Subgroups — (C₁₀₅₁⋊C₃)⋊C₄ #27162176

Order 12612.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₅₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₀₅₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₀₅₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₀₅₁	C₂×C₃	1	1	yes	characteristic
5	C₁₀₅₁	C₃×C₄	1	1	yes	characteristic, complemented, Sylow
6	C₃×C₄	—	1051	1	no	maximal, Hall
7	C₂×C₃	—	1051	1	no	—
8	C₄	—	1051	1	no	Sylow
9	C₃	—	1051	1	no	Sylow
10	C₂	D₁₀₅₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₀₅₁⋊C₃
commutator, hypocenter	C₁₀₅₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₀₅₁	C₂×C₃
prime radical	C₂×C₁₀₅₁⋊C₃	C₂
LCS	G ▷ C₁₀₅₁
UCS	C₁ ◁ C₂

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.