Subgroups — C₃²×C₂²⋊A₄ #89124

Order 432.

316 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂²⋊A₄	C₃	1	12	yes	maximal, direct product factor
3	C₃²×A₄	—	4	5	no	maximal
4	C₂³×C₃²	—	3	5	no	—
5	C₂⁴×C₃	C₃²	1	4	yes	complemented
6	C₂²⋊A₄	C₃²	1	9	yes	direct product factor
7	C₂²×C₃²	—	3	10	no	—
8	C₂²×C₃²	A₄	1	5	yes	complemented
9	C₃×A₄	—	4	60	no	—
10	C₃³	—	16	1	no	Sylow
11	C₂³×C₃	—	3	20	no	—
12	C₂×C₃²	—	3	5	no	—
13	C₂⁴	C₃³	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₃	—	3	40	no	—
15	C₂²×C₃	C₃×A₄	1	20	yes	complemented
16	A₄	—	4	45	no	—
17	C₃²	—	16	12	no	—
18	C₃²	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
19	C₂³	—	3	5	no	—
20	C₂×C₃	—	3	20	no	—
21	C₂²	—	3	10	no	—
22	C₂²	C₃²×A₄	1	5	yes	complemented
23	C₃	—	16	9	no	—
24	C₃	C₃×C₂²⋊A₄	1	4	yes	direct product factor
25	C₂	—	3	5	no	—

	subgroup	G/H
center, hypercenter	C₃²	C₂²⋊A₄
commutator, cosocle, hypocenter	C₂⁴	C₃³
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃²	C₃
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₃²

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.