Subgroups — D₁₂₂₉₃ #37589639

Order 24586.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₆₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₄₇	—	19	1	no	maximal, Hall
3	C₆₄₇	D₁₉	1	1	yes	characteristic, complemented, Sylow
4	D₁₉	—	647	1	no	maximal, Hall
5	C₁₉	D₆₄₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	12293	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉×C₆₄₇	C₂
LCS	G ▷ C₁₉×C₆₄₇
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.