Subgroups — C₇×#25968 #13203184

Order 1792.

1136 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic
3	C₇×#2441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₇×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2065	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2025	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1864	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1809	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1786	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₄×C₇×D₄	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×C₇×C₂²⋊C₄	—	2	1	no	—
23	C₇×#478	—	2	4	no	—
24	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
30	C₇×#418	—	2	4	no	—
31	C₂×C₇×#102	C₂²	1	1	yes	characteristic
32	C₂×C₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₇×#102	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	C₇×#399	—	2	1	no	—
41	C₇×#396	—	2	1	no	—
42	C₇×#390	C₂²	1	1	yes	characteristic
43	C₇×#390	C₂²	1	1	yes	characteristic
44	C₇×#389	—	2	1	no	—
45	C₇×#389	C₂²	1	1	yes	characteristic, complemented
46	C₇×#389	C₂²	1	1	yes	characteristic, complemented
47	C₇×#387	—	2	1	no	—
48	C₇×#386	—	2	1	no	—
49	C₇×#386	—	2	1	no	—
50	C₇×#384	C₂²	1	1	yes	characteristic, complemented
51	C₇×#380	C₂²	1	1	yes	characteristic
52	C₇×#380	C₂²	1	1	yes	characteristic
53	C₇×#379	—	2	1	no	—
54	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₇×#340	C₂²	1	1	yes	characteristic, complemented
56	C₇×#340	C₂²	1	1	yes	characteristic, complemented
57	C₇×#340	C₂²	1	1	yes	characteristic, complemented
58	C₇×#340	C₂²	1	1	yes	characteristic, complemented
59	C₇×#336	C₂²	1	1	yes	characteristic, complemented
60	C₇×#336	C₂²	1	1	yes	characteristic, complemented
61	#25968	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁵×C₇	—	2	1	no	—
63	C₂²×C₇×D₄	—	2	2	no	—
64	C₂²×C₇×D₄	—	2	2	no	—
65	C₂²×C₇×D₄	—	2	1	no	—
66	C₂²×C₇×D₄	—	2	2	no	—
67	C₂²×C₇×D₄	—	4	1	no	—
68	C₂²×C₇×D₄	—	4	1	no	—
69	C₂²×C₇×D₄	Q₈	1	4	yes	—
70	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
71	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂³×C₄×C₇	—	2	1	no	—
74	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₇×M₁₆	—	2	2	no	—
76	C₂×C₇×M₁₆	—	2	2	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×#125	—	2	2	no	—
83	C₇×#125	—	4	1	no	—
84	C₄×C₇×D₄	—	2	2	no	—
85	C₄×C₇×D₄	—	2	2	no	—
86	C₄×C₇×D₄	—	4	1	no	—
87	C₄×C₇×D₄	—	4	1	no	—
88	C₇×#117	—	2	2	no	—
89	C₇×#117	—	4	1	no	—
90	C₂×C₇×C₄⋊C₄	—	2	1	no	—
91	C₂×C₇×C₄⋊C₄	—	2	1	no	—
92	C₂×C₇×C₄⋊C₄	—	2	1	no	—
93	C₂×C₇×C₄⋊C₄	—	2	1	no	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	—	2	1	no	—
96	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
112	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₇	—	2	1	no	—
115	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
117	C₇×#107	—	2	2	no	—
118	C₇×#107	—	4	1	no	—
119	C₇×#106	—	2	2	no	—
120	C₇×#106	—	4	1	no	—
121	C₇×C₄⋊C₈	—	2	2	no	—
122	C₇×C₄⋊C₈	—	4	1	no	—
123	C₇×#102	—	2	2	no	—
124	C₇×#102	—	2	2	no	—
125	C₇×#102	—	2	2	no	—
126	C₇×#102	—	2	2	no	—
127	C₇×#102	—	2	2	no	—
128	C₇×#102	—	4	1	no	—
129	C₇×#102	—	4	1	no	—
