Finite Group Databasebeta

← