Subgroups — D₃₂₂₇₉ #72302000

Order 64558.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆₉×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₄₈₃	—	13	1	no	maximal
3	C₁₃×C₁₉₁	D₁₃	1	1	yes	characteristic
4	D₁₉₁	—	169	1	no	Hall
5	D₁₆₉	—	191	1	no	maximal, Hall
6	C₁₉₁	D₁₆₉	1	1	yes	characteristic, complemented, Sylow
7	C₁₆₉	D₁₉₁	1	1	yes	characteristic, complemented, Sylow
8	D₁₃	—	2483	1	no	—
9	C₁₃	D₂₄₈₃	1	1	yes	characteristic
10	C₂	—	32279	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₆₉×C₁₉₁	C₂
Frattini	C₁₃	D₂₄₈₃
socle	C₁₃×C₁₉₁	D₁₃
LCS	G ▷ C₁₆₉×C₁₉₁
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.