Subgroups — #23782075

Order 10432.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19104735	C₂	1	1	yes	maximal, characteristic
2	#19104668	C₂	1	2	yes	maximal
3	#19104666	C₂	1	2	yes	maximal
4	#19104646	C₂	1	1	yes	maximal, characteristic
5	#125×C₁₆₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₂₆	—	2	1	no	—
7	C₂×C₁₆₃⋊C₈	C₂²	1	2	yes	—
8	C₄⋊Dic₁₆₃	—	2	1	no	—
9	C₄⋊Dic₁₆₃	C₂²	1	2	yes	—
10	C₄⋊C₄×C₁₆₃	—	2	1	no	—
11	C₄⋊C₄×C₁₆₃	—	2	1	no	—
12	C₄⋊C₄×C₁₆₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₆₃	C₂²	1	1	yes	characteristic
14	C₄²×C₁₆₃	C₂²	1	1	yes	characteristic
15	Dic₃₂₆	—	4	2	no	—
16	C₂×Dic₁₆₃	—	2	2	no	—
17	C₁₆₃⋊C₈	Q₈	1	4	yes	complemented
18	C₂×C₄×C₁₆₃	—	2	1	no	—
19	C₂×C₄×C₁₆₃	—	2	1	no	—
20	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
23	C₂²×C₁₆₃	C₂×D₄	1	1	yes	characteristic
24	C₄×C₁₆₃	—	2	1	no	—
25	C₄×C₁₆₃	—	2	1	no	—
26	C₄×C₁₆₃	—	4	1	no	—
27	C₄×C₁₆₃	—	4	1	no	—
28	C₄×C₁₆₃	C₂×Q₈	1	2	yes	—
29	Dic₁₆₃	—	4	2	no	—
30	C₂×C₁₆₃	C₄⋊Q₈	1	1	yes	characteristic
31	C₂×C₁₆₃	AGL(1,ℤ/8)	1	1	yes	characteristic
32	C₂×C₁₆₃	#137	1	1	yes	characteristic
33	C₁₆₃	#501	1	1	yes	characteristic, complemented, Sylow
34	#501	—	163	1	no	maximal, Sylow
35	C₄⋊Q₈	—	163	1	no	—
36	#125	D₁₆₃	1	1	yes	characteristic
37	#107	—	163	2	no	—
38	#106	—	163	2	no	—
39	#97	—	163	1	no	—
40	C₂×Q₈	—	326	1	no	—
41	C₂×C₈	—	163	2	no	—
42	C₄⋊C₄	—	2	1	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	326	1	no	—
45	C₄⋊C₄	—	163	2	no	—
46	C₄⋊C₄	C₂×D₁₆₃	1	1	yes	characteristic
47	C₄⋊C₄	C₂×D₁₆₃	1	1	yes	characteristic
48	C₄²	C₂×D₁₆₃	1	1	yes	characteristic
49	Q₈	—	652	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	326	2	no	—
53	C₂×C₄	C₂²⋊D₁₆₃	1	1	yes	characteristic
54	C₂×C₄	C₂²⋊D₁₆₃	1	1	yes	characteristic
55	C₂×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
56	C₈	—	163	4	no	—
57	C₂²	C₂×C₂²⋊D₁₆₃	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	4	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	652	2	no	—
63	C₄	Q₈×D₁₆₃	1	2	yes	—
64	C₂	#19104733	1	1	yes	characteristic
65	C₂	#19104760	1	1	yes	characteristic
66	C₂	#19104765	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₆₃
commutator, cosocle	C₂×C₄×C₁₆₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₆₃
Fitting	#125×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	C₂×D₄
hypercenter	#125	D₁₆₃
hypocenter	C₁₆₃	#501
LCS	G ▷ C₂×C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
17. C₁₆₃⋊C₈	Q₈	semidirect
33. C₁₆₃	#501	semidirect