Subgroups — D₂₇₂₉₃ #72290613

Order 54586.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₅₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₈₉₉	—	7	1	no	maximal
3	C₇×C₅₅₇	D₇	1	1	yes	characteristic
4	D₅₅₇	—	49	1	no	Hall
5	C₅₅₇	D₄₉	1	1	yes	characteristic, complemented, Sylow
6	D₄₉	—	557	1	no	maximal, Hall
7	C₄₉	D₅₅₇	1	1	yes	characteristic, complemented, Sylow
8	D₇	—	3899	1	no	—
9	C₇	D₃₈₉₉	1	1	yes	characteristic
10	C₂	—	27293	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄₉×C₅₅₇	C₂
Frattini	C₇	D₃₈₉₉
socle	C₇×C₅₅₇	D₇
LCS	G ▷ C₄₉×C₅₅₇
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.