Finite Group Databasebeta

← C23×C3×C7×C9×C11 #72194635

Subgroups — C23×C3×C7×C9×C11 #72194635

Order 16632.

640 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C7×C9×C11C217yesmaximal, direct product factor
2C23×C32×C7×C11C311yesmaximal, characteristic
3C23×C7×C9×C11C313yesmaximal, direct product factor
4C2×C3×C7×C9×C11C2217yesdirect product factor
5C23×C3×C9×C11C711yesmaximal, characteristic, direct product factor, Hall
6C3×C7×C9×C11C2311yescharacteristic, direct product factor, Hall
7C22×C32×C7×C11C2×C317yes—
8C22×C7×C9×C11C2×C3121yesdirect product factor
9C23×C3×C7×C11C913yesdirect product factor
10C23×C3×C7×C11C3211yescharacteristic
11C23×C3×C7×C9C1111yesmaximal, characteristic, direct product factor, Hall
12C2×C32×C7×C11C22×C317yes—
13C2×C7×C9×C11C22×C3121yesdirect product factor
14C22×C3×C9×C11C2×C717yesdirect product factor
15C22×C3×C7×C11C2×C9121yesdirect product factor
16C22×C3×C7×C11C2×C3217yes—
17C23×C32×C11C3×C711yescharacteristic
18C23×C9×C11C3×C713yesdirect product factor
19C22×C3×C7×C9C2×C1117yesdirect product factor
20C32×C7×C11C23×C311yescharacteristic
21C7×C9×C11C23×C313yesdirect product factor
22C23×C7×C11C3×C911yescharacteristic, direct product factor, Hall
23C2×C3×C9×C11C22×C717yesdirect product factor
24C23×C32×C7C3×C1111yescharacteristic
25C23×C7×C9C3×C1113yesdirect product factor
26C2×C3×C7×C11C22×C9121yesdirect product factor
27C2×C3×C7×C11C22×C3217yes—
28C22×C32×C11C2×C3×C717yes—
29C22×C9×C11C2×C3×C7121yesdirect product factor
30C2×C3×C7×C9C22×C1117yesdirect product factor
31C22×C7×C11C2×C3×C917yesdirect product factor
32C3×C9×C11C23×C711yescharacteristic, direct product factor, Hall
33C23×C3×C11C7×C913yesdirect product factor
34C23×C3×C11C32×C711yescharacteristic
35C22×C32×C7C2×C3×C1117yes—
36C22×C7×C9C2×C3×C11121yesdirect product factor
37C3×C7×C11C23×C913yesdirect product factor
38C3×C7×C11C23×C3211yescharacteristic
39C23×C3×C9C7×C1111yescharacteristic, direct product factor, Hall
40C2×C32×C11C22×C3×C717yes—
41C2×C9×C11C22×C3×C7121yesdirect product factor
42C3×C7×C9C23×C1111yescharacteristic, direct product factor, Hall
43C23×C3×C7C9×C1113yesdirect product factor
44C23×C3×C7C32×C1111yescharacteristic
45C2×C7×C11C22×C3×C917yesdirect product factor
46C22×C3×C11C2×C7×C9121yesdirect product factor
47C22×C3×C11C2×C32×C717yes—
48C2×C32×C7C22×C3×C1117yes—
49C2×C7×C9C22×C3×C11121yesdirect product factor
50C22×C3×C9C2×C7×C1117yesdirect product factor
51C32×C11C23×C3×C711yescharacteristic
52C9×C11C23×C3×C713yesdirect product factor
53C23×C11C3×C7×C911yescharacteristic, direct product factor, Hall
54C22×C3×C7C2×C9×C11121yesdirect product factor
55C22×C3×C7C2×C32×C1117yes—
56C7×C11C23×C3×C911yescharacteristic, direct product factor, Hall
57C23×C32C3×C7×C1111yescharacteristic
58C23×C9C3×C7×C1113yesdirect product factor
59C2×C3×C11C22×C7×C9121yesdirect product factor
60C2×C3×C11C22×C32×C717yes—
61C32×C7C23×C3×C1111yescharacteristic
62C7×C9C23×C3×C1113yesdirect product factor
63C23×C7C3×C9×C1111yescharacteristic, direct product factor, Hall
64C2×C3×C9C22×C7×C1117yesdirect product factor
65C22×C11C2×C3×C7×C917yesdirect product factor
66C2×C3×C7C22×C9×C11121yesdirect product factor
67C2×C3×C7C22×C32×C1117yes—
68C22×C32C2×C3×C7×C1117yes—
69C22×C9C2×C3×C7×C11121yesdirect product factor
70C3×C11C23×C7×C913yesdirect product factor
71C3×C11C23×C32×C711yescharacteristic
72C22×C7C2×C3×C9×C1117yesdirect product factor
73C3×C9C23×C7×C1111yescharacteristic, direct product factor, Sylow
74C23×C3C7×C9×C1113yesdirect product factor
75C23×C3C32×C7×C1111yescharacteristic
76C2×C11C22×C3×C7×C917yesdirect product factor
77C3×C7C23×C9×C1113yesdirect product factor
78C3×C7C23×C32×C1111yescharacteristic
79C2×C32C22×C3×C7×C1117yes—
80C2×C9C22×C3×C7×C11121yesdirect product factor
81C2×C7C22×C3×C9×C1117yesdirect product factor
82C22×C3C2×C7×C9×C11121yesdirect product factor
83C22×C3C2×C32×C7×C1117yes—
84C11C23×C3×C7×C911yescharacteristic, direct product factor, Sylow
85C32C23×C3×C7×C1111yescharacteristic
86C9C23×C3×C7×C1113yesdirect product factor
87C23C3×C7×C9×C1111yescharacteristic, direct product factor, Sylow
88C7C23×C3×C9×C1111yescharacteristic, direct product factor, Sylow
89C2×C3C22×C7×C9×C11121yesdirect product factor
90C2×C3C22×C32×C7×C1117yes—
91C22C2×C3×C7×C9×C1117yesdirect product factor
92C3C23×C7×C9×C1113yesdirect product factor
93C3C23×C32×C7×C1111yescharacteristic
94C2C22×C3×C7×C9×C1117yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C23×C32×C7×C11
socle, prime radicalC23×C32×C7×C11C3
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C7×C9×C11C2direct (N × H)
3. C23×C7×C9×C11C3direct (N × H)
4. C2×C3×C7×C9×C11C22direct (N × H)
5. C23×C3×C9×C11C7direct (N × H)
6. C3×C7×C9×C11C23direct (N × H)
8. C22×C7×C9×C11C2×C3direct (N × H)
9. C23×C3×C7×C11C9direct (N × H)
11. C23×C3×C7×C9C11direct (N × H)
13. C2×C7×C9×C11C22×C3direct (N × H)
14. C22×C3×C9×C11C2×C7direct (N × H)
15. C22×C3×C7×C11C2×C9direct (N × H)
18. C23×C9×C11C3×C7direct (N × H)
19. C22×C3×C7×C9C2×C11direct (N × H)
21. C7×C9×C11C23×C3direct (N × H)
22. C23×C7×C11C3×C9direct (N × H)
23. C2×C3×C9×C11C22×C7direct (N × H)
25. C23×C7×C9C3×C11direct (N × H)
26. C2×C3×C7×C11C22×C9direct (N × H)
29. C22×C9×C11C2×C3×C7direct (N × H)
30. C2×C3×C7×C9C22×C11direct (N × H)
31. C22×C7×C11C2×C3×C9direct (N × H)
32. C3×C9×C11C23×C7direct (N × H)
33. C23×C3×C11C7×C9direct (N × H)
36. C22×C7×C9C2×C3×C11direct (N × H)
37. C3×C7×C11C23×C9direct (N × H)
39. C23×C3×C9C7×C11direct (N × H)
41. C2×C9×C11C22×C3×C7direct (N × H)
42. C3×C7×C9C23×C11direct (N × H)
43. C23×C3×C7C9×C11direct (N × H)
45. C2×C7×C11C22×C3×C9direct (N × H)
46. C22×C3×C11C2×C7×C9direct (N × H)
49. C2×C7×C9C22×C3×C11direct (N × H)
50. C22×C3×C9C2×C7×C11direct (N × H)
52. C9×C11C23×C3×C7direct (N × H)
53. C23×C11C3×C7×C9direct (N × H)
54. C22×C3×C7C2×C9×C11direct (N × H)
56. C7×C11C23×C3×C9direct (N × H)
58. C23×C9C3×C7×C11direct (N × H)
59. C2×C3×C11C22×C7×C9direct (N × H)
62. C7×C9C23×C3×C11direct (N × H)
63. C23×C7C3×C9×C11direct (N × H)
64. C2×C3×C9C22×C7×C11direct (N × H)
65. C22×C11C2×C3×C7×C9direct (N × H)
66. C2×C3×C7C22×C9×C11direct (N × H)
69. C22×C9C2×C3×C7×C11direct (N × H)
70. C3×C11C23×C7×C9direct (N × H)
72. C22×C7C2×C3×C9×C11direct (N × H)
73. C3×C9C23×C7×C11direct (N × H)
74. C23×C3C7×C9×C11direct (N × H)
76. C2×C11C22×C3×C7×C9direct (N × H)
77. C3×C7C23×C9×C11direct (N × H)
80. C2×C9C22×C3×C7×C11direct (N × H)
81. C2×C7C22×C3×C9×C11direct (N × H)
82. C22×C3C2×C7×C9×C11direct (N × H)
84. C11C23×C3×C7×C9direct (N × H)
86. C9C23×C3×C7×C11direct (N × H)
87. C23C3×C7×C9×C11direct (N × H)
88. C7C23×C3×C9×C11direct (N × H)
89. C2×C3C22×C7×C9×C11direct (N × H)
91. C22C2×C3×C7×C9×C11direct (N × H)
92. C3C23×C7×C9×C11direct (N × H)
94. C2C22×C3×C7×C9×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C7×C9×C112
C23×C32×C7×C113
C23×C7×C9×C113
C23×C3×C9×C117
C23×C3×C7×C911