Subgroups — C₇×#23759 #13200975

Order 1792.

752 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₇×#2283	C₂	1	1	yes	maximal, characteristic
3	C₇×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2097	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2077	C₂	1	1	yes	maximal, characteristic
7	C₇×#2075	C₂	1	1	yes	maximal, characteristic
8	C₇×#2074	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2036	C₂	1	1	yes	maximal, characteristic
10	C₇×#2035	C₂	1	1	yes	maximal, characteristic
11	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
16	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
19	C₂×C₇×#107	C₂²	1	1	yes	characteristic
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#106	C₂²	1	1	yes	characteristic
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×#103	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	1	yes	characteristic
25	C₂×C₇×#103	C₂²	1	1	yes	characteristic
26	C₂×C₇×#103	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₇×#391	C₂²	1	1	yes	characteristic
32	C₇×#389	C₂²	1	1	yes	characteristic
33	C₇×#387	—	2	1	no	—
34	C₇×#385	—	2	1	no	—
35	C₇×#383	—	2	1	no	—
36	C₇×#382	C₂²	1	1	yes	characteristic
37	C₇×#382	C₂²	1	1	yes	characteristic
38	C₇×#381	—	2	1	no	—
39	C₇×#380	C₂²	1	1	yes	characteristic
40	C₇×#380	C₂²	1	1	yes	characteristic
41	C₇×#380	C₂²	1	1	yes	characteristic
42	C₄×C₇×C₄⋊C₄	—	2	1	no	—
43	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
47	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
48	C₇×#376	—	2	1	no	—
49	C₇×#340	C₂²	1	1	yes	characteristic
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×#336	C₂²	1	1	yes	characteristic
58	C₇×#336	C₂²	1	1	yes	characteristic
59	#23759	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₇×C₂²⋊Q₈	—	2	2	no	—
69	C₇×C₂²⋊Q₈	—	2	2	no	—
70	C₄×C₇×Q₈	—	2	2	no	—
71	C₄×C₇×Q₈	—	2	2	no	—
72	C₂×C₇×C₄⋊C₄	—	2	1	no	—
73	C₂×C₇×C₄⋊C₄	—	2	1	no	—
74	C₂×C₇×C₄⋊C₄	—	2	1	no	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₇	—	2	2	no	—
87	C₂×C₄²×C₇	—	2	2	no	—
88	C₂×C₄²×C₇	—	2	1	no	—
89	C₂×C₄²×C₇	—	2	1	no	—
90	C₂×C₄²×C₇	—	2	1	no	—
91	C₂×C₄²×C₇	—	2	1	no	—
92	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
96	C₇×#107	—	2	2	no	—
97	C₇×#107	—	2	2	no	—
98	C₇×#106	—	2	2	no	—
99	C₇×#106	—	2	2	no	—
100	C₇×#103	—	2	2	no	—
101	C₇×#103	—	2	2	no	—
102	C₇×#103	—	2	2	no	—
103	C₇×#103	—	2	2	no	—
104	C₇×C₂²⋊C₈	—	2	2	no	—
105	C₇×C₂²⋊C₈	—	2	2	no	—
106	C₄×C₇×C₈	—	2	2	no	—
107	C₄×C₇×C₈	—	2	2	no	—
108	C₇×#95	—	2	1	no	—
109	C₇×#95	—	2	1	no	—
110	C₇×#95	—	2	1	no	—
111	C₇×#95	—	2	1	no	—
112	C₇×#95	—	2	1	no	—
113	C₇×#95	—	2	1	no	—
114	C₇×#95	—	2	1	no	—
115	C₇×#95	—	2	1	no	—
116	C₇×#95	—	2	1	no	—
117	C₇×#95	—	2	1	no	—
