Subgroups — #23781492

Order 10432.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#19104669	C₂	1	1	yes	maximal, characteristic
3	#107×C₁₆₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₆₃	—	2	1	no	—
5	C₁₆₃⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₆₃	—	2	1	no	—
8	C₂×Dic₁₆₃	—	4	1	no	—
9	C₂×C₄×C₁₆₃	—	4	1	no	—
10	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
11	C₈×C₁₆₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₆₃	Q₈	1	1	yes	characteristic
13	C₂²×C₁₆₃	D₈	1	1	yes	characteristic
14	C₄×C₁₆₃	—	8	1	no	—
15	C₄×C₁₆₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₆₃	Q₁₆	1	1	yes	characteristic
17	Dic₁₆₃	—	8	1	no	—
18	C₂×C₁₆₃	#107	1	1	yes	characteristic
19	C₂×C₁₆₃	SD₃₂	1	1	yes	characteristic
20	C₂×C₁₆₃	SD₃₂	1	1	yes	characteristic
21	C₁₆₃	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	163	1	no	maximal, Sylow
23	C₂×C₁₆	—	163	1	no	—
24	#107	—	163	1	no	—
25	#107	D₁₆₃	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	326	1	no	—
29	C₁₆	—	163	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	652	1	no	—
32	C₂×C₄	C₂²⋊D₁₆₃	1	1	yes	characteristic
33	C₈	C₄×D₁₆₃	1	1	yes	characteristic
34	C₈	Dic₃₂₆	1	1	yes	characteristic
35	C₂²	#14579684	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	1304	1	no	—
38	C₄	Dic₁₆₃⋊C₄	1	1	yes	characteristic
39	C₄	#14579689	1	1	yes	characteristic
40	C₂	#19104668	1	1	yes	characteristic
41	C₂	#19104678	1	1	yes	characteristic
42	C₂	#19104679	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14579684
commutator	C₈×C₁₆₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₆₃
Fitting	#107×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	D₈
cosocle	C₂×C₈×C₁₆₃	C₂²
hypercenter	#107	D₁₆₃
hypocenter	C₁₆₃	#367
LCS	G ▷ C₈×C₁₆₃ ▷ C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. C₁₆₃⋊C₁₆	C₄	semidirect
21. C₁₆₃	#367	semidirect