Subgroups — C₃×C₄²×D₃ #63994

Order 288.

231 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₃	C₂	1	3	yes	maximal
2	C₃²×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×Dic₃	C₂	1	3	yes	maximal, complemented
4	C₂×C₃×C₄²	—	3	1	no	maximal
5	C₄²×D₃	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃×D₃	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₄	C₂²	1	3	yes	—
8	C₂×C₃×Dic₃	C₂²	1	3	yes	—
9	C₃×C₄×D₃	C₄	1	12	yes	direct product factor
10	C₂²×C₃×C₄	—	3	3	no	—
11	C₂×C₄×D₃	C₂×C₃	1	3	yes	—
12	C₃×C₄²	—	2	1	no	—
13	C₃×C₄²	—	3	3	no	—
14	C₃×C₄²	D₃	1	1	yes	characteristic, direct product factor
15	C₃×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
16	C₄×Dic₃	C₂×C₃	1	3	yes	complemented
17	C₂²×C₃²	C₂³	1	1	yes	characteristic
18	C₂×C₃×D₃	C₂×C₄	1	6	yes	—
19	C₃²×C₄	C₂×C₄	1	6	yes	complemented
20	C₃×Dic₃	C₂×C₄	1	6	yes	complemented
21	C₂×C₄²	—	3	1	no	Sylow
22	C₂³×C₃	—	3	1	no	—
23	C₂²×D₃	C₂²×C₃	1	1	yes	characteristic
24	C₂×C₃×C₄	—	2	3	no	—
25	C₂×C₃×C₄	—	3	3	no	—
26	C₂×C₃×C₄	—	3	12	no	—
27	C₂×C₃×C₄	C₂×D₃	1	3	yes	—
28	C₂×C₃×C₄	C₂²×C₃	1	3	yes	—
29	C₂×Dic₃	C₂²×C₃	1	3	yes	—
30	C₄×D₃	C₃×C₄	1	12	yes	direct product factor
31	C₂×C₃²	C₂²×C₄	1	3	yes	—
32	C₃×D₃	C₄²	1	4	yes	direct product factor
33	C₂²×C₄	—	3	3	no	—
34	C₄²	—	3	3	no	—
35	C₄²	C₃×D₃	1	1	yes	characteristic, direct product factor
36	C₂²×C₃	—	2	1	no	—
37	C₂²×C₃	—	3	6	no	—
38	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
39	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
40	C₂×D₃	C₂×C₃×C₄	1	6	yes	—
41	C₃×C₄	—	2	6	no	—
42	C₃×C₄	—	3	6	no	—
43	C₃×C₄	C₄×D₃	1	6	yes	direct product factor
44	C₃×C₄	C₂×C₃×C₄	1	6	yes	complemented
45	Dic₃	C₂×C₃×C₄	1	6	yes	complemented
46	C₃²	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
47	C₂³	—	3	1	no	—
48	C₂×C₄	—	3	3	no	—
49	C₂×C₄	—	3	12	no	—
50	C₂×C₄	C₂×C₃×D₃	1	3	yes	—
51	C₂×C₃	—	2	3	no	—
52	C₂×C₃	—	3	4	no	—
53	C₂×C₃	C₂×C₄×D₃	1	3	yes	—
54	C₂×C₃	C₂²×C₃×C₄	1	3	yes	—
55	D₃	C₃×C₄²	1	4	yes	direct product factor
56	C₂²	—	3	6	no	—
57	C₂²	C₂²×C₃×D₃	1	1	yes	characteristic
58	C₄	—	3	6	no	—
59	C₄	C₃×C₄×D₃	1	6	yes	direct product factor
60	C₃	—	2	1	no	—
61	C₃	C₄²×D₃	1	1	yes	characteristic, direct product factor
62	C₃	C₂×C₃×C₄²	1	1	yes	characteristic, complemented
63	C₂	—	3	4	no	—
64	C₂	C₂×C₃×C₄×D₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₃×C₄²	D₃
commutator, hypocenter	C₃	C₂×C₃×C₄²
Frattini	C₂²	C₂²×C₃×D₃
Fitting	C₃²×C₄²	C₂
socle	C₂²×C₃²	C₂³
prime radical	C₂²×C₃×D₃	C₂²
cosocle	C₂²×C₃	C₂³×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄²	C₂	semidirect
3. C₃×C₄×Dic₃	C₂	semidirect
5. C₄²×D₃	C₃	direct (N × H)
9. C₃×C₄×D₃	C₄	direct (N × H)
14. C₃×C₄²	D₃	direct (N × H)
15. C₃×C₄²	C₂×C₃	semidirect
16. C₄×Dic₃	C₂×C₃	semidirect
19. C₃²×C₄	C₂×C₄	semidirect
20. C₃×Dic₃	C₂×C₄	semidirect
30. C₄×D₃	C₃×C₄	direct (N × H)
32. C₃×D₃	C₄²	direct (N × H)
35. C₄²	C₃×D₃	direct (N × H)
43. C₃×C₄	C₄×D₃	direct (N × H)
44. C₃×C₄	C₂×C₃×C₄	semidirect
45. Dic₃	C₂×C₃×C₄	semidirect
46. C₃²	C₂×C₄²	semidirect
55. D₃	C₃×C₄²	direct (N × H)
59. C₄	C₃×C₄×D₃	direct (N × H)
61. C₃	C₄²×D₃	direct (N × H)
62. C₃	C₂×C₃×C₄²	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×D₃	2
C₃²×C₄²	2
C₃×C₄×Dic₃	2
C₂×C₃×C₄²	3
C₄²×D₃	3

Subgroups — C3×C42×D3 #63994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄²×D₃ #63994