130	C₇×#102	D₄	1	4	yes	—
131	C₇×C₂²⋊C₈	—	2	2	no	—
132	C₇×#95	—	2	1	no	—
133	C₇×#95	—	2	1	no	—
134	C₇×#95	—	2	1	no	—
135	C₇×#95	—	2	1	no	—
136	C₇×#95	D₄	1	1	yes	characteristic
137	C₇×#95	D₄	1	1	yes	characteristic
138	C₂×#478	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂×#418	C₂×C₇	1	1	yes	characteristic
140	#2441	C₂×C₇	1	1	yes	characteristic, complemented
141	D₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
142	#2093	C₂×C₇	1	1	yes	characteristic, complemented
143	#2065	C₂×C₇	1	1	yes	characteristic, complemented
144	#2065	C₂×C₇	1	1	yes	characteristic, complemented
145	#2025	C₂×C₇	1	1	yes	characteristic, complemented
146	#1864	C₂×C₇	1	1	yes	characteristic, complemented
147	#1862	C₂×C₇	1	1	yes	characteristic, complemented
148	#1854	C₂×C₇	1	1	yes	characteristic, complemented
149	#1851	C₂×C₇	1	1	yes	characteristic, complemented
150	#1809	C₂×C₇	1	1	yes	characteristic, complemented
151	#1802	C₂×C₇	1	1	yes	characteristic, complemented
152	#1786	C₂×C₇	1	1	yes	characteristic
153	C₂⁴×C₇	—	2	1	no	—
154	C₂⁴×C₇	—	2	1	no	—
155	C₂⁴×C₇	—	2	4	no	—
156	C₂⁴×C₇	—	4	2	no	—
157	C₂⁴×C₇	—	4	2	no	—
158	C₂⁴×C₇	—	4	2	no	—
159	C₂⁴×C₇	—	4	2	no	—
160	C₂⁴×C₇	—	8	1	no	—
161	C₂⁴×C₇	—	8	1	no	—
162	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
163	C₂×C₇×D₄	—	2	8	no	—
164	C₂×C₇×D₄	—	2	4	no	—
165	C₂×C₇×D₄	—	2	1	no	—
166	C₂×C₇×D₄	—	2	1	no	—
167	C₂×C₇×D₄	—	2	1	no	—
168	C₂×C₇×D₄	—	2	1	no	—
169	C₂×C₇×D₄	—	2	1	no	—
170	C₂×C₇×D₄	—	2	1	no	—
171	C₂×C₇×D₄	—	2	1	no	—
172	C₂×C₇×D₄	—	2	1	no	—
173	C₂×C₇×D₄	—	4	4	no	—
174	C₂×C₇×D₄	—	4	4	no	—
175	C₂×C₇×D₄	—	4	4	no	—
176	C₂×C₇×D₄	—	4	2	no	—
177	C₂×C₇×D₄	—	4	2	no	—
178	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
179	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
180	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
181	C₂×C₇×D₄	#41	1	2	yes	—
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	1	no	—
188	C₂²×C₄×C₇	—	2	1	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	—	4	2	no	—
195	C₂²×C₄×C₇	—	4	2	no	—
196	C₂²×C₄×C₇	—	8	1	no	—
197	C₂²×C₄×C₇	—	8	1	no	—
198	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	2	yes	—
204	C₂²×C₄×C₇	#41	1	2	yes	—
205	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
206	C₇×M₁₆	—	4	4	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	C₂×D₄	1	2	yes	—
219	C₇×C₄⋊C₄	—	2	1	no	—
220	C₇×C₄⋊C₄	—	2	1	no	—
221	C₇×C₄⋊C₄	—	2	1	no	—
222	C₇×C₄⋊C₄	—	2	1	no	—
223	C₇×C₄⋊C₄	—	2	1	no	—
224	C₇×C₄⋊C₄	—	2	1	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	—	4	2	no	—
231	C₇×C₄⋊C₄	—	4	2	no	—
232	C₇×C₄⋊C₄	—	4	2	no	—
233	C₇×C₄⋊C₄	—	4	2	no	—
234	C₇×C₄⋊C₄	—	8	1	no	—
235	C₇×C₄⋊C₄	—	8	1	no	—
236	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
237	C₇×C₂²⋊C₄	—	2	2	no	—
238	C₇×C₂²⋊C₄	—	4	1	no	—
239	C₇×C₂²⋊C₄	—	4	2	no	—
240	C₇×C₂²⋊C₄	—	4	2	no	—
241	C₇×C₂²⋊C₄	—	4	2	no	—
242	C₇×C₂²⋊C₄	—	4	2	no	—
243	C₇×C₂²⋊C₄	—	4	2	no	—
244	C₇×C₂²⋊C₄	—	4	2	no	—
245	C₇×C₂²⋊C₄	—	8	1	no	—
246	C₇×C₂²⋊C₄	—	8	1	no	—
247	C₇×C₂²⋊C₄	—	8	1	no	—
248	C₄²×C₇	—	2	1	no	—
249	C₄²×C₇	—	2	1	no	—
250	C₄²×C₇	—	2	1	no	—
251	C₄²×C₇	—	2	1	no	—
252	C₄²×C₇	—	4	2	no	—
