Finite Group Databasebeta

← C₃×C₁₃₇⋊C₁₇ #20296140

Subgroups — C₃×C₁₃₇⋊C₁₇ #20296140

Order 6987.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃₇⋊C₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₃₇	C₁₇	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃₇	C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₁₇	—	137	1	no	maximal, Hall
5	C₁₇	—	137	1	no	Sylow
6	C₃	C₁₃₇⋊C₁₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₃₇⋊C₁₇
commutator, hypocenter	C₁₃₇	C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₃₇	C₁₇
LCS	G ▷ C₁₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₁₃₇⋊C₁₇	C₃	direct (N × H)
2. C₃×C₁₃₇	C₁₇	semidirect
3. C₁₃₇	C₃×C₁₇	semidirect
6. C₃	C₁₃₇⋊C₁₇	direct (N × H)