Subgroups — H(3,𝔽₁₇) #19096831

Order 4913.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²	C₁₇	1	18	yes	maximal, complemented
2	C₁₇	—	17	18	no	—
3	C₁₇	C₁₇²	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle	C₁₇	C₁₇²
LCS	G ▷ C₁₇ ▷ C₁
UCS	C₁ ◁ C₁₇ ◁ G
LECS	G ▷ C₁₇ ▷ C₁

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

N	H ≅ G/N	type
1. C₁₇²	C₁₇	semidirect