Subgroups — #46782356

Order 33664.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30682343	C₂	1	1	yes	maximal, characteristic
2	#30682290	C₂	1	2	yes	maximal
3	#30682288	C₂	1	2	yes	maximal
4	C₈×C₂₆₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#500×C₂₆₃	C₂	1	1	yes	maximal, characteristic
6	#22554470	C₂²	1	2	yes	—
7	#22554404	—	2	2	no	—
8	#22554394	—	2	4	no	—
9	#22554393	—	2	4	no	—
10	C₄×C₂₆₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₄×C₂₆₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Q₈×C₂₆₃	C₂²	1	2	yes	—
13	#107×C₂₆₃	—	2	2	no	—
14	C₄×C₈×C₂₆₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₂₆	—	2	2	no	—
16	C₂×C₂₆₃⋊C₈	D₄	1	2	yes	—
17	C₂×C₂₆₃⋊C₈	D₄	1	2	yes	—
18	C₄⋊Dic₂₆₃	—	2	2	no	—
19	C₄⋊Dic₂₆₃	—	2	2	no	—
20	C₂×Q₈×C₂₆₃	—	2	2	no	—
21	C₂×C₈×C₂₆₃	D₄	1	2	yes	—
22	C₄⋊C₄×C₂₆₃	—	2	2	no	—
23	C₄⋊C₄×C₂₆₃	—	2	2	no	—
24	C₄²×C₂₆₃	C₂³	1	1	yes	characteristic
25	Dic₅₂₆	—	4	4	no	—
26	C₂×Dic₂₆₃	—	4	2	no	—
27	C₂₆₃⋊C₈	—	2	2	no	—
28	C₂₆₃⋊C₈	—	2	2	no	—
29	Q₈×C₂₆₃	—	4	4	no	—
30	C₂×C₄×C₂₆₃	—	4	2	no	—
31	C₂×C₄×C₂₆₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₂₆₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₆₃	C₂×D₄	1	1	yes	characteristic
34	C₈×C₂₆₃	Q₁₆	1	4	yes	—
35	C₂²×C₂₆₃	#127	1	1	yes	characteristic
36	C₄×C₂₆₃	—	8	2	no	—
37	C₄×C₂₆₃	C₂×Q₁₆	1	2	yes	—
38	C₄×C₂₆₃	#135	1	2	yes	—
39	C₄×C₂₆₃	#135	1	2	yes	—
40	Dic₂₆₃	—	8	2	no	—
41	C₂×C₂₆₃	#494	1	1	yes	characteristic
42	C₂×C₂₆₃	#495	1	1	yes	characteristic
43	C₂×C₂₆₃	#495	1	1	yes	characteristic
44	C₂₆₃	#1710	1	1	yes	characteristic, complemented, Sylow
45	#1710	—	263	1	no	maximal, Sylow
46	#500	—	263	1	no	—
47	#500	D₂₆₃	1	1	yes	characteristic
48	#487	—	263	2	no	—
49	#487	—	263	2	no	—
50	C₈²	—	263	1	no	—
51	C₄⋊Q₈	—	263	2	no	—
52	C₄⋊Q₈	C₂×D₂₆₃	1	2	yes	—
53	#107	—	2	2	no	—
54	#107	—	526	2	no	—
55	#103	—	526	4	no	—
56	#103	—	526	4	no	—
57	C₄×C₈	—	263	1	no	—
58	C₄×C₈	—	263	1	no	—
59	C₄×C₈	C₂×D₂₆₃	1	1	yes	characteristic
60	C₂×Q₈	—	2	2	no	—
61	C₂×Q₈	—	526	2	no	—
62	C₂×C₈	—	263	2	no	—
63	C₂×C₈	—	263	2	no	—
64	C₂×C₈	C₂²⋊D₂₆₃	1	2	yes	—
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	526	2	no	—
68	C₄⋊C₄	—	526	2	no	—
69	C₄²	C₂²×D₂₆₃	1	1	yes	characteristic
70	Q₈	—	4	4	no	—
71	Q₈	—	1052	4	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	—	1052	2	no	—
74	C₂×C₄	D₄×D₂₆₃	1	1	yes	characteristic
75	C₂×C₄	D₄×D₂₆₃	1	1	yes	characteristic
76	C₂×C₄	C₂×C₂²⋊D₂₆₃	1	1	yes	characteristic
77	C₈	—	526	2	no	—
78	C₈	—	526	2	no	—
79	C₈	#16862366	1	4	yes	—
80	C₂²	#22554466	1	1	yes	characteristic
81	C₄	—	8	2	no	—
82	C₄	—	2104	2	no	—
83	C₄	C₂×#16862366	1	2	yes	—
84	C₄	#22554489	1	2	yes	—
85	C₄	#22554493	1	2	yes	—
86	C₂	#30682317	1	1	yes	characteristic
87	C₂	#30682321	1	1	yes	characteristic
88	C₂	#30682323	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22554466
commutator, cosocle	C₄²×C₂₆₃	C₂³
Frattini	C₄²	C₂²×D₂₆₃
Fitting	#500×C₂₆₃	C₂
socle, prime radical	C₂²×C₂₆₃	#127
hypercenter	#500	D₂₆₃
hypocenter	C₂₆₃	#1710
LCS	G ▷ C₄²×C₂₆₃ ▷ C₂²×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

Complements

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

N	H ≅ G/N	type
44. C₂₆₃	#1710	semidirect

Maximal subgroups

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

subgroup	index
#30682343	2
#30682290	2
#30682288	2
C₈×C₂₆₃⋊C₈	2
#500×C₂₆₃	2
#1710	263