Subgroups — C₇×#22584 #13199800

Order 1792.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic
2	C₇×#2346	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1934	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1926	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1925	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1864	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1862	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1825	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1809	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1786	C₂	1	1	yes	maximal, characteristic
13	C₇×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₇×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
22	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
24	C₇×#418	C₄	1	8	yes	complemented
25	C₂×C₇×#102	C₂²	1	1	yes	characteristic
26	C₂×C₇×#102	C₂²	1	1	yes	characteristic
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₇×#102	C₂²	1	1	yes	characteristic
29	C₂×C₇×#102	C₂²	1	1	yes	characteristic
30	C₂×C₇×#102	C₂²	1	1	yes	characteristic
31	C₂×C₇×#102	C₂²	1	1	yes	characteristic
32	C₂×C₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
36	C₇×#390	C₂²	1	1	yes	characteristic
37	C₇×#390	C₂²	1	1	yes	characteristic
38	C₇×#389	C₂²	1	1	yes	characteristic, complemented
39	C₇×#389	C₂²	1	1	yes	characteristic, complemented
40	C₇×#388	—	2	1	no	—
41	C₇×#388	—	2	1	no	—
42	C₇×#386	—	2	1	no	—
43	C₇×#386	—	2	1	no	—
44	C₇×#382	—	2	1	no	—
45	C₇×#380	C₂²	1	1	yes	characteristic
46	C₇×#380	C₂²	1	1	yes	characteristic
47	C₇×#379	—	2	1	no	—
48	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₇×#376	—	2	1	no	—
52	C₇×#340	C₂²	1	1	yes	characteristic, complemented
53	C₇×#340	C₂²	1	1	yes	characteristic, complemented
54	C₇×#340	C₂²	1	1	yes	characteristic, complemented
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×#336	C₂²	1	1	yes	characteristic, complemented
59	C₇×#336	C₂²	1	1	yes	characteristic, complemented
60	#22584	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁵×C₇	—	2	1	no	—
62	C₂²×C₇×D₄	—	2	2	no	—
63	C₂²×C₇×D₄	—	2	2	no	—
64	C₂²×C₇×D₄	—	2	1	no	—
65	C₂²×C₇×D₄	—	2	2	no	—
66	C₂²×C₇×D₄	—	4	1	no	—
67	C₂²×C₇×D₄	—	4	1	no	—
68	C₂²×C₇×D₄	C₂×C₄	1	4	yes	—
69	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₇	—	2	1	no	—
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₇×M₁₆	—	4	1	no	—
75	C₂×C₇×M₁₆	—	4	1	no	—
76	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	complemented
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	C₄×C₇×D₄	—	2	2	no	—
82	C₄×C₇×D₄	—	2	2	no	—
83	C₄×C₇×D₄	—	4	1	no	—
84	C₄×C₇×D₄	—	4	1	no	—
85	C₇×#117	—	2	2	no	—
86	C₇×#117	C₂×C₄	1	4	yes	complemented
87	C₂×C₇×C₄⋊C₄	—	2	1	no	—
88	C₂×C₇×C₄⋊C₄	—	2	1	no	—
89	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
105	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₇	—	2	1	no	—
108	C₂×C₄²×C₇	—	2	1	no	—
109	C₂×C₄²×C₇	—	2	1	no	—
110	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
112	C₇×#107	—	4	1	no	—
113	C₇×#106	—	4	1	no	—
114	C₇×#102	—	2	2	no	—
115	C₇×#102	—	2	2	no	—
116	C₇×#102	—	4	1	no	—
117	C₇×#102	—	4	1	no	—
118	C₇×#102	C₂×C₄	1	4	yes	—
