Subgroups — H(3,𝔽₁₁) #13050604

Order 1331.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²	C₁₁	1	12	yes	maximal, complemented
2	C₁₁	—	11	12	no	—
3	C₁₁	C₁₁²	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₁₁	C₁₁²
LCS	G ▷ C₁₁ ▷ C₁
UCS	C₁ ◁ C₁₁ ◁ G
LECS	G ▷ C₁₁ ▷ C₁

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

N	H ≅ G/N	type
1. C₁₁²	C₁₁	semidirect

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

subgroup	index
C₁₁²	11