118	C₇×#95	—	2	1	no	—
119	C₇×#95	—	2	1	no	—
120	C₇×#95	—	2	1	no	—
121	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
122	#2283	C₂×C₇	1	1	yes	characteristic
123	#2101	C₂×C₇	1	1	yes	characteristic, complemented
124	#2097	C₂×C₇	1	1	yes	characteristic, complemented
125	#2085	C₂×C₇	1	1	yes	characteristic, complemented
126	#2077	C₂×C₇	1	1	yes	characteristic
127	#2075	C₂×C₇	1	1	yes	characteristic
128	#2074	C₂×C₇	1	1	yes	characteristic, complemented
129	#2036	C₂×C₇	1	1	yes	characteristic
130	#2035	C₂×C₇	1	1	yes	characteristic
131	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
132	C₄×#106	C₂×C₇	1	1	yes	characteristic, complemented
133	C₄×#103	C₂×C₇	1	1	yes	characteristic, complemented
134	C₄×#103	C₂×C₇	1	1	yes	characteristic, complemented
135	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic
136	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₇×Q₈	—	2	1	no	—
138	C₂×C₇×Q₈	—	2	1	no	—
139	C₂×C₇×Q₈	—	2	1	no	—
140	C₂×C₇×Q₈	—	2	1	no	—
141	C₂×C₇×Q₈	—	2	1	no	—
142	C₂×C₇×Q₈	#41	1	2	yes	—
143	C₂²×C₄×C₇	—	2	2	no	—
144	C₂²×C₄×C₇	—	2	1	no	—
145	C₂²×C₄×C₇	—	2	1	no	—
146	C₂²×C₄×C₇	—	2	2	no	—
147	C₂²×C₄×C₇	—	2	2	no	—
148	C₂²×C₄×C₇	—	2	2	no	—
149	C₂²×C₄×C₇	—	2	2	no	—
150	C₂²×C₄×C₇	—	2	1	no	—
151	C₂²×C₄×C₇	—	2	1	no	—
152	C₂²×C₄×C₇	—	2	1	no	—
153	C₂²×C₄×C₇	—	2	1	no	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	2	1	no	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	1	no	—
159	C₂²×C₄×C₇	—	2	1	no	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	4	1	no	—
163	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
169	C₂×C₇×C₈	—	2	1	no	—
170	C₂×C₇×C₈	—	2	1	no	—
171	C₂×C₇×C₈	—	2	1	no	—
172	C₂×C₇×C₈	—	2	1	no	—
173	C₂×C₇×C₈	—	2	1	no	—
174	C₂×C₇×C₈	—	2	1	no	—
175	C₂×C₇×C₈	—	2	1	no	—
176	C₂×C₇×C₈	—	2	1	no	—
177	C₂×C₇×C₈	—	2	1	no	—
178	C₂×C₇×C₈	—	2	1	no	—
179	C₂×C₇×C₈	#41	1	2	yes	—
180	C₂×C₇×C₈	#41	1	2	yes	—
181	C₇×C₄⋊C₄	—	2	4	no	—
182	C₇×C₄⋊C₄	—	2	1	no	—
183	C₇×C₄⋊C₄	—	2	1	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	—	2	1	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	1	no	—
191	C₇×C₄⋊C₄	—	2	1	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	—	2	1	no	—
194	C₇×C₄⋊C₄	—	2	1	no	—
195	C₇×C₄⋊C₄	—	4	2	no	—
196	C₇×C₄⋊C₄	—	4	2	no	—
197	C₇×C₄⋊C₄	#41	1	2	yes	—
198	C₇×C₂²⋊C₄	—	2	4	no	—
199	C₇×C₂²⋊C₄	—	4	2	no	—
200	C₇×C₂²⋊C₄	—	4	2	no	—
201	C₇×C₂²⋊C₄	—	4	2	no	—
202	C₄²×C₇	—	2	2	no	—
203	C₄²×C₇	—	2	2	no	—
204	C₄²×C₇	—	2	1	no	—
205	C₄²×C₇	—	2	1	no	—
206	C₄²×C₇	—	4	2	no	—
207	C₄²×C₇	—	4	2	no	—
208	C₄²×C₇	—	4	2	no	—
209	C₄²×C₇	—	4	2	no	—
210	C₄²×C₇	#41	1	2	yes	—
211	C₄²×C₇	#41	1	2	yes	—
212	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
