Subgroups — D₃₂₃₉₁ #72302111

Order 64782.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₅₉×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₇₉₇	—	3	1	no	maximal
3	C₃×C₅₉×C₆₁	D₃	1	1	yes	characteristic
4	D₃₅₉₉	—	9	1	no	Hall
5	C₅₉×C₆₁	D₉	1	1	yes	characteristic, complemented, Hall
6	D₅₄₉	—	59	1	no	maximal, Hall
7	D₅₃₁	—	61	1	no	maximal, Hall
8	C₉×C₆₁	D₅₉	1	1	yes	characteristic, complemented, Hall
9	C₉×C₅₉	D₆₁	1	1	yes	characteristic, complemented, Hall
10	D₁₈₃	—	177	1	no	—
11	D₁₇₇	—	183	1	no	—
12	C₃×C₆₁	D₁₇₇	1	1	yes	characteristic
13	C₃×C₅₉	D₁₈₃	1	1	yes	characteristic
14	D₆₁	—	531	1	no	Hall
15	D₅₉	—	549	1	no	Hall
16	C₆₁	D₅₃₁	1	1	yes	characteristic, complemented, Sylow
17	C₅₉	D₅₄₉	1	1	yes	characteristic, complemented, Sylow
18	D₉	—	3599	1	no	Hall
19	C₉	D₃₅₉₉	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	10797	1	no	—
21	C₃	D₁₀₇₉₇	1	1	yes	characteristic
22	C₂	—	32391	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₅₉×C₆₁	C₂
Frattini	C₃	D₁₀₇₉₇
socle	C₃×C₅₉×C₆₁	D₃
LCS	G ▷ C₉×C₅₉×C₆₁
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.