Subgroups — C₇×#22501 #13199717

Order 1792.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#553	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1895	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1874	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1825	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1736	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1736	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	C₇×#553	—	2	4	no	—
19	C₇×#553	C₄	1	8	yes	complemented
20	C₂×C₇×#126	—	2	1	no	—
21	C₂×C₇×#125	C₂²	1	1	yes	characteristic
22	C₂×C₇×#123	—	2	1	no	—
23	C₂×C₇×#121	—	2	1	no	—
24	C₂×C₇×#121	C₂²	1	1	yes	characteristic
25	C₂×C₇×#121	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×D₄	—	2	1	no	—
27	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂×C₇×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₇×#436	—	2	4	no	—
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×#102	C₂²	1	1	yes	characteristic
36	C₂×C₇×#102	C₂²	1	1	yes	characteristic
37	C₂×C₇×#102	C₂²	1	1	yes	characteristic
38	C₂×C₇×#102	C₂²	1	1	yes	characteristic
39	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
42	C₇×#388	—	2	1	no	—
43	C₇×#387	—	2	1	no	—
44	C₇×#386	—	2	1	no	—
45	C₇×#382	C₂²	1	1	yes	characteristic
46	C₇×#380	C₂²	1	1	yes	characteristic
47	C₇×#380	C₂²	1	1	yes	characteristic
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
50	C₇×#340	C₂²	1	1	yes	characteristic
51	C₇×#340	C₂²	1	1	yes	characteristic
52	C₇×#340	C₂²	1	1	yes	characteristic
53	C₇×#340	C₂²	1	1	yes	characteristic
54	C₇×#340	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#340	C₂²	1	1	yes	characteristic
61	C₇×#340	C₂²	1	1	yes	characteristic
62	#22501	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×D₄	—	2	1	no	—
64	C₂²×C₇×D₄	—	2	1	no	—
65	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	—	2	1	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	—	2	1	no	—
70	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂×C₇×M₁₆	—	2	2	no	—
73	C₂×C₇×M₁₆	—	2	2	no	—
74	C₂×C₇×M₁₆	—	2	2	no	—
75	C₂×C₇×M₁₆	—	2	2	no	—
76	C₂×C₇×M₁₆	—	4	1	no	—
77	C₂×C₇×M₁₆	—	4	1	no	—
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	C₇×#126	—	2	8	no	—
83	C₇×#125	—	2	2	no	—
84	C₇×#125	C₂×C₄	1	4	yes	complemented
85	C₇×#123	—	2	8	no	—
86	C₇×#121	—	2	8	no	—
87	C₇×#121	—	2	2	no	—
88	C₇×#121	—	2	2	no	—
89	C₇×#121	C₂×C₄	1	4	yes	—
90	C₇×#121	C₂×C₄	1	4	yes	complemented
91	C₄×C₇×D₄	—	2	8	no	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
94	C₄×C₇×D₄	C₂×C₄	1	4	yes	complemented
95	C₄×C₇×D₄	D₄	1	4	yes	—
96	C₇×#117	—	2	2	no	—
97	C₇×#117	—	2	2	no	—
98	C₇×#117	—	4	1	no	—
99	C₇×#117	C₂×C₄	1	4	yes	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	2	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	—	2	1	no	—
104	C₂×C₇×C₄⋊C₄	—	2	2	no	—
105	C₂×C₇×C₄⋊C₄	—	2	1	no	—
106	C₂×C₇×C₄⋊C₄	—	4	1	no	—
107	C₂×C₇×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
108	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
124	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₇	—	2	1	no	—
126	C₂×C₄²×C₇	—	2	1	no	—
127	C₂×C₄²×C₇	—	2	1	no	—
128	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
129	C₇×C₄⋊C₈	—	2	2	no	—
130	C₇×#102	—	2	2	no	—
131	C₇×#102	—	2	2	no	—
132	C₇×#102	—	4	1	no	—
133	C₇×#102	—	4	1	no	—
134	C₇×C₂²⋊C₈	—	2	2	no	—
135	C₇×C₂²⋊C₈	—	2	2	no	—
136	C₄×C₇×C₈	—	2	2	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₂×#553	C₂×C₇	1	1	yes	characteristic
143	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
144	#2352	C₂×C₇	1	1	yes	characteristic, complemented
145	#1991	C₂×C₇	1	1	yes	characteristic, complemented
146	#1989	C₂×C₇	1	1	yes	characteristic, complemented
