797	C₂	1	1	yes	maximal, characteristic
10	C₇×#1771	C₂	1	2	yes	maximal, complemented
11	C₇×#1749	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂²×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
17	C₇×#432	—	2	4	no	—
18	C₇×#431	—	2	4	no	—
19	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₇×C₂²⋊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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×#97	C₂²	1	2	yes	—
27	C₂×C₇×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
29	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
30	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
31	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
32	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
33	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₇×#95	C₄	1	1	yes	characteristic
38	C₂×C₇×#95	C₄	1	1	yes	characteristic
39	C₇×#336	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	C₇×#336	C₂²	1	2	yes	—
44	C₇×#336	C₂²	1	2	yes	—
45	#22601	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	2	yes	—
55	C₂²×C₇×C₈	C₂³	1	2	yes	—
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂×C₇×C₄⋊C₄	—	2	4	no	—
58	C₂×C₇×C₄⋊C₄	—	2	4	no	—
59	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇	—	2	2	no	—
68	C₂×C₄²×C₇	—	2	2	no	—
69	C₂×C₄²×C₇	—	2	2	no	—
70	C₂×C₄²×C₇	—	2	2	no	—
71	C₂×C₄²×C₇	—	2	4	no	—
72	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
84	C₇×C₄⋊C₈	—	2	4	no	—
85	C₇×C₄⋊C₈	—	2	4	no	—
86	C₇×C₄⋊C₈	—	2	4	no	—
87	C₇×C₂²⋊C₈	—	2	2	no	—
88	C₇×C₂²⋊C₈	—	2	2	no	—
89	C₇×C₂²⋊C₈	—	2	2	no	—
90	C₇×C₂²⋊C₈	D₄	1	4	yes	—
91	C₇×#97	—	2	4	no	—
92	C₇×#97	—	2	4	no	—
93	C₄×C₇×C₈	—	2	4	no	—
94	C₇×#95	C₂×C₄	1	1	yes	characteristic
95	C₇×#95	C₂×C₄	1	1	yes	characteristic
96	C₇×#95	C₂×C₄	1	1	yes	characteristic
97	C₇×#95	C₂×C₄	1	1	yes	characteristic
98	C₇×#95	C₂×C₄	1	1	yes	characteristic
99	C₇×#95	C₂×C₄	1	1	yes	characteristic
100	C₇×#95	C₂×C₄	1	1	yes	characteristic
101	C₇×#95	C₂×C₄	1	1	yes	characteristic
102	C₂×#432	C₂×C₇	1	1	yes	characteristic
103	C₂×#431	C₂×C₇	1	1	yes	characteristic
104	C₂×C₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
105	#1940	C₂×C₇	1	2	yes	complemented
106	#1917	C₂×C₇	1	2	yes	complemented
107	#1916	C₂×C₇	1	2	yes	complemented
108	#1817	C₂×C₇	1	1	yes	characteristic
109	#1817	C₂×C₇	1	1	yes	characteristic
110	#1797	C₂×C₇	1	1	yes	characteristic
111	#1771	C₂×C₇	1	2	yes	complemented
112	#1749	C₂×C₇	1	1	yes	characteristic
113	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	2	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	2	no	—
127	C₂²×C₄×C₇	—	2	2	no	—
128	C₂²×C₄×C₇	—	2	2	no	—
129	C₂²×C₄×C₇	—	2	2	no	—
130	C₂²×C₄×C₇	—	4	1	no	—
131	C₂²×C₄×C₇	—	4	1	no	—
132	C₂²×C₄×C₇	—	4	1	no	—
133	C₂²×C₄×C₇	M₁₆	1	4	yes	—
134	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇	#41	1	2	yes	—
149	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
150	C₂×C₇×C₈	—	2	2	no	—
151	C₂×C₇×C₈	—	2	2	no	—
152	C₂×C₇×C₈	—	2	2	no	—
153	C₂×C₇×C₈	—	2	2	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	—	2	2	no	—
156	C₂×C₇×C₈	—	2	2	no	—
157	C₂×C₇×C₈	—	2	2	no	—
158	C₂×C₇×C₈	—	2	2	no	—
159	C₂×C₇×C₈	—	2	2	no	—
160	C₂×C₇×C₈	—	2	2	no	—
161	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	—	2	2	no	—
164	C₇×C₄⋊C₄	—	2	2	no	—
165	C₇×C₄⋊C₄	—	2	2	no	—
166	C₇×C₄⋊C₄	—	2	2	no	—
167	C₇×C₄⋊C₄	—	2	2	no	—
168	C₇×C₄⋊C₄	—	2	2	no	—
169	C₇×C₄⋊C₄	M₁₆	1	4	yes	—
170	C₄²×C₇	—	2	2	no	—
171	C₄²×C₇	—	2	2	no	—
172	C₄²×C₇	—	2	2	no	—
173	C₄²×C₇	—	2	2	no	—
174	C₄²×C₇	—	2	2	no	—
175	C₄²×C₇	—	2	2	no	—
176	C₄²×C₇	—	2	1	no	—
177	C₄²×C₇	—	2	1	no	—
178	C₄²×C₇	—	2	1	no	—
179	C₄²×C₇	—	2	1	no	—
180	C₄²×C₇	—	2	2	no	—
181	C₄²×C₇	—	2	1	no	—
182	C₄²×C₇	—	2	1	no	—
183	C₄²×C₇	—	2	1	no	—
184	C₄²×C₇	—	2	1	no	—
185	C₄²×C₇	#41	1	4	yes	—
186	C₂²×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
187	C₂²×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
188	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
189	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
