Finite Group Databasebeta

← C2×C32×C5×C17×D11 #46778195

Subgroups — C2×C32×C5×C17×D11 #46778195

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C17×D11C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C3×C5×C17×D11C314yesmaximal, direct product factor
4C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
5C2×C32×C17×D11C511yesmaximal, characteristic, direct product factor, Hall
6C3×C5×C17×D11C2×C318yesdirect product factor
7C2×C3×C5×C11×C17C2×C314yescomplemented
8C2×C5×C17×D11C3211yescharacteristic, direct product factor, Hall
9C32×C17×D11C2×C512yesdirect product factor
10C2×C32×C11×C17C2×C511yescharacteristic, complemented
11C22×C32×C5×C17—111nomaximal, Hall
12C3×C5×C11×C17C22×C314yescomplemented
13C2×C3×C17×D11C3×C514yesdirect product factor
14C2×C32×C5×D11C1711yesmaximal, characteristic, direct product factor, Hall
15C2×C5×C11×C17C2×C3211yescharacteristic, complemented
16C5×C17×D11C2×C3212yesdirect product factor
17C32×C11×C17C22×C511yescharacteristic, complemented, Hall
18C2×C32×C5×C17—112no—
19C2×C32×C5×C17D1111yescharacteristic, direct product factor
20C2×C3×C11×C17C2×C3×C514yescomplemented
21C3×C17×D11C2×C3×C518yesdirect product factor
22C22×C3×C5×C17—114no—
23C2×C32×C5×C11C2×C1711yescharacteristic, complemented
24C32×C5×D11C2×C1712yesdirect product factor
25C5×C11×C17C22×C3211yescharacteristic, complemented, Hall
26C32×C5×C17C2×D1111yescharacteristic, direct product factor, Hall
27C2×C17×D11C32×C511yescharacteristic, direct product factor, Hall
28C2×C3×C5×D11C3×C1714yesdirect product factor
29C22×C32×C17—111noHall
30C3×C11×C17C22×C3×C514yescomplemented
31C2×C3×C5×C17—118no—
32C2×C3×C5×C17C3×D1114yesdirect product factor
33C32×C5×C11C22×C1711yescharacteristic, complemented, Hall
34C2×C32×D11C5×C1711yescharacteristic, direct product factor, Hall
35C2×C11×C17C2×C32×C511yescharacteristic, complemented
36C17×D11C2×C32×C512yesdirect product factor
37C22×C5×C17—111noHall
38C2×C3×C5×C11C2×C3×C1714yescomplemented
39C3×C5×D11C2×C3×C1718yesdirect product factor
40C2×C32×C17—112no—
41C2×C32×C17C5×D1111yescharacteristic, direct product factor
42C3×C5×C17C2×C3×D1114yesdirect product factor
43C2×C5×D11C32×C1711yescharacteristic, direct product factor, Hall
44C22×C3×C17—114no—
45C2×C32×C11C2×C5×C1711yescharacteristic, complemented
46C32×D11C2×C5×C1712yesdirect product factor
47C11×C17C22×C32×C511yescharacteristic, complemented, Hall
48C22×C32×C5—111noHall
49C2×C5×C17—112no—
50C2×C5×C17C32×D1111yescharacteristic, direct product factor
51C3×C5×C11C22×C3×C1714yescomplemented
52C32×C17C2×C5×D1111yescharacteristic, direct product factor, Hall
53C2×C3×D11C3×C5×C1714yesdirect product factor
54C2×C5×C11C2×C32×C1711yescharacteristic, complemented
55C5×D11C2×C32×C1712yesdirect product factor
56C2×C3×C17—118no—
57C2×C3×C17C3×C5×D1114yesdirect product factor
58C32×C11C22×C5×C1711yescharacteristic, complemented, Hall
59C2×C32×C5—112no—
60C2×C32×C5C17×D1111yescharacteristic, direct product factor
61C5×C17C2×C32×D1111yescharacteristic, direct product factor, Hall
62C22×C17—111noHall
63C2×C3×C11C2×C3×C5×C1714yescomplemented
64C3×D11C2×C3×C5×C1718yesdirect product factor
65C22×C3×C5—114no—
66C5×C11C22×C32×C1711yescharacteristic, complemented, Hall
67C3×C17C2×C3×C5×D1114yesdirect product factor
68C32×C5C2×C17×D1111yescharacteristic, direct product factor, Hall
69C2×D11C32×C5×C1711yescharacteristic, direct product factor, Hall
70C22×C32—111noHall
71C2×C17—112no—
72C2×C17C32×C5×D1111yescharacteristic, direct product factor
73C3×C11C22×C3×C5×C1714yescomplemented
74C2×C3×C5—118no—
75C2×C3×C5C3×C17×D1114yesdirect product factor
76C2×C11C2×C32×C5×C1711yescharacteristic, complemented
77D11C2×C32×C5×C1712yesdirect product factor
78C22×C5—111noHall
79C2×C32—112no—
80C2×C32C5×C17×D1111yescharacteristic, direct product factor
81C17C2×C32×C5×D1111yescharacteristic, direct product factor, Sylow
82C3×C5C2×C3×C17×D1114yesdirect product factor
83C22×C3—114no—
84C11C22×C32×C5×C1711yescharacteristic, complemented, Sylow
85C2×C5—112no—
86C2×C5C32×C17×D1111yescharacteristic, direct product factor
87C32C2×C5×C17×D1111yescharacteristic, direct product factor, Sylow
88C2×C3—118no—
89C2×C3C3×C5×C17×D1114yesdirect product factor
90C5C2×C32×C17×D1111yescharacteristic, direct product factor, Sylow
91C22—111noSylow
92C3C2×C3×C5×C17×D1114yesdirect product factor
93C2—112no—
94C2C32×C5×C17×D1111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C5×C17D11
commutator, cosocle, hypocenterC11C22×C32×C5×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C11
UCSC1 ◁ C2×C32×C5×C17

