Subgroups — #23781473

Order 10432.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19104757	C₂	1	1	yes	maximal, characteristic
2	#19104671	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14579699	—	2	1	no	—
5	Dic₆₅₂	C₄	1	1	yes	characteristic
6	#14579688	—	2	1	no	—
7	D₁₃₀₄	C₄	1	1	yes	characteristic
8	#14579683	—	2	1	no	—
9	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
10	C₁₆×C₁₆₃	—	2	1	no	—
11	Dic₃₂₆	—	2	1	no	—
12	D₆₅₂	—	2	1	no	—
13	C₂²⋊D₁₆₃	—	4	1	no	—
14	C₄×D₁₆₃	—	4	1	no	—
15	C₁₆₃⋊C₈	—	4	1	no	—
16	C₂×C₄×C₁₆₃	D₄	1	1	yes	characteristic
17	C₈×C₁₆₃	C₂×C₄	1	1	yes	characteristic
18	C₈×C₁₆₃	D₄	1	1	yes	characteristic
19	C₂²×C₁₆₃	SD₁₆	1	1	yes	characteristic
20	C₂×D₁₆₃	—	4	1	no	—
21	C₄×C₁₆₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₆₃	D₈	1	1	yes	characteristic
23	Dic₁₆₃	—	4	1	no	—
24	C₂×C₁₆₃	—	2	1	no	—
25	C₂×C₁₆₃	#102	1	1	yes	characteristic
26	D₁₆₃	—	8	1	no	—
27	C₁₆₃	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	163	1	no	maximal, Sylow
29	#135	—	163	1	no	—
30	C₂×C₁₆	D₁₆₃	1	1	yes	characteristic, complemented
31	#108	—	163	1	no	—
32	#41	—	326	1	no	—
33	Q₁₆	—	163	1	no	—
34	SD₁₆	—	326	1	no	—
35	D₈	—	163	1	no	—
36	M₁₆	—	326	1	no	—
37	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	Q₈	—	326	1	no	—
40	D₄	—	326	1	no	—
41	D₄	—	652	1	no	—
42	C₂×C₄	—	652	1	no	—
43	C₂×C₄	D₆₅₂	1	1	yes	characteristic
44	C₈	—	652	1	no	—
45	C₈	C₄×D₁₆₃	1	1	yes	characteristic
46	C₈	C₂²⋊D₁₆₃	1	1	yes	characteristic
47	C₂²	—	652	1	no	—
48	C₂²	#14579688	1	1	yes	characteristic
49	C₄	—	652	1	no	—
50	C₄	(C₂×D₁₆₃)⋊C₄	1	1	yes	characteristic
51	C₄	D₁₃₀₄	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	1304	1	no	—
54	C₂	#19104657	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃₀₄
commutator	C₈×C₁₆₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₆₃
Fitting	C₂×C₁₆×C₁₆₃	C₂
socle	C₂×C₁₆₃	#102
prime radical	#19104757	C₂
cosocle	C₂×C₈×C₁₆₃	C₂²
hypercenter	C₂×C₁₆	D₁₆₃
hypocenter	C₁₆₃	#359
LCS	G ▷ C₈×C₁₆₃ ▷ C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #19104671	C₂	semidirect
3. C₂×C₁₆×C₁₆₃	C₂	semidirect
27. C₁₆₃	#359	semidirect
30. C₂×C₁₆	D₁₆₃	semidirect