Subgroups — #23781410

Order 10432.

64 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	C₄⋊(C₁₆₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₁₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₂₆	—	2	1	no	—
5	C₂×C₁₆₃⋊C₈	—	2	1	no	—
6	C₄⋊Dic₁₆₃	—	2	1	no	—
7	C₄⋊Dic₁₆₃	C₄	1	2	yes	—
8	C₂×C₈×C₁₆₃	—	2	1	no	—
9	C₄²×C₁₆₃	C₂²	1	1	yes	characteristic
10	Dic₃₂₆	—	4	1	no	—
11	Dic₃₂₆	—	4	1	no	—
12	C₂×Dic₁₆₃	—	2	2	no	—
13	C₁₆₃⋊C₈	—	4	1	no	—
14	C₂×C₄×C₁₆₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
17	C₈×C₁₆₃	—	4	1	no	—
18	C₂²×C₁₆₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₆₃	—	2	1	no	—
20	C₄×C₁₆₃	D₈	1	1	yes	characteristic
21	C₄×C₁₆₃	SD₁₆	1	1	yes	characteristic
22	C₄×C₁₆₃	SD₁₆	1	1	yes	characteristic
23	C₄×C₁₆₃	Q₁₆	1	1	yes	characteristic
24	Dic₁₆₃	—	4	2	no	—
25	C₂×C₁₆₃	#101	1	1	yes	characteristic
26	C₂×C₁₆₃	#102	1	1	yes	characteristic
27	C₂×C₁₆₃	#103	1	1	yes	characteristic
28	C₁₆₃	#332	1	1	yes	characteristic, complemented, Sylow
29	#332	—	163	1	no	maximal, Sylow
30	C₄⋊Q₈	—	163	1	no	—
31	C₄⋊C₈	—	163	1	no	—
32	C₄⋊C₈	D₁₆₃	1	1	yes	characteristic
33	C₂×Q₈	—	326	1	no	—
34	C₂×C₈	—	2	1	no	—
35	C₂×C₈	—	326	1	no	—
36	C₄⋊C₄	—	326	1	no	—
37	C₄⋊C₄	—	163	2	no	—
38	C₄²	C₂×D₁₆₃	1	1	yes	characteristic
39	Q₈	—	652	1	no	—
40	Q₈	—	652	1	no	—
41	C₂×C₄	—	326	2	no	—
42	C₂×C₄	C₄×D₁₆₃	1	1	yes	characteristic
43	C₂×C₄	C₂²⋊D₁₆₃	1	1	yes	characteristic
44	C₂×C₄	D₆₅₂	1	1	yes	characteristic
45	C₈	—	4	1	no	—
46	C₈	—	652	1	no	—
47	C₂²	(C₂×D₁₆₃)⋊C₄	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	—	652	2	no	—
50	C₄	D₁₃₀₄	1	1	yes	characteristic
51	C₄	#14579687	1	1	yes	characteristic
52	C₄	#14579688	1	1	yes	characteristic
53	C₄	#14579689	1	1	yes	characteristic
54	C₂	#19104653	1	1	yes	characteristic
55	C₂	#19104657	1	1	yes	characteristic
56	C₂	#19104658	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₁₆₃)⋊C₄
commutator	C₂×C₄×C₁₆₃	C₂×C₄
Frattini	C₄²	C₂×D₁₆₃
Fitting	C₄⋊C₈×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	C₂²⋊C₄
cosocle	C₄²×C₁₆₃	C₂²
hypercenter	C₄⋊C₈	D₁₆₃
hypocenter	C₁₆₃	#332
LCS	G ▷ C₂×C₄×C₁₆₃ ▷ C₂²×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
28. C₁₆₃	#332	semidirect