Subgroups — C₂²×D₃×C₉² #14518454

Order 1944.

936 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₉²	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×D₃×C₉	C₃	1	4	yes	maximal
4	C₂³×C₉²	—	3	1	no	maximal
5	C₂×C₃×C₉²	C₂²	1	3	yes	complemented
6	D₃×C₉²	C₂²	1	4	yes	direct product factor
7	C₂²×C₃²×C₉	C₂×C₃	1	4	yes	—
8	C₂×C₃×D₃×C₉	C₂×C₃	1	24	yes	—
9	C₂²×C₉²	—	2	4	no	—
10	C₂²×C₉²	—	3	6	no	—
11	C₂²×C₉²	D₃	1	1	yes	characteristic, direct product factor
12	C₃×C₉²	C₂³	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₃²×D₃	C₃²	1	1	yes	characteristic
14	C₂³×C₃×C₉	—	3	4	no	—
15	C₂²×D₃×C₉	C₉	1	12	yes	direct product factor
16	C₂×C₃²×C₉	C₂²×C₃	1	12	yes	—
17	C₃×D₃×C₉	C₂²×C₃	1	16	yes	—
18	C₂×C₉²	—	2	12	no	—
19	C₂×C₉²	—	3	4	no	—
20	C₂×C₉²	C₂×D₃	1	3	yes	direct product factor
21	C₂²×C₃³	C₂×C₃²	1	1	yes	characteristic
22	C₂×C₃²×D₃	C₂×C₃²	1	6	yes	—
23	C₂²×C₃×C₉	—	2	4	no	—
24	C₂²×C₃×C₉	—	2	12	no	—
25	C₂²×C₃×C₉	—	3	24	no	—
26	C₂²×C₃×C₉	C₂×C₉	1	12	yes	complemented
27	C₂²×C₃×C₉	C₃×D₃	1	4	yes	—
28	C₂×D₃×C₉	C₂×C₉	1	72	yes	direct product factor
29	C₃²×C₉	C₂³×C₃	1	4	yes	—
30	C₉²	—	2	4	no	—
31	C₉²	C₂²×D₃	1	1	yes	characteristic, direct product factor
32	C₂³×C₃²	—	3	1	no	—
33	C₂²×C₃×D₃	C₃×C₉	1	4	yes	—
34	C₂³×C₉	—	3	12	no	—
35	C₂×C₃³	C₂²×C₃²	1	3	yes	—
36	C₃²×D₃	C₂²×C₃²	1	4	yes	—
37	C₂×C₃×C₉	—	2	12	no	—
38	C₂×C₃×C₉	—	2	36	no	—
39	C₂×C₃×C₉	—	3	16	no	—
40	C₂×C₃×C₉	C₂²×C₉	1	36	yes	complemented
41	C₂×C₃×C₉	C₂×C₃×D₃	1	12	yes	—
42	D₃×C₉	C₂²×C₉	1	48	yes	direct product factor
43	C₂²×C₃²	—	2	4	no	—
44	C₂²×C₃²	—	3	6	no	—
45	C₂²×C₃²	C₂×C₃×C₉	1	4	yes	—
46	C₂²×C₃²	C₃²×D₃	1	1	yes	characteristic
47	C₂×C₃×D₃	C₂×C₃×C₉	1	24	yes	—
48	C₂²×C₉	—	2	12	no	—
49	C₂²×C₉	—	3	72	no	—
50	C₂²×C₉	D₃×C₉	1	12	yes	direct product factor
51	C₃³	C₂³×C₃²	1	1	yes	characteristic
52	C₃×C₉	—	2	4	no	—
53	C₃×C₉	—	2	12	no	—
54	C₃×C₉	C₂³×C₉	1	12	yes	complemented
55	C₃×C₉	C₂²×C₃×D₃	1	4	yes	—
56	C₂³×C₃	—	3	4	no	—
57	C₂²×D₃	C₉²	1	1	yes	characteristic, direct product factor
58	C₂×C₃²	—	2	12	no	—
59	C₂×C₃²	—	3	4	no	—
60	C₂×C₃²	C₂²×C₃×C₉	1	12	yes	—
61	C₂×C₃²	C₂×C₃²×D₃	1	3	yes	—
