Subgroups — D₁₂₄₂₇ #38733207

Order 24854.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇₃₁	—	17	1	no	maximal
3	C₁₇×C₄₃	D₁₇	1	1	yes	characteristic
4	D₂₈₉	—	43	1	no	maximal, Hall
5	C₂₈₉	D₄₃	1	1	yes	characteristic, complemented, Sylow
6	D₄₃	—	289	1	no	Hall
7	C₄₃	D₂₈₉	1	1	yes	characteristic, complemented, Sylow
8	D₁₇	—	731	1	no	—
9	C₁₇	D₇₃₁	1	1	yes	characteristic
10	C₂	—	12427	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄₃×C₂₈₉	C₂
Frattini	C₁₇	D₇₃₁
socle	C₁₇×C₄₃	D₁₇
LCS	G ▷ C₄₃×C₂₈₉
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.