253	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
254	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
255	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
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	C₂²×C₂²⋊C₄	—	2	1	no	—
260	#478	—	2	4	no	—
261	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
262	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
263	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
264	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
265	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
266	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
267	#418	—	2	4	no	—
268	C₂×#102	C₂²×C₇	1	1	yes	characteristic
269	C₂×#102	C₂²×C₇	1	1	yes	characteristic
270	C₂×#102	C₂²×C₇	1	1	yes	characteristic
271	C₂×#102	C₂²×C₇	1	1	yes	characteristic
272	C₂×#102	C₂²×C₇	1	1	yes	characteristic
273	C₂×#102	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×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
277	#399	—	2	1	no	—
278	#396	—	2	1	no	—
279	#390	C₂²×C₇	1	1	yes	characteristic
280	#390	C₂²×C₇	1	1	yes	characteristic
281	#389	—	2	1	no	—
282	#389	C₂²×C₇	1	1	yes	characteristic, complemented
283	#389	C₂²×C₇	1	1	yes	characteristic, complemented
284	#387	—	2	1	no	—
285	#386	—	2	1	no	—
286	#386	—	2	1	no	—
287	#384	C₂²×C₇	1	1	yes	characteristic, complemented
288	#380	C₂²×C₇	1	1	yes	characteristic
289	#380	C₂²×C₇	1	1	yes	characteristic
290	#379	—	2	1	no	—
291	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
292	#340	C₂²×C₇	1	1	yes	characteristic, complemented
293	#340	C₂²×C₇	1	1	yes	characteristic, complemented
294	#340	C₂²×C₇	1	1	yes	characteristic, complemented
295	#340	C₂²×C₇	1	1	yes	characteristic, complemented
296	#336	C₂²×C₇	1	1	yes	characteristic, complemented
297	#336	C₂²×C₇	1	1	yes	characteristic, complemented
298	C₂³×C₇	—	2	2	no	—
299	C₂³×C₇	—	2	1	no	—
300	C₂³×C₇	—	2	2	no	—
301	C₂³×C₇	—	2	2	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	2	no	—
308	C₂³×C₇	—	4	8	no	—
309	C₂³×C₇	—	4	8	no	—
310	C₂³×C₇	—	4	1	no	—
311	C₂³×C₇	—	4	1	no	—
312	C₂³×C₇	—	4	1	no	—
313	C₂³×C₇	—	4	1	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	—	8	4	no	—
321	C₂³×C₇	—	8	4	no	—
322	C₂³×C₇	—	8	4	no	—
323	C₂³×C₇	—	8	4	no	—
324	C₂³×C₇	—	8	4	no	—
325	C₂³×C₇	C₂²⋊Q₈	1	2	yes	—
326	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
327	C₇×D₄	—	2	2	no	—
328	C₇×D₄	—	2	2	no	—
329	C₇×D₄	—	2	2	no	—
330	C₇×D₄	—	2	2	no	—
331	C₇×D₄	—	2	2	no	—
332	C₇×D₄	—	4	8	no	—
333	C₇×D₄	—	4	1	no	—
334	C₇×D₄	—	4	1	no	—
335	C₇×D₄	C₂²⋊Q₈	1	4	yes	—
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	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	1	no	—
345	C₂×C₄×C₇	—	2	1	no	—
346	C₂×C₄×C₇	—	2	2	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	—	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	—	4	1	no	—
368	C₂×C₄×C₇	—	4	1	no	—
369	C₂×C₄×C₇	—	4	1	no	—
370	C₂×C₄×C₇	—	4	1	no	—
371	C₂×C₄×C₇	—	8	4	no	—
372	C₂×C₄×C₇	—	8	4	no	—
373	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
374	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
