Subgroups — C₃×A₄² #89103

Order 432.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊A₄	C₃	1	2	yes	maximal, complemented
2	C₂²×C₃×A₄	C₃	1	2	yes	maximal, complemented
3	A₄²	C₃	1	9	yes	maximal, direct product factor
4	C₃²×A₄	—	4	2	no	maximal
5	C₂×C₃×A₄	—	3	2	no	—
6	C₂⁴×C₃	C₃²	1	1	yes	characteristic, complemented
7	C₂²⋊A₄	C₃²	1	6	yes	complemented
8	C₂²×A₄	C₃²	1	6	yes	complemented
9	C₂²×C₃²	—	4	2	no	—
10	C₃×A₄	—	4	4	no	—
11	C₃×A₄	—	4	18	no	—
12	C₃×A₄	—	12	2	no	—
13	C₃×A₄	A₄	1	2	yes	direct product factor
14	C₃³	—	16	1	no	Sylow
15	C₂³×C₃	—	3	2	no	—
16	C₂³×C₃	—	9	1	no	—
17	C₂×A₄	—	3	6	no	—
18	C₂×C₃²	—	12	2	no	—
19	C₂⁴	C₃³	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₃	—	3	2	no	—
21	C₂²×C₃	—	4	6	no	—
22	C₂²×C₃	—	9	1	no	—
23	C₂²×C₃	—	9	2	no	—
24	C₂²×C₃	C₃×A₄	1	2	yes	complemented
25	A₄	—	4	12	no	—
26	A₄	—	12	6	no	—
27	A₄	C₃×A₄	1	6	yes	direct product factor
28	C₃²	—	4	2	no	—
29	C₃²	—	16	9	no	—
30	C₃²	—	16	2	no	—
31	C₂³	—	3	2	no	—
32	C₂³	—	9	1	no	—
33	C₂×C₃	—	3	2	no	—
34	C₂×C₃	—	9	1	no	—
35	C₂×C₃	—	12	6	no	—
36	C₂²	—	3	2	no	—
37	C₂²	—	9	1	no	—
38	C₂²	—	9	2	no	—
39	C₂²	C₃²×A₄	1	2	yes	complemented
40	C₃	—	4	6	no	—
41	C₃	—	16	6	no	—
42	C₃	A₄²	1	1	yes	characteristic, direct product factor
43	C₂	—	3	2	no	—
44	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₃	A₄²
commutator, cosocle, hypocenter	C₂⁴	C₃³
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃	C₃²
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₃

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.