Subgroups — D₃₁₇₉₇ #72301749

Order 63594.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₅₃₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₅₉₉	—	3	1	no	maximal
3	C₃×C₃₅₃₃	D₃	1	1	yes	characteristic
4	D₃₅₃₃	—	9	1	no	Hall
5	C₃₅₃₃	D₉	1	1	yes	characteristic, complemented, Sylow
6	D₉	—	3533	1	no	maximal, Hall
7	C₉	D₃₅₃₃	1	1	yes	characteristic, complemented, Sylow
8	D₃	—	10599	1	no	—
9	C₃	D₁₀₅₉₉	1	1	yes	characteristic
10	C₂	—	31797	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₃₅₃₃	C₂
Frattini	C₃	D₁₀₅₉₉
socle	C₃×C₃₅₃₃	D₃
LCS	G ▷ C₉×C₃₅₃₃
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.