Subgroups — C₇×#21871 #13199087

Order 1792.

1086 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2317	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1959	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1958	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1875	C₂	1	1	yes	maximal, characteristic
9	C₇×#1874	C₂	1	1	yes	maximal, characteristic
10	C₇×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1805	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1804	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#542	—	2	4	no	—
17	C₇×#542	C₄	1	8	yes	complemented
18	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×#126	—	2	1	no	—
20	C₂×C₇×#124	—	2	1	no	—
21	C₂×C₇×#124	C₂²	1	1	yes	characteristic
22	C₂×C₇×#123	—	2	1	no	—
23	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#121	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₇×#117	C₂²	1	1	yes	characteristic
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₇×#433	—	2	4	no	—
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	1	yes	characteristic
37	C₂×C₇×#103	C₂²	1	1	yes	characteristic
38	C₂×C₇×#102	C₂²	1	1	yes	characteristic
39	C₂×C₇×#102	C₂²	1	1	yes	characteristic
40	C₂×C₇×#102	C₂²	1	1	yes	characteristic
41	C₂×C₇×#102	C₂²	1	1	yes	characteristic
42	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₇×#97	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
46	C₇×#389	—	2	1	no	—
47	C₇×#389	—	2	1	no	—
48	C₇×#385	—	2	1	no	—
49	C₇×#385	—	2	1	no	—
50	C₇×#384	C₂²	1	1	yes	characteristic
51	C₇×#384	C₂²	1	1	yes	characteristic
52	C₇×#382	C₂²	1	1	yes	characteristic
53	C₇×#382	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	#21871	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×Q₈	—	2	1	no	—
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₇×C₄⋊Q₈	—	2	2	no	—
75	C₇×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
76	C₇×#126	—	2	8	no	—
77	C₇×#124	—	2	8	no	—
78	C₇×#124	—	2	2	no	—
79	C₇×#124	C₂×C₄	1	4	yes	complemented
80	C₇×#123	—	2	8	no	—
81	C₇×C₂²⋊Q₈	—	2	2	no	—
82	C₇×C₂²⋊Q₈	—	2	8	no	—
83	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
84	C₇×#121	—	2	2	no	—
85	C₇×#121	C₂×C₄	1	4	yes	—
86	C₄×C₇×Q₈	—	2	2	no	—
87	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
88	C₄×C₇×D₄	—	2	2	no	—
89	C₄×C₇×D₄	C₂×C₄	1	4	yes	complemented
90	C₇×#117	—	4	1	no	—
91	C₇×#117	—	4	1	no	—
92	C₇×#117	C₂×C₄	1	4	yes	—
93	C₇×#117	D₄	1	4	yes	—
94	C₂×C₇×C₄⋊C₄	—	2	1	no	—
95	C₂×C₇×C₄⋊C₄	—	2	1	no	—
96	C₂×C₇×C₄⋊C₄	—	2	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	4	1	no	—
103	C₂×C₇×C₄⋊C₄	—	4	1	no	—
104	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₇	—	2	1	no	—
121	C₂×C₄²×C₇	—	2	1	no	—
122	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
124	C₇×C₄⋊C₈	—	2	2	no	—
125	C₇×C₄⋊C₈	—	2	2	no	—
126	C₇×#103	—	4	1	no	—
127	C₇×#103	—	4	1	no	—
128	C₇×#103	—	4	1	no	—
129	C₇×#103	—	4	1	no	—
130	C₇×#102	—	4	1	no	—
131	C₇×#102	—	4	1	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	C₇×#97	—	2	2	no	—
137	C₄×C₇×C₈	—	2	2	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×#542	C₂×C₇	1	1	yes	characteristic
143	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
144	#2317	C₂×C₇	1	1	yes	characteristic, complemented
