Subgroups — #28385168

Order 14356.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇×C₉₇	C₂	1	1	yes	maximal, characteristic
2	C₃₇×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₉₇	—	37	1	no	maximal, Hall
4	C₂×C₉₇	—	37	1	no	—
5	#3866	—	97	1	no	maximal, Hall
6	C₉₇	#3866	1	1	yes	characteristic, complemented, Sylow
7	D₃₇	D₉₇	1	1	yes	characteristic
8	C₃₇	Dic₉₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	3589	1	no	Sylow
10	C₂	—	37	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃₇×C₉₇	C₄
prime radical, cosocle	D₃₇×C₉₇	C₂
LCS	G ▷ C₃₇×C₉₇
UCS	C₁

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.