Subgroups — #23782098

Order 10432.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19104758	C₂	1	2	yes	maximal, complemented
2	#19104678	C₂	1	2	yes	maximal, complemented
3	D₂₆₀₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₃₂×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14579700	—	2	2	no	—
7	#14579686	—	2	2	no	—
8	D₁₃₀₄	C₂²	1	2	yes	—
9	C₈×D₁₆₃	C₂²	1	1	yes	characteristic
10	C₁₆₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	Q₁₆×C₁₆₃	C₂²	1	2	yes	—
12	C₁₆×C₁₆₃	C₂²	1	1	yes	characteristic
13	D₆₅₂	—	2	2	no	—
14	D₆₅₂	—	4	2	no	—
15	C₄×D₁₆₃	—	4	2	no	—
16	C₄×D₁₆₃	D₄	1	1	yes	characteristic
17	C₁₆₃⋊C₈	D₄	1	1	yes	characteristic
18	Q₈×C₁₆₃	—	2	2	no	—
19	C₈×C₁₆₃	C₂³	1	1	yes	characteristic
20	C₂×D₁₆₃	—	4	2	no	—
21	C₂×D₁₆₃	D₈	1	1	yes	characteristic
22	C₄×C₁₆₃	—	4	2	no	—
23	C₄×C₁₆₃	C₂×D₄	1	1	yes	characteristic
24	Dic₁₆₃	D₈	1	1	yes	characteristic
25	C₂×C₁₆₃	C₂×D₈	1	1	yes	characteristic
26	D₁₆₃	—	2	1	no	—
27	D₁₆₃	—	8	2	no	—
28	C₁₆₃	#508	1	1	yes	characteristic, complemented, Sylow
29	#508	—	163	1	no	maximal, Sylow
30	#135	—	163	2	no	—
31	Q₃₂	D₁₆₃	1	1	yes	characteristic, complemented
32	SD₃₂	—	163	2	no	—
33	D₁₆	—	163	1	no	—
34	C₂×C₁₆	—	163	1	no	—
35	#41	—	326	2	no	—
36	Q₁₆	C₂×D₁₆₃	1	2	yes	—
37	SD₁₆	—	326	2	no	—
38	D₈	—	163	2	no	—
39	C₂×C₈	—	163	1	no	—
40	C₁₆	—	163	1	no	—
41	C₁₆	C₂×D₁₆₃	1	1	yes	characteristic
42	Q₈	—	2	2	no	—
43	D₄	—	326	2	no	—
44	D₄	—	652	2	no	—
45	C₂×C₄	—	652	2	no	—
46	C₂×C₄	—	163	1	no	—
47	C₈	—	163	1	no	—
48	C₈	C₂²×D₁₆₃	1	1	yes	characteristic
49	C₂²	—	652	2	no	—
50	C₂²	—	163	1	no	—
51	C₄	—	4	2	no	—
52	C₄	—	163	1	no	—
53	C₄	D₄×D₁₆₃	1	1	yes	characteristic
54	C₂	—	1304	2	no	—
55	C₂	—	326	1	no	—
56	C₂	D₈×D₁₆₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₆₃
commutator, cosocle	C₈×C₁₆₃	C₂³
Frattini	C₈	C₂²×D₁₆₃
Fitting	Q₃₂×C₁₆₃	C₂
socle	C₂×C₁₆₃	C₂×D₈
hypercenter	Q₃₂	D₁₆₃
hypocenter	C₁₆₃	#508
LCS	G ▷ C₈×C₁₆₃ ▷ C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #19104758	C₂	semidirect
2. #19104678	C₂	semidirect
3. D₂₆₀₈	C₂	semidirect
4. C₁₆×D₁₆₃	C₂	semidirect
5. Q₃₂×C₁₆₃	C₂	semidirect
28. C₁₆₃	#508	semidirect
31. Q₃₂	D₁₆₃	semidirect