Subgroups — C₃²×D₁₇ #64560

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	C₃×D₁₇	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₁₇	C₂×C₃	1	4	yes	complemented
4	D₁₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃²	—	17	1	no	maximal, Hall
6	C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented, Sylow
7	C₃²	D₁₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₃	—	17	4	no	—
9	C₃	C₃×D₁₇	1	4	yes	direct product factor
10	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃²

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.