Subgroups — C₂²×C₃³×D₉ #14519352

Order 1944.

2124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃³×D₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃³×D₃	—	3	1	no	maximal
4	C₂²×C₃²×D₉	C₃	1	13	yes	maximal, direct product factor
5	C₂×C₃³×C₉	C₂²	1	3	yes	complemented
6	C₃³×D₉	C₂²	1	4	yes	direct product factor
7	C₂²×C₃⁴	D₃	1	1	yes	characteristic
8	C₂×C₃³×D₃	—	3	6	no	—
9	C₂²×C₃²×C₉	—	2	13	no	—
10	C₂²×C₃²×C₉	C₂×C₃	1	13	yes	complemented
11	C₂×C₃²×D₉	C₂×C₃	1	78	yes	direct product factor
12	C₃³×C₉	C₂³	1	1	yes	characteristic, complemented, Sylow
13	C₂³×C₃³	—	9	1	no	—
14	C₂²×C₃²×D₃	—	3	13	no	—
15	C₂²×C₃×D₉	C₃²	1	13	yes	direct product factor
16	C₂×C₃⁴	C₂×D₃	1	3	yes	—
17	C₃³×D₃	—	3	4	no	—
18	C₂×C₃²×C₉	—	2	39	no	—
19	C₂×C₃²×C₉	C₂²×C₃	1	39	yes	complemented
20	C₃²×D₉	C₂²×C₃	1	52	yes	direct product factor
21	C₂²×C₃³	—	2	13	no	—
22	C₂²×C₃³	—	9	6	no	—
23	C₂²×C₃³	D₉	1	1	yes	characteristic, direct product factor
24	C₂²×C₃³	C₃×D₃	1	13	yes	—
25	C₂×C₃²×D₃	—	3	78	no	—
26	C₂²×C₃×C₉	—	2	52	no	—
27	C₂²×C₃×C₉	C₂×C₃²	1	13	yes	complemented
28	C₂×C₃×D₉	C₂×C₃²	1	78	yes	direct product factor
29	C₃⁴	C₂²×D₃	1	1	yes	characteristic
30	C₃²×C₉	—	2	13	no	—
31	C₃²×C₉	C₂³×C₃	1	13	yes	complemented
32	C₂³×C₃²	—	9	13	no	—
33	C₂²×C₃×D₃	—	3	13	no	—
34	C₂²×D₉	C₃³	1	1	yes	characteristic, direct product factor
35	C₂×C₃³	—	2	39	no	—
36	C₂×C₃³	—	9	4	no	—
37	C₂×C₃³	C₂×D₉	1	3	yes	direct product factor
38	C₂×C₃³	C₂×C₃×D₃	1	39	yes	—
39	C₃²×D₃	—	3	52	no	—
40	C₂×C₃×C₉	—	2	156	no	—
41	C₂×C₃×C₉	C₂²×C₃²	1	39	yes	complemented
42	C₃×D₉	C₂²×C₃²	1	52	yes	direct product factor
43	C₂²×C₃²	—	2	52	no	—
44	C₂²×C₃²	—	9	78	no	—
45	C₂²×C₃²	C₃×D₉	1	13	yes	direct product factor
46	C₂²×C₃²	C₃²×D₃	1	13	yes	—
47	C₂×C₃×D₃	—	3	78	no	—
48	C₂²×C₉	—	2	13	no	—
49	C₂²×C₉	C₂×C₃³	1	1	yes	characteristic, complemented
50	C₂×D₉	C₂×C₃³	1	6	yes	direct product factor
51	C₃³	—	2	13	no	—
52	C₃³	C₂²×D₉	1	1	yes	characteristic, direct product factor
53	C₃³	C₂²×C₃×D₃	1	13	yes	—
54	C₃×C₉	—	2	52	no	—
55	C₃×C₉	C₂³×C₃²	1	13	yes	complemented
56	C₂³×C₃	—	9	13	no	—
57	C₂²×D₃	—	3	1	no	—
58	C₂×C₃²	—	2	156	no	—
59	C₂×C₃²	—	9	52	no	—
60	C₂×C₃²	C₂×C₃×D₉	1	39	yes	direct product factor
61	C₂×C₃²	C₂×C₃²×D₃	1	39	yes	—
62	C₃×D₃	—	3	52	no	—
63	C₂×C₉	—	2	39	no	—
64	C₂×C₉	C₂²×C₃³	1	3	yes	complemented
65	D₉	C₂²×C₃³	1	4	yes	direct product factor
66	C₂²×C₃	—	2	13	no	—
67	C₂²×C₃	—	9	78	no	—
68	C₂²×C₃	C₃²×D₉	1	13	yes	direct product factor
69	C₂²×C₃	C₃³×D₃	1	1	yes	characteristic
70	C₂×D₃	—	3	6	no	—
71	C₃²	—	2	52	no	—
72	C₃²	C₂²×C₃×D₉	1	13	yes	direct product factor
73	C₃²	C₂²×C₃²×D₃	1	13	yes	—
74	C₉	—	2	13	no	—
75	C₉	C₂³×C₃³	1	1	yes	characteristic, complemented
76	C₂³	—	9	1	no	Sylow
77	C₂×C₃	—	2	39	no	—
78	C₂×C₃	—	9	52	no	—
79	C₂×C₃	C₂×C₃²×D₉	1	39	yes	direct product factor
80	C₂×C₃	C₂×C₃³×D₃	1	3	yes	—
81	D₃	—	3	4	no	—
82	C₂²	—	9	6	no	—
83	C₂²	C₃³×D₉	1	1	yes	characteristic, direct product factor
84	C₃	—	2	13	no	—
85	C₃	C₂²×C₃²×D₉	1	13	yes	direct product factor
86	C₃	C₂²×C₃³×D₃	1	1	yes	characteristic
87	C₂	—	9	4	no	—
88	C₂	C₂×C₃³×D₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃³	D₉
commutator, cosocle, hypocenter	C₉	C₂³×C₃³
Frattini	C₃	C₂²×C₃³×D₃
Fitting	C₂²×C₃³×C₉	C₂
socle	C₂²×C₃⁴	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂²×C₃³

