Subgroups — 37₋¹⁺² #61797874

Order 50653.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇²	C₃₇	1	1	yes	maximal, characteristic
2	C₁₃₆₉	C₃₇	1	37	yes	maximal, complemented
3	C₃₇	—	37	1	no	—
4	C₃₇	C₃₇²	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₃₇	C₃₇²
prime radical	C₃₇²	C₃₇
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
2. C₁₃₆₉	C₃₇	semidirect

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

subgroup	index
C₃₇²	37
C₁₃₆₉	37