Subgroups — #46780947

Order 33664.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30681764	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₂₆₃	C₂	1	1	yes	maximal, characteristic
3	#22554404	—	2	2	no	—
4	C₂×C₁₆×C₂₆₃	C₂²	1	1	yes	characteristic
5	C₃₂×C₂₆₃	C₄	1	2	yes	complemented
6	C₄⋊Dic₂₆₃	—	4	2	no	—
7	C₂×C₈×C₂₆₃	D₄	1	1	yes	characteristic
8	C₁₆×C₂₆₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₆₃	Q₈	1	1	yes	characteristic
10	C₂×Dic₂₆₃	—	8	2	no	—
11	C₂×C₄×C₂₆₃	D₈	1	1	yes	characteristic
12	C₈×C₂₆₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₆₃	Q₁₆	1	1	yes	characteristic
14	C₂²×C₂₆₃	D₁₆	1	1	yes	characteristic
15	C₄×C₂₆₃	#107	1	1	yes	characteristic
16	C₄×C₂₆₃	Q₃₂	1	1	yes	characteristic
17	Dic₂₆₃	—	16	2	no	—
18	C₂×C₂₆₃	#366	1	1	yes	characteristic
19	C₂×C₂₆₃	D₃₂	1	1	yes	characteristic
20	C₂×C₂₆₃	Q₆₄	1	1	yes	characteristic
21	C₂₆₃	#1423	1	1	yes	characteristic, complemented, Sylow
22	#1423	—	263	1	no	maximal, Sylow
23	C₂×C₃₂	D₂₆₃	1	1	yes	characteristic
24	#366	—	263	2	no	—
25	C₂×C₁₆	C₂×D₂₆₃	1	1	yes	characteristic
26	#107	—	526	2	no	—
27	C₃₂	Dic₂₆₃	1	2	yes	complemented
28	C₂×C₈	D₁₀₅₂	1	1	yes	characteristic
29	C₄⋊C₄	—	1052	2	no	—
30	C₁₆	C₂×Dic₂₆₃	1	1	yes	characteristic
31	C₁₆	Dic₅₂₆	1	1	yes	characteristic
32	C₂×C₄	—	2104	2	no	—
33	C₂×C₄	D₂₁₀₄	1	1	yes	characteristic
34	C₈	C₄⋊Dic₂₆₃	1	1	yes	characteristic
35	C₈	Dic₁₀₅₂	1	1	yes	characteristic
36	C₂²	D₄₂₀₈	1	1	yes	characteristic
37	C₄	—	4208	2	no	—
38	C₄	#22554404	1	1	yes	characteristic
39	C₄	Dic₂₁₀₄	1	1	yes	characteristic
40	C₂	#30681764	1	1	yes	characteristic
41	C₂	D₈₄₁₆	1	1	yes	characteristic
42	C₂	Dic₄₂₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₂₀₈
commutator	C₁₆×C₂₆₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₆₃
Fitting	C₂×C₃₂×C₂₆₃	C₂
socle, prime radical	C₂²×C₂₆₃	D₁₆
cosocle	C₂×C₁₆×C₂₆₃	C₂²
hypercenter	C₂×C₃₂	D₂₆₃
hypocenter	C₂₆₃	#1423
LCS	G ▷ C₁₆×C₂₆₃ ▷ C₈×C₂₆₃ ▷ C₄×C₂₆₃ ▷ C₂×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₂₆₃	C₄	semidirect
21. C₂₆₃	#1423	semidirect
27. C₃₂	Dic₂₆₃	semidirect

Maximal subgroups

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

subgroup	index
#30681764	2
C₂×C₃₂×C₂₆₃	2
#1423	263