Complements

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

NH ≅ G/Ntype
1. C32×C5×C17×D11C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
3. C2×C3×C5×C17×D11C3direct (N × H)
4. C32×C5×C11×C17C22semidirect
5. C2×C32×C17×D11C5direct (N × H)
6. C3×C5×C17×D11C2×C3direct (N × H)
7. C2×C3×C5×C11×C17C2×C3semidirect
8. C2×C5×C17×D11C32direct (N × H)
9. C32×C17×D11C2×C5direct (N × H)
10. C2×C32×C11×C17C2×C5semidirect
12. C3×C5×C11×C17C22×C3semidirect
13. C2×C3×C17×D11C3×C5direct (N × H)
14. C2×C32×C5×D11C17direct (N × H)
15. C2×C5×C11×C17C2×C32semidirect
16. C5×C17×D11C2×C32direct (N × H)
17. C32×C11×C17C22×C5semidirect
19. C2×C32×C5×C17D11direct (N × H)
20. C2×C3×C11×C17C2×C3×C5semidirect
21. C3×C17×D11C2×C3×C5direct (N × H)
23. C2×C32×C5×C11C2×C17semidirect
24. C32×C5×D11C2×C17direct (N × H)
25. C5×C11×C17C22×C32semidirect
26. C32×C5×C17C2×D11direct (N × H)
27. C2×C17×D11C32×C5direct (N × H)
28. C2×C3×C5×D11C3×C17direct (N × H)
30. C3×C11×C17C22×C3×C5semidirect
32. C2×C3×C5×C17C3×D11direct (N × H)
33. C32×C5×C11C22×C17semidirect
34. C2×C32×D11C5×C17direct (N × H)
35. C2×C11×C17C2×C32×C5semidirect
36. C17×D11C2×C32×C5direct (N × H)
38. C2×C3×C5×C11C2×C3×C17semidirect
39. C3×C5×D11C2×C3×C17direct (N × H)
41. C2×C32×C17C5×D11direct (N × H)
42. C3×C5×C17C2×C3×D11direct (N × H)
43. C2×C5×D11C32×C17direct (N × H)
45. C2×C32×C11C2×C5×C17semidirect
46. C32×D11C2×C5×C17direct (N × H)
47. C11×C17C22×C32×C5semidirect
50. C2×C5×C17C32×D11direct (N × H)
51. C3×C5×C11C22×C3×C17semidirect
52. C32×C17C2×C5×D11direct (N × H)
53. C2×C3×D11C3×C5×C17direct (N × H)
54. C2×C5×C11C2×C32×C17semidirect
55. C5×D11C2×C32×C17direct (N × H)
57. C2×C3×C17C3×C5×D11direct (N × H)
58. C32×C11C22×C5×C17semidirect
60. C2×C32×C5C17×D11direct (N × H)
61. C5×C17C2×C32×D11direct (N × H)
63. C2×C3×C11C2×C3×C5×C17semidirect
64. C3×D11C2×C3×C5×C17direct (N × H)
66. C5×C11C22×C32×C17semidirect
67. C3×C17C2×C3×C5×D11direct (N × H)
68. C32×C5C2×C17×D11direct (N × H)
69. C2×D11C32×C5×C17direct (N × H)
72. C2×C17C32×C5×D11direct (N × H)
73. C3×C11C22×C3×C5×C17semidirect
75. C2×C3×C5C3×C17×D11direct (N × H)
76. C2×C11C2×C32×C5×C17semidirect
77. D11C2×C32×C5×C17direct (N × H)
80. C2×C32C5×C17×D11direct (N × H)
81. C17C2×C32×C5×D11direct (N × H)
82. C3×C5C2×C3×C17×D11direct (N × H)
84. C11C22×C32×C5×C17semidirect
86. C2×C5C32×C17×D11direct (N × H)
87. C32C2×C5×C17×D11direct (N × H)
89. C2×C3C3×C5×C17×D11direct (N × H)
90. C5C2×C32×C17×D11direct (N × H)
92. C3C2×C3×C5×C17×D11direct (N × H)
94. C2C32×C5×C17×D11direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C17×D112
C2×C32×C5×C11×C172
C2×C3×C5×C17×D113
C2×C32×C17×D115
C22×C32×C5×C1711
C2×C32×C5×D1117