375	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
377	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
378	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
379	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
381	C₇×C₈	—	2	2	no	—
382	C₇×C₈	—	4	1	no	—
383	C₇×C₈	—	4	1	no	—
384	C₇×C₈	—	4	1	no	—
385	C₂⁵	—	2	1	no	—
386	C₂²×D₄	—	2	2	no	—
387	C₂²×D₄	—	2	2	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	—	4	1	no	—
391	C₂²×D₄	—	4	1	no	—
392	C₂²×D₄	C₇×Q₈	1	4	yes	—
393	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
394	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
395	C₂³×C₄	—	2	1	no	—
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
398	C₂×M₁₆	—	2	2	no	—
399	C₂×M₁₆	—	2	2	no	—
400	C₂×M₁₆	—	4	1	no	—
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	#125	—	2	2	no	—
406	#125	—	4	1	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	4	1	no	—
410	C₄×D₄	—	4	1	no	—
411	#117	—	2	2	no	—
412	#117	—	4	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	4	4	no	—
435	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
440	#107	—	2	2	no	—
441	#107	—	4	1	no	—
442	#106	—	2	2	no	—
443	#106	—	4	1	no	—
444	C₄⋊C₈	—	2	2	no	—
445	C₄⋊C₈	—	4	1	no	—
446	#102	—	2	2	no	—
447	#102	—	2	2	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	—	4	1	no	—
452	#102	—	4	1	no	—
453	#102	C₇×D₄	1	4	yes	—
454	C₂²⋊C₈	—	2	2	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	C₇×D₄	1	1	yes	characteristic
460	#95	C₇×D₄	1	1	yes	characteristic
461	C₂²×C₇	—	2	2	no	—
462	C₂²×C₇	—	2	2	no	—
463	C₂²×C₇	—	2	2	no	—
464	C₂²×C₇	—	2	4	no	—
465	C₂²×C₇	—	4	2	no	—
466	C₂²×C₇	—	4	2	no	—
467	C₂²×C₇	—	4	1	no	—
468	C₂²×C₇	—	4	2	no	—
469	C₂²×C₇	—	4	2	no	—
470	C₂²×C₇	—	4	1	no	—
471	C₂²×C₇	—	4	2	no	—
472	C₂²×C₇	—	4	1	no	—
473	C₂²×C₇	—	4	1	no	—
474	C₂²×C₇	—	4	2	no	—
475	C₂²×C₇	—	4	2	no	—
476	C₂²×C₇	—	4	2	no	—
477	C₂²×C₇	—	4	2	no	—
478	C₂²×C₇	—	8	16	no	—
479	C₂²×C₇	—	8	1	no	—
480	C₂²×C₇	—	8	1	no	—
481	C₂²×C₇	—	8	1	no	—
482	C₂²×C₇	—	8	1	no	—
483	C₂²×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
484	C₂²×C₇	D₄²	1	1	yes	characteristic
485	C₂²×C₇	#546	1	1	yes	characteristic
486	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
487	C₂²×C₇	#575	1	1	yes	characteristic
488	C₂²×C₇	#576	1	1	yes	characteristic
489	C₂²×C₇	#577	1	1	yes	characteristic
490	C₄×C₇	—	2	2	no	—
491	C₄×C₇	—	2	2	no	—
492	C₄×C₇	—	4	1	no	—
493	C₄×C₇	—	4	2	no	—
494	C₄×C₇	—	4	1	no	—
495	C₄×C₇	—	4	1	no	—
496	C₄×C₇	—	8	1	no	—
497	C₄×C₇	—	8	1	no	—
498	C₄×C₇	—	8	1	no	—
499	C₄×C₇	—	8	1	no	—
500	C₄×C₇	—	8	1	no	—
501	C₄×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
502	C₄×C₇	#543	1	1	yes	characteristic
503	C₄×C₇	#546	1	1	yes	characteristic
504	C₄×C₇	#551	1	1	yes	characteristic
505	C₂⁴	—	2	1	no	—
506	C₂⁴	—	2	1	no	—
507	C₂⁴	—	2	4	no	—
508	C₂⁴	—	4	2	no	—
509	C₂⁴	—	4	2	no	—
510	C₂⁴	—	4	2	no	—
511	C₂⁴	—	4	2	no	—
512	C₂⁴	—	8	1	no	—
513	C₂⁴	—	8	1	no	—
514	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
515	C₂×D₄	—	2	8	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	4	4	no	—
526	C₂×D₄	—	4	4	no	—
527	C₂×D₄	—	4	4	no	—
528	C₂×D₄	—	4	2	no	—
