Subgroups — C₃⋊#3633 #87997

Order 408.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#595	C₂	1	1	yes	maximal, characteristic
2	#3633	—	3	1	no	maximal, Hall
3	C₃×D₁₇	C₄	1	1	yes	characteristic
4	#595	D₃	1	1	yes	characteristic
5	C₃×C₁₇	C₈	1	1	yes	characteristic, complemented, Hall
6	D₁₇	Dic₃	1	1	yes	characteristic
7	C₃⋊C₈	—	17	1	no	maximal, Hall
8	C₁₇	C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₄	—	17	1	no	—
10	C₈	—	51	1	no	Sylow
11	C₂×C₃	—	17	1	no	—
12	C₄	—	17	1	no	—
13	C₃	#3633	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₇	C₈
prime radical	C₃×D₁₇	C₄
cosocle	C₃×#595	C₂
LCS	G ▷ C₃×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.