145	#1993	C₂×C₇	1	1	yes	characteristic, complemented
146	#1990	C₂×C₇	1	1	yes	characteristic, complemented
147	#1959	C₂×C₇	1	1	yes	characteristic, complemented
148	#1958	C₂×C₇	1	1	yes	characteristic, complemented
149	#1875	C₂×C₇	1	1	yes	characteristic
150	#1874	C₂×C₇	1	1	yes	characteristic
151	#1873	C₂×C₇	1	1	yes	characteristic, complemented
152	#1872	C₂×C₇	1	1	yes	characteristic, complemented
153	#1805	C₂×C₇	1	1	yes	characteristic, complemented
154	#1804	C₂×C₇	1	1	yes	characteristic, complemented
155	#1803	C₂×C₇	1	1	yes	characteristic, complemented
156	#1802	C₂×C₇	1	1	yes	characteristic, complemented
157	C₂⁴×C₇	—	2	1	no	—
158	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
159	C₂×C₇×Q₈	—	2	4	no	—
160	C₂×C₇×Q₈	—	2	1	no	—
161	C₂×C₇×Q₈	—	2	1	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
165	C₂×C₇×Q₈	—	8	1	no	—
166	C₂×C₇×Q₈	—	8	1	no	—
167	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
168	C₂×C₇×D₄	—	2	4	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	—	2	1	no	—
174	C₂×C₇×D₄	—	8	1	no	—
175	C₂×C₇×D₄	—	8	1	no	—
176	C₂×C₇×D₄	C₂²×C₄	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	4	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	—	4	2	no	—
190	C₂²×C₄×C₇	—	8	1	no	—
191	C₂²×C₄×C₇	—	8	1	no	—
192	C₂²×C₄×C₇	—	8	1	no	—
193	C₂²×C₄×C₇	—	8	1	no	—
194	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
213	C₂×C₇×C₈	—	2	1	no	—
214	C₇×C₄⋊C₄	—	2	4	no	—
215	C₇×C₄⋊C₄	—	2	4	no	—
216	C₇×C₄⋊C₄	—	2	4	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	—	2	1	no	—
225	C₇×C₄⋊C₄	—	2	1	no	—
226	C₇×C₄⋊C₄	—	2	1	no	—
227	C₇×C₄⋊C₄	—	4	2	no	—
228	C₇×C₄⋊C₄	—	8	1	no	—
229	C₇×C₄⋊C₄	—	8	1	no	—
230	C₇×C₄⋊C₄	—	8	1	no	—
231	C₇×C₄⋊C₄	—	8	1	no	—
232	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
233	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
234	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
235	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
236	C₇×C₂²⋊C₄	—	2	4	no	—
237	C₇×C₂²⋊C₄	—	2	4	no	—
238	C₇×C₂²⋊C₄	—	2	4	no	—
239	C₇×C₂²⋊C₄	—	2	4	no	—
240	C₇×C₂²⋊C₄	—	2	4	no	—
241	C₇×C₂²⋊C₄	—	4	2	no	—
242	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
243	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
244	C₄²×C₇	—	2	4	no	—
245	C₄²×C₇	—	4	2	no	—
246	C₄²×C₇	C₂²×C₄	1	2	yes	—
247	C₄²×C₇	C₂²×C₄	1	2	yes	—
248	C₄²×C₇	C₂×D₄	1	2	yes	—
249	C₄²×C₇	C₂×D₄	1	2	yes	—
250	#542	—	2	4	no	—
251	#542	C₄×C₇	1	8	yes	complemented
252	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
253	C₂×#126	—	2	1	no	—
254	C₂×#124	—	2	1	no	—
255	C₂×#124	C₂²×C₇	1	1	yes	characteristic
256	C₂×#123	—	2	1	no	—
257	C₂×C₂²⋊Q₈	—	2	1	no	—
258	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
259	C₂×#121	C₂²×C₇	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
262	C₂×#117	C₂²×C₇	1	1	yes	characteristic
263	C₂×#117	C₂²×C₇	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
265	#433	—	2	4	no	—
266	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
268	C₂×#103	C₂²×C₇	1	1	yes	characteristic
269	C₂×#103	C₂²×C₇	1	1	yes	characteristic
270	C₂×#103	C₂²×C₇	1	1	yes	characteristic
271	C₂×#103	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	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
