Subgroups — D₃₂₂₈₃ #72302002

Order 64566.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₇₆₁	—	3	1	no	maximal
3	C₃×C₁₇×C₂₁₁	D₃	1	1	yes	characteristic
4	D₃₅₈₇	—	9	1	no	Hall
5	D₁₈₉₉	—	17	1	no	maximal, Hall
6	C₁₇×C₂₁₁	D₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₂₁₁	D₁₇	1	1	yes	characteristic, complemented, Hall
8	D₆₃₃	—	51	1	no	—
9	C₃×C₂₁₁	D₅₁	1	1	yes	characteristic
10	D₂₁₁	—	153	1	no	Hall
11	D₁₅₃	—	211	1	no	maximal, Hall
12	C₂₁₁	D₁₅₃	1	1	yes	characteristic, complemented, Sylow
13	C₉×C₁₇	D₂₁₁	1	1	yes	characteristic, complemented, Hall
14	D₅₁	—	633	1	no	—
15	C₃×C₁₇	D₆₃₃	1	1	yes	characteristic
16	D₁₇	—	1899	1	no	Hall
17	D₉	—	3587	1	no	Hall
18	C₁₇	D₁₈₉₉	1	1	yes	characteristic, complemented, Sylow
19	C₉	D₃₅₈₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	10761	1	no	—
21	C₃	D₁₀₇₆₁	1	1	yes	characteristic
22	C₂	—	32283	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₇×C₂₁₁	C₂
Frattini	C₃	D₁₀₇₆₁
socle	C₃×C₁₇×C₂₁₁	D₃
LCS	G ▷ C₉×C₁₇×C₂₁₁
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.