119	C₇×#102	C₂×C₄	1	4	yes	—
120	C₇×#102	C₂×C₄	1	4	yes	complemented
121	C₇×#102	C₂×C₄	1	4	yes	complemented
122	C₇×C₂²⋊C₈	—	2	2	no	—
123	C₇×#97	—	4	1	no	—
124	C₄×C₇×C₈	—	4	1	no	—
125	C₇×#95	—	2	1	no	—
126	C₇×#95	—	2	1	no	—
127	C₇×#95	—	2	1	no	—
128	C₇×#95	—	2	1	no	—
129	C₇×#95	—	2	1	no	—
130	C₇×#95	—	2	1	no	—
131	C₇×#95	D₄	1	1	yes	characteristic
132	C₇×#95	D₄	1	1	yes	characteristic
133	C₂×#418	C₂×C₇	1	1	yes	characteristic
134	#2346	C₂×C₇	1	1	yes	characteristic, complemented
135	D₄×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
136	#1936	C₂×C₇	1	1	yes	characteristic, complemented
137	#1934	C₂×C₇	1	1	yes	characteristic, complemented
138	#1926	C₂×C₇	1	1	yes	characteristic, complemented
139	#1925	C₂×C₇	1	1	yes	characteristic, complemented
140	#1864	C₂×C₇	1	1	yes	characteristic, complemented
141	#1862	C₂×C₇	1	1	yes	characteristic, complemented
142	#1825	C₂×C₇	1	1	yes	characteristic, complemented
143	#1809	C₂×C₇	1	1	yes	characteristic, complemented
144	#1786	C₂×C₇	1	1	yes	characteristic
145	#1762	C₂×C₇	1	1	yes	characteristic, complemented
146	C₄×#102	C₂×C₇	1	1	yes	characteristic, complemented
147	#1753	C₂×C₇	1	1	yes	characteristic, complemented
148	C₂⁴×C₇	—	2	1	no	—
149	C₂⁴×C₇	—	2	1	no	—
150	C₂⁴×C₇	—	2	4	no	—
151	C₂⁴×C₇	—	4	2	no	—
152	C₂⁴×C₇	—	4	2	no	—
153	C₂⁴×C₇	—	4	2	no	—
154	C₂⁴×C₇	—	4	2	no	—
155	C₂⁴×C₇	—	8	1	no	—
156	C₂⁴×C₇	—	8	1	no	—
157	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
158	C₂×C₇×D₄	—	2	8	no	—
159	C₂×C₇×D₄	—	2	4	no	—
160	C₂×C₇×D₄	—	2	1	no	—
161	C₂×C₇×D₄	—	2	1	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	—	2	1	no	—
168	C₂×C₇×D₄	—	4	4	no	—
169	C₂×C₇×D₄	—	4	4	no	—
170	C₂×C₇×D₄	—	4	4	no	—
171	C₂×C₇×D₄	—	4	2	no	—
172	C₂×C₇×D₄	—	4	2	no	—
173	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
174	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
175	C₂×C₇×D₄	#41	1	2	yes	—
176	C₂×C₇×D₄	#41	1	2	yes	—
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	—	4	2	no	—
188	C₂²×C₄×C₇	—	4	2	no	—
189	C₂²×C₄×C₇	—	4	2	no	—
190	C₂²×C₄×C₇	—	4	2	no	—
191	C₂²×C₄×C₇	—	8	1	no	—
192	C₂²×C₄×C₇	—	8	1	no	—
193	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	#41	1	2	yes	—
200	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
201	C₇×M₁₆	—	4	4	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	C₂²×C₄	1	2	yes	—
213	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
214	C₇×C₄⋊C₄	—	2	1	no	—
215	C₇×C₄⋊C₄	—	2	1	no	—
216	C₇×C₄⋊C₄	—	2	1	no	—
217	C₇×C₄⋊C₄	—	2	1	no	—
218	C₇×C₄⋊C₄	—	2	1	no	—
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	—	8	1	no	—
225	C₇×C₄⋊C₄	—	8	1	no	—
226	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
227	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
228	C₇×C₂²⋊C₄	—	2	4	no	—
229	C₇×C₂²⋊C₄	—	2	2	no	—
230	C₇×C₂²⋊C₄	—	4	1	no	—
231	C₇×C₂²⋊C₄	—	4	2	no	—
232	C₇×C₂²⋊C₄	—	4	2	no	—
233	C₇×C₂²⋊C₄	—	4	2	no	—
234	C₇×C₂²⋊C₄	—	4	2	no	—
235	C₇×C₂²⋊C₄	—	4	2	no	—
236	C₇×C₂²⋊C₄	—	8	1	no	—
237	C₇×C₂²⋊C₄	—	8	1	no	—
238	C₇×C₂²⋊C₄	—	8	1	no	—
239	C₄²×C₇	—	2	4	no	—
240	C₄²×C₇	—	2	1	no	—
241	C₄²×C₇	—	2	1	no	—
242	C₄²×C₇	—	2	1	no	—
243	C₄²×C₇	—	2	1	no	—
244	C₄²×C₇	—	4	2	no	—
245	C₄²×C₇	—	4	2	no	—
