Finite Group Databasebeta

← C₃×C₄₁×D₁₀₁ #38733014

Subgroups — C₃×C₄₁×D₁₀₁ #38733014

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	C₄₁×D₁₀₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₁×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₀₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₀₁	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₄₁	—	101	1	no	maximal, Hall
7	D₁₀₁	C₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₄₁	D₁₀₁	1	1	yes	characteristic, direct product factor, Hall
9	C₁₀₁	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₄₁	—	101	1	no	Hall
11	C₄₁	C₃×D₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	101	1	no	Hall
13	C₃	C₄₁×D₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	101	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₁	D₁₀₁
commutator, cosocle, hypocenter	C₁₀₁	C₂×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₄₁×C₁₀₁	C₂
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₃×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₁×C₁₀₁	C₂	semidirect
2. C₄₁×D₁₀₁	C₃	direct (N × H)
3. C₄₁×C₁₀₁	C₂×C₃	semidirect
4. C₃×D₁₀₁	C₄₁	direct (N × H)
5. C₃×C₁₀₁	C₂×C₄₁	semidirect
7. D₁₀₁	C₃×C₄₁	direct (N × H)
8. C₃×C₄₁	D₁₀₁	direct (N × H)
9. C₁₀₁	C₂×C₃×C₄₁	semidirect
11. C₄₁	C₃×D₁₀₁	direct (N × H)
13. C₃	C₄₁×D₁₀₁	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
C₄₁×D₁₀₁	3
C₃×D₁₀₁	41
C₂×C₃×C₄₁	101