147	#1895	C₂×C₇	1	1	yes	characteristic, complemented
148	#1895	C₂×C₇	1	1	yes	characteristic, complemented
149	#1875	C₂×C₇	1	1	yes	characteristic, complemented
150	#1874	C₂×C₇	1	1	yes	characteristic, complemented
151	#1825	C₂×C₇	1	1	yes	characteristic, complemented
152	#1823	C₂×C₇	1	1	yes	characteristic, complemented
153	#1804	C₂×C₇	1	1	yes	characteristic, complemented
154	C₄×#102	C₂×C₇	1	1	yes	characteristic, complemented
155	#1736	C₂×C₇	1	1	yes	characteristic, complemented
156	#1736	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂⁴×C₇	—	2	1	no	—
158	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
159	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
160	C₂×C₇×D₄	—	2	4	no	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	—	2	1	no	—
163	C₂×C₇×D₄	—	2	1	no	—
164	C₂×C₇×D₄	—	2	1	no	—
165	C₂×C₇×D₄	—	2	1	no	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	—	4	1	no	—
168	C₂×C₇×D₄	—	4	1	no	—
169	C₂×C₇×D₄	—	4	2	no	—
170	C₂×C₇×D₄	—	4	2	no	—
171	C₂×C₇×D₄	—	8	1	no	—
172	C₂×C₇×D₄	—	8	1	no	—
173	C₂×C₇×D₄	C₂²⋊C₄	1	4	yes	—
174	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	1	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	1	no	—
186	C₂²×C₄×C₇	—	2	1	no	—
187	C₂²×C₄×C₇	—	2	4	no	—
188	C₂²×C₄×C₇	—	2	4	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	4	2	no	—
193	C₂²×C₄×C₇	—	4	2	no	—
194	C₂²×C₄×C₇	—	8	1	no	—
195	C₂²×C₄×C₇	—	8	1	no	—
196	C₂²×C₄×C₇	—	8	1	no	—
197	C₂²×C₄×C₇	—	8	1	no	—
198	C₂²×C₄×C₇	—	8	1	no	—
199	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
208	C₇×M₁₆	—	4	4	no	—
209	C₇×M₁₆	—	4	4	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	—	2	1	no	—
221	C₂×C₇×C₈	#41	1	2	yes	—
222	C₇×C₄⋊C₄	—	2	4	no	—
223	C₇×C₄⋊C₄	—	2	4	no	—
224	C₇×C₄⋊C₄	—	2	4	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	2	1	no	—
228	C₇×C₄⋊C₄	—	2	1	no	—
229	C₇×C₄⋊C₄	—	2	1	no	—
230	C₇×C₄⋊C₄	—	2	1	no	—
231	C₇×C₄⋊C₄	—	2	1	no	—
232	C₇×C₄⋊C₄	—	2	1	no	—
233	C₇×C₄⋊C₄	—	2	1	no	—
234	C₇×C₄⋊C₄	—	2	1	no	—
235	C₇×C₄⋊C₄	—	4	2	no	—
236	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
237	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
238	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
239	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
240	C₇×C₄⋊C₄	#41	1	2	yes	—
241	C₇×C₂²⋊C₄	—	2	4	no	—
242	C₇×C₂²⋊C₄	—	2	4	no	—
243	C₇×C₂²⋊C₄	—	2	4	no	—
244	C₇×C₂²⋊C₄	—	2	4	no	—
245	C₇×C₂²⋊C₄	—	4	2	no	—
246	C₇×C₂²⋊C₄	—	4	2	no	—
247	C₇×C₂²⋊C₄	—	8	1	no	—
248	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
249	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
250	C₄²×C₇	—	2	4	no	—
251	C₄²×C₇	—	4	2	no	—
252	C₄²×C₇	—	8	1	no	—
253	C₄²×C₇	C₂²×C₄	1	2	yes	—
254	C₄²×C₇	C₂×D₄	1	2	yes	—
255	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
256	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
257	#553	—	2	4	no	—
258	#553	C₄×C₇	1	8	yes	complemented
259	C₂×#126	—	2	1	no	—
260	C₂×#125	C₂²×C₇	1	1	yes	characteristic
261	C₂×#123	—	2	1	no	—
262	C₂×#121	—	2	1	no	—
263	C₂×#121	C₂²×C₇	1	1	yes	characteristic
264	C₂×#121	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₄×D₄	—	2	1	no	—
266	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
268	C₂×#117	C₂²×C₇	1	1	yes	characteristic
269	C₂×#117	C₂²×C₇	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
272	#436	—	2	4	no	—
273	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
274	C₂×#102	C₂²×C₇	1	1	yes	characteristic
275	C₂×#102	C₂²×C₇	1	1	yes	characteristic
276	C₂×#102	C₂²×C₇	1	1	yes	characteristic
277	C₂×#102	C₂²×C₇	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
281	#388	—	2	1	no	—
282	#387	—	2	1	no	—
283	#386	—	2	1	no	—
284	#382	C₂²×C₇	1	1	yes	characteristic
