Finite Group Databasebeta

← C₃×C₄₁×D₁₃₁ #44567410

Subgroups — C₃×C₄₁×D₁₃₁ #44567410

Order 32226.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁×D₁₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₁×C₁₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₃₁	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
6	D₁₃₁	C₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₄₁	—	131	1	no	maximal, Hall
8	C₁₃₁	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₄₁	D₁₃₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₄₁	—	131	1	no	Hall
11	C₄₁	C₃×D₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	131	1	no	Hall
13	C₃	C₄₁×D₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	131	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₁	D₁₃₁
commutator, cosocle, hypocenter	C₁₃₁	C₂×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₄₁×C₁₃₁	C₂
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₃×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₁×C₁₃₁	C₂	semidirect
2. C₄₁×D₁₃₁	C₃	direct (N × H)
3. C₄₁×C₁₃₁	C₂×C₃	semidirect
4. C₃×D₁₃₁	C₄₁	direct (N × H)
5. C₃×C₁₃₁	C₂×C₄₁	semidirect
6. D₁₃₁	C₃×C₄₁	direct (N × H)
8. C₁₃₁	C₂×C₃×C₄₁	semidirect
9. C₃×C₄₁	D₁₃₁	direct (N × H)
11. C₄₁	C₃×D₁₃₁	direct (N × H)
13. C₃	C₄₁×D₁₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄₁×C₁₃₁	2
C₄₁×D₁₃₁	3
C₃×D₁₃₁	41
C₂×C₃×C₄₁	131