529	C₂×D₄	—	4	2	no	—
530	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
531	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
532	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
533	C₂×D₄	C₇×#41	1	2	yes	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	8	1	no	—
549	C₂²×C₄	—	8	1	no	—
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	1	yes	characteristic
555	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
556	C₂²×C₄	C₇×#41	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
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	C₂×C₇×D₄	1	2	yes	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	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	—	4	2	no	—
583	C₄⋊C₄	—	4	2	no	—
584	C₄⋊C₄	—	4	2	no	—
585	C₄⋊C₄	—	4	2	no	—
586	C₄⋊C₄	—	8	1	no	—
587	C₄⋊C₄	—	8	1	no	—
588	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	2	no	—
592	C₂²⋊C₄	—	4	2	no	—
593	C₂²⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	4	2	no	—
595	C₂²⋊C₄	—	4	2	no	—
596	C₂²⋊C₄	—	4	2	no	—
597	C₂²⋊C₄	—	8	1	no	—
598	C₂²⋊C₄	—	8	1	no	—
599	C₂²⋊C₄	—	8	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	1	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	4	2	no	—
605	C₂×C₇	—	4	2	no	—
606	C₂×C₇	—	4	4	no	—
607	C₂×C₇	—	8	2	no	—
608	C₂×C₇	#2437	1	1	yes	characteristic
609	C₂×C₇	#3077	1	1	yes	characteristic
610	C₂×C₇	#3081	1	1	yes	characteristic
611	C₂×C₇	#3267	1	1	yes	characteristic
612	C₂×C₇	#3274	1	1	yes	characteristic
613	C₂×C₇	#3310	1	1	yes	characteristic
614	C₂×C₇	#3322	1	1	yes	characteristic
615	C₂³	—	2	2	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	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	2	no	—
625	C₂³	—	4	8	no	—
626	C₂³	—	4	8	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	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	8	4	no	—
638	C₂³	—	8	4	no	—
639	C₂³	—	8	4	no	—
640	C₂³	—	8	4	no	—
641	C₂³	—	8	4	no	—
642	C₂³	C₇×C₂²⋊Q₈	1	2	yes	—
643	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
644	D₄	—	2	2	no	—
645	D₄	—	2	2	no	—
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	2	no	—
649	D₄	—	4	8	no	—
650	D₄	—	4	1	no	—
651	D₄	—	4	1	no	—
652	D₄	C₇×C₂²⋊Q₈	1	4	yes	—
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	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	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	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	8	4	no	—
689	C₂×C₄	—	8	4	no	—
690	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
691	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
692	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
693	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
694	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
695	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
696	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
697	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
698	C₈	—	2	2	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₈	—	4	1	no	—
702	C₇	#25968	1	1	yes	characteristic, direct product factor, Sylow
703	C₂²	—	2	2	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	8	16	no	—