278	C₂×#97	C₂²×C₇	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
280	#389	—	2	1	no	—
281	#389	—	2	1	no	—
282	#385	—	2	1	no	—
283	#385	—	2	1	no	—
284	#384	C₂²×C₇	1	1	yes	characteristic
285	#384	C₂²×C₇	1	1	yes	characteristic
286	#382	C₂²×C₇	1	1	yes	characteristic
287	#382	C₂²×C₇	1	1	yes	characteristic
288	#340	C₂²×C₇	1	1	yes	characteristic
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	C₂³×C₇	—	2	1	no	—
297	C₂³×C₇	—	2	1	no	—
298	C₂³×C₇	—	2	1	no	—
299	C₂³×C₇	—	2	1	no	—
300	C₂³×C₇	—	2	1	no	—
301	C₂³×C₇	—	2	1	no	—
302	C₂³×C₇	—	2	2	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	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
311	C₇×Q₈	—	2	2	no	—
312	C₇×Q₈	—	2	2	no	—
313	C₇×Q₈	—	4	1	no	—
314	C₇×Q₈	—	4	1	no	—
315	C₇×Q₈	—	8	4	no	—
316	C₇×D₄	—	2	2	no	—
317	C₇×D₄	—	2	2	no	—
318	C₇×D₄	—	4	1	no	—
319	C₇×D₄	—	4	1	no	—
320	C₇×D₄	—	8	4	no	—
321	C₂×C₄×C₇	—	2	1	no	—
322	C₂×C₄×C₇	—	2	1	no	—
323	C₂×C₄×C₇	—	2	1	no	—
324	C₂×C₄×C₇	—	2	1	no	—
325	C₂×C₄×C₇	—	2	1	no	—
326	C₂×C₄×C₇	—	2	1	no	—
327	C₂×C₄×C₇	—	2	1	no	—
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	2	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	—	4	1	no	—
339	C₂×C₄×C₇	—	4	1	no	—
340	C₂×C₄×C₇	—	4	1	no	—
341	C₂×C₄×C₇	—	4	1	no	—
342	C₂×C₄×C₇	—	4	1	no	—
343	C₂×C₄×C₇	—	4	1	no	—
344	C₂×C₄×C₇	—	4	1	no	—
345	C₂×C₄×C₇	—	4	1	no	—
346	C₂×C₄×C₇	—	4	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	—	8	4	no	—
357	C₂×C₄×C₇	—	8	4	no	—
358	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
359	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
360	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
361	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
362	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
363	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
364	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
368	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
369	C₇×C₈	—	4	1	no	—
370	C₇×C₈	—	4	1	no	—
371	C₇×C₈	—	4	1	no	—
372	C₇×C₈	—	4	1	no	—
373	C₂²×Q₈	—	2	1	no	—
374	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
375	C₂²×D₄	—	2	1	no	—
376	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
377	C₂³×C₄	—	2	1	no	—
378	C₂³×C₄	—	2	1	no	—
379	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	C₂×C₄×C₇	1	4	yes	complemented
386	#126	—	2	8	no	—
387	#124	—	2	8	no	—
388	#124	—	2	2	no	—
389	#124	C₂×C₄×C₇	1	4	yes	complemented
390	#123	—	2	8	no	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	—	2	8	no	—
393	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
394	#121	—	2	2	no	—
395	#121	C₂×C₄×C₇	1	4	yes	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	C₂×C₄×C₇	1	4	yes	complemented
400	#117	—	4	1	no	—
401	#117	—	4	1	no	—
402	#117	C₂×C₄×C₇	1	4	yes	—
403	#117	C₇×D₄	1	4	yes	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	4	1	no	—
413	C₂×C₄⋊C₄	—	4	1	no	—
414	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
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	C₇×D₄	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
434	C₄⋊C₈	—	2	2	no	—
435	C₄⋊C₈	—	2	2	no	—
436	#103	—	4	1	no	—
437	#103	—	4	1	no	—
438	#103	—	4	1	no	—
439	#103	—	4	1	no	—
440	#102	—	4	1	no	—
441	#102	—	4	1	no	—
442	#102	—	4	1	no	—