246	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
250	C₂×#117	C₂²×C₇	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	—	2	1	no	—
252	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
253	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
254	#418	C₄×C₇	1	8	yes	complemented
255	C₂×#102	C₂²×C₇	1	1	yes	characteristic
256	C₂×#102	C₂²×C₇	1	1	yes	characteristic
257	C₂×#102	C₂²×C₇	1	1	yes	characteristic
258	C₂×#102	C₂²×C₇	1	1	yes	characteristic
259	C₂×#102	C₂²×C₇	1	1	yes	characteristic
260	C₂×#102	C₂²×C₇	1	1	yes	characteristic
261	C₂×#102	C₂²×C₇	1	1	yes	characteristic
262	C₂×#102	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
265	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
266	#390	C₂²×C₇	1	1	yes	characteristic
267	#390	C₂²×C₇	1	1	yes	characteristic
268	#389	C₂²×C₇	1	1	yes	characteristic, complemented
269	#389	C₂²×C₇	1	1	yes	characteristic, complemented
270	#388	—	2	1	no	—
271	#388	—	2	1	no	—
272	#386	—	2	1	no	—
273	#386	—	2	1	no	—
274	#382	—	2	1	no	—
275	#380	C₂²×C₇	1	1	yes	characteristic
276	#380	C₂²×C₇	1	1	yes	characteristic
277	#379	—	2	1	no	—
278	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
279	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
280	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
281	#376	—	2	1	no	—
282	#340	C₂²×C₇	1	1	yes	characteristic, complemented
283	#340	C₂²×C₇	1	1	yes	characteristic, complemented
284	#340	C₂²×C₇	1	1	yes	characteristic, complemented
285	#340	C₂²×C₇	1	1	yes	characteristic, complemented
286	#340	C₂²×C₇	1	1	yes	characteristic, complemented
287	#340	C₂²×C₇	1	1	yes	characteristic, complemented
288	#336	C₂²×C₇	1	1	yes	characteristic, complemented
289	#336	C₂²×C₇	1	1	yes	characteristic, complemented
290	C₂³×C₇	—	2	2	no	—
291	C₂³×C₇	—	2	2	no	—
292	C₂³×C₇	—	2	2	no	—
293	C₂³×C₇	—	2	1	no	—
294	C₂³×C₇	—	2	1	no	—
295	C₂³×C₇	—	2	1	no	—
296	C₂³×C₇	—	2	1	no	—
297	C₂³×C₇	—	2	1	no	—
298	C₂³×C₇	—	2	1	no	—
299	C₂³×C₇	—	2	2	no	—
300	C₂³×C₇	—	4	8	no	—
301	C₂³×C₇	—	4	8	no	—
302	C₂³×C₇	—	4	1	no	—
303	C₂³×C₇	—	4	1	no	—
304	C₂³×C₇	—	4	1	no	—
305	C₂³×C₇	—	4	1	no	—
306	C₂³×C₇	—	4	1	no	—
307	C₂³×C₇	—	4	1	no	—
308	C₂³×C₇	—	4	1	no	—
309	C₂³×C₇	—	4	1	no	—
310	C₂³×C₇	—	4	1	no	—
311	C₂³×C₇	—	4	1	no	—
312	C₂³×C₇	—	8	4	no	—
313	C₂³×C₇	—	8	4	no	—
314	C₂³×C₇	—	8	4	no	—
315	C₂³×C₇	—	8	4	no	—
316	C₂³×C₇	—	8	4	no	—
317	C₂³×C₇	C₄×D₄	1	2	yes	—
318	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
319	C₇×D₄	—	2	2	no	—
320	C₇×D₄	—	2	2	no	—
321	C₇×D₄	—	2	2	no	—
322	C₇×D₄	—	2	2	no	—
323	C₇×D₄	—	2	2	no	—
324	C₇×D₄	—	4	8	no	—
325	C₇×D₄	—	4	1	no	—
326	C₇×D₄	—	4	1	no	—
327	C₇×D₄	#117	1	4	yes	—
328	C₂×C₄×C₇	—	2	1	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	2	no	—
333	C₂×C₄×C₇	—	2	2	no	—
334	C₂×C₄×C₇	—	2	2	no	—
335	C₂×C₄×C₇	—	2	2	no	—
336	C₂×C₄×C₇	—	2	2	no	—
337	C₂×C₄×C₇	—	2	2	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	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	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	—	8	4	no	—
364	C₂×C₄×C₇	—	8	4	no	—
365	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
366	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
