Subgroups — A₄² #3841

Order 144.

41 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊A₄	C₃	1	2	yes	maximal, complemented
2	C₂²×A₄	C₃	1	2	yes	maximal, complemented
3	C₃×A₄	—	4	2	no	maximal
4	C₂×A₄	—	3	2	no	—
5	C₂⁴	C₃²	1	1	yes	characteristic, complemented, Sylow
6	C₂²×C₃	—	4	2	no	—
7	A₄	—	4	4	no	—
8	A₄	—	12	2	no	—
9	A₄	A₄	1	2	yes	direct product factor
10	C₃²	—	16	1	no	Sylow
11	C₂³	—	3	2	no	—
12	C₂³	—	9	1	no	—
13	C₂×C₃	—	12	2	no	—
14	C₂²	—	3	2	no	—
15	C₂²	—	9	1	no	—
16	C₂²	—	9	2	no	—
17	C₂²	C₃×A₄	1	2	yes	complemented
18	C₃	—	4	2	no	—
19	C₃	—	16	2	no	—
20	C₂	—	3	2	no	—
21	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂⁴	C₃²
LCS	G ▷ C₂⁴
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.