Subgroups — #36376404

Order 22468.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×D₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₄₁×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#10587739	—	41	1	no	maximal, Hall
4	D₁₃₇	D₄₁	1	1	yes	characteristic
5	Dic₄₁	—	137	1	no	maximal, Hall
6	C₁₃₇	Dic₄₁	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₄₁	—	137	1	no	—
8	C₄₁	#10587739	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	5617	1	no	Sylow
10	C₂	—	137	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₄₁×C₁₃₇	C₄
prime radical, cosocle	C₄₁×D₁₃₇	C₂
LCS	G ▷ C₄₁×C₁₃₇
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.