Subgroups — C₃×D₃×A₄ #6329

Order 216.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₃²×A₄	C₂	semidirect
2. C₂²×C₃×D₃	C₃	semidirect
4. D₃×A₄	C₃	direct (N × H)
6. C₂²×C₃²	C₂×C₃	semidirect
11. C₃×A₄	D₃	direct (N × H)
12. C₃×A₄	C₂×C₃	semidirect
15. C₂²×D₃	C₃²	semidirect
21. C₃×D₃	A₄	direct (N × H)
25. C₂²×C₃	C₃×D₃	semidirect
26. C₂²×C₃	C₂×C₃²	semidirect
30. A₄	C₃×D₃	direct (N × H)
35. C₃²	C₂×A₄	semidirect
44. D₃	C₃×A₄	direct (N × H)
47. C₂²	C₃²×D₃	semidirect
51. C₃	D₃×A₄	direct (N × H)
52. C₃	C₂×C₃×A₄	semidirect

Maximal subgroups

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

subgroup	index
C₃²×A₄	2
C₂²×C₃×D₃	3
C₂×C₃×A₄	3
D₃×A₄	3
C₃²×D₃	4

Subgroups — C3×D3×A4 #6329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×A₄ #6329