285	#380	C₂²×C₇	1	1	yes	characteristic
286	#380	C₂²×C₇	1	1	yes	characteristic
287	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
288	C₄×C₂²⋊C₄	—	2	1	no	—
289	#340	C₂²×C₇	1	1	yes	characteristic
290	#340	C₂²×C₇	1	1	yes	characteristic
291	#340	C₂²×C₇	1	1	yes	characteristic
292	#340	C₂²×C₇	1	1	yes	characteristic
293	#340	C₂²×C₇	1	1	yes	characteristic
294	#340	C₂²×C₇	1	1	yes	characteristic
295	#340	C₂²×C₇	1	1	yes	characteristic
296	#340	C₂²×C₇	1	1	yes	characteristic
297	#340	C₂²×C₇	1	1	yes	characteristic
298	#340	C₂²×C₇	1	1	yes	characteristic
299	#340	C₂²×C₇	1	1	yes	characteristic
300	#340	C₂²×C₇	1	1	yes	characteristic
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	2	no	—
314	C₂³×C₇	—	4	1	no	—
315	C₂³×C₇	—	4	1	no	—
316	C₂³×C₇	—	4	1	no	—
317	C₂³×C₇	—	4	1	no	—
318	C₂³×C₇	—	4	1	no	—
319	C₂³×C₇	—	4	1	no	—
320	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
321	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
322	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
323	C₇×D₄	—	2	2	no	—
324	C₇×D₄	—	2	2	no	—
325	C₇×D₄	—	4	4	no	—
326	C₇×D₄	—	4	8	no	—
327	C₇×D₄	—	4	1	no	—
328	C₇×D₄	—	4	1	no	—
329	C₇×D₄	—	8	4	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	2	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	2	no	—
341	C₂×C₄×C₇	—	2	2	no	—
342	C₂×C₄×C₇	—	2	2	no	—
343	C₂×C₄×C₇	—	2	2	no	—
344	C₂×C₄×C₇	—	2	2	no	—
345	C₂×C₄×C₇	—	2	2	no	—
346	C₂×C₄×C₇	—	2	2	no	—
347	C₂×C₄×C₇	—	2	2	no	—
348	C₂×C₄×C₇	—	2	2	no	—
349	C₂×C₄×C₇	—	2	2	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	4	1	no	—
354	C₂×C₄×C₇	—	4	1	no	—
355	C₂×C₄×C₇	—	4	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	—	4	1	no	—
365	C₂×C₄×C₇	—	4	1	no	—
366	C₂×C₄×C₇	—	4	1	no	—
367	C₂×C₄×C₇	—	8	4	no	—
368	C₂×C₄×C₇	—	8	4	no	—
369	C₂×C₄×C₇	—	8	4	no	—
370	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
371	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
372	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
373	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
374	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
375	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
377	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
378	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
380	C₇×C₈	—	2	2	no	—
381	C₇×C₈	—	4	1	no	—
382	C₇×C₈	—	4	1	no	—
383	C₇×C₈	—	4	1	no	—
384	C₂²×D₄	—	2	1	no	—
385	C₂²×D₄	—	2	1	no	—
386	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	—	2	1	no	—
391	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
393	C₂×M₁₆	—	2	2	no	—
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	2	2	no	—
397	C₂×M₁₆	—	4	1	no	—
398	C₂×M₁₆	—	4	1	no	—
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	#126	—	2	8	no	—
404	#125	—	2	2	no	—
405	#125	C₂×C₄×C₇	1	4	yes	complemented
406	#123	—	2	8	no	—
407	#121	—	2	8	no	—
408	#121	—	2	2	no	—
409	#121	—	2	2	no	—
410	#121	C₂×C₄×C₇	1	4	yes	—
411	#121	C₂×C₄×C₇	1	4	yes	complemented
412	C₄×D₄	—	2	8	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
415	C₄×D₄	C₂×C₄×C₇	1	4	yes	complemented
416	C₄×D₄	C₇×D₄	1	4	yes	—
417	#117	—	2	2	no	—
418	#117	—	2	2	no	—
419	#117	—	4	1	no	—
420	#117	C₂×C₄×C₇	1	4	yes	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	2	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	2	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	4	1	no	—
428	C₂×C₄⋊C₄	C₂×C₄×C₇	1	4	yes	complemented
429	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	—	2	1	no	—
449	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
450	C₄⋊C₈	—	2	2	no	—
451	#102	—	2	2	no	—
452	#102	—	2	2	no	—
453	#102	—	4	1	no	—
454	#102	—	4	1	no	—
455	C₂²⋊C₈	—	2	2	no	—
456	C₂²⋊C₈	—	2	2	no	—
