Subgroups — Dic₂₃⋊C₁₁ #11759793

Order 1012.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂₃⋊C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₂₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₂₃	C₂×C₁₁	1	1	yes	characteristic
5	C₄×C₁₁	—	23	1	no	maximal, Hall
6	C₂₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₁₁	—	23	1	no	—
8	C₁₁	—	23	1	no	Sylow
9	C₄	—	23	1	no	Sylow
10	C₂	AGL(1,𝔽₂₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	AGL(1,𝔽₂₃)
commutator, hypocenter	C₂₃	C₄×C₁₁
Fitting, socle, cosocle	C₂×C₂₃	C₂×C₁₁
prime radical	C₂×C₂₃⋊C₁₁	C₂
LCS	G ▷ C₂₃
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.