Subgroups — #24923094

Order 10688.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#19128766	C₂	1	1	yes	maximal, characteristic
3	#107×C₁₆₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₆₇	—	2	1	no	—
5	C₁₆₇⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₆₇	—	2	1	no	—
8	C₂×Dic₁₆₇	—	4	1	no	—
9	C₂×C₄×C₁₆₇	—	4	1	no	—
10	C₂×C₄×C₁₆₇	D₄	1	1	yes	characteristic
11	C₈×C₁₆₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₆₇	Q₈	1	1	yes	characteristic
13	C₂²×C₁₆₇	D₈	1	1	yes	characteristic
14	C₄×C₁₆₇	—	8	1	no	—
15	C₄×C₁₆₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₆₇	Q₁₆	1	1	yes	characteristic
17	Dic₁₆₇	—	8	1	no	—
18	C₂×C₁₆₇	#107	1	1	yes	characteristic
19	C₂×C₁₆₇	D₁₆	1	1	yes	characteristic
20	C₂×C₁₆₇	Q₃₂	1	1	yes	characteristic
21	C₁₆₇	#366	1	1	yes	characteristic, complemented, Sylow
22	#366	—	167	1	no	maximal, Sylow
23	C₂×C₁₆	—	167	1	no	—
24	#107	—	167	1	no	—
25	#107	D₁₆₇	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₆₇	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	334	1	no	—
29	C₁₆	—	167	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	668	1	no	—
32	C₂×C₄	C₂²⋊D₁₆₇	1	1	yes	characteristic
33	C₈	C₄×D₁₆₇	1	1	yes	characteristic
34	C₈	Dic₃₃₄	1	1	yes	characteristic
35	C₂²	#14581935	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	1336	1	no	—
38	C₄	Dic₁₆₇⋊C₄	1	1	yes	characteristic
39	C₄	#14581940	1	1	yes	characteristic
40	C₂	#19128765	1	1	yes	characteristic
41	C₂	#19128773	1	1	yes	characteristic
42	C₂	#19128778	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14581935
commutator	C₈×C₁₆₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₆₇
Fitting	#107×C₁₆₇	C₂
socle, prime radical	C₂²×C₁₆₇	D₈
cosocle	C₂×C₈×C₁₆₇	C₂²
hypercenter	#107	D₁₆₇
hypocenter	C₁₆₇	#366
LCS	G ▷ C₈×C₁₆₇ ▷ C₄×C₁₆₇ ▷ C₂×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. C₁₆₇⋊C₁₆	C₄	semidirect
21. C₁₆₇	#366	semidirect