Subgroups — C₃⋊D₃×C₃⋊Dic₃ #10620149

Order 648.

552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊(C₃⋊Dic₃))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃×C₃⋊D₃	—	3	4	no	maximal
5	D₃×C₃⋊Dic₃	—	3	4	no	maximal
6	C₂×C₃⁴	C₂²	1	1	yes	characteristic
7	C₃²×C₃⋊D₃	C₄	1	2	yes	complemented
8	C₂×C₃×C₃⋊D₃	D₃	1	4	yes	—
9	C₂×C₃²×D₃	—	3	4	no	—
10	C₃⋊(C₃⋊Dic₃)	—	3	4	no	—
11	C₃⋊(C₃⋊Dic₃)	—	3	4	no	—
12	C₃⋊(C₃⋊Dic₃)	—	6	16	no	—
13	C₃×C₃⋊Dic₃	D₃	1	4	yes	complemented
14	C₃²×Dic₃	—	3	4	no	—
15	C₃⁴	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃⋊Dic₃	—	9	1	no	—
17	C₄×C₃⋊D₃	—	9	1	no	—
18	D₃×Dic₃	—	9	16	no	—
19	C₂×C₃³	—	2	16	no	—
20	C₂×C₃³	C₂×D₃	1	4	yes	—
21	C₂×C₃³	C₂×D₃	1	4	yes	—
22	C₃×C₃⋊D₃	Dic₃	1	8	yes	complemented
23	C₃²×D₃	—	3	8	no	—
24	C₂²×C₃²	—	9	1	no	—
25	C₂×C₃⋊D₃	C₃⋊D₃	1	1	yes	characteristic
26	C₂×C₃×D₃	—	3	16	no	—
27	C₃²×C₄	—	9	1	no	—
28	C₃⋊Dic₃	—	9	1	no	—
29	C₃⋊Dic₃	—	9	1	no	—
30	C₃⋊Dic₃	—	9	16	no	—
31	C₃⋊Dic₃	—	18	16	no	—
32	C₃⋊Dic₃	—	18	16	no	—
33	C₃⋊Dic₃	—	18	24	no	—
34	C₃⋊Dic₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
35	C₃×Dic₃	—	3	16	no	—
36	C₃³	—	2	16	no	—
37	C₃³	C₄×D₃	1	4	yes	complemented
38	C₃³	C₂×Dic₃	1	4	yes	complemented
39	C₂×Dic₃	—	27	4	no	—
40	C₄×D₃	—	27	4	no	—
41	C₂×C₃²	—	2	24	no	—
42	C₂×C₃²	—	2	16	no	—
43	C₂×C₃²	—	2	16	no	—
44	C₂×C₃²	—	9	2	no	—
45	C₂×C₃²	D₃²	1	16	yes	—
46	C₂×C₃²	C₂×C₃⋊D₃	1	1	yes	characteristic
47	C₂×C₃²	C₂×C₃⋊D₃	1	1	yes	characteristic
48	C₃⋊D₃	C₃⋊Dic₃	1	2	yes	direct product factor
49	C₃×D₃	—	3	32	no	—
50	C₂²×C₃	—	9	4	no	—
51	C₂×D₃	—	3	4	no	—
52	C₃×C₄	—	9	4	no	—
53	Dic₃	—	3	4	no	—
54	Dic₃	—	27	4	no	—
55	Dic₃	—	27	4	no	—
56	Dic₃	—	54	16	no	—
57	C₃²	—	2	24	no	—
58	C₃²	—	2	16	no	—
59	C₃²	—	2	16	no	—
60	C₃²	D₃×Dic₃	1	16	yes	complemented
61	C₃²	C₄×C₃⋊D₃	1	1	yes	characteristic, complemented
62	C₃²	C₂×C₃⋊Dic₃	1	1	yes	characteristic, complemented
63	C₂×C₄	—	81	1	no	Sylow
64	C₂×C₃	—	2	16	no	—
65	C₂×C₃	—	9	8	no	—
66	C₂×C₃	D₃×C₃⋊D₃	1	4	yes	—
67	C₂×C₃	D₃×C₃⋊D₃	1	4	yes	—
68	D₃	—	3	8	no	—
69	C₂²	—	9	1	no	—
70	C₄	—	9	1	no	—
71	C₄	—	81	1	no	—
72	C₃	—	2	16	no	—
73	C₃	D₃×C₃⋊Dic₃	1	4	yes	complemented
74	C₃	Dic₃×C₃⋊D₃	1	4	yes	complemented
75	C₂	—	9	2	no	—
76	C₂	C₃⋊D₃²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊D₃²
commutator, hypocenter	C₃⁴	C₂×C₄
Fitting, socle, cosocle	C₂×C₃⁴	C₂²
prime radical	C₂×C₃²×C₃⋊D₃	C₂
LCS	G ▷ C₃⁴
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃⋊(C₃⋊Dic₃))	C₂	semidirect
3. C₃²×C₃⋊Dic₃	C₂	semidirect
7. C₃²×C₃⋊D₃	C₄	semidirect
13. C₃×C₃⋊Dic₃	D₃	semidirect
15. C₃⁴	C₂×C₄	semidirect
22. C₃×C₃⋊D₃	Dic₃	semidirect
34. C₃⋊Dic₃	C₃⋊D₃	direct (N × H)
37. C₃³	C₄×D₃	semidirect
38. C₃³	C₂×Dic₃	semidirect
48. C₃⋊D₃	C₃⋊Dic₃	direct (N × H)
60. C₃²	D₃×Dic₃	semidirect
61. C₃²	C₄×C₃⋊D₃	semidirect
62. C₃²	C₂×C₃⋊Dic₃	semidirect
73. C₃	D₃×C₃⋊Dic₃	semidirect
74. C₃	Dic₃×C₃⋊D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₃⋊D₃	2
C₃⋊(C₃⋊(C₃⋊Dic₃))	2
C₃²×C₃⋊Dic₃	2
Dic₃×C₃⋊D₃	3
D₃×C₃⋊Dic₃	3

Subgroups — C3⋊D3×C3⋊Dic3 #10620149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×C₃⋊Dic₃ #10620149