Subgroups — D₃×D₁₂ #3801

Order 144.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃²	C₂	1	2	yes	maximal, complemented
2	C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#626	C₂	1	2	yes	maximal, complemented
6	D₃×D₄	—	3	1	no	maximal
7	C₂×D₁₂	—	3	1	no	maximal
8	C₂×C₃⋊D₃	C₂²	1	2	yes	complemented
9	C₂×C₃×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×D₃	C₂²	1	2	yes	complemented
11	D₃²	—	2	4	no	—
12	C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
13	C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
14	C₂²×D₃	—	3	2	no	—
15	C₂²×D₃	—	3	2	no	—
16	C₃×D₄	—	3	1	no	—
17	C₂×C₃×C₄	—	3	1	no	—
18	#67	—	3	2	no	—
19	D₁₂	—	3	2	no	—
20	D₁₂	—	3	1	no	—
21	D₁₂	—	3	1	no	—
22	D₁₂	—	6	1	no	—
23	D₁₂	D₃	1	1	yes	characteristic, direct product factor
24	C₄×D₃	D₃	1	1	yes	characteristic, complemented
25	C₂×C₃²	C₂³	1	1	yes	characteristic
26	C₃⋊D₃	—	2	2	no	—
27	C₃×D₃	—	2	2	no	—
28	C₃×D₃	D₄	1	2	yes	complemented
29	C₂×D₄	—	9	1	no	Sylow
30	C₂²×C₃	—	3	1	no	—
31	C₂²×C₃	—	3	2	no	—
32	C₂×D₃	—	3	2	no	—
33	C₂×D₃	—	3	2	no	—
34	C₂×D₃	—	6	2	no	—
35	C₂×D₃	—	6	4	no	—
36	C₂×D₃	—	6	4	no	—
37	C₂×D₃	C₂×D₃	1	1	yes	characteristic
38	C₂×D₃	C₂×D₃	1	2	yes	complemented
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	—	3	1	no	—
41	C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
42	C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
43	Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
44	C₃²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
45	C₂³	—	9	2	no	—
46	D₄	—	3	1	no	—
47	D₄	—	9	2	no	—
48	D₄	—	9	1	no	—
49	C₂×C₄	—	3	1	no	—
50	C₂×C₃	—	2	1	no	—
51	C₂×C₃	—	3	2	no	—
52	C₂×C₃	—	6	2	no	—
53	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
54	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
55	D₃	—	2	2	no	—
56	D₃	—	6	2	no	—
57	D₃	—	6	2	no	—
58	D₃	—	12	2	no	—
59	D₃	D₁₂	1	2	yes	direct product factor
60	C₂²	—	3	1	no	—
61	C₂²	—	3	2	no	—
62	C₂²	—	9	2	no	—
63	C₂²	—	18	4	no	—
64	C₄	—	3	1	no	—
65	C₄	D₃²	1	1	yes	characteristic, complemented
66	C₃	—	2	1	no	—
67	C₃	C₂×D₁₂	1	1	yes	characteristic, complemented
68	C₃	D₃×D₄	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	—	6	2	no	—
71	C₂	—	18	2	no	—
72	C₂	C₂×D₃²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃²
commutator, socle, cosocle	C₂×C₃²	C₂³
Fitting	C₃²×C₄	C₂²
hypercenter	C₄	D₃²
hypocenter	C₃²	C₂×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₃²	C₂	semidirect
2. C₄⋊(C₃⋊D₃)	C₂	semidirect
3. C₃×D₁₂	C₂	semidirect
4. C₃×C₄×D₃	C₂	semidirect
5. #626	C₂	semidirect
8. C₂×C₃⋊D₃	C₂²	semidirect
10. C₂×C₃×D₃	C₂²	semidirect
12. C₃²×C₄	C₂²	semidirect
13. C₃×Dic₃	C₂²	semidirect
23. D₁₂	D₃	direct (N × H)
24. C₄×D₃	D₃	semidirect
28. C₃×D₃	D₄	semidirect
38. C₂×D₃	C₂×D₃	semidirect
41. C₃×C₄	C₂×D₃	semidirect
42. C₃×C₄	C₂×D₃	semidirect
43. Dic₃	C₂×D₃	semidirect
44. C₃²	C₂×D₄	semidirect
59. D₃	D₁₂	direct (N × H)
65. C₄	D₃²	semidirect
67. C₃	C₂×D₁₂	semidirect
68. C₃	D₃×D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃²	2
C₄⋊(C₃⋊D₃)	2
C₃×D₁₂	2
C₃×C₄×D₃	2
#626	2
D₃×D₄	3
C₂×D₁₂	3

Subgroups — D3×D12 #3801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₂ #3801