213	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
215	C₂×#107	C₂²×C₇	1	1	yes	characteristic
216	C₂×#107	C₂²×C₇	1	1	yes	characteristic
217	C₂×#106	C₂²×C₇	1	1	yes	characteristic
218	C₂×#106	C₂²×C₇	1	1	yes	characteristic
219	C₂×#103	C₂²×C₇	1	1	yes	characteristic
220	C₂×#103	C₂²×C₇	1	1	yes	characteristic
221	C₂×#103	C₂²×C₇	1	1	yes	characteristic
222	C₂×#103	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
227	#391	C₂²×C₇	1	1	yes	characteristic
228	#389	C₂²×C₇	1	1	yes	characteristic
229	#387	—	2	1	no	—
230	#385	—	2	1	no	—
231	#383	—	2	1	no	—
232	#382	C₂²×C₇	1	1	yes	characteristic
233	#382	C₂²×C₇	1	1	yes	characteristic
234	#381	—	2	1	no	—
235	#380	C₂²×C₇	1	1	yes	characteristic
236	#380	C₂²×C₇	1	1	yes	characteristic
237	#380	C₂²×C₇	1	1	yes	characteristic
238	C₄×C₄⋊C₄	—	2	1	no	—
239	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	—	2	1	no	—
243	C₄×C₂²⋊C₄	—	2	1	no	—
244	#376	—	2	1	no	—
245	#340	C₂²×C₇	1	1	yes	characteristic
246	#340	C₂²×C₇	1	1	yes	characteristic
247	#340	C₂²×C₇	1	1	yes	characteristic
248	#340	C₂²×C₇	1	1	yes	characteristic
249	#340	C₂²×C₇	1	1	yes	characteristic
250	#340	C₂²×C₇	1	1	yes	characteristic
251	#340	C₂²×C₇	1	1	yes	characteristic
252	#340	C₂²×C₇	1	1	yes	characteristic
253	#336	C₂²×C₇	1	1	yes	characteristic
254	#336	C₂²×C₇	1	1	yes	characteristic
255	C₂³×C₇	—	2	1	no	—
256	C₂³×C₇	—	2	1	no	—
257	C₂³×C₇	—	2	1	no	—
258	C₂³×C₇	—	2	1	no	—
259	C₂³×C₇	—	2	1	no	—
260	C₂³×C₇	—	2	1	no	—
261	C₂³×C₇	#135	1	2	yes	—
262	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
263	C₇×Q₈	—	2	2	no	—
264	C₇×Q₈	—	2	2	no	—
265	C₇×Q₈	—	4	1	no	—
266	C₇×Q₈	—	4	1	no	—
267	C₂×C₄×C₇	—	2	1	no	—
268	C₂×C₄×C₇	—	2	1	no	—
269	C₂×C₄×C₇	—	2	1	no	—
270	C₂×C₄×C₇	—	2	1	no	—
271	C₂×C₄×C₇	—	2	1	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	1	no	—
275	C₂×C₄×C₇	—	2	1	no	—
276	C₂×C₄×C₇	—	2	1	no	—
277	C₂×C₄×C₇	—	2	1	no	—
278	C₂×C₄×C₇	—	2	1	no	—
279	C₂×C₄×C₇	—	2	1	no	—
280	C₂×C₄×C₇	—	4	4	no	—
281	C₂×C₄×C₇	—	4	1	no	—
282	C₂×C₄×C₇	—	4	1	no	—
283	C₂×C₄×C₇	—	4	1	no	—
284	C₂×C₄×C₇	—	4	1	no	—
285	C₂×C₄×C₇	—	4	1	no	—
286	C₂×C₄×C₇	—	4	1	no	—
287	C₂×C₄×C₇	—	4	1	no	—
288	C₂×C₄×C₇	—	4	1	no	—
289	C₂×C₄×C₇	—	4	4	no	—
290	C₂×C₄×C₇	—	4	1	no	—
291	C₂×C₄×C₇	—	4	1	no	—
292	C₂×C₄×C₇	—	4	1	no	—
293	C₂×C₄×C₇	—	4	1	no	—
294	C₂×C₄×C₇	—	4	1	no	—
295	C₂×C₄×C₇	—	4	1	no	—
296	C₂×C₄×C₇	—	4	1	no	—
297	C₂×C₄×C₇	—	4	1	no	—
298	C₂×C₄×C₇	—	4	1	no	—
299	C₂×C₄×C₇	—	4	1	no	—
300	C₂×C₄×C₇	—	4	1	no	—
301	C₂×C₄×C₇	—	4	1	no	—
302	C₂×C₄×C₇	—	4	1	no	—
303	C₂×C₄×C₇	—	4	1	no	—
304	C₂×C₄×C₇	—	4	1	no	—
305	C₂×C₄×C₇	—	4	1	no	—
306	C₂×C₄×C₇	—	4	1	no	—
307	C₂×C₄×C₇	—	4	1	no	—
308	C₂×C₄×C₇	#123	1	2	yes	—
309	C₂×C₄×C₇	#123	1	2	yes	—
