Finite Group Databasebeta

← C₃×D₄₁×C₁₀₁ #38733015

Subgroups — C₃×D₄₁×C₁₀₁ #38733015

Order 24846.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₁×C₁₀₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₁×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₀₁	—	41	1	no	maximal, Hall
5	C₃×C₁₀₁	D₄₁	1	1	yes	characteristic, direct product factor, Hall
6	C₃×D₄₁	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₀₁	—	41	1	no	Hall
8	C₃×C₄₁	C₂×C₁₀₁	1	1	yes	characteristic, complemented, Hall
9	C₁₀₁	C₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
10	D₄₁	C₃×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
11	C₄₁	C₂×C₃×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	41	1	no	Hall
13	C₃	D₄₁×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	41	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₀₁	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂×C₃×C₁₀₁
Frattini	C₁	G
Fitting, socle	C₃×C₄₁×C₁₀₁	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₃×C₁₀₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₁×C₁₀₁	C₂	semidirect
2. D₄₁×C₁₀₁	C₃	direct (N × H)
3. C₄₁×C₁₀₁	C₂×C₃	semidirect
5. C₃×C₁₀₁	D₄₁	direct (N × H)
6. C₃×D₄₁	C₁₀₁	direct (N × H)
8. C₃×C₄₁	C₂×C₁₀₁	semidirect
9. C₁₀₁	C₃×D₄₁	direct (N × H)
10. D₄₁	C₃×C₁₀₁	direct (N × H)
11. C₄₁	C₂×C₃×C₁₀₁	semidirect
13. C₃	D₄₁×C₁₀₁	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×C₁₀₁	2
D₄₁×C₁₀₁	3
C₂×C₃×C₁₀₁	41
C₃×D₄₁	101