Subgroups — C₂²⋊(C₁₆₃⋊C₁₆) #23781445

Order 10432.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
2	C₂²×C₈×C₁₆₃	C₂	1	1	yes	maximal, characteristic
3	C₁₆₃⋊C₁₆	—	2	2	no	—
4	C₂²×C₄×C₁₆₃	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₆₃	—	2	2	no	—
6	C₂×C₈×C₁₆₃	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
8	C₂³×C₁₆₃	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₆₃	—	2	1	no	—
10	C₂×C₄×C₁₆₃	—	2	1	no	—
11	C₂×C₄×C₁₆₃	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₆₃	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₆₃	—	2	1	no	—
14	C₈×C₁₆₃	D₄	1	2	yes	—
15	C₂²×C₁₆₃	—	2	1	no	—
16	C₂²×C₁₆₃	—	2	1	no	—
17	C₂²×C₁₆₃	C₁₆	1	2	yes	complemented
18	C₂²×C₁₆₃	C₂×C₈	1	1	yes	characteristic
19	C₄×C₁₆₃	—	2	1	no	—
20	C₄×C₁₆₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₆₃	M₁₆	1	1	yes	characteristic
22	C₂×C₁₆₃	—	2	2	no	—
23	C₂×C₁₆₃	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₁₆₃	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₁₆₃	M₃₂	1	1	yes	characteristic
26	C₁₆₃	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	163	1	no	maximal, Sylow
28	C₂²×C₈	D₁₆₃	1	1	yes	characteristic
29	C₂×C₁₆	—	163	2	no	—
30	C₂²×C₄	Dic₁₆₃	1	1	yes	characteristic
31	C₂×C₈	—	2	2	no	—
32	C₂×C₈	Dic₁₆₃	1	1	yes	characteristic
33	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
34	C₁₆	—	326	2	no	—
35	C₂³	C₁₆₃⋊C₈	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	C₁₆₃⋊C₈	1	1	yes	characteristic
39	C₂×C₄	C₂×Dic₁₆₃	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	C₂²⋊D₁₆₃	1	2	yes	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	C₁₆₃⋊C₁₆	1	2	yes	complemented
45	C₂²	C₂×C₁₆₃⋊C₈	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	C₂²⋊Dic₁₆₃	1	1	yes	characteristic
48	C₄	#14579683	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊(C₁₆₃⋊C₈)	1	1	yes	characteristic
51	C₂	C₂×C₁₆₃⋊C₁₆	1	1	yes	characteristic
52	C₂	#19104675	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₆₃
commutator	C₂×C₁₆₃	C₂×C₁₆
Fitting	C₂²×C₈×C₁₆₃	C₂
socle	C₂²×C₁₆₃	C₂×C₈
prime radical	C₂³×C₁₆₃	C₈
cosocle	C₂×C₈×C₁₆₃	C₂²
hypercenter	C₂²×C₈	D₁₆₃
hypocenter	C₁₆₃	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₆₃⋊C₁₆	C₂	semidirect
17. C₂²×C₁₆₃	C₁₆	semidirect
26. C₁₆₃	C₂²⋊C₁₆	semidirect
44. C₂²	C₁₆₃⋊C₁₆	semidirect

Subgroups — C22⋊(C163⋊C16) #23781445

Conjugacy classes of subgroups

Complements

Subgroups — C₂²⋊(C₁₆₃⋊C₁₆) #23781445