310	C₂×C₄×C₇	#135	1	2	yes	—
311	C₂×C₄×C₇	#137	1	2	yes	—
312	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
313	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
315	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
318	C₇×C₈	—	2	2	no	—
319	C₇×C₈	—	2	2	no	—
320	C₇×C₈	—	4	1	no	—
321	C₇×C₈	—	4	1	no	—
322	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
323	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
324	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
355	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
358	#107	—	2	2	no	—
359	#107	—	2	2	no	—
360	#106	—	2	2	no	—
361	#106	—	2	2	no	—
362	#103	—	2	2	no	—
363	#103	—	2	2	no	—
364	#103	—	2	2	no	—
365	#103	—	2	2	no	—
366	C₂²⋊C₈	—	2	2	no	—
367	C₂²⋊C₈	—	2	2	no	—
368	C₄×C₈	—	2	2	no	—
369	C₄×C₈	—	2	2	no	—
370	#95	—	2	1	no	—
371	#95	—	2	1	no	—
372	#95	—	2	1	no	—
373	#95	—	2	1	no	—
374	#95	—	2	1	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	C₂²×C₇	—	2	2	no	—
384	C₂²×C₇	—	2	2	no	—
385	C₂²×C₇	—	2	2	no	—
386	C₂²×C₇	—	4	1	no	—
387	C₂²×C₇	—	4	1	no	—
388	C₂²×C₇	—	4	1	no	—
389	C₂²×C₇	—	4	1	no	—
390	C₂²×C₇	C₂×#123	1	1	yes	characteristic
391	C₂²×C₇	#525	1	1	yes	characteristic
392	C₂²×C₇	#532	1	1	yes	characteristic
393	C₂²×C₇	C₂×#135	1	1	yes	characteristic
394	C₂²×C₇	C₂×#135	1	1	yes	characteristic
395	C₂²×C₇	C₂×#137	1	1	yes	characteristic
396	C₂²×C₇	#575	1	1	yes	characteristic
397	C₄×C₇	—	2	2	no	—
398	C₄×C₇	—	4	1	no	—
399	C₄×C₇	—	4	1	no	—
400	C₄×C₇	—	4	2	no	—
401	C₄×C₇	—	4	1	no	—
402	C₄×C₇	—	4	2	no	—
403	C₄×C₇	—	8	1	no	—
404	C₄×C₇	—	8	1	no	—
405	C₄×C₇	—	8	1	no	—
406	C₄×C₇	—	8	1	no	—
407	C₄×C₇	—	8	1	no	—
408	C₄×C₇	—	8	1	no	—
409	C₄×C₇	#485	1	4	yes	—
410	C₄×C₇	#529	1	1	yes	characteristic
411	C₄×C₇	#529	1	1	yes	characteristic
412	C₄×C₇	#529	1	1	yes	characteristic
413	C₄×C₇	#529	1	1	yes	characteristic
414	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₇×#41	1	2	yes	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	C₇×#41	1	2	yes	—
458	C₂×C₈	C₇×#41	1	2	yes	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	C₇×#41	1	2	yes	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	2	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	2	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	4	2	no	—
485	C₄²	—	4	2	no	—
486	C₄²	—	4	2	no	—
487	C₄²	—	4	2	no	—
488	C₄²	C₇×#41	1	2	yes	—
489	C₄²	C₇×#41	1	2	yes	—
490	C₂×C₇	—	4	2	no	—
491	C₂×C₇	#2395	1	1	yes	characteristic
492	C₂×C₇	C₂×#485	1	1	yes	characteristic
493	C₂×C₇	#3091	1	1	yes	characteristic
494	C₂×C₇	#3102	1	1	yes	characteristic
495	C₂×C₇	#3108	1	1	yes	characteristic
496	C₂×C₇	#3168	1	1	yes	characteristic
497	C₂×C₇	#3172	1	1	yes	characteristic
