Subgroups — #23782070

Order 10432.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19104735	C₂	1	2	yes	maximal
2	#19104669	C₂	1	4	yes	maximal
3	C₄×C₈×C₁₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₂₆	—	2	2	no	—
5	C₄⋊Dic₁₆₃	—	2	2	no	—
6	C₄⋊Dic₁₆₃	C₂²	1	4	yes	—
7	C₂×C₈×C₁₆₃	C₂²	1	2	yes	—
8	C₄²×C₁₆₃	C₂²	1	1	yes	characteristic
9	Dic₃₂₆	—	4	4	no	—
10	C₂×Dic₁₆₃	—	2	4	no	—
11	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
12	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
13	C₂×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
14	C₈×C₁₆₃	Q₈	1	4	yes	complemented
15	C₂²×C₁₆₃	C₂×D₄	1	1	yes	characteristic
16	C₄×C₁₆₃	D₈	1	2	yes	—
17	C₄×C₁₆₃	Q₁₆	1	2	yes	—
18	C₄×C₁₆₃	C₂×Q₈	1	2	yes	—
19	Dic₁₆₃	—	4	4	no	—
20	C₂×C₁₆₃	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₁₆₃	C₂×D₈	1	1	yes	characteristic
22	C₂×C₁₆₃	C₂×Q₁₆	1	1	yes	characteristic
23	C₁₆₃	#500	1	1	yes	characteristic, complemented, Sylow
24	#500	—	163	1	no	maximal, Sylow
25	C₄⋊Q₈	—	163	2	no	—
26	#107	—	163	4	no	—
27	C₄×C₈	D₁₆₃	1	1	yes	characteristic
28	C₂×Q₈	—	326	2	no	—
29	C₂×C₈	C₂×D₁₆₃	1	2	yes	—
30	C₄⋊C₄	—	326	2	no	—
31	C₄⋊C₄	—	163	4	no	—
32	C₄²	C₂×D₁₆₃	1	1	yes	characteristic
33	Q₈	—	652	4	no	—
34	C₂×C₄	—	326	4	no	—
35	C₂×C₄	D₆₅₂	1	1	yes	characteristic
36	C₂×C₄	D₆₅₂	1	1	yes	characteristic
37	C₂×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
38	C₈	Dic₃₂₆	1	4	yes	complemented
39	C₂²	C₂×D₆₅₂	1	1	yes	characteristic
40	C₄	—	652	4	no	—
41	C₄	D₁₃₀₄	1	2	yes	—
42	C₄	Dic₆₅₂	1	2	yes	—
43	C₄	C₂×Dic₃₂₆	1	2	yes	—
44	C₂	#19104735	1	1	yes	characteristic
45	C₂	C₂×D₁₃₀₄	1	1	yes	characteristic
46	C₂	C₂×Dic₆₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₆₅₂
commutator, cosocle	C₂×C₄×C₁₆₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₆₃
Fitting	C₄×C₈×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	C₂×D₄
hypercenter	C₄×C₈	D₁₆₃
hypocenter	C₁₆₃	#500
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
14. C₈×C₁₆₃	Q₈	semidirect
23. C₁₆₃	#500	semidirect
38. C₈	Dic₃₂₆	semidirect