Subgroups — A₄×C₃⋊Dic₃ #88980

Order 432.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×A₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊Dic₃	C₃	1	1	yes	maximal, characteristic, complemented
3	Dic₃×A₄	—	3	4	no	maximal
4	C₃²×A₄	C₄	1	1	yes	characteristic, complemented
5	C₃×C₃⋊Dic₃	—	4	1	no	maximal
6	C₂³×C₃²	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×A₄	—	2	4	no	—
8	C₂×C₃×A₄	D₃	1	4	yes	—
9	C₂×C₃⋊Dic₃	—	3	1	no	—
10	C₂×C₃⋊Dic₃	—	3	1	no	—
11	C₂×C₃³	—	4	1	no	—
12	C₂²×Dic₃	—	3	4	no	—
13	C₄×A₄	—	9	1	no	—
14	C₂²×C₃²	—	3	1	no	—
15	C₂²×C₃²	—	3	1	no	—
16	C₂²×C₃²	C₃×C₄	1	1	yes	characteristic, complemented
17	C₃×A₄	—	2	4	no	—
18	C₃×A₄	Dic₃	1	4	yes	complemented
19	C₃⋊Dic₃	—	3	1	no	—
20	C₃⋊Dic₃	A₄	1	1	yes	characteristic, direct product factor
21	C₃×Dic₃	—	12	4	no	—
22	C₃³	—	4	1	no	Sylow
23	C₂³×C₃	C₃×D₃	1	4	yes	—
24	C₂×A₄	—	2	4	no	—
25	C₂×A₄	C₃⋊D₃	1	1	yes	characteristic
26	C₂×Dic₃	—	9	4	no	—
27	C₂×Dic₃	—	9	4	no	—
28	C₂×C₃²	—	3	1	no	—
29	C₂×C₃²	—	3	1	no	—
30	C₂×C₃²	—	4	4	no	—
31	C₂×C₃²	—	8	4	no	—
32	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
33	C₂²×C₄	—	9	1	no	Sylow
34	C₂²×C₃	—	3	4	no	—
35	C₂²×C₃	—	3	4	no	—
36	C₂²×C₃	C₃×Dic₃	1	4	yes	complemented
37	A₄	—	2	4	no	—
38	A₄	C₃⋊Dic₃	1	1	yes	characteristic, direct product factor
39	C₃×C₄	—	36	1	no	—
40	Dic₃	—	3	4	no	—
41	Dic₃	—	9	4	no	—
42	C₃²	—	4	4	no	—
43	C₃²	—	8	4	no	—
44	C₃²	C₄×A₄	1	1	yes	characteristic, complemented
45	C₂³	C₃×C₃⋊D₃	1	1	yes	characteristic
46	C₂×C₄	—	27	1	no	—
47	C₂×C₄	—	27	1	no	—
48	C₂×C₃	—	3	4	no	—
49	C₂×C₃	—	3	4	no	—
50	C₂×C₃	—	4	1	no	—
51	C₂×C₃	—	8	4	no	—
52	C₂×C₃	D₃×A₄	1	4	yes	—
53	C₂²	—	3	1	no	—
54	C₂²	—	3	1	no	—
55	C₂²	C₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented
56	C₄	—	9	1	no	—
57	C₄	—	27	1	no	—
58	C₃	—	4	1	no	—
59	C₃	—	8	4	no	—
60	C₃	Dic₃×A₄	1	4	yes	complemented
61	C₂	—	3	1	no	—
62	C₂	—	3	1	no	—
63	C₂	A₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄×C₃⋊D₃
commutator, hypocenter	C₂²×C₃²	C₃×C₄
Fitting, socle, cosocle	C₂³×C₃²	C₂×C₃
prime radical	C₂×C₃²×A₄	C₂
LCS	G ▷ C₂²×C₃²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃⋊Dic₃	C₃	semidirect
4. C₃²×A₄	C₄	semidirect
16. C₂²×C₃²	C₃×C₄	semidirect
18. C₃×A₄	Dic₃	semidirect
20. C₃⋊Dic₃	A₄	direct (N × H)
36. C₂²×C₃	C₃×Dic₃	semidirect
38. A₄	C₃⋊Dic₃	direct (N × H)
44. C₃²	C₄×A₄	semidirect
55. C₂²	C₃×C₃⋊Dic₃	semidirect
60. C₃	Dic₃×A₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×A₄	2
C₂²×C₃⋊Dic₃	3
Dic₃×A₄	3
C₃×C₃⋊Dic₃	4

Subgroups — A4×C3⋊Dic3 #88980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×C₃⋊Dic₃ #88980