Subgroups — D₃₃₃₉ #20269239

Order 6678.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁₁₃	—	3	1	no	maximal
3	C₃×C₇×C₅₃	D₃	1	1	yes	characteristic
4	D₄₇₇	—	7	1	no	maximal, Hall
5	D₃₇₁	—	9	1	no	Hall
6	C₉×C₅₃	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₅₃	D₉	1	1	yes	characteristic, complemented, Hall
8	D₁₅₉	—	21	1	no	—
9	C₃×C₅₃	D₂₁	1	1	yes	characteristic
10	D₆₃	—	53	1	no	maximal, Hall
11	D₅₃	—	63	1	no	Hall
12	C₇×C₉	D₅₃	1	1	yes	characteristic, complemented, Hall
13	C₅₃	D₆₃	1	1	yes	characteristic, complemented, Sylow
14	D₂₁	—	159	1	no	—
15	C₃×C₇	D₁₅₉	1	1	yes	characteristic
16	D₉	—	371	1	no	Hall
17	D₇	—	477	1	no	Hall
18	C₉	D₃₇₁	1	1	yes	characteristic, complemented, Sylow
19	C₇	D₄₇₇	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	1113	1	no	—
21	C₃	D₁₁₁₃	1	1	yes	characteristic
22	C₂	—	3339	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₇×C₉×C₅₃	C₂
Frattini	C₃	D₁₁₁₃
socle	C₃×C₇×C₅₃	D₃
LCS	G ▷ C₇×C₉×C₅₃
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.