721	C₂²	—	8	1	no	—
722	C₂²	—	8	1	no	—
723	C₂²	—	8	1	no	—
724	C₂²	—	8	1	no	—
725	C₂²	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
726	C₂²	C₇×D₄²	1	1	yes	characteristic
727	C₂²	C₇×#546	1	1	yes	characteristic
728	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
729	C₂²	C₇×#575	1	1	yes	characteristic
730	C₂²	C₇×#576	1	1	yes	characteristic
731	C₂²	C₇×#577	1	1	yes	characteristic
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	1	no	—
738	C₄	—	8	1	no	—
739	C₄	—	8	1	no	—
740	C₄	—	8	1	no	—
741	C₄	—	8	1	no	—
742	C₄	—	8	1	no	—
743	C₄	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
744	C₄	C₇×#543	1	1	yes	characteristic
745	C₄	C₇×#546	1	1	yes	characteristic
746	C₄	C₇×#551	1	1	yes	characteristic
747	C₂	—	4	2	no	—
748	C₂	—	4	4	no	—
749	C₂	—	8	2	no	—
750	C₂	C₇×#2437	1	1	yes	characteristic
751	C₂	C₇×#3077	1	1	yes	characteristic
752	C₂	C₇×#3081	1	1	yes	characteristic
753	C₂	C₇×#3267	1	1	yes	characteristic
754	C₂	C₇×#3274	1	1	yes	characteristic
755	C₂	C₇×#3310	1	1	yes	characteristic
756	C₂	C₇×#3322	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#478	C₂	semidirect
3. C₇×#2441	C₂	semidirect
5. C₇×#2093	C₂	semidirect
6. C₇×#2065	C₂	semidirect
7. C₇×#2065	C₂	semidirect
8. C₇×#2025	C₂	semidirect
9. C₇×#1864	C₂	semidirect
10. C₇×#1862	C₂	semidirect
11. C₇×#1854	C₂	semidirect
12. C₇×#1851	C₂	semidirect
13. C₇×#1809	C₂	semidirect
14. C₇×#1802	C₂	semidirect
18. C₂×C₇×#125	C₂²	semidirect
24. C₂×C₇×#107	C₂²	semidirect
25. C₂×C₇×#107	C₂²	semidirect
26. C₂×C₇×#106	C₂²	semidirect
27. C₂×C₇×#106	C₂²	semidirect
28. C₂×C₇×C₄⋊C₈	C₂²	semidirect
29. C₂×C₇×C₄⋊C₈	C₂²	semidirect
45. C₇×#389	C₂²	semidirect
46. C₇×#389	C₂²	semidirect
50. C₇×#384	C₂²	semidirect
55. C₇×#340	C₂²	semidirect
56. C₇×#340	C₂²	semidirect
57. C₇×#340	C₂²	semidirect
58. C₇×#340	C₂²	semidirect
59. C₇×#336	C₂²	semidirect
60. C₇×#336	C₂²	semidirect
61. #25968	C₇	direct (N × H)
138. C₂×#478	C₂×C₇	semidirect
140. #2441	C₂×C₇	semidirect
142. #2093	C₂×C₇	semidirect
143. #2065	C₂×C₇	semidirect
144. #2065	C₂×C₇	semidirect
145. #2025	C₂×C₇	semidirect
146. #1864	C₂×C₇	semidirect
147. #1862	C₂×C₇	semidirect
148. #1854	C₂×C₇	semidirect
149. #1851	C₂×C₇	semidirect
150. #1809	C₂×C₇	semidirect
151. #1802	C₂×C₇	semidirect
255. C₂×#125	C₂²×C₇	semidirect
261. C₂×#107	C₂²×C₇	semidirect
262. C₂×#107	C₂²×C₇	semidirect
263. C₂×#106	C₂²×C₇	semidirect
264. C₂×#106	C₂²×C₇	semidirect
265. C₂×C₄⋊C₈	C₂²×C₇	semidirect
266. C₂×C₄⋊C₈	C₂²×C₇	semidirect
282. #389	C₂²×C₇	semidirect
283. #389	C₂²×C₇	semidirect
287. #384	C₂²×C₇	semidirect
292. #340	C₂²×C₇	semidirect
293. #340	C₂²×C₇	semidirect
294. #340	C₂²×C₇	semidirect
295. #340	C₂²×C₇	semidirect
296. #336	C₂²×C₇	semidirect
297. #336	C₂²×C₇	semidirect
702. C₇	#25968	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×#478	2
C₂×C₇×#418	2
C₇×#2441	2
C₇×D₄×C₂²⋊C₄	2
C₇×#2093	2
C₇×#2065	2
C₇×#2025	2
C₇×#1864	2
C₇×#1862	2
C₇×#1854	2
C₇×#1851	2
C₇×#1809	2
C₇×#1802	2
C₇×#1786	2
#25968	7

Subgroups — C7×#25968 #13203184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#25968 #13203184