Subgroups — D₄₄₃₇ #22580025

Order 8874.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₄₇₉	—	3	1	no	maximal
3	C₃×C₁₇×C₂₉	D₃	1	1	yes	characteristic
4	D₄₉₃	—	9	1	no	Hall
5	D₂₆₁	—	17	1	no	maximal, Hall
6	C₁₇×C₂₉	D₉	1	1	yes	characteristic, complemented, Hall
7	D₁₅₃	—	29	1	no	maximal, Hall
8	C₉×C₂₉	D₁₇	1	1	yes	characteristic, complemented, Hall
9	D₈₇	—	51	1	no	—
10	C₉×C₁₇	D₂₉	1	1	yes	characteristic, complemented, Hall
11	D₅₁	—	87	1	no	—
12	C₃×C₂₉	D₅₁	1	1	yes	characteristic
13	D₂₉	—	153	1	no	Hall
14	C₃×C₁₇	D₈₇	1	1	yes	characteristic
15	D₁₇	—	261	1	no	Hall
16	C₂₉	D₁₅₃	1	1	yes	characteristic, complemented, Sylow
17	D₉	—	493	1	no	Hall
18	C₁₇	D₂₆₁	1	1	yes	characteristic, complemented, Sylow
19	C₉	D₄₉₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	1479	1	no	—
21	C₃	D₁₄₇₉	1	1	yes	characteristic
22	C₂	—	4437	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₇×C₂₉	C₂
Frattini	C₃	D₁₄₇₉
socle	C₃×C₁₇×C₂₉	D₃
LCS	G ▷ C₉×C₁₇×C₂₉
UCS	C₁

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