Subgroups — C₃⋊C₁₆ #199

Order 48.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₁₆	—	3	1	no	maximal, Sylow
3	C₃×C₄	C₄	1	1	yes	characteristic
4	C₈	D₃	1	1	yes	characteristic
5	C₂×C₃	C₈	1	1	yes	characteristic
6	C₄	Dic₃	1	1	yes	characteristic
7	C₃	C₁₆	1	1	yes	characteristic, complemented, Sylow
8	C₂	C₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₃
commutator, hypocenter	C₃	C₁₆
Fitting, cosocle	C₃×C₈	C₂
socle, prime radical	C₂×C₃	C₈
LCS	G ▷ C₃
UCS	C₁ ◁ C₈

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
7. C₃	C₁₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₈	2
C₁₆	3