Subgroups — C₂²⋊(C₁₆₇⋊C₁₆) #24923049

Order 10688.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆₇⋊C₁₆	C₂	1	2	yes	maximal, complemented
2	C₂²×C₈×C₁₆₇	C₂	1	1	yes	maximal, characteristic
3	C₁₆₇⋊C₁₆	—	2	2	no	—
4	C₂²×C₄×C₁₆₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₆₇	—	2	2	no	—
6	C₂×C₈×C₁₆₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
8	C₂³×C₁₆₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₆₇	—	2	1	no	—
10	C₂×C₄×C₁₆₇	—	2	1	no	—
11	C₂×C₄×C₁₆₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₆₇	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₆₇	—	2	1	no	—
14	C₈×C₁₆₇	D₄	1	2	yes	—
15	C₂²×C₁₆₇	—	2	1	no	—
16	C₂²×C₁₆₇	—	2	1	no	—
17	C₂²×C₁₆₇	C₁₆	1	2	yes	complemented
18	C₂²×C₁₆₇	C₂×C₈	1	1	yes	characteristic
19	C₄×C₁₆₇	—	2	1	no	—
20	C₄×C₁₆₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₆₇	M₁₆	1	1	yes	characteristic
22	C₂×C₁₆₇	—	2	2	no	—
23	C₂×C₁₆₇	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₁₆₇	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₁₆₇	M₃₂	1	1	yes	characteristic
26	C₁₆₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	167	1	no	maximal, Sylow
28	C₂²×C₈	D₁₆₇	1	1	yes	characteristic
29	C₂×C₁₆	—	167	2	no	—
30	C₂²×C₄	Dic₁₆₇	1	1	yes	characteristic
31	C₂×C₈	—	2	2	no	—
32	C₂×C₈	Dic₁₆₇	1	1	yes	characteristic
33	C₂×C₈	C₂×D₁₆₇	1	1	yes	characteristic
34	C₁₆	—	334	2	no	—
35	C₂³	C₁₆₇⋊C₈	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	C₁₆₇⋊C₈	1	1	yes	characteristic
39	C₂×C₄	C₂×Dic₁₆₇	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	C₂²⋊D₁₆₇	1	2	yes	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	C₁₆₇⋊C₁₆	1	2	yes	complemented
45	C₂²	C₂×C₁₆₇⋊C₈	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	C₂²⋊Dic₁₆₇	1	1	yes	characteristic
48	C₄	#14581934	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊(C₁₆₇⋊C₈)	1	1	yes	characteristic
51	C₂	C₂×C₁₆₇⋊C₁₆	1	1	yes	characteristic
52	C₂	#19128772	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₆₇
commutator	C₂×C₁₆₇	C₂×C₁₆
Fitting	C₂²×C₈×C₁₆₇	C₂
socle	C₂²×C₁₆₇	C₂×C₈
prime radical	C₂³×C₁₆₇	C₈
cosocle	C₂×C₈×C₁₆₇	C₂²
hypercenter	C₂²×C₈	D₁₆₇
hypocenter	C₁₆₇	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₆₇⋊C₁₆	C₂	semidirect
17. C₂²×C₁₆₇	C₁₆	semidirect
26. C₁₆₇	C₂²⋊C₁₆	semidirect
44. C₂²	C₁₆₇⋊C₁₆	semidirect

Subgroups — C22⋊(C167⋊C16) #24923049

Conjugacy classes of subgroups

Complements

Subgroups — C₂²⋊(C₁₆₇⋊C₁₆) #24923049