190	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
191	#432	—	2	4	no	—
192	#431	—	2	4	no	—
193	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
195	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
197	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
198	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
199	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
200	C₂×#97	C₂²×C₇	1	2	yes	—
201	C₂×#97	C₂²×C₇	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
203	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
205	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
208	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
209	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
210	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
211	C₂×#95	C₄×C₇	1	1	yes	characteristic
212	C₂×#95	C₄×C₇	1	1	yes	characteristic
213	#336	C₂²×C₇	1	2	yes	—
214	#336	C₂²×C₇	1	2	yes	—
215	#336	C₂²×C₇	1	2	yes	—
216	#336	C₂²×C₇	1	2	yes	—
217	#336	C₂²×C₇	1	2	yes	—
218	#336	C₂²×C₇	1	2	yes	—
219	C₂³×C₇	—	2	1	no	—
220	C₂³×C₇	—	2	1	no	—
221	C₂³×C₇	—	2	1	no	—
222	C₂³×C₇	—	2	1	no	—
223	C₂³×C₇	C₄×D₄	1	2	yes	—
224	C₂³×C₇	C₂×M₁₆	1	2	yes	—
225	C₂³×C₇	#131	1	2	yes	—
226	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₇	—	2	8	no	—
228	C₂×C₄×C₇	—	2	1	no	—
229	C₂×C₄×C₇	—	2	1	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	1	no	—
233	C₂×C₄×C₇	—	2	1	no	—
234	C₂×C₄×C₇	—	2	1	no	—
235	C₂×C₄×C₇	—	2	1	no	—
236	C₂×C₄×C₇	—	2	1	no	—
237	C₂×C₄×C₇	—	2	1	no	—
238	C₂×C₄×C₇	—	2	1	no	—
239	C₂×C₄×C₇	—	2	1	no	—
240	C₂×C₄×C₇	—	2	1	no	—
241	C₂×C₄×C₇	—	2	1	no	—
242	C₂×C₄×C₇	—	2	1	no	—
243	C₂×C₄×C₇	—	2	1	no	—
244	C₂×C₄×C₇	—	2	8	no	—
245	C₂×C₄×C₇	—	2	4	no	—
246	C₂×C₄×C₇	—	2	4	no	—
247	C₂×C₄×C₇	—	2	1	no	—
248	C₂×C₄×C₇	—	2	1	no	—
249	C₂×C₄×C₇	—	2	1	no	—
250	C₂×C₄×C₇	—	2	1	no	—
251	C₂×C₄×C₇	—	2	1	no	—
252	C₂×C₄×C₇	—	2	1	no	—
253	C₂×C₄×C₇	—	2	1	no	—
254	C₂×C₄×C₇	—	2	1	no	—
255	C₂×C₄×C₇	—	2	1	no	—
256	C₂×C₄×C₇	—	2	1	no	—
257	C₂×C₄×C₇	—	2	1	no	—
258	C₂×C₄×C₇	—	2	1	no	—
259	C₂×C₄×C₇	—	2	1	no	—
260	C₂×C₄×C₇	—	2	1	no	—
261	C₂×C₄×C₇	—	2	1	no	—
262	C₂×C₄×C₇	—	4	4	no	—
263	C₂×C₄×C₇	—	4	4	no	—
264	C₂×C₄×C₇	—	4	4	no	—
265	C₂×C₄×C₇	—	4	4	no	—
266	C₂×C₄×C₇	#117	1	2	yes	—
267	C₂×C₄×C₇	#117	1	2	yes	—
268	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
269	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
270	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
271	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
272	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
273	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
274	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₇	C₂×#41	1	2	yes	—
276	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
278	C₇×C₈	—	2	4	no	—
279	C₇×C₈	—	4	2	no	—
280	C₇×C₈	—	4	2	no	—
281	C₇×C₈	—	4	2	no	—
282	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
283	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
284	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
285	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
286	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
287	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₇	1	2	yes	—
290	C₂²×C₈	C₂³×C₇	1	2	yes	—
291	C₂²×C₈	C₂³×C₇	1	2	yes	—
292	C₂²×C₈	C₂³×C₇	1	2	yes	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	4	no	—
308	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
309	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
310	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
311	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
312	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
313	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
320	C₄⋊C₈	—	2	4	no	—
321	C₄⋊C₈	—	2	4	no	—
322	C₄⋊C₈	—	2	4	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	C₇×D₄	1	4	yes	—
327	#97	—	2	4	no	—
328	#97	—	2	4	no	—
329	C₄×C₈	—	2	4	no	—
330	#95	C₂×C₄×C₇	1	1	yes	characteristic
331	#95	C₂×C₄×C₇	1	1	yes	characteristic
332	#95	C₂×C₄×C₇	1	1	yes	characteristic