367	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
369	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
370	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
372	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
373	C₇×C₈	—	2	2	no	—
374	C₇×C₈	—	2	2	no	—
375	C₇×C₈	—	4	1	no	—
376	C₇×C₈	—	4	1	no	—
377	C₂⁵	—	2	1	no	—
378	C₂²×D₄	—	2	2	no	—
379	C₂²×D₄	—	2	2	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	—	2	2	no	—
382	C₂²×D₄	—	4	1	no	—
383	C₂²×D₄	—	4	1	no	—
384	C₂²×D₄	C₂×C₄×C₇	1	4	yes	—
385	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
386	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
390	C₂×M₁₆	—	4	1	no	—
391	C₂×M₁₆	—	4	1	no	—
392	C₂×M₁₆	C₂×C₄×C₇	1	4	yes	complemented
393	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	4	1	no	—
400	C₄×D₄	—	4	1	no	—
401	#117	—	2	2	no	—
402	#117	C₂×C₄×C₇	1	4	yes	complemented
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	4	4	no	—
421	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
428	#107	—	4	1	no	—
429	#106	—	4	1	no	—
430	#102	—	2	2	no	—
431	#102	—	2	2	no	—
432	#102	—	4	1	no	—
433	#102	—	4	1	no	—
434	#102	C₂×C₄×C₇	1	4	yes	—
435	#102	C₂×C₄×C₇	1	4	yes	—
436	#102	C₂×C₄×C₇	1	4	yes	complemented
437	#102	C₂×C₄×C₇	1	4	yes	complemented
438	C₂²⋊C₈	—	2	2	no	—
439	#97	—	4	1	no	—
440	C₄×C₈	—	4	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	C₇×D₄	1	1	yes	characteristic
448	#95	C₇×D₄	1	1	yes	characteristic
449	C₂²×C₇	—	2	2	no	—
450	C₂²×C₇	—	2	4	no	—
451	C₂²×C₇	—	2	2	no	—
452	C₂²×C₇	—	2	2	no	—
453	C₂²×C₇	—	4	2	no	—
454	C₂²×C₇	—	4	2	no	—
455	C₂²×C₇	—	4	2	no	—
456	C₂²×C₇	—	4	1	no	—
457	C₂²×C₇	—	4	1	no	—
458	C₂²×C₇	—	4	2	no	—
459	C₂²×C₇	—	4	1	no	—
460	C₂²×C₇	—	4	2	no	—
461	C₂²×C₇	—	4	2	no	—
462	C₂²×C₇	—	4	1	no	—
463	C₂²×C₇	—	4	2	no	—
464	C₂²×C₇	—	4	2	no	—
465	C₂²×C₇	—	4	2	no	—
466	C₂²×C₇	—	8	16	no	—
467	C₂²×C₇	—	8	1	no	—
468	C₂²×C₇	—	8	1	no	—
469	C₂²×C₇	—	8	1	no	—
470	C₂²×C₇	—	8	1	no	—
471	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
472	C₂²×C₇	#546	1	1	yes	characteristic
473	C₂²×C₇	#546	1	1	yes	characteristic
474	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
475	C₂²×C₇	#575	1	1	yes	characteristic
476	C₂²×C₇	#576	1	1	yes	characteristic
477	C₂²×C₇	#577	1	1	yes	characteristic
478	C₄×C₇	—	2	2	no	—
479	C₄×C₇	—	2	2	no	—
480	C₄×C₇	—	4	2	no	—
481	C₄×C₇	—	4	2	no	—
482	C₄×C₇	—	4	1	no	—
483	C₄×C₇	—	4	1	no	—
484	C₄×C₇	—	4	1	no	—
485	C₄×C₇	—	8	1	no	—
486	C₄×C₇	—	8	1	no	—
487	C₄×C₇	—	8	1	no	—
488	C₄×C₇	—	8	1	no	—
489	C₄×C₇	C₂×#117	1	1	yes	characteristic
490	C₄×C₇	#518	1	1	yes	characteristic
491	C₄×C₇	#551	1	1	yes	characteristic
492	C₄×C₇	#551	1	1	yes	characteristic
493	C₂⁴	—	2	1	no	—
494	C₂⁴	—	2	1	no	—
495	C₂⁴	—	2	4	no	—
496	C₂⁴	—	4	2	no	—
497	C₂⁴	—	4	2	no	—
498	C₂⁴	—	4	2	no	—
499	C₂⁴	—	4	2	no	—
500	C₂⁴	—	8	1	no	—
501	C₂⁴	—	8	1	no	—
502	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
503	C₂×D₄	—	2	8	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	4	4	no	—
514	C₂×D₄	—	4	4	no	—
515	C₂×D₄	—	4	4	no	—
516	C₂×D₄	—	4	2	no	—
517	C₂×D₄	—	4	2	no	—
518	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
519	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
