Subgroups — C₂×C₃×C₄×D₃ #3816

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

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×C₄	C₂	semidirect
3. C₂×C₃×Dic₃	C₂	semidirect
4. C₃×C₄×D₃	C₂	direct (N × H)
6. C₂×C₄×D₃	C₃	direct (N × H)
8. C₂×C₃×D₃	C₄	direct (N × H)
10. C₃²×C₄	C₂²	semidirect
11. C₃×Dic₃	C₂²	semidirect
17. C₂×C₃×C₄	D₃	direct (N × H)
18. C₂×C₃×C₄	C₂×C₃	semidirect
19. C₂×Dic₃	C₂×C₃	semidirect
20. C₄×D₃	C₂×C₃	direct (N × H)
21. C₂×C₃²	C₂×C₄	semidirect
23. C₃×D₃	C₂×C₄	direct (N × H)
30. C₂×D₃	C₃×C₄	direct (N × H)
34. C₃×C₄	C₂×D₃	direct (N × H)
35. C₃×C₄	C₂²×C₃	semidirect
36. Dic₃	C₂²×C₃	semidirect
37. C₃²	C₂²×C₄	semidirect
41. C₂×C₄	C₃×D₃	direct (N × H)
45. C₂×C₃	C₄×D₃	direct (N × H)
46. C₂×C₃	C₂×C₃×C₄	semidirect
49. D₃	C₂×C₃×C₄	direct (N × H)
54. C₄	C₂×C₃×D₃	direct (N × H)
56. C₃	C₂×C₄×D₃	direct (N × H)
57. C₃	C₂²×C₃×C₄	semidirect
59. C₂	C₃×C₄×D₃	direct (N × H)

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
C₂×C₃²×C₄	2
C₂×C₃×Dic₃	2
C₃×C₄×D₃	2
C₂²×C₃×C₄	3
C₂×C₄×D₃	3

Subgroups — C2×C3×C4×D3 #3816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×D₃ #3816