Subgroups — #23782042

Order 10432.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃₀₄	C₂	1	4	yes	maximal, complemented
2	#19104732	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₅₂	—	2	4	no	—
5	C₂×D₆₅₂	C₂²	1	4	yes	—
6	D₁₃₀₄	—	2	8	no	—
7	C₂×C₈×C₁₆₃	C₂²	1	2	yes	—
8	C₄²×C₁₆₃	C₂²	1	1	yes	characteristic
9	C₂²×D₁₆₃	—	2	4	no	—
10	D₆₅₂	—	2	8	no	—
11	D₆₅₂	—	4	8	no	—
12	C₂×C₄×C₁₆₃	D₄	1	2	yes	—
13	C₂×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
14	C₈×C₁₆₃	D₄	1	4	yes	complemented
15	C₂²×C₁₆₃	C₂×D₄	1	1	yes	characteristic
16	C₂×D₁₆₃	—	4	4	no	—
17	C₂×D₁₆₃	—	4	8	no	—
18	C₄×C₁₆₃	D₈	1	4	yes	complemented
19	C₄×C₁₆₃	C₂×D₄	1	2	yes	—
20	C₂×C₁₆₃	#127	1	1	yes	characteristic
21	C₂×C₁₆₃	C₂×D₈	1	2	yes	—
22	D₁₆₃	—	8	4	no	—
23	C₁₆₃	#493	1	1	yes	characteristic, complemented, Sylow
24	#493	—	163	1	no	maximal, Sylow
25	C₂×D₈	—	163	4	no	—
26	#127	—	163	2	no	—
27	C₄×C₈	D₁₆₃	1	1	yes	characteristic, complemented
28	C₂×D₄	—	326	4	no	—
29	C₂×D₄	—	163	4	no	—
30	D₈	—	326	8	no	—
31	C₂×C₈	C₂×D₁₆₃	1	2	yes	—
32	C₄²	C₂×D₁₆₃	1	1	yes	characteristic
33	C₂³	—	326	4	no	—
34	D₄	—	326	8	no	—
35	D₄	—	652	8	no	—
36	C₂×C₄	D₆₅₂	1	2	yes	—
37	C₂×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
38	C₈	D₆₅₂	1	4	yes	complemented
39	C₂²	—	652	4	no	—
40	C₂²	—	652	8	no	—
41	C₂²	C₂×D₆₅₂	1	1	yes	characteristic
42	C₄	D₁₃₀₄	1	4	yes	complemented
43	C₄	C₂×D₆₅₂	1	2	yes	—
44	C₂	—	1304	4	no	—
45	C₂	#19104732	1	1	yes	characteristic
46	C₂	C₂×D₁₃₀₄	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₆₅₂
commutator, cosocle	C₂×C₄×C₁₆₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₆₃
Fitting	C₄×C₈×C₁₆₃	C₂
socle	C₂²×C₁₆₃	C₂×D₄
hypercenter	C₄×C₈	D₁₆₃
hypocenter	C₁₆₃	#493
LCS	G ▷ C₂×C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₃₀₄	C₂	semidirect
2. #19104732	C₂	semidirect
3. C₄×C₈×C₁₆₃	C₂	semidirect
14. C₈×C₁₆₃	D₄	semidirect
18. C₄×C₁₆₃	D₈	semidirect
23. C₁₆₃	#493	semidirect
27. C₄×C₈	D₁₆₃	semidirect
38. C₈	D₆₅₂	semidirect
42. C₄	D₁₃₀₄	semidirect