520	C₂×D₄	C₇×#41	1	2	yes	—
521	C₂×D₄	C₇×#41	1	2	yes	—
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	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	8	1	no	—
537	C₂²×C₄	—	8	1	no	—
538	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
539	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
540	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
541	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
542	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
543	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
544	C₂²×C₄	C₇×#41	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
546	M₁₆	—	4	4	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	C₂²×C₄×C₇	1	2	yes	—
558	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	8	1	no	—
570	C₄⋊C₄	—	8	1	no	—
571	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
572	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	8	1	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₂²⋊C₄	—	8	1	no	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	4	2	no	—
590	C₄²	—	4	2	no	—
591	C₂×C₇	—	4	2	no	—
592	C₂×C₇	—	4	4	no	—
593	C₂×C₇	—	8	2	no	—
594	C₂×C₇	#2342	1	1	yes	characteristic
595	C₂×C₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
596	C₂×C₇	#2946	1	1	yes	characteristic
597	C₂×C₇	#3310	1	1	yes	characteristic
598	C₂×C₇	#3319	1	1	yes	characteristic
599	C₂×C₇	#3323	1	1	yes	characteristic
600	C₂×C₇	#3325	1	1	yes	characteristic
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	4	8	no	—
612	C₂³	—	4	8	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	8	4	no	—
624	C₂³	—	8	4	no	—
625	C₂³	—	8	4	no	—
626	C₂³	—	8	4	no	—
627	C₂³	—	8	4	no	—
628	C₂³	C₄×C₇×D₄	1	2	yes	—
629	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
630	D₄	—	2	2	no	—
631	D₄	—	2	2	no	—
632	D₄	—	2	2	no	—
633	D₄	—	2	2	no	—
634	D₄	—	2	2	no	—
635	D₄	—	4	8	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	C₇×#117	1	4	yes	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	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	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	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	—	8	4	no	—
675	C₂×C₄	—	8	4	no	—
676	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
677	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
678	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
679	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
680	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
681	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
682	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
683	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
684	C₈	—	2	2	no	—
685	C₈	—	2	2	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₇	#22584	1	1	yes	characteristic, direct product factor, Sylow
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	4	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	8	16	no	—
707	C₂²	—	8	1	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
712	C₂²	C₇×#546	1	1	yes	characteristic
713	C₂²	C₇×#546	1	1	yes	characteristic
714	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