443	#102	—	4	1	no	—
444	C₂²⋊C₈	—	2	2	no	—
445	C₂²⋊C₈	—	2	2	no	—
446	#97	—	2	2	no	—
447	C₄×C₈	—	2	2	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	C₂²×C₇	—	2	2	no	—
453	C₂²×C₇	—	2	2	no	—
454	C₂²×C₇	—	2	2	no	—
455	C₂²×C₇	—	4	1	no	—
456	C₂²×C₇	—	4	1	no	—
457	C₂²×C₇	—	4	1	no	—
458	C₂²×C₇	—	4	1	no	—
459	C₂²×C₇	—	4	2	no	—
460	C₂²×C₇	—	4	2	no	—
461	C₂²×C₇	—	4	2	no	—
462	C₂²×C₇	—	8	1	no	—
463	C₂²×C₇	—	8	1	no	—
464	C₂²×C₇	—	8	1	no	—
465	C₂²×C₇	—	8	1	no	—
466	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
467	C₂²×C₇	#535	1	1	yes	characteristic
468	C₂²×C₇	#536	1	1	yes	characteristic
469	C₂²×C₇	#576	1	1	yes	characteristic
470	C₂²×C₇	#577	1	1	yes	characteristic
471	C₂²×C₇	#577	1	1	yes	characteristic
472	C₂²×C₇	#578	1	1	yes	characteristic
473	C₄×C₇	—	2	2	no	—
474	C₄×C₇	—	2	2	no	—
475	C₄×C₇	—	2	2	no	—
476	C₄×C₇	—	2	2	no	—
477	C₄×C₇	—	2	2	no	—
478	C₄×C₇	—	4	2	no	—
479	C₄×C₇	—	4	2	no	—
480	C₄×C₇	—	4	2	no	—
481	C₄×C₇	—	8	1	no	—
482	C₄×C₇	—	8	1	no	—
483	C₄×C₇	—	8	1	no	—
484	C₄×C₇	—	8	1	no	—
485	C₄×C₇	#520	1	1	yes	characteristic
486	C₄×C₇	#520	1	1	yes	characteristic
487	C₄×C₇	#537	1	1	yes	characteristic
488	C₄×C₇	#537	1	1	yes	characteristic
489	C₂⁴	—	2	1	no	—
490	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
491	C₂×Q₈	—	2	4	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	8	1	no	—
498	C₂×Q₈	—	8	1	no	—
499	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	8	1	no	—
507	C₂×D₄	—	8	1	no	—
508	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	8	1	no	—
523	C₂²×C₄	—	8	1	no	—
524	C₂²×C₄	—	8	1	no	—
525	C₂²×C₄	—	8	1	no	—
526	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
527	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
528	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
529	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
530	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
531	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
532	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	—	8	1	no	—
561	C₄⋊C₄	—	8	1	no	—
562	C₄⋊C₄	—	8	1	no	—
563	C₄⋊C₄	—	8	1	no	—
564	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
565	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
566	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
567	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
575	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
576	C₄²	—	2	4	no	—
577	C₄²	—	4	2	no	—
578	C₄²	C₂²×C₄×C₇	1	2	yes	—
579	C₄²	C₂²×C₄×C₇	1	2	yes	—
580	C₄²	C₂×C₇×D₄	1	2	yes	—
581	C₄²	C₂×C₇×D₄	1	2	yes	—
582	C₂×C₇	—	4	2	no	—
583	C₂×C₇	—	8	2	no	—
584	C₂×C₇	#2311	1	1	yes	characteristic
585	C₂×C₇	#2897	1	1	yes	characteristic
586	C₂×C₇	#2898	1	1	yes	characteristic
587	C₂×C₇	#3224	1	1	yes	characteristic
588	C₂×C₇	#3225	1	1	yes	characteristic
589	C₂×C₇	#3243	1	1	yes	characteristic
590	C₂×C₇	#3244	1	1	yes	characteristic
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
605	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
606	Q₈	—	2	2	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	4	1	no	—
609	Q₈	—	4	1	no	—
610	Q₈	—	8	4	no	—
611	D₄	—	2	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	1	no	—
615	D₄	—	8	4	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	8	4	no	—
