Subgroups — C₃⋊D₃×C₁₀₅₁ #34038708

Order 18918.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₀₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₀₅₁	—	3	4	no	maximal
3	C₃×C₁₀₅₁	D₃	1	4	yes	complemented
4	C₂×C₁₀₅₁	—	9	1	no	Hall
5	C₁₀₅₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃⋊D₃	C₁₀₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃²	C₂×C₁₀₅₁	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	3	4	no	—
9	C₃	D₃×C₁₀₅₁	1	4	yes	complemented
10	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₀₅₁	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₁₀₅₁
Frattini	C₁	G
Fitting, socle	C₃²×C₁₀₅₁	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₀₅₁

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

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