Subgroups — (C₃×A₄)⋊A₄ #88879

Order 432.

90 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	C₂²⋊H(3,𝔽₃)	—	4	2	no	maximal
4	C₂×C₃×A₄	—	3	2	no	—
5	C₂⁴×C₃	C₃²	1	1	yes	characteristic
6	C₂²⋊A₄	—	3	2	no	—
7	C₂²×A₄	—	3	2	no	—
8	C₂²×C₃²	—	4	2	no	—
9	C₃×A₄	—	4	4	no	—
10	C₃×A₄	—	12	2	no	—
11	C₃×A₄	A₄	1	2	yes	complemented
12	H(3,𝔽₃)	—	16	1	no	Sylow
13	C₂³×C₃	—	3	2	no	—
14	C₂³×C₃	—	9	1	no	—
15	C₂×A₄	—	3	6	no	—
16	C₂×C₃²	—	12	2	no	—
17	C₂⁴	H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₃	—	3	2	no	—
19	C₂²×C₃	—	9	1	no	—
20	C₂²×C₃	—	9	2	no	—
21	C₂²×C₃	—	12	2	no	—
22	C₂²×C₃	C₃×A₄	1	2	yes	—
23	A₄	—	3	2	no	—
24	A₄	—	12	6	no	—
25	A₄	—	12	4	no	—
26	C₃²	—	4	2	no	—
27	C₃²	—	16	2	no	—
28	C₂³	—	3	2	no	—
29	C₂³	—	9	1	no	—
30	C₂×C₃	—	3	2	no	—
31	C₂×C₃	—	9	1	no	—
32	C₂×C₃	—	12	6	no	—
33	C₂²	—	3	2	no	—
34	C₂²	—	9	1	no	—
35	C₂²	—	9	2	no	—
36	C₂²	C₂²⋊H(3,𝔽₃)	1	2	yes	complemented
37	C₃	—	12	2	no	—
38	C₃	—	48	2	no	—
39	C₃	A₄²	1	1	yes	characteristic
40	C₂	—	3	2	no	—
41	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	A₄²
commutator, Fitting, socle, cosocle	C₂⁴×C₃	C₃²
hypocenter	C₂⁴	H(3,𝔽₃)
LCS	G ▷ C₂⁴×C₃ ▷ 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.