Subgroups — Dic₅₈₄₇ #37552669

Order 23388.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉₄₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₉₄₉	—	3	1	no	maximal, Hall
3	C₃×C₁₉₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉₄₉	D₃	1	1	yes	characteristic
5	C₁₉₄₉	Dic₃	1	1	yes	characteristic, complemented, Sylow
6	Dic₃	—	1949	1	no	maximal, Hall
7	C₂×C₃	D₁₉₄₉	1	1	yes	characteristic
8	C₄	—	5847	1	no	Sylow
9	C₃	Dic₁₉₄₉	1	1	yes	characteristic, complemented, Sylow
10	C₂	D₅₈₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅₈₄₇
commutator, hypocenter	C₃×C₁₉₄₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₉₄₉	C₂
LCS	G ▷ C₃×C₁₉₄₉
UCS	C₁ ◁ C₂

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.