652	C₂×C₄	—	8	4	no	—
653	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
654	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
655	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
656	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
657	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
658	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
659	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
660	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
662	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
663	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
664	C₈	—	4	1	no	—
665	C₈	—	4	1	no	—
666	C₈	—	4	1	no	—
667	C₈	—	4	1	no	—
668	C₇	#21871	1	1	yes	characteristic, direct product factor, Sylow
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	1	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	—	8	1	no	—
682	C₂²	—	8	1	no	—
683	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
684	C₂²	C₇×#535	1	1	yes	characteristic
685	C₂²	C₇×#536	1	1	yes	characteristic
686	C₂²	C₇×#576	1	1	yes	characteristic
687	C₂²	C₇×#577	1	1	yes	characteristic
688	C₂²	C₇×#577	1	1	yes	characteristic
689	C₂²	C₇×#578	1	1	yes	characteristic
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	8	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	—	8	1	no	—
702	C₄	C₇×#520	1	1	yes	characteristic
703	C₄	C₇×#520	1	1	yes	characteristic
704	C₄	C₇×#537	1	1	yes	characteristic
705	C₄	C₇×#537	1	1	yes	characteristic
706	C₂	—	4	2	no	—
707	C₂	—	8	2	no	—
708	C₂	C₇×#2311	1	1	yes	characteristic
709	C₂	C₇×#2897	1	1	yes	characteristic
710	C₂	C₇×#2898	1	1	yes	characteristic
711	C₂	C₇×#3224	1	1	yes	characteristic
712	C₂	C₇×#3225	1	1	yes	characteristic
713	C₂	C₇×#3243	1	1	yes	characteristic
714	C₂	C₇×#3244	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×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#433	C₂	semidirect
3. C₇×#2317	C₂	semidirect
4. C₇×#1993	C₂	semidirect
5. C₇×#1990	C₂	semidirect
6. C₇×#1959	C₂	semidirect
7. C₇×#1958	C₂	semidirect
10. C₇×#1873	C₂	semidirect
11. C₇×#1872	C₂	semidirect
12. C₇×#1805	C₂	semidirect
13. C₇×#1804	C₂	semidirect
14. C₇×#1803	C₂	semidirect
15. C₇×#1802	C₂	semidirect
17. C₇×#542	C₄	semidirect
62. #21871	C₇	direct (N × H)
75. C₇×C₄⋊Q₈	C₂×C₄	semidirect
79. C₇×#124	C₂×C₄	semidirect
87. C₄×C₇×Q₈	C₂×C₄	semidirect
89. C₄×C₇×D₄	C₂×C₄	semidirect
143. C₂×#433	C₂×C₇	semidirect
144. #2317	C₂×C₇	semidirect
145. #1993	C₂×C₇	semidirect
146. #1990	C₂×C₇	semidirect
147. #1959	C₂×C₇	semidirect
148. #1958	C₂×C₇	semidirect
151. #1873	C₂×C₇	semidirect
152. #1872	C₂×C₇	semidirect
153. #1805	C₂×C₇	semidirect
154. #1804	C₂×C₇	semidirect
155. #1803	C₂×C₇	semidirect
156. #1802	C₂×C₇	semidirect
251. #542	C₄×C₇	semidirect
385. C₄⋊Q₈	C₂×C₄×C₇	semidirect
389. #124	C₂×C₄×C₇	semidirect
397. C₄×Q₈	C₂×C₄×C₇	semidirect
399. C₄×D₄	C₂×C₄×C₇	semidirect
668. C₇	#21871	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×#542	2
C₂×C₇×#433	2
C₇×#2317	2
C₇×#1993	2
C₇×#1990	2
C₇×#1959	2
C₇×#1958	2
C₇×#1875	2
C₇×#1874	2
C₇×#1873	2
C₇×#1872	2
C₇×#1805	2
C₇×#1804	2
C₇×#1803	2
C₇×#1802	2
#21871	7

Subgroups — C7×#21871 #13199087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21871 #13199087