Finite Group Databasebeta

← D₃×C₃₁×C₁₈₁ #46797571

Subgroups — D₃×C₃₁×C₁₈₁ #46797571

Order 33666.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃₁×C₁₈₁	—	3	1	no	maximal, Hall
3	C₃₁×C₁₈₁	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₈₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₈₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₈₁	—	3	1	no	Hall
7	D₃×C₃₁	C₁₈₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₈₁	D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×C₃₁	C₂×C₁₈₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃₁	—	3	1	no	Hall
11	C₃₁	D₃×C₁₈₁	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₃₁×C₁₈₁	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₃₁×C₁₈₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁×C₁₈₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃₁×C₁₈₁
Frattini	C₁	G
Fitting, socle	C₃×C₃₁×C₁₈₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃₁×C₁₈₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₁₈₁	C₂	semidirect
3. C₃₁×C₁₈₁	D₃	direct (N × H)
4. D₃×C₁₈₁	C₃₁	direct (N × H)
5. C₃×C₁₈₁	C₂×C₃₁	semidirect
7. D₃×C₃₁	C₁₈₁	direct (N × H)
8. C₁₈₁	D₃×C₃₁	direct (N × H)
9. C₃×C₃₁	C₂×C₁₈₁	semidirect
11. C₃₁	D₃×C₁₈₁	direct (N × H)
12. D₃	C₃₁×C₁₈₁	direct (N × H)
13. C₃	C₂×C₃₁×C₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃₁×C₁₈₁	2
C₂×C₃₁×C₁₈₁	3
D₃×C₁₈₁	31
D₃×C₃₁	181