Subgroups — C₃⋊D₃×C₂₃ #88030

Order 414.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₂₃	—	3	4	no	maximal
3	C₃×C₂₃	D₃	1	4	yes	complemented
4	C₂×C₂₃	—	9	1	no	Hall
5	C₂₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃⋊D₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃²	C₂×C₂₃	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	3	4	no	—
9	C₃	D₃×C₂₃	1	4	yes	complemented
10	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂₃

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.