Finite Group Databasebeta

← C₁₀₁⋊(D₆₁⋊C₃) #49149331

Subgroups — C₁₀₁⋊(D₆₁⋊C₃) #49149331

Order 36966.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₁₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₆₁×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₀₁	—	61	1	no	maximal, Hall
5	D₆₁⋊C₃	—	101	1	no	maximal, Hall
6	C₃×C₁₀₁	—	61	1	no	Hall
7	D₁₀₁	—	61	1	no	Hall
8	C₆₁⋊C₃	D₁₀₁	1	1	yes	characteristic, complemented, Hall
9	D₆₁	—	101	1	no	Hall
10	C₁₀₁	D₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
11	C₆₁	C₃×D₁₀₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	6161	1	no	Hall
13	C₃	—	61	1	no	Sylow
14	C₂	—	6161	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₆₁×C₁₀₁	C₂×C₃
LCS	G ▷ C₆₁×C₁₀₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₀₁×C₆₁⋊C₃	C₂	semidirect
2. D₆₁₆₁	C₃	semidirect
3. C₆₁×C₁₀₁	C₂×C₃	semidirect
8. C₆₁⋊C₃	D₁₀₁	semidirect
10. C₁₀₁	D₆₁⋊C₃	semidirect
11. C₆₁	C₃×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×C₆₁⋊C₃	2
D₆₁₆₁	3
C₃×D₁₀₁	61
D₆₁⋊C₃	101