Subgroups — #46780943

Order 33664.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₆₃⋊C₃₂	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₂₆₃	C₂	1	1	yes	maximal, characteristic
3	C₂₆₃⋊C₃₂	—	2	2	no	—
4	C₂×C₁₆×C₂₆₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₂₆₃	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₂₆₃	C₄	1	1	yes	characteristic
7	C₂×C₈×C₂₆₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₂₆₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₂₆₃	C₈	1	1	yes	characteristic
10	C₁₆×C₂₆₃	—	2	1	no	—
11	C₁₆×C₂₆₃	D₄	1	1	yes	characteristic
12	C₁₆×C₂₆₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₆₃	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₂₆₃	C₁₆	1	1	yes	characteristic
15	C₂×C₄×C₂₆₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₂₆₃	—	2	1	no	—
17	C₈×C₂₆₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₂₆₃	M₁₆	1	1	yes	characteristic
19	C₂²×C₂₆₃	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₂₆₃	—	2	1	no	—
21	C₄×C₂₆₃	C₃₂	1	2	yes	complemented
22	C₄×C₂₆₃	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₂₆₃	M₃₂	1	1	yes	characteristic
24	C₂×C₂₆₃	C₄⋊C₁₆	1	1	yes	characteristic
25	C₂×C₂₆₃	C₂×C₃₂	1	1	yes	characteristic
26	C₂×C₂₆₃	M₆₄	1	1	yes	characteristic
27	C₂₆₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₄⋊C₃₂	—	263	1	no	maximal, Sylow
29	C₂×C₃₂	—	263	2	no	—
30	C₄×C₁₆	D₂₆₃	1	1	yes	characteristic
31	C₂×C₁₆	Dic₂₆₃	1	1	yes	characteristic
32	C₂×C₁₆	C₂×D₂₆₃	1	1	yes	characteristic
33	C₄×C₈	Dic₂₆₃	1	1	yes	characteristic
34	C₃₂	—	526	2	no	—
35	C₂×C₈	C₂₆₃⋊C₈	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₂₆₃	1	1	yes	characteristic
37	C₄²	C₂₆₃⋊C₈	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	D₁₀₅₂	1	1	yes	characteristic
40	C₁₆	Dic₅₂₆	1	1	yes	characteristic
41	C₂×C₄	C₂₆₃⋊C₁₆	1	1	yes	characteristic
42	C₂×C₄	C₂₆₃⋊C₁₆	1	1	yes	characteristic
43	C₂×C₄	C₂×C₂₆₃⋊C₈	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	C₄⋊Dic₂₆₃	1	1	yes	characteristic
46	C₈	#16862360	1	1	yes	characteristic
47	C₂²	C₂×C₂₆₃⋊C₁₆	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	C₂₆₃⋊C₃₂	1	2	yes	complemented
50	C₄	C₄⋊(C₂₆₃⋊C₈)	1	1	yes	characteristic
51	C₄	#22554410	1	1	yes	characteristic
52	C₂	C₄⋊(C₂₆₃⋊C₁₆)	1	1	yes	characteristic
53	C₂	C₂×C₂₆₃⋊C₃₂	1	1	yes	characteristic
54	C₂	#30681772	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₂₆₃
commutator	C₂×C₂₆₃	C₂×C₃₂
Fitting	C₄×C₁₆×C₂₆₃	C₂
socle, prime radical	C₂²×C₂₆₃	C₂×C₁₆
cosocle	C₂×C₁₆×C₂₆₃	C₂²
hypercenter	C₄×C₁₆	D₂₆₃
hypocenter	C₂₆₃	C₄⋊C₃₂
LCS	G ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
21. C₄×C₂₆₃	C₃₂	semidirect
27. C₂₆₃	C₄⋊C₃₂	semidirect
49. C₄	C₂₆₃⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₆₃⋊C₃₂	2
C₄×C₁₆×C₂₆₃	2
C₄⋊C₃₂	263