Subgroups — C₃×D₃×D₄ #3819

Order 144.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₃	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂³×C₃
Frattini	C₂	C₂²×C₃×D₃
Fitting	C₃²×D₄	C₂
socle	C₂×C₃²	C₂³
hypercenter	C₃×D₄	D₃
hypocenter	C₃	C₂×C₃×D₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₃	C₂	semidirect
2. C₃²×D₄	C₂	semidirect
3. C₃×#67	C₂	semidirect
4. C₃×D₁₂	C₂	semidirect
5. C₃×C₄×D₃	C₂	semidirect
7. D₃×D₄	C₃	direct (N × H)
8. C₂²×C₃²	C₂²	semidirect
11. C₂×C₃×D₃	C₂²	semidirect
12. C₃²×C₄	C₂²	semidirect
13. C₃×Dic₃	C₂²	semidirect
15. C₂²×D₃	C₂×C₃	semidirect
19. C₃×D₄	D₃	direct (N × H)
20. C₃×D₄	C₂×C₃	semidirect
22. #67	C₂×C₃	semidirect
23. D₁₂	C₂×C₃	semidirect
24. C₄×D₃	C₂×C₃	semidirect
28. C₃×D₃	D₄	direct (N × H)
34. C₂²×C₃	C₂×D₃	semidirect
35. C₂²×C₃	C₂²×C₃	semidirect
38. C₂×D₃	C₂²×C₃	semidirect
41. C₃×C₄	C₂×D₃	semidirect
42. C₃×C₄	C₂²×C₃	semidirect
43. Dic₃	C₂²×C₃	semidirect
44. C₃²	C₂×D₄	semidirect
48. D₄	C₃×D₃	direct (N × H)
59. D₃	C₃×D₄	direct (N × H)
63. C₂²	C₂×C₃×D₃	semidirect
65. C₄	C₂×C₃×D₃	semidirect
67. C₃	D₃×D₄	direct (N × H)
68. C₃	C₂×C₃×D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃	2
C₃²×D₄	2
C₃×#67	2
C₃×D₁₂	2
C₃×C₄×D₃	2
C₂×C₃×D₄	3
D₃×D₄	3

Subgroups — C3×D3×D4 #3819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×D₄ #3819