Subgroups — C₂³×C₉×D₉ #13048183

Order 1296.

715 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₉²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×D₉	C₂	1	14	yes	maximal, direct product factor
3	C₂³×D₃×C₉	—	3	1	no	maximal
4	C₂³×C₃×D₉	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₉²	C₂²	1	7	yes	complemented
6	C₂×C₉×D₉	C₂²	1	28	yes	direct product factor
7	C₂³×C₃×C₉	—	2	1	no	—
8	C₂³×C₃×C₉	D₃	1	1	yes	characteristic
9	C₂³×C₃×C₉	C₂×C₃	1	1	yes	characteristic
10	C₂²×D₃×C₉	—	3	14	no	—
11	C₂²×C₃×D₉	C₂×C₃	1	14	yes	—
12	C₂×C₉²	C₂³	1	7	yes	complemented
13	C₉×D₉	C₂³	1	8	yes	direct product factor
14	C₂³×C₃×D₃	—	3	1	no	—
15	C₂⁴×C₉	—	9	1	no	—
16	C₂³×D₉	C₉	1	1	yes	characteristic, direct product factor
17	C₂²×C₃×C₉	—	2	7	no	—
18	C₂²×C₃×C₉	C₂×D₃	1	7	yes	—
19	C₂²×C₃×C₉	C₂²×C₃	1	7	yes	—
20	C₂×D₃×C₉	—	3	28	no	—
21	C₂×C₃×D₉	C₂²×C₃	1	28	yes	—
22	C₉²	C₂⁴	1	1	yes	characteristic, complemented, Sylow
23	C₂³×C₃²	C₃×D₃	1	1	yes	characteristic
24	C₂²×C₃×D₃	—	3	14	no	—
25	C₂³×C₉	—	2	3	no	—
26	C₂³×C₉	—	2	1	no	—
27	C₂³×C₉	—	2	1	no	—
28	C₂³×C₉	—	9	14	no	—
29	C₂³×C₉	D₉	1	1	yes	characteristic, direct product factor
30	C₂³×C₉	C₂×C₉	1	1	yes	characteristic, complemented
31	C₂²×D₉	C₂×C₉	1	14	yes	direct product factor
32	C₂×C₃×C₉	—	2	7	no	—
33	C₂×C₃×C₉	C₂²×D₃	1	7	yes	—
34	C₂×C₃×C₉	C₂³×C₃	1	7	yes	—
35	D₃×C₉	—	3	8	no	—
36	C₃×D₉	C₂³×C₃	1	8	yes	—
37	C₂⁴×C₃	—	9	1	no	—
38	C₂³×D₃	—	3	1	no	—
39	C₂²×C₃²	C₂×C₃×D₃	1	7	yes	—
40	C₂×C₃×D₃	—	3	28	no	—
41	C₂²×C₉	—	2	21	no	—
42	C₂²×C₉	—	2	7	no	—
43	C₂²×C₉	—	2	7	no	—
44	C₂²×C₉	—	9	28	no	—
45	C₂²×C₉	C₂×D₉	1	7	yes	direct product factor
46	C₂²×C₉	C₂²×C₉	1	7	yes	complemented
47	C₂×D₉	C₂²×C₉	1	28	yes	direct product factor
48	C₃×C₉	—	2	1	no	—
49	C₃×C₉	C₂³×D₃	1	1	yes	characteristic
50	C₃×C₉	C₂⁴×C₃	1	1	yes	characteristic
51	C₂³×C₃	—	2	1	no	—
52	C₂³×C₃	—	9	14	no	—
53	C₂³×C₃	C₃×D₉	1	1	yes	characteristic
54	C₂³×C₃	D₃×C₉	1	1	yes	characteristic
55	C₂²×D₃	—	3	14	no	—
56	C₂×C₃²	C₂²×C₃×D₃	1	7	yes	—
57	C₃×D₃	—	3	8	no	—
58	C₂×C₉	—	2	21	no	—
59	C₂×C₉	—	2	7	no	—
60	C₂×C₉	—	2	7	no	—
61	C₂×C₉	—	9	8	no	—
62	C₂×C₉	C₂²×D₉	1	7	yes	direct product factor
63	C₂×C₉	C₂³×C₉	1	7	yes	complemented
64	D₉	C₂³×C₉	1	8	yes	direct product factor
65	C₂⁴	—	9	1	no	Sylow
66	C₂²×C₃	—	2	7	no	—
67	C₂²×C₃	—	9	28	no	—
68	C₂²×C₃	C₂×C₃×D₉	1	7	yes	—
69	C₂²×C₃	C₂×D₃×C₉	1	7	yes	—
70	C₂×D₃	—	3	28	no	—
71	C₃²	C₂³×C₃×D₃	1	1	yes	characteristic
72	C₉	—	2	3	no	—
73	C₉	—	2	1	no	—
74	C₉	—	2	1	no	—
75	C₉	C₂³×D₉	1	1	yes	characteristic, direct product factor
76	C₉	C₂⁴×C₉	1	1	yes	characteristic, complemented
77	C₂³	—	9	14	no	—
78	C₂³	C₉×D₉	1	1	yes	characteristic, direct product factor
79	C₂×C₃	—	2	7	no	—
80	C₂×C₃	—	9	8	no	—
81	C₂×C₃	C₂²×C₃×D₉	1	7	yes	—
82	C₂×C₃	C₂²×D₃×C₉	1	7	yes	—
83	D₃	—	3	8	no	—
84	C₂²	—	9	28	no	—
85	C₂²	C₂×C₉×D₉	1	7	yes	direct product factor
86	C₃	—	2	1	no	—
87	C₃	C₂³×C₃×D₉	1	1	yes	characteristic
88	C₃	C₂³×D₃×C₉	1	1	yes	characteristic
89	C₂	—	9	8	no	—
90	C₂	C₂²×C₉×D₉	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³×C₉	D₉
commutator, hypocenter	C₉	C₂⁴×C₉
Frattini	C₃²	C₂³×C₃×D₃
Fitting	C₂³×C₉²	C₂
socle	C₂³×C₃²	C₃×D₃
prime radical	C₂³×C₃×D₉	C₃
cosocle	C₃×C₉	C₂⁴×C₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂³×C₉

Complements

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

N	H ≅ G/N	type
1. C₂³×C₉²	C₂	semidirect
2. C₂²×C₉×D₉	C₂	direct (N × H)
5. C₂²×C₉²	C₂²	semidirect
6. C₂×C₉×D₉	C₂²	direct (N × H)
12. C₂×C₉²	C₂³	semidirect
13. C₉×D₉	C₂³	direct (N × H)
16. C₂³×D₉	C₉	direct (N × H)
22. C₉²	C₂⁴	semidirect
29. C₂³×C₉	D₉	direct (N × H)
30. C₂³×C₉	C₂×C₉	semidirect
31. C₂²×D₉	C₂×C₉	direct (N × H)
45. C₂²×C₉	C₂×D₉	direct (N × H)
46. C₂²×C₉	C₂²×C₉	semidirect
47. C₂×D₉	C₂²×C₉	direct (N × H)
62. C₂×C₉	C₂²×D₉	direct (N × H)
63. C₂×C₉	C₂³×C₉	semidirect
64. D₉	C₂³×C₉	direct (N × H)
75. C₉	C₂³×D₉	direct (N × H)
76. C₉	C₂⁴×C₉	semidirect
78. C₂³	C₉×D₉	direct (N × H)
85. C₂²	C₂×C₉×D₉	direct (N × H)
90. C₂	C₂²×C₉×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
C₂³×C₉²	2
C₂²×C₉×D₉	2
C₂³×D₃×C₉	3
C₂³×C₃×D₉	3

Subgroups — C23×C9×D9 #13048183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₉×D₉ #13048183