Subgroups — A₄×Dic₉ #88619

Order 432.

65 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×A₄	C₂	1	1	yes	maximal, characteristic
2	Dic₃×A₄	—	3	1	no	maximal
3	C₂²×Dic₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₉×A₄	C₄	1	1	yes	characteristic, complemented
5	C₃×Dic₉	—	4	1	no	maximal
6	C₂×C₃×A₄	D₃	1	1	yes	characteristic
7	C₂³×C₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₂²⋊C₉	—	2	1	no	—
9	C₂×Dic₉	—	3	1	no	—
10	C₂×Dic₉	—	3	1	no	—
11	C₂×C₃×C₉	—	4	1	no	—
12	C₂²×Dic₃	—	3	1	no	—
13	C₄×A₄	—	9	1	no	—
14	C₃×A₄	Dic₃	1	1	yes	characteristic
15	C₃×Dic₃	—	12	1	no	—
16	C₂²×C₉	—	3	1	no	—
17	C₂²×C₉	—	3	1	no	—
18	C₂²×C₉	C₃×C₄	1	1	yes	characteristic, complemented
19	C₂²⋊C₉	—	2	1	no	—
20	Dic₉	—	3	1	no	—
21	Dic₉	A₄	1	1	yes	characteristic, direct product factor
22	C₃×C₉	—	4	1	no	Sylow
23	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
24	C₂×A₄	—	2	1	no	—
25	C₂×A₄	D₉	1	1	yes	characteristic
26	C₂×Dic₃	—	9	1	no	—
27	C₂×Dic₃	—	9	1	no	—
28	C₂×C₃²	—	4	1	no	—
29	C₂×C₉	—	3	1	no	—
30	C₂×C₉	—	3	1	no	—
31	C₂×C₉	—	8	1	no	—
32	C₂×C₉	C₂×A₄	1	1	yes	characteristic
33	C₂²×C₄	—	9	1	no	Sylow
34	C₂²×C₃	—	3	1	no	—
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	C₃×Dic₃	1	1	yes	characteristic
37	A₄	—	2	1	no	—
38	A₄	Dic₉	1	1	yes	characteristic, direct product factor
39	C₃×C₄	—	36	1	no	—
40	Dic₃	—	3	1	no	—
41	Dic₃	—	9	1	no	—
42	C₃²	—	4	1	no	—
43	C₉	—	8	1	no	—
44	C₉	C₄×A₄	1	1	yes	characteristic, complemented
45	C₂³	C₃×D₉	1	1	yes	characteristic
46	C₂×C₄	—	27	1	no	—
47	C₂×C₄	—	27	1	no	—
48	C₂×C₃	—	3	1	no	—
49	C₂×C₃	—	3	1	no	—
50	C₂×C₃	—	4	1	no	—
51	C₂×C₃	—	8	1	no	—
52	C₂×C₃	D₃×A₄	1	1	yes	characteristic
53	C₂²	—	3	1	no	—
54	C₂²	—	3	1	no	—
55	C₂²	C₃×Dic₉	1	1	yes	characteristic, complemented
56	C₄	—	9	1	no	—
57	C₄	—	27	1	no	—
58	C₃	—	4	1	no	—
59	C₃	—	8	1	no	—
60	C₃	Dic₃×A₄	1	1	yes	characteristic
61	C₂	—	3	1	no	—
62	C₂	—	3	1	no	—
63	C₂	A₄×D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	A₄×D₉
commutator, hypocenter	C₂²×C₉	C₃×C₄
Frattini	C₂×C₃	D₃×A₄
Fitting, cosocle	C₂³×C₉	C₂×C₃
socle	C₂³×C₃	C₃×D₃
prime radical	C₂×C₃×A₄	D₃
LCS	G ▷ C₂²×C₉
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂²×Dic₉	C₃	semidirect
4. C₉×A₄	C₄	semidirect
18. C₂²×C₉	C₃×C₄	semidirect
21. Dic₉	A₄	direct (N × H)
38. A₄	Dic₉	direct (N × H)
44. C₉	C₄×A₄	semidirect
55. C₂²	C₃×Dic₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×A₄	2
Dic₃×A₄	3
C₂²×Dic₉	3
C₃×Dic₉	4

Subgroups — A4×Dic9 #88619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×Dic₉ #88619