Subgroups — #23782062

Order 10432.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19104734	C₂	1	2	yes	maximal
2	#19104667	C₂	1	1	yes	maximal, characteristic
3	#19104666	C₂	1	2	yes	maximal
4	C₈×Dic₁₆₃	C₂	1	1	yes	maximal, characteristic
5	#106×C₁₆₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₂₆	—	2	2	no	—
7	C₂×C₁₆₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₁₆₃	C₂²	1	2	yes	—
9	Dic₁₆₃⋊C₄	—	2	2	no	—
10	C₄×Dic₁₆₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₆₃	C₂²	1	2	yes	—
13	Dic₃₂₆	—	4	4	no	—
14	C₂×Dic₁₆₃	—	2	2	no	—
15	C₂×Dic₁₆₃	D₄	1	2	yes	—
16	C₁₆₃⋊C₈	Q₈	1	2	yes	complemented
17	C₂×C₄×C₁₆₃	—	2	2	no	—
18	C₂×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
19	C₈×C₁₆₃	Q₈	1	2	yes	complemented
20	C₂²×C₁₆₃	C₂×D₄	1	1	yes	characteristic
21	C₄×C₁₆₃	—	4	2	no	—
22	C₄×C₁₆₃	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₁₆₃	C₂×Q₈	1	1	yes	characteristic
24	Dic₁₆₃	—	4	2	no	—
25	Dic₁₆₃	SD₁₆	1	4	yes	—
26	C₂×C₁₆₃	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₁₆₃	C₂×SD₁₆	1	2	yes	—
28	C₁₆₃	#498	1	1	yes	characteristic, complemented, Sylow
29	#498	—	163	1	no	maximal, Sylow
30	C₄⋊Q₈	—	163	2	no	—
31	#106	—	163	1	no	—
32	#106	—	163	2	no	—
33	#106	D₁₆₃	1	1	yes	characteristic
34	C₄×C₈	—	163	1	no	—
35	C₂×Q₈	—	326	2	no	—
36	C₂×C₈	—	163	1	no	—
37	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
38	C₄⋊C₄	—	326	2	no	—
39	C₄⋊C₄	—	163	2	no	—
40	C₄⋊C₄	C₂×D₁₆₃	1	2	yes	—
41	C₄²	—	163	1	no	—
42	Q₈	—	652	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	326	2	no	—
45	C₂×C₄	—	163	2	no	—
46	C₂×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
47	C₈	—	163	2	no	—
48	C₈	Dic₃₂₆	1	2	yes	complemented
49	C₂²	D₄×D₁₆₃	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	652	2	no	—
52	C₄	—	163	4	no	—
53	C₄	Q₈×D₁₆₃	1	1	yes	characteristic
54	C₄	C₂×Dic₃₂₆	1	1	yes	characteristic
55	C₂	#19104734	1	1	yes	characteristic
56	C₂	SD₁₆×D₁₆₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₆₃
commutator, cosocle	C₂×C₄×C₁₆₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₆₃
Fitting	#106×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	C₂×D₄
hypercenter	#106	D₁₆₃
hypocenter	C₁₆₃	#498
LCS	G ▷ C₂×C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
16. C₁₆₃⋊C₈	Q₈	semidirect
19. C₈×C₁₆₃	Q₈	semidirect
28. C₁₆₃	#498	semidirect
48. C₈	Dic₃₂₆	semidirect