Subgroups — #46780807

Order 33664.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30682340	C₂	1	1	yes	maximal, characteristic
2	#30681759	C₂	1	1	yes	maximal, characteristic
3	#364×C₂₆₃	C₂	1	1	yes	maximal, characteristic
4	#22554462	C₄	1	2	yes	—
5	#22554410	—	2	1	no	—
6	#22554404	—	2	1	no	—
7	#22554402	—	2	1	no	—
8	M₃₂×C₂₆₃	—	2	1	no	—
9	C₄×C₈×C₂₆₃	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₂₆₃	—	2	2	no	—
11	Dic₂₆₃⋊C₄	—	4	2	no	—
12	C₂₆₃⋊C₁₆	—	4	1	no	—
13	C₂×C₈×C₂₆₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₆₃	D₄	1	1	yes	characteristic
15	C₄²×C₂₆₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₆₃	—	4	1	no	—
17	C₂×Dic₂₆₃	—	4	2	no	—
18	C₂×C₄×C₂₆₃	—	2	1	no	—
19	C₂×C₄×C₂₆₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₂₆₃	SD₁₆	1	1	yes	characteristic
21	C₈×C₂₆₃	SD₁₆	1	1	yes	characteristic
22	C₈×C₂₆₃	Q₁₆	1	1	yes	characteristic
23	C₈×C₂₆₃	Q₁₆	1	1	yes	characteristic
24	C₂²×C₂₆₃	#100	1	1	yes	characteristic
25	C₄×C₂₆₃	—	4	1	no	—
26	C₄×C₂₆₃	#103	1	1	yes	characteristic
27	C₄×C₂₆₃	#103	1	1	yes	characteristic
28	Dic₂₆₃	—	8	2	no	—
29	C₂×C₂₆₃	—	2	1	no	—
30	C₂×C₂₆₃	#333	1	1	yes	characteristic
31	C₂₆₃	#1366	1	1	yes	characteristic, complemented, Sylow
32	#1366	—	263	1	no	maximal, Sylow
33	#499	—	263	1	no	—
34	#364	—	263	1	no	—
35	#364	D₂₆₃	1	1	yes	characteristic
36	#125	—	263	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	526	1	no	—
39	#107	—	526	1	no	—
40	#106	—	526	1	no	—
41	C₄×C₈	C₂×D₂₆₃	1	1	yes	characteristic
42	C₂×C₈	C₂²⋊D₂₆₃	1	1	yes	characteristic
43	C₂×C₈	D₁₀₅₂	1	1	yes	characteristic
44	C₄⋊C₄	—	526	2	no	—
45	C₄⋊C₄	—	1052	2	no	—
46	C₄²	C₄×D₂₆₃	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	1052	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	1052	2	no	—
51	C₂×C₄	(C₂×D₂₆₃)⋊C₄	1	1	yes	characteristic
52	C₈	#16862364	1	1	yes	characteristic
53	C₈	#16862365	1	1	yes	characteristic
54	C₈	#16862366	1	1	yes	characteristic
55	C₈	Dic₁₀₅₂	1	1	yes	characteristic
56	C₂²	#22554386	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	2104	2	no	—
59	C₄	#22554393	1	1	yes	characteristic
60	C₄	#22554395	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#30681686	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#30681686
commutator	C₄²×C₂₆₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₆₃
Fitting	#364×C₂₆₃	C₂
socle	C₂×C₂₆₃	#333
prime radical	C₂²×C₂₆₃	#100
cosocle	C₄×C₈×C₂₆₃	C₂²
hypercenter	#364	D₂₆₃
hypocenter	C₂₆₃	#1366
LCS	G ▷ C₄²×C₂₆₃ ▷ C₂×C₄×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
31. C₂₆₃	#1366	semidirect

Maximal subgroups

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

subgroup	index
#30682340	2
#30681759	2
#364×C₂₆₃	2
#1366	263