Subgroups — C₃×C₁₁₂₃⋊C₁₁ #49150367

Order 37059.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₂₃⋊C₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₁₂₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁₂₃	C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₁₁	—	1123	1	no	maximal, Hall
5	C₁₁	—	1123	1	no	Sylow
6	C₃	C₁₁₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₁₂₃⋊C₁₁
commutator, cosocle, hypocenter	C₁₁₂₃	C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁₂₃	C₁₁
LCS	G ▷ C₁₁₂₃
UCS	C₁ ◁ C₃

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.