457	C₄×C₈	—	2	2	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	C₂²×C₇	—	2	2	no	—
464	C₂²×C₇	—	2	2	no	—
465	C₂²×C₇	—	2	2	no	—
466	C₂²×C₇	—	2	2	no	—
467	C₂²×C₇	—	2	2	no	—
468	C₂²×C₇	—	2	2	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	2	no	—
478	C₂²×C₇	—	4	2	no	—
479	C₂²×C₇	—	4	2	no	—
480	C₂²×C₇	—	8	1	no	—
481	C₂²×C₇	—	8	1	no	—
482	C₂²×C₇	—	8	1	no	—
483	C₂²×C₇	—	8	1	no	—
484	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
485	C₂²×C₇	#546	1	1	yes	characteristic
486	C₂²×C₇	#547	1	1	yes	characteristic
487	C₂²×C₇	#575	1	1	yes	characteristic
488	C₂²×C₇	#575	1	1	yes	characteristic
489	C₂²×C₇	#576	1	1	yes	characteristic
490	C₂²×C₇	#577	1	1	yes	characteristic
491	C₄×C₇	—	2	2	no	—
492	C₄×C₇	—	2	2	no	—
493	C₄×C₇	—	2	2	no	—
494	C₄×C₇	—	2	2	no	—
495	C₄×C₇	—	4	2	no	—
496	C₄×C₇	—	4	2	no	—
497	C₄×C₇	—	4	2	no	—
498	C₄×C₇	—	4	2	no	—
499	C₄×C₇	—	8	1	no	—
500	C₄×C₇	—	8	1	no	—
501	C₄×C₇	—	8	1	no	—
502	C₄×C₇	C₄×#41	1	1	yes	characteristic
503	C₄×C₇	#520	1	1	yes	characteristic
504	C₄×C₇	#546	1	1	yes	characteristic
505	C₄×C₇	#547	1	1	yes	characteristic
506	C₂⁴	—	2	1	no	—
507	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
508	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	—	4	1	no	—
518	C₂×D₄	—	4	2	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	8	1	no	—
521	C₂×D₄	—	8	1	no	—
522	C₂×D₄	C₇×C₂²⋊C₄	1	4	yes	—
523	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
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	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	8	1	no	—
544	C₂²×C₄	—	8	1	no	—
545	C₂²×C₄	—	8	1	no	—
546	C₂²×C₄	—	8	1	no	—
547	C₂²×C₄	—	8	1	no	—
548	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
549	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
550	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
551	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
552	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
553	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
554	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
555	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
557	M₁₆	—	4	4	no	—
558	M₁₆	—	4	4	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	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	C₇×#41	1	2	yes	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	4	2	no	—
585	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
586	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
587	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
588	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
589	C₄⋊C₄	C₇×#41	1	2	yes	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	—	4	2	no	—
596	C₂²⋊C₄	—	8	1	no	—
597	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
598	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
599	C₄²	—	2	4	no	—
600	C₄²	—	4	2	no	—
601	C₄²	—	8	1	no	—
602	C₄²	C₂²×C₄×C₇	1	2	yes	—
603	C₄²	C₂×C₇×D₄	1	2	yes	—
604	C₂×C₇	—	4	2	no	—
605	C₂×C₇	—	4	2	no	—
606	C₂×C₇	—	8	2	no	—
607	C₂×C₇	#2339	1	1	yes	characteristic
608	C₂×C₇	#2896	1	1	yes	characteristic
609	C₂×C₇	#2897	1	1	yes	characteristic
610	C₂×C₇	#3322	1	1	yes	characteristic
611	C₂×C₇	#3326	1	1	yes	characteristic
612	C₂×C₇	#3351	1	1	yes	characteristic
613	C₂×C₇	#3355	1	1	yes	characteristic
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	—	2	2	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
634	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
635	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
636	D₄	—	2	2	no	—
637	D₄	—	2	2	no	—
638	D₄	—	4	4	no	—
639	D₄	—	4	8	no	—
640	D₄	—	4	1	no	—
641	D₄	—	4	1	no	—
