Subgroups — C₄⋊(C₁₆₇⋊C₁₆) #24923088

Order 10688.

50 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
2	C₄×C₈×C₁₆₇	C₂	1	1	yes	maximal, characteristic
3	C₁₆₇⋊C₁₆	—	2	2	no	—
4	C₂×C₈×C₁₆₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
6	C₄²×C₁₆₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₆₇	C₈	1	1	yes	characteristic
8	C₂×C₄×C₁₆₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₆₇	C₂×C₄	1	1	yes	characteristic
10	C₈×C₁₆₇	—	2	1	no	—
11	C₈×C₁₆₇	D₄	1	1	yes	characteristic
12	C₈×C₁₆₇	Q₈	1	1	yes	characteristic
13	C₂²×C₁₆₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₆₇	—	2	1	no	—
15	C₄×C₁₆₇	C₁₆	1	2	yes	complemented
16	C₄×C₁₆₇	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₆₇	M₁₆	1	1	yes	characteristic
18	C₂×C₁₆₇	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₆₇	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₁₆₇	M₃₂	1	1	yes	characteristic
21	C₁₆₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	167	1	no	maximal, Sylow
23	C₂×C₁₆	—	167	2	no	—
24	C₄×C₈	D₁₆₇	1	1	yes	characteristic
25	C₂×C₈	Dic₁₆₇	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₆₇	1	1	yes	characteristic
27	C₄²	Dic₁₆₇	1	1	yes	characteristic
28	C₁₆	—	334	2	no	—
29	C₂×C₄	C₁₆₇⋊C₈	1	1	yes	characteristic
30	C₂×C₄	C₁₆₇⋊C₈	1	1	yes	characteristic
31	C₂×C₄	C₂×Dic₁₆₇	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	D₆₆₈	1	1	yes	characteristic
34	C₈	Dic₃₃₄	1	1	yes	characteristic
35	C₂²	C₂×C₁₆₇⋊C₈	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	C₁₆₇⋊C₁₆	1	2	yes	complemented
38	C₄	C₄⋊Dic₁₆₇	1	1	yes	characteristic
39	C₄	#14581934	1	1	yes	characteristic
40	C₂	C₄⋊(C₁₆₇⋊C₈)	1	1	yes	characteristic
41	C₂	C₂×C₁₆₇⋊C₁₆	1	1	yes	characteristic
42	C₂	#19128772	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₆₇
commutator	C₂×C₁₆₇	C₂×C₁₆
Fitting	C₄×C₈×C₁₆₇	C₂
socle, prime radical	C₂²×C₁₆₇	C₂×C₈
cosocle	C₂×C₈×C₁₆₇	C₂²
hypercenter	C₄×C₈	D₁₆₇
hypocenter	C₁₆₇	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
15. C₄×C₁₆₇	C₁₆	semidirect
21. C₁₆₇	C₄⋊C₁₆	semidirect
37. C₄	C₁₆₇⋊C₁₆	semidirect

Subgroups — C4⋊(C167⋊C16) #24923088

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊(C₁₆₇⋊C₁₆) #24923088