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	C₇×#135	1	2	yes	—
505	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
506	Q₈	—	2	2	no	—
507	Q₈	—	2	2	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	C₇×#123	1	2	yes	—
552	C₂×C₄	C₇×#123	1	2	yes	—
553	C₂×C₄	C₇×#135	1	2	yes	—
554	C₂×C₄	C₇×#137	1	2	yes	—
555	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
556	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
557	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
558	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
559	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
560	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
561	C₈	—	2	2	no	—
562	C₈	—	2	2	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₇	#23759	1	1	yes	characteristic, direct product factor, Sylow
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	C₂×C₇×#123	1	1	yes	characteristic
574	C₂²	C₇×#525	1	1	yes	characteristic
575	C₂²	C₇×#532	1	1	yes	characteristic
576	C₂²	C₂×C₇×#135	1	1	yes	characteristic
577	C₂²	C₂×C₇×#135	1	1	yes	characteristic
578	C₂²	C₂×C₇×#137	1	1	yes	characteristic
579	C₂²	C₇×#575	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	2	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₄	C₇×#485	1	4	yes	—
593	C₄	C₇×#529	1	1	yes	characteristic
594	C₄	C₇×#529	1	1	yes	characteristic
595	C₄	C₇×#529	1	1	yes	characteristic
596	C₄	C₇×#529	1	1	yes	characteristic
597	C₂	—	4	2	no	—
598	C₂	C₇×#2395	1	1	yes	characteristic
599	C₂	C₂×C₇×#485	1	1	yes	characteristic
600	C₂	C₇×#3091	1	1	yes	characteristic
601	C₂	C₇×#3102	1	1	yes	characteristic
602	C₂	C₇×#3108	1	1	yes	characteristic
603	C₂	C₇×#3168	1	1	yes	characteristic
604	C₂	C₇×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂²×D₄
prime radical	C₂⁴×C₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#2101	C₂	semidirect
4. C₇×#2097	C₂	semidirect
5. C₇×#2085	C₂	semidirect
8. C₇×#2074	C₂	semidirect
11. C₄×C₇×#107	C₂	semidirect
12. C₄×C₇×#106	C₂	semidirect
13. C₄×C₇×#103	C₂	semidirect
14. C₄×C₇×#103	C₂	semidirect
59. #23759	C₇	direct (N × H)
123. #2101	C₂×C₇	semidirect
124. #2097	C₂×C₇	semidirect
125. #2085	C₂×C₇	semidirect
128. #2074	C₂×C₇	semidirect
131. C₄×#107	C₂×C₇	semidirect
132. C₄×#106	C₂×C₇	semidirect
133. C₄×#103	C₂×C₇	semidirect
134. C₄×#103	C₂×C₇	semidirect
565. C₇	#23759	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₇×C₂²⋊Q₈	2
C₇×#2283	2
C₇×#2101	2
C₇×#2097	2
C₇×#2085	2
C₇×#2077	2
C₇×#2075	2
C₇×#2074	2
C₇×#2036	2
C₇×#2035	2
C₄×C₇×#107	2
C₄×C₇×#106	2
C₄×C₇×#103	2
C₄×C₇×C₂²⋊C₈	2
#23759	7

Subgroups — C7×#23759 #13200975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23759 #13200975