642	D₄	—	8	4	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	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	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	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	8	4	no	—
681	C₂×C₄	—	8	4	no	—
682	C₂×C₄	—	8	4	no	—
683	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
684	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
685	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
686	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
687	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
688	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
689	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
690	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
691	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
692	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
693	C₈	—	2	2	no	—
694	C₈	—	4	1	no	—
695	C₈	—	4	1	no	—
696	C₈	—	4	1	no	—
697	C₇	#22501	1	1	yes	characteristic, direct product factor, Sylow
698	C₂²	—	2	2	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	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	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	8	1	no	—
716	C₂²	—	8	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	8	1	no	—
719	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
720	C₂²	C₇×#546	1	1	yes	characteristic
721	C₂²	C₇×#547	1	1	yes	characteristic
722	C₂²	C₇×#575	1	1	yes	characteristic
723	C₂²	C₇×#575	1	1	yes	characteristic
724	C₂²	C₇×#576	1	1	yes	characteristic
725	C₂²	C₇×#577	1	1	yes	characteristic
726	C₄	—	2	2	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	8	1	no	—
735	C₄	—	8	1	no	—
736	C₄	—	8	1	no	—
737	C₄	C₄×C₇×#41	1	1	yes	characteristic
738	C₄	C₇×#520	1	1	yes	characteristic
739	C₄	C₇×#546	1	1	yes	characteristic
740	C₄	C₇×#547	1	1	yes	characteristic
741	C₂	—	4	2	no	—
742	C₂	—	4	2	no	—
743	C₂	—	8	2	no	—
744	C₂	C₇×#2339	1	1	yes	characteristic
745	C₂	C₇×#2896	1	1	yes	characteristic
746	C₂	C₇×#2897	1	1	yes	characteristic
747	C₂	C₇×#3322	1	1	yes	characteristic
748	C₂	C₇×#3326	1	1	yes	characteristic
749	C₂	C₇×#3351	1	1	yes	characteristic
750	C₂	C₇×#3355	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#553	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#436	C₂	semidirect
3. C₇×#2352	C₂	semidirect
4. C₇×#1991	C₂	semidirect
5. C₇×#1989	C₂	semidirect
6. C₇×#1895	C₂	semidirect
7. C₇×#1895	C₂	semidirect
8. C₇×#1875	C₂	semidirect
9. C₇×#1874	C₂	semidirect
10. C₇×#1825	C₂	semidirect
11. C₇×#1823	C₂	semidirect
12. C₇×#1804	C₂	semidirect
13. C₄×C₇×#102	C₂	semidirect
14. C₇×#1736	C₂	semidirect
15. C₇×#1736	C₂	semidirect
19. C₇×#553	C₄	semidirect
62. #22501	C₇	direct (N × H)
84. C₇×#125	C₂×C₄	semidirect
90. C₇×#121	C₂×C₄	semidirect
94. C₄×C₇×D₄	C₂×C₄	semidirect
107. C₂×C₇×C₄⋊C₄	C₂×C₄	semidirect
143. C₂×#436	C₂×C₇	semidirect
144. #2352	C₂×C₇	semidirect
145. #1991	C₂×C₇	semidirect
146. #1989	C₂×C₇	semidirect
147. #1895	C₂×C₇	semidirect
148. #1895	C₂×C₇	semidirect
149. #1875	C₂×C₇	semidirect
150. #1874	C₂×C₇	semidirect
151. #1825	C₂×C₇	semidirect
152. #1823	C₂×C₇	semidirect
153. #1804	C₂×C₇	semidirect
154. C₄×#102	C₂×C₇	semidirect
155. #1736	C₂×C₇	semidirect
156. #1736	C₂×C₇	semidirect
258. #553	C₄×C₇	semidirect
405. #125	C₂×C₄×C₇	semidirect
411. #121	C₂×C₄×C₇	semidirect
415. C₄×D₄	C₂×C₄×C₇	semidirect
428. C₂×C₄⋊C₄	C₂×C₄×C₇	semidirect
697. C₇	#22501	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×#553	2
C₂×C₇×#436	2
C₇×#2352	2
C₇×#1991	2
C₇×#1989	2
C₇×#1895	2
C₇×#1875	2
C₇×#1874	2
C₇×#1825	2
C₇×#1823	2
C₇×#1804	2
C₄×C₇×#102	2
C₇×#1736	2
#22501	7

Subgroups — C7×#22501 #13199717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22501 #13199717