Subgroups — #37567425

Order 24411.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₀₃⋊C₃	—	79	1	no	maximal, Hall
3	C₇₉⋊C₃	—	103	1	no	maximal, Hall
4	C₁₀₃	C₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
5	C₇₉	C₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
6	C₃	—	8137	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇₉×C₁₀₃	C₃
LCS	G ▷ C₇₉×C₁₀₃
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.