62	C₃×D₃	C₂²×C₃×C₉	1	16	yes	—
63	C₂×C₉	—	2	36	no	—
64	C₂×C₉	—	3	48	no	—
65	C₂×C₉	C₂×D₃×C₉	1	36	yes	direct product factor
66	C₂²×C₃	—	2	4	no	—
67	C₂²×C₃	—	3	24	no	—
68	C₂²×C₃	C₂×C₉²	1	1	yes	characteristic, complemented
69	C₂²×C₃	C₃×D₃×C₉	1	4	yes	—
70	C₂×D₃	C₂×C₉²	1	6	yes	direct product factor
71	C₃²	—	2	4	no	—
72	C₃²	C₂³×C₃×C₉	1	4	yes	—
73	C₃²	C₂²×C₃²×D₃	1	1	yes	characteristic
74	C₉	—	2	12	no	—
75	C₉	C₂²×D₃×C₉	1	12	yes	direct product factor
76	C₂³	—	3	1	no	Sylow
77	C₂×C₃	—	2	12	no	—
78	C₂×C₃	—	3	16	no	—
79	C₂×C₃	C₂²×C₉²	1	3	yes	complemented
80	C₂×C₃	C₂×C₃×D₃×C₉	1	12	yes	—
81	D₃	C₂²×C₉²	1	4	yes	direct product factor
82	C₂²	—	3	6	no	—
83	C₂²	D₃×C₉²	1	1	yes	characteristic, direct product factor
84	C₃	—	2	4	no	—
85	C₃	C₂³×C₉²	1	1	yes	characteristic, complemented
86	C₃	C₂²×C₃×D₃×C₉	1	4	yes	—
87	C₂	—	3	4	no	—
88	C₂	C₂×D₃×C₉²	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₉²	D₃
commutator, hypocenter	C₃	C₂³×C₉²
Frattini	C₃²	C₂²×C₃²×D₃
Fitting	C₂²×C₃×C₉²	C₂
socle	C₂²×C₃³	C₂×C₃²
prime radical	C₂²×C₃²×D₃	C₃²
cosocle	C₃³	C₂³×C₃²
LCS	G ▷ C₃
UCS	C₁ ◁ C₂²×C₉²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₉²	C₂	semidirect
2. C₂×D₃×C₉²	C₂	direct (N × H)
5. C₂×C₃×C₉²	C₂²	semidirect
6. D₃×C₉²	C₂²	direct (N × H)
11. C₂²×C₉²	D₃	direct (N × H)
12. C₃×C₉²	C₂³	semidirect
15. C₂²×D₃×C₉	C₉	direct (N × H)
20. C₂×C₉²	C₂×D₃	direct (N × H)
26. C₂²×C₃×C₉	C₂×C₉	semidirect
28. C₂×D₃×C₉	C₂×C₉	direct (N × H)
31. C₉²	C₂²×D₃	direct (N × H)
40. C₂×C₃×C₉	C₂²×C₉	semidirect
42. D₃×C₉	C₂²×C₉	direct (N × H)
50. C₂²×C₉	D₃×C₉	direct (N × H)
54. C₃×C₉	C₂³×C₉	semidirect
57. C₂²×D₃	C₉²	direct (N × H)
65. C₂×C₉	C₂×D₃×C₉	direct (N × H)
68. C₂²×C₃	C₂×C₉²	semidirect
70. C₂×D₃	C₂×C₉²	direct (N × H)
75. C₉	C₂²×D₃×C₉	direct (N × H)
79. C₂×C₃	C₂²×C₉²	semidirect
81. D₃	C₂²×C₉²	direct (N × H)
83. C₂²	D₃×C₉²	direct (N × H)
85. C₃	C₂³×C₉²	semidirect
88. C₂	C₂×D₃×C₉²	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×C₉²	2
C₂×D₃×C₉²	2
C₂²×C₃×D₃×C₉	3
C₂³×C₉²	3

Subgroups — C22×D3×C92 #14518454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₃×C₉² #14518454