Subgroups — C₁₁⋊(C₂₃⋊D₂₃) #26042813

Order 11638.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₂₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃⋊D₂₃	—	11	1	no	maximal, Hall
3	C₂₃²	D₁₁	1	1	yes	characteristic, complemented, Sylow
4	D₂₅₃	—	23	24	no	maximal
5	C₁₁×C₂₃	D₂₃	1	24	yes	complemented
6	D₂₃	—	253	24	no	—
7	C₂₃	D₂₅₃	1	24	yes	complemented
8	D₁₁	—	529	1	no	Hall
9	C₁₁	C₂₃⋊D₂₃	1	1	yes	characteristic, complemented, Sylow
10	C₂	—	5819	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₂₃²	C₂
LCS	G ▷ C₁₁×C₂₃²
UCS	C₁

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.