Subgroups — C₃×D₃₃×C₁₆₇ #45683402

Order 33066.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₃×C₁₆₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₁×C₁₆₇	—	3	1	no	maximal
4	C₃×C₁₁×C₁₆₇	—	2	1	no	—
5	C₃×C₁₁×C₁₆₇	D₃	1	1	yes	characteristic, complemented
6	C₃×C₁₁×C₁₆₇	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₁×C₁₆₇	—	3	1	no	Hall
8	C₃×D₃×C₁₆₇	—	11	1	no	maximal, Hall
9	C₁₁×C₁₆₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₁₆₇	D₁₁	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₆₇	—	33	1	no	—
12	D₃×C₁₆₇	—	11	1	no	—
13	C₃×C₁₆₇	—	2	1	no	—
14	C₃×C₁₆₇	C₃×D₁₁	1	1	yes	characteristic, complemented
15	C₃×C₁₆₇	D₃₃	1	1	yes	characteristic, direct product factor
16	C₂×C₁₆₇	—	33	1	no	Hall
17	C₃×D₃₃	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₆₇	C₃×D₃₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²×C₁₁	C₂×C₁₆₇	1	1	yes	characteristic, complemented, Hall
20	D₃₃	C₃×C₁₆₇	1	1	yes	characteristic, direct product factor
21	C₃×D₁₁	—	3	1	no	—
22	C₃×C₁₁	—	2	1	no	—
23	C₃×C₁₁	D₃×C₁₆₇	1	1	yes	characteristic, complemented
24	C₃×C₁₁	C₂×C₃×C₁₆₇	1	1	yes	characteristic, complemented
25	D₁₁	—	3	1	no	Hall
26	C₃×D₃	—	11	1	no	Hall
27	C₁₁	C₃×D₃×C₁₆₇	1	1	yes	characteristic, complemented, Sylow
28	C₃²	D₁₁×C₁₆₇	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	33	1	no	—
30	D₃	—	11	1	no	—
31	C₃	—	2	1	no	—
32	C₃	C₃×D₁₁×C₁₆₇	1	1	yes	characteristic, complemented
33	C₃	D₃₃×C₁₆₇	1	1	yes	characteristic, direct product factor
34	C₂	—	33	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₆₇	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₃×C₁₆₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₆₇	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₃×C₁₆₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₁×C₁₆₇	C₂	semidirect
2. D₃₃×C₁₆₇	C₃	direct (N × H)
5. C₃×C₁₁×C₁₆₇	D₃	semidirect
6. C₃×C₁₁×C₁₆₇	C₂×C₃	semidirect
9. C₁₁×C₁₆₇	C₃×D₃	semidirect
10. C₃²×C₁₆₇	D₁₁	semidirect
14. C₃×C₁₆₇	C₃×D₁₁	semidirect
15. C₃×C₁₆₇	D₃₃	direct (N × H)
17. C₃×D₃₃	C₁₆₇	direct (N × H)
18. C₁₆₇	C₃×D₃₃	direct (N × H)
19. C₃²×C₁₁	C₂×C₁₆₇	semidirect
20. D₃₃	C₃×C₁₆₇	direct (N × H)
23. C₃×C₁₁	D₃×C₁₆₇	semidirect
24. C₃×C₁₁	C₂×C₃×C₁₆₇	semidirect
27. C₁₁	C₃×D₃×C₁₆₇	semidirect
28. C₃²	D₁₁×C₁₆₇	semidirect
32. C₃	C₃×D₁₁×C₁₆₇	semidirect
33. C₃	D₃₃×C₁₆₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₁₁×C₁₆₇	2
D₃₃×C₁₆₇	3
C₃×D₁₁×C₁₆₇	3
C₃×D₃×C₁₆₇	11
C₃×D₃₃	167

Subgroups — C3×D33×C167 #45683402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₃×C₁₆₇ #45683402