Subgroups — C₂×D₃×Dic₃ #3803

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×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×Dic₃	C₂	1	4	yes	maximal, direct product factor
5	C₂²×Dic₃	—	3	1	no	maximal
6	C₂×C₄×D₃	—	3	1	no	maximal
7	C₂²×C₃²	C₂²	1	1	yes	characteristic
8	C₂×C₃×D₃	C₄	1	4	yes	complemented
9	C₂×C₃×D₃	C₂²	1	2	yes	—
10	C₃⋊Dic₃	C₂²	1	2	yes	complemented
11	C₃×Dic₃	C₂²	1	2	yes	complemented
12	C₂³×C₃	—	3	1	no	—
13	C₂²×D₃	D₃	1	1	yes	characteristic
14	C₂×C₃×C₄	—	3	1	no	—
15	C₂×Dic₃	—	3	1	no	—
16	C₂×Dic₃	—	3	1	no	—
17	C₂×Dic₃	—	3	4	no	—
18	C₂×Dic₃	—	6	1	no	—
19	C₂×Dic₃	D₃	1	1	yes	characteristic, direct product factor
20	C₄×D₃	—	3	4	no	—
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	complemented
24	C₂²×C₄	—	9	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	C₂×D₃	1	1	yes	characteristic
30	C₂×D₃	Dic₃	1	4	yes	direct product factor
31	C₂×D₃	C₂×D₃	1	2	yes	—
32	C₃×C₄	—	3	2	no	—
33	Dic₃	—	3	2	no	—
34	Dic₃	—	3	2	no	—
35	Dic₃	—	6	2	no	—
36	Dic₃	C₂×D₃	1	2	yes	direct product factor
37	C₃²	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
38	C₂³	—	3	1	no	—
39	C₂×C₄	—	3	1	no	—
40	C₂×C₄	—	9	4	no	—
41	C₂×C₄	—	9	1	no	—
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	complemented
46	C₂×C₃	C₂×Dic₃	1	2	yes	complemented
47	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
48	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
49	D₃	C₂×Dic₃	1	4	yes	direct product factor
50	C₂²	—	3	4	no	—
51	C₂²	—	3	2	no	—
52	C₂²	D₃²	1	1	yes	characteristic
53	C₄	—	3	2	no	—
54	C₄	—	9	2	no	—
55	C₃	—	2	1	no	—
56	C₃	C₂×C₄×D₃	1	1	yes	characteristic, complemented
57	C₃	C₂²×Dic₃	1	1	yes	characteristic, complemented
58	C₂	—	3	4	no	—
59	C₂	D₃×Dic₃	1	2	yes	direct product factor
60	C₂	C₂×D₃²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃²
commutator, hypocenter	C₃²	C₂²×C₄
Frattini	C₂	C₂×D₃²
Fitting, socle	C₂²×C₃²	C₂²
prime radical	C₂²×C₃×D₃	C₂
cosocle	C₂×C₃²	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²

Complements

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

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

Subgroups — C2×D3×Dic3 #3803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×Dic₃ #3803