Subgroups — C₂×Dic₃×C₃⋊D₃ #89030

Order 432.

388 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃×C₃⋊D₃	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄×C₃⋊D₃	—	3	1	no	maximal
6	C₂×D₃×Dic₃	—	3	4	no	maximal
7	C₂²×C₃³	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₃⋊D₃	C₄	1	4	yes	complemented
9	C₂×C₃×C₃⋊D₃	C₂²	1	2	yes	—
10	C₃⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
11	C₃²×Dic₃	C₂²	1	2	yes	complemented
12	C₂²×C₃⋊D₃	D₃	1	1	yes	characteristic
13	C₂²×C₃×D₃	—	3	4	no	—
14	C₂×C₃²×C₄	—	3	1	no	—
15	C₂×C₃⋊Dic₃	—	3	1	no	—
16	C₂×C₃⋊Dic₃	—	3	4	no	—
17	C₂×C₃⋊Dic₃	—	6	4	no	—
18	C₄×C₃⋊D₃	—	3	4	no	—
19	C₂×C₃×Dic₃	D₃	1	4	yes	complemented
20	D₃×Dic₃	—	3	16	no	—
21	C₂×C₃³	C₂×C₄	1	2	yes	complemented
22	C₂×C₃³	C₂³	1	1	yes	characteristic
23	C₃×C₃⋊D₃	C₂×C₄	1	4	yes	complemented
24	C₂²×Dic₃	—	9	1	no	—
25	C₂×C₄×D₃	—	9	4	no	—
26	C₂²×C₃²	—	2	4	no	—
27	C₂²×C₃²	C₂×D₃	1	4	yes	—
28	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
29	C₂×C₃⋊D₃	Dic₃	1	4	yes	direct product factor
30	C₂×C₃⋊D₃	C₂×D₃	1	2	yes	—
31	C₂×C₃×D₃	—	3	16	no	—
32	C₂×C₃×D₃	—	3	8	no	—
33	C₃²×C₄	—	3	2	no	—
34	C₃⋊Dic₃	—	3	2	no	—
35	C₃⋊Dic₃	—	3	8	no	—
36	C₃⋊Dic₃	—	6	8	no	—
37	C₃×Dic₃	C₂×D₃	1	8	yes	complemented
38	C₃³	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
39	C₂³×C₃	—	9	1	no	—
40	C₂²×D₃	—	3	4	no	—
41	C₂×C₃×C₄	—	3	4	no	—
42	C₂×Dic₃	—	9	4	no	—
43	C₂×Dic₃	—	9	1	no	—
44	C₂×Dic₃	—	9	4	no	—
45	C₂×Dic₃	—	18	4	no	—
46	C₂×Dic₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
47	C₄×D₃	—	9	16	no	—
48	C₂×C₃²	—	2	8	no	—
49	C₂×C₃²	—	2	4	no	—
50	C₂×C₃²	C₄×D₃	1	8	yes	complemented
51	C₂×C₃²	C₂×Dic₃	1	2	yes	complemented
52	C₂×C₃²	C₂²×D₃	1	4	yes	—
53	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
54	C₃⋊D₃	C₂×Dic₃	1	4	yes	direct product factor
55	C₃×D₃	—	3	16	no	—
56	C₂²×C₄	—	27	1	no	Sylow
57	C₂²×C₃	—	2	4	no	—
58	C₂²×C₃	—	9	4	no	—
59	C₂²×C₃	—	9	2	no	—
60	C₂²×C₃	D₃²	1	4	yes	—
61	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
62	C₂×D₃	—	3	16	no	—
63	C₂×D₃	—	3	8	no	—
64	C₃×C₄	—	3	8	no	—
65	Dic₃	—	9	8	no	—
66	Dic₃	—	9	2	no	—
67	Dic₃	—	18	8	no	—
68	Dic₃	C₂×C₃⋊D₃	1	2	yes	direct product factor
69	C₃²	—	2	4	no	—
70	C₃²	C₂×C₄×D₃	1	4	yes	complemented
71	C₃²	C₂²×Dic₃	1	1	yes	characteristic, complemented
72	C₂³	—	9	1	no	—
73	C₂×C₄	—	3	1	no	—
74	C₂×C₄	—	27	4	no	—
75	C₂×C₄	—	27	1	no	—
76	C₂×C₃	—	2	8	no	—
77	C₂×C₃	—	2	4	no	—
78	C₂×C₃	—	9	4	no	—
79	C₂×C₃	D₃×Dic₃	1	8	yes	complemented
80	C₂×C₃	C₄×C₃⋊D₃	1	2	yes	complemented
81	C₂×C₃	C₂×D₃²	1	4	yes	—
82	C₂×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
83	D₃	—	3	16	no	—
84	C₂²	—	9	4	no	—
85	C₂²	—	9	2	no	—
86	C₂²	D₃×C₃⋊D₃	1	1	yes	characteristic
87	C₄	—	3	2	no	—
88	C₄	—	27	2	no	—
89	C₃	—	2	4	no	—
90	C₃	C₂×D₃×Dic₃	1	4	yes	complemented
91	C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic, complemented
92	C₂	—	9	4	no	—
93	C₂	Dic₃×C₃⋊D₃	1	2	yes	direct product factor
94	C₂	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×C₃⋊D₃
commutator, hypocenter	C₃³	C₂²×C₄
Frattini	C₂	C₂×D₃×C₃⋊D₃
Fitting, socle	C₂²×C₃³	C₂²
prime radical	C₂²×C₃×C₃⋊D₃	C₂
cosocle	C₂×C₃³	C₂³
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊(C₃⋊Dic₃)	C₂	semidirect
3. C₂×C₃²×Dic₃	C₂	semidirect
4. Dic₃×C₃⋊D₃	C₂	direct (N × H)
8. C₂×C₃×C₃⋊D₃	C₄	semidirect
10. C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
11. C₃²×Dic₃	C₂²	semidirect
19. C₂×C₃×Dic₃	D₃	semidirect
21. C₂×C₃³	C₂×C₄	semidirect
23. C₃×C₃⋊D₃	C₂×C₄	semidirect
29. C₂×C₃⋊D₃	Dic₃	direct (N × H)
37. C₃×Dic₃	C₂×D₃	semidirect
38. C₃³	C₂²×C₄	semidirect
46. C₂×Dic₃	C₃⋊D₃	direct (N × H)
50. C₂×C₃²	C₄×D₃	semidirect
51. C₂×C₃²	C₂×Dic₃	semidirect
54. C₃⋊D₃	C₂×Dic₃	direct (N × H)
68. Dic₃	C₂×C₃⋊D₃	direct (N × H)
70. C₃²	C₂×C₄×D₃	semidirect
71. C₃²	C₂²×Dic₃	semidirect
79. C₂×C₃	D₃×Dic₃	semidirect
80. C₂×C₃	C₄×C₃⋊D₃	semidirect
90. C₃	C₂×D₃×Dic₃	semidirect
91. C₃	C₂×C₄×C₃⋊D₃	semidirect
93. C₂	Dic₃×C₃⋊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×C₃⋊D₃	2
C₂×C₃⋊(C₃⋊Dic₃)	2
C₂×C₃²×Dic₃	2
Dic₃×C₃⋊D₃	2
C₂×C₄×C₃⋊D₃	3
C₂×D₃×Dic₃	3

Subgroups — C2×Dic3×C3⋊D3 #89030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃×C₃⋊D₃ #89030