333	#95	C₂×C₄×C₇	1	1	yes	characteristic
334	#95	C₂×C₄×C₇	1	1	yes	characteristic
335	#95	C₂×C₄×C₇	1	1	yes	characteristic
336	#95	C₂×C₄×C₇	1	1	yes	characteristic
337	#95	C₂×C₄×C₇	1	1	yes	characteristic
338	C₂²×C₇	—	2	2	no	—
339	C₂²×C₇	—	2	2	no	—
340	C₂²×C₇	—	2	2	no	—
341	C₂²×C₇	—	2	2	no	—
342	C₂²×C₇	—	2	2	no	—
343	C₂²×C₇	—	2	2	no	—
344	C₂²×C₇	#435	1	4	yes	—
345	C₂²×C₇	C₂×#117	1	1	yes	characteristic
346	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
347	C₂²×C₇	#519	1	1	yes	characteristic
348	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
349	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
350	C₂²×C₇	C₂×#131	1	1	yes	characteristic
351	C₂²×C₇	#568	1	1	yes	characteristic
352	C₄×C₇	—	2	2	no	—
353	C₄×C₇	—	2	2	no	—
354	C₄×C₇	—	2	2	no	—
355	C₄×C₇	—	2	2	no	—
356	C₄×C₇	—	2	2	no	—
357	C₄×C₇	—	2	2	no	—
358	C₄×C₇	—	2	2	no	—
359	C₄×C₇	—	2	2	no	—
360	C₄×C₇	—	4	1	no	—
361	C₄×C₇	—	4	1	no	—
362	C₄×C₇	—	4	1	no	—
363	C₄×C₇	—	4	1	no	—
364	C₄×C₇	—	4	1	no	—
365	C₄×C₇	#547	1	2	yes	—
366	C₄×C₇	#552	1	2	yes	—
367	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	C₇×M₁₆	1	4	yes	—
388	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
402	C₂²×C₄	C₇×#41	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	C₇×M₁₆	1	4	yes	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	C₇×#41	1	4	yes	—
440	C₂×C₇	—	2	4	no	—
441	C₂×C₇	#2344	1	1	yes	characteristic
442	C₂×C₇	#2920	1	1	yes	characteristic
443	C₂×C₇	#2924	1	1	yes	characteristic
444	C₂×C₇	C₂×#435	1	1	yes	characteristic
445	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
446	C₂×C₇	#2983	1	1	yes	characteristic
447	C₂×C₇	#2984	1	1	yes	characteristic
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	C₄×C₇×D₄	1	2	yes	—
453	C₂³	C₂×C₇×M₁₆	1	2	yes	—
454	C₂³	C₇×#131	1	2	yes	—
455	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	C₇×#117	1	2	yes	—
496	C₂×C₄	C₇×#117	1	2	yes	—
497	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
498	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
499	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
500	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
501	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
502	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
503	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
504	C₂×C₄	C₂×C₇×#41	1	2	yes	—
505	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
506	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
507	C₈	—	2	4	no	—
508	C₈	—	4	2	no	—
509	C₈	—	4	2	no	—
510	C₈	—	4	2	no	—
511	C₇	#22601	1	1	yes	characteristic, direct product factor, Sylow
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	C₇×#435	1	4	yes	—
519	C₂²	C₂×C₇×#117	1	1	yes	characteristic
520	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
521	C₂²	C₇×#519	1	1	yes	characteristic
522	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
523	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
524	C₂²	C₂×C₇×#131	1	1	yes	characteristic
525	C₂²	C₇×#568	1	1	yes	characteristic
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	C₇×#547	1	2	yes	—
540	C₄	C₇×#552	1	2	yes	—
541	C₂	—	2	4	no	—
542	C₂	C₇×#2344	1	1	yes	characteristic
543	C₂	C₇×#2920	1	1	yes	characteristic
544	C₂	C₇×#2924	1	1	yes	characteristic
545	C₂	C₂×C₇×#435	1	1	yes	characteristic
546	C₂	C₇×D₄×M₁₆	1	1	yes	characteristic
547	C₂	C₇×#2983	1	1	yes	characteristic
548	C₂	C₇×#2984	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
4. C₇×#1940	C₂	semidirect
5. C₇×#1917	C₂	semidirect
6. C₇×#1916	C₂	semidirect
10. C₇×#1771	C₂	semidirect
45. #22601	C₇	direct (N × H)
105. #1940	C₂×C₇	semidirect
106. #1917	C₂×C₇	semidirect
107. #1916	C₂×C₇	semidirect
111. #1771	C₂×C₇	semidirect
511. C₇	#22601	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×#432	2
C₂×C₇×#431	2
C₂×C₄×C₇×C₄⋊C₄	2
C₇×#1940	2
C₇×#1917	2
C₇×#1916	2
C₇×#1817	2
C₇×#1797	2
C₇×#1771	2
C₇×#1749	2
#22601	7

Subgroups — C7×#22601 #13199817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22601 #13199817