Subgroups — C₂²×D₃₇ #64448

Order 296.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃₇	C₂	1	6	yes	maximal, direct product factor
3	C₂×C₃₇	C₂²	1	3	yes	complemented
4	D₃₇	C₂²	1	4	yes	direct product factor
5	C₃₇	C₂³	1	1	yes	characteristic, complemented, Sylow
6	C₂³	—	37	1	no	maximal, Sylow
7	C₂²	—	37	6	no	—
8	C₂²	D₃₇	1	1	yes	characteristic, direct product factor
9	C₂	—	37	4	no	—
10	C₂	C₂×D₃₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂³
Frattini	C₁	G
Fitting, socle	C₂²×C₃₇	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂²

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

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