Finite Group Databasebeta

← C₁₀₁⋊(D₄₃⋊C₃) #39907584

Subgroups — C₁₀₁⋊(D₄₃⋊C₃) #39907584

Order 26058.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₃₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₃×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₀₁	—	43	1	no	maximal, Hall
5	C₃×C₁₀₁	—	43	1	no	Hall
6	D₄₃⋊C₃	—	101	1	no	maximal, Hall
7	D₁₀₁	—	43	1	no	Hall
8	C₄₃⋊C₃	D₁₀₁	1	1	yes	characteristic, complemented, Hall
9	C₁₀₁	D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
10	D₄₃	—	101	1	no	Hall
11	C₄₃	C₃×D₁₀₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	4343	1	no	Hall
13	C₃	—	43	1	no	Sylow
14	C₂	—	4343	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₄₃×C₁₀₁	C₂×C₃
LCS	G ▷ C₄₃×C₁₀₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₀₁×C₄₃⋊C₃	C₂	semidirect
2. D₄₃₄₃	C₃	semidirect
3. C₄₃×C₁₀₁	C₂×C₃	semidirect
8. C₄₃⋊C₃	D₁₀₁	semidirect
9. C₁₀₁	D₄₃⋊C₃	semidirect
11. C₄₃	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×C₄₃⋊C₃	2
D₄₃₄₃	3
C₃×D₁₀₁	43
D₄₃⋊C₃	101