Subgroups — D₅₄₉₉ #24926951

Order 10998.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₈₃₃	—	3	1	no	maximal
3	C₃×C₁₃×C₄₇	D₃	1	1	yes	characteristic
4	D₆₁₁	—	9	1	no	Hall
5	D₄₂₃	—	13	1	no	maximal, Hall
6	C₁₃×C₄₇	D₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₄₇	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₁₄₁	—	39	1	no	—
9	D₁₁₇	—	47	1	no	maximal, Hall
10	C₃×C₄₇	D₃₉	1	1	yes	characteristic
11	C₉×C₁₃	D₄₇	1	1	yes	characteristic, complemented, Hall
12	D₄₇	—	117	1	no	Hall
13	D₃₉	—	141	1	no	—
14	C₄₇	D₁₁₇	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₃	D₁₄₁	1	1	yes	characteristic
16	D₁₃	—	423	1	no	Hall
17	D₉	—	611	1	no	Hall
18	C₁₃	D₄₂₃	1	1	yes	characteristic, complemented, Sylow
19	C₉	D₆₁₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	1833	1	no	—
21	C₃	D₁₈₃₃	1	1	yes	characteristic
22	C₂	—	5499	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃×C₄₇	C₂
Frattini	C₃	D₁₈₃₃
socle	C₃×C₁₃×C₄₇	D₃
LCS	G ▷ C₉×C₁₃×C₄₇
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.