Subgroups — #24923044

Order 10688.

54 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	C₈×Dic₁₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆₇⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₁₆₇	C₄	1	1	yes	characteristic
6	C₁₆₇⋊C₁₆	C₄	1	2	yes	complemented
7	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₆₇	C₄	1	2	yes	complemented
9	C₂×Dic₁₆₇	C₈	1	2	yes	—
10	C₁₆₇⋊C₈	C₈	1	2	yes	—
11	C₂×C₄×C₁₆₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₆₇	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₆₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₁₆₇	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₆₇	C₄²	1	1	yes	characteristic
16	C₄×C₁₆₇	C₂×C₈	1	1	yes	characteristic
17	Dic₁₆₇	—	2	2	no	—
18	C₂×C₁₆₇	C₄×C₈	1	1	yes	characteristic
19	C₂×C₁₆₇	M₃₂	1	2	yes	—
20	C₁₆₇	#346	1	1	yes	characteristic, complemented, Sylow
21	#346	—	167	1	no	maximal, Sylow
22	C₂×C₁₆	—	167	1	no	—
23	C₂×C₁₆	D₁₆₇	1	1	yes	characteristic
24	C₄×C₈	—	167	1	no	—
25	C₂×C₈	—	167	1	no	—
26	C₂×C₈	C₂×D₁₆₇	1	1	yes	characteristic
27	C₄²	—	167	1	no	—
28	C₁₆	—	167	2	no	—
29	C₁₆	Dic₁₆₇	1	2	yes	complemented
30	C₂×C₄	—	167	2	no	—
31	C₂×C₄	C₄×D₁₆₇	1	1	yes	characteristic
32	C₈	—	167	2	no	—
33	C₈	C₄×D₁₆₇	1	1	yes	characteristic
34	C₈	C₂×Dic₁₆₇	1	1	yes	characteristic
35	C₂²	C₈×D₁₆₇	1	1	yes	characteristic
36	C₄	—	334	2	no	—
37	C₄	C₄×Dic₁₆₇	1	1	yes	characteristic
38	C₄	C₈×D₁₆₇	1	1	yes	characteristic
39	C₂	C₈×Dic₁₆₇	1	1	yes	characteristic
40	C₂	#19128771	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₆₇
commutator	C₂×C₁₆₇	C₄×C₈
Fitting	C₂×C₁₆×C₁₆₇	C₂
socle, prime radical	C₂²×C₁₆₇	C₂×C₈
cosocle	C₂×C₈×C₁₆₇	C₂²
hypercenter	C₂×C₁₆	D₁₆₇
hypocenter	C₁₆₇	#346
LCS	G ▷ C₂×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. C₁₆₇⋊C₁₆	C₄	semidirect
8. C₁₆×C₁₆₇	C₄	semidirect
20. C₁₆₇	#346	semidirect
29. C₁₆	Dic₁₆₇	semidirect