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×C₉	C₂	semidirect
2. C₂×C₃³×D₉	C₂	direct (N × H)
4. C₂²×C₃²×D₉	C₃	direct (N × H)
5. C₂×C₃³×C₉	C₂²	semidirect
6. C₃³×D₉	C₂²	direct (N × H)
10. C₂²×C₃²×C₉	C₂×C₃	semidirect
11. C₂×C₃²×D₉	C₂×C₃	direct (N × H)
12. C₃³×C₉	C₂³	semidirect
15. C₂²×C₃×D₉	C₃²	direct (N × H)
19. C₂×C₃²×C₉	C₂²×C₃	semidirect
20. C₃²×D₉	C₂²×C₃	direct (N × H)
23. C₂²×C₃³	D₉	direct (N × H)
27. C₂²×C₃×C₉	C₂×C₃²	semidirect
28. C₂×C₃×D₉	C₂×C₃²	direct (N × H)
31. C₃²×C₉	C₂³×C₃	semidirect
34. C₂²×D₉	C₃³	direct (N × H)
37. C₂×C₃³	C₂×D₉	direct (N × H)
41. C₂×C₃×C₉	C₂²×C₃²	semidirect
42. C₃×D₉	C₂²×C₃²	direct (N × H)
45. C₂²×C₃²	C₃×D₉	direct (N × H)
49. C₂²×C₉	C₂×C₃³	semidirect
50. C₂×D₉	C₂×C₃³	direct (N × H)
52. C₃³	C₂²×D₉	direct (N × H)
55. C₃×C₉	C₂³×C₃²	semidirect
60. C₂×C₃²	C₂×C₃×D₉	direct (N × H)
64. C₂×C₉	C₂²×C₃³	semidirect
65. D₉	C₂²×C₃³	direct (N × H)
68. C₂²×C₃	C₃²×D₉	direct (N × H)
72. C₃²	C₂²×C₃×D₉	direct (N × H)
75. C₉	C₂³×C₃³	semidirect
79. C₂×C₃	C₂×C₃²×D₉	direct (N × H)
83. C₂²	C₃³×D₉	direct (N × H)
85. C₃	C₂²×C₃²×D₉	direct (N × H)
88. C₂	C₂×C₃³×D₉	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×C₃³×C₉	2
C₂×C₃³×D₉	2
C₂²×C₃³×D₃	3
C₂²×C₃²×D₉	3

Subgroups — C22×C33×D9 #14519352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃³×D₉ #14519352