Subgroups — C₂×D₃×A₄ #3847

Order 144.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×A₄	C₂	1	2	yes	maximal, direct product factor
3	C₂³×D₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×A₄	—	3	1	no	maximal
5	C₂×C₃×D₃	—	4	1	no	maximal
6	C₃×A₄	C₂²	1	1	yes	characteristic, complemented
7	C₂³×C₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂²×D₃	—	3	1	no	—
9	C₂²×D₃	—	3	1	no	—
10	C₂²×D₃	—	3	2	no	—
11	C₂²×D₃	C₂×C₃	1	2	yes	complemented
12	C₂×A₄	—	2	1	no	—
13	C₂×A₄	—	3	2	no	—
14	C₂×A₄	D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃²	—	4	1	no	—
16	C₃×D₃	—	4	2	no	—
17	C₂⁴	—	3	1	no	Sylow
18	C₂²×C₃	—	3	1	no	—
19	C₂²×C₃	—	3	1	no	—
20	C₂²×C₃	—	12	1	no	—
21	C₂²×C₃	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂×D₃	—	3	2	no	—
23	C₂×D₃	—	3	1	no	—
24	C₂×D₃	—	3	2	no	—
25	C₂×D₃	—	3	2	no	—
26	C₂×D₃	—	3	2	no	—
27	C₂×D₃	A₄	1	1	yes	characteristic, direct product factor
28	A₄	—	2	1	no	—
29	A₄	C₂×D₃	1	1	yes	characteristic, direct product factor
30	C₃²	—	4	1	no	Sylow
31	C₂³	—	3	2	no	—
32	C₂³	—	9	1	no	—
33	C₂³	—	9	2	no	—
34	C₂³	—	9	1	no	—
35	C₂³	C₃×D₃	1	1	yes	characteristic, complemented
36	C₂×C₃	—	3	1	no	—
37	C₂×C₃	—	3	1	no	—
38	C₂×C₃	—	4	1	no	—
39	C₂×C₃	—	8	1	no	—
40	C₂×C₃	—	12	2	no	—
41	C₂×C₃	C₂×A₄	1	1	yes	characteristic, complemented
42	D₃	—	3	2	no	—
43	D₃	C₂×A₄	1	2	yes	direct product factor
44	C₂²	—	3	1	no	—
45	C₂²	—	3	1	no	—
46	C₂²	—	3	1	no	—
47	C₂²	—	9	2	no	—
48	C₂²	—	9	2	no	—
49	C₂²	—	9	2	no	—
50	C₂²	—	9	2	no	—
51	C₂²	—	9	1	no	—
52	C₂²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
53	C₃	—	4	1	no	—
54	C₃	—	8	1	no	—
55	C₃	C₂²×A₄	1	1	yes	characteristic, complemented
56	C₂	—	3	1	no	—
57	C₂	—	3	1	no	—
58	C₂	—	3	2	no	—
59	C₂	—	9	2	no	—
60	C₂	D₃×A₄	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×A₄	C₂	semidirect
2. D₃×A₄	C₂	direct (N × H)
3. C₂³×D₃	C₃	semidirect
6. C₃×A₄	C₂²	semidirect
7. C₂³×C₃	C₂×C₃	semidirect
11. C₂²×D₃	C₂×C₃	semidirect
14. C₂×A₄	D₃	direct (N × H)
21. C₂²×C₃	C₂²×C₃	semidirect
27. C₂×D₃	A₄	direct (N × H)
29. A₄	C₂×D₃	direct (N × H)
35. C₂³	C₃×D₃	semidirect
41. C₂×C₃	C₂×A₄	semidirect
43. D₃	C₂×A₄	direct (N × H)
52. C₂²	C₂×C₃×D₃	semidirect
55. C₃	C₂²×A₄	semidirect
60. C₂	D₃×A₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×A₄	2
D₃×A₄	2
C₂³×D₃	3
C₂²×A₄	3
C₂×C₃×D₃	4

Subgroups — C2×D3×A4 #3847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×A₄ #3847