Subgroups — A₄⋊D₈₃ #14521950

Order 1992.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₈₃	—	3	1	no	maximal, Hall
3	D₂₄₉	—	4	1	no	maximal
4	C₂²×C₈₃	D₃	1	1	yes	characteristic, complemented
5	C₂×D₈₃	—	3	1	no	—
6	Dic₈₃	—	3	1	no	—
7	C₃×C₈₃	—	4	1	no	Hall
8	C₂×C₈₃	—	3	1	no	—
9	D₈₃	—	6	1	no	—
10	C₈₃	S₄	1	1	yes	characteristic, complemented, Sylow
11	S₄	—	83	1	no	maximal, Hall
12	A₄	D₈₃	1	1	yes	characteristic, complemented
13	D₄	—	249	1	no	Sylow
14	D₃	—	332	1	no	—
15	C₂²	—	249	1	no	—
16	C₂²	D₂₄₉	1	1	yes	characteristic, complemented
17	C₄	—	249	1	no	—
18	C₃	—	4	1	no	Sylow
19	C₂	—	3	1	no	—
20	C₂	—	498	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	A₄×C₈₃	C₂
Fitting, socle	C₂²×C₈₃	D₃
LCS	G ▷ A₄×C₈₃
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.