715	C₂²	C₇×#575	1	1	yes	characteristic
716	C₂²	C₇×#576	1	1	yes	characteristic
717	C₂²	C₇×#577	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	8	1	no	—
726	C₄	—	8	1	no	—
727	C₄	—	8	1	no	—
728	C₄	—	8	1	no	—
729	C₄	C₂×C₇×#117	1	1	yes	characteristic
730	C₄	C₇×#518	1	1	yes	characteristic
731	C₄	C₇×#551	1	1	yes	characteristic
732	C₄	C₇×#551	1	1	yes	characteristic
733	C₂	—	4	2	no	—
734	C₂	—	4	4	no	—
735	C₂	—	8	2	no	—
736	C₂	C₇×#2342	1	1	yes	characteristic
737	C₂	C₄×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
738	C₂	C₇×#2946	1	1	yes	characteristic
739	C₂	C₇×#3310	1	1	yes	characteristic
740	C₂	C₇×#3319	1	1	yes	characteristic
741	C₂	C₇×#3323	1	1	yes	characteristic
742	C₂	C₇×#3325	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	C₂³×C₇×D₄	C₂²
LCS	G ▷ C₂×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
2. C₇×#2346	C₂	semidirect
4. C₇×#1936	C₂	semidirect
5. C₇×#1934	C₂	semidirect
6. C₇×#1926	C₂	semidirect
7. C₇×#1925	C₂	semidirect
8. C₇×#1864	C₂	semidirect
9. C₇×#1862	C₂	semidirect
10. C₇×#1825	C₂	semidirect
11. C₇×#1809	C₂	semidirect
13. C₇×#1762	C₂	semidirect
14. C₄×C₇×#102	C₂	semidirect
15. C₇×#1753	C₂	semidirect
22. C₂×C₇×#107	C₂²	semidirect
23. C₂×C₇×#106	C₂²	semidirect
24. C₇×#418	C₄	semidirect
34. C₂×C₇×#97	C₂²	semidirect
35. C₂×C₄×C₇×C₈	C₂²	semidirect
38. C₇×#389	C₂²	semidirect
39. C₇×#389	C₂²	semidirect
48. C₄×C₇×C₄⋊C₄	C₂²	semidirect
49. C₄×C₇×C₄⋊C₄	C₂²	semidirect
52. C₇×#340	C₂²	semidirect
53. C₇×#340	C₂²	semidirect
54. C₇×#340	C₂²	semidirect
55. C₇×#340	C₂²	semidirect
56. C₇×#340	C₂²	semidirect
57. C₇×#340	C₂²	semidirect
58. C₇×#336	C₂²	semidirect
59. C₇×#336	C₂²	semidirect
60. #22584	C₇	direct (N × H)
76. C₂×C₇×M₁₆	C₂×C₄	semidirect
86. C₇×#117	C₂×C₄	semidirect
120. C₇×#102	C₂×C₄	semidirect
121. C₇×#102	C₂×C₄	semidirect
134. #2346	C₂×C₇	semidirect
136. #1936	C₂×C₇	semidirect
137. #1934	C₂×C₇	semidirect
138. #1926	C₂×C₇	semidirect
139. #1925	C₂×C₇	semidirect
140. #1864	C₂×C₇	semidirect
141. #1862	C₂×C₇	semidirect
142. #1825	C₂×C₇	semidirect
143. #1809	C₂×C₇	semidirect
145. #1762	C₂×C₇	semidirect
146. C₄×#102	C₂×C₇	semidirect
147. #1753	C₂×C₇	semidirect
252. C₂×#107	C₂²×C₇	semidirect
253. C₂×#106	C₂²×C₇	semidirect
254. #418	C₄×C₇	semidirect
264. C₂×#97	C₂²×C₇	semidirect
265. C₂×C₄×C₈	C₂²×C₇	semidirect
268. #389	C₂²×C₇	semidirect
269. #389	C₂²×C₇	semidirect
278. C₄×C₄⋊C₄	C₂²×C₇	semidirect
279. C₄×C₄⋊C₄	C₂²×C₇	semidirect
282. #340	C₂²×C₇	semidirect
283. #340	C₂²×C₇	semidirect
284. #340	C₂²×C₇	semidirect
285. #340	C₂²×C₇	semidirect
286. #340	C₂²×C₇	semidirect
287. #340	C₂²×C₇	semidirect
288. #336	C₂²×C₇	semidirect
289. #336	C₂²×C₇	semidirect
392. C₂×M₁₆	C₂×C₄×C₇	semidirect
402. #117	C₂×C₄×C₇	semidirect
436. #102	C₂×C₄×C₇	semidirect
437. #102	C₂×C₄×C₇	semidirect
688. C₇	#22584	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×#418	2
C₇×#2346	2
C₇×D₄×C₂²⋊C₄	2
C₇×#1936	2
C₇×#1934	2
C₇×#1926	2
C₇×#1925	2
C₇×#1864	2
C₇×#1862	2
C₇×#1825	2
C₇×#1809	2
C₇×#1786	2
C₇×#1762	2
C₄×C₇×#102	2
C₇×#1753	2
#22584	7

Subgroups — C7×#22584 #13199800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22584 #13199800