Subgroups — C₃⋊D₅₁ #64564

Order 306.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₁	—	3	4	no	maximal
3	C₃×C₁₇	D₃	1	4	yes	complemented
4	D₁₇	—	9	1	no	Hall
5	C₃⋊D₃	—	17	1	no	maximal, Hall
6	C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
7	C₃²	D₁₇	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	51	4	no	—
9	C₃	D₅₁	1	4	yes	complemented
10	C₂	—	153	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₇	C₂
LCS	G ▷ C₃²×C₁₇
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.