Subgroups — H(3,𝔽₂₃) #27131580

Order 12167.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃²	C₂₃	1	24	yes	maximal, complemented
2	C₂₃	—	23	24	no	—
3	C₂₃	C₂₃²	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂₃	C₂₃²
LCS	G ▷ C₂₃ ▷ C₁
UCS	C₁ ◁ C₂₃ ◁ G
LECS	G ▷ C₂₃ ▷ C₁

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

N	H ≅ G/N	type
1. C₂₃²	C₂₃	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃²	23