Subgroups — H(3,𝔽₃₇) #61797873

Order 50653.

79 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇²	C₃₇	1	38	yes	maximal, complemented
2	C₃₇	—	37	38	no	—
3	C₃₇	C₃₇²	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₃₇	C₃₇²
LCS	G ▷ C₃₇ ▷ C₁
UCS	C₁ ◁ C₃₇ ◁ G
LECS	G ▷ C₃₇ ▷ C₁

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

N	H ≅ G/N	type
1. C₃₇²	C₃₇	semidirect

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

subgroup	index
C₃₇²	37