Subgroups — (C₂²⋊A₄)⋊C₉ #88878

Order 432.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊A₄	C₃	1	1	yes	maximal, characteristic
2	C₂²⋊(C₂²⋊C₉)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₉×A₄	—	4	2	no	maximal
5	C₂×C₂²⋊C₉	—	3	2	no	—
6	C₂⁴×C₃	C₃²	1	1	yes	characteristic
7	C₂²⋊A₄	C₉	1	3	yes	complemented
8	C₃×A₄	—	4	2	no	—
9	C₃×A₄	—	12	1	no	—
10	C₂²×C₉	—	4	2	no	—
11	C₂²⋊C₉	—	4	2	no	—
12	C₂²⋊C₉	—	12	1	no	—
13	C₂²⋊C₉	A₄	1	2	yes	complemented
14	C₃×C₉	—	16	1	no	Sylow
15	C₂³×C₃	—	3	2	no	—
16	C₂³×C₃	—	9	1	no	—
17	C₂×C₉	—	12	2	no	—
18	C₂⁴	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₃	—	3	1	no	—
20	C₂²×C₃	—	3	1	no	—
21	C₂²×C₃	—	9	1	no	—
22	C₂²×C₃	—	9	2	no	—
23	C₂²×C₃	C₃×A₄	1	2	yes	—
24	A₄	—	4	6	no	—
25	A₄	—	12	3	no	—
26	C₃²	—	16	1	no	—
27	C₉	—	4	2	no	—
28	C₉	—	16	1	no	—
29	C₂³	—	3	2	no	—
30	C₂³	—	9	1	no	—
31	C₂×C₃	—	3	2	no	—
32	C₂×C₃	—	9	1	no	—
33	C₂²	—	3	1	no	—
34	C₂²	—	3	1	no	—
35	C₂²	—	9	1	no	—
36	C₂²	—	9	2	no	—
37	C₂²	C₉×A₄	1	2	yes	complemented
38	C₃	—	16	3	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, hypocenter	C₂⁴	C₃×C₉
Fitting, socle, cosocle	C₂⁴×C₃	C₃²
prime radical	C₃×C₂²⋊A₄	C₃
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.