Subgroups — C₁₁×D₁₁₂₃ #37612708

Order 24706.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₁₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₁₁	—	1123	1	no	maximal, Hall
5	C₁₁	D₁₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	1123	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₁₁₂₃
commutator, cosocle, hypocenter	C₁₁₂₃	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₁₂₃	C₂
LCS	G ▷ C₁₁₂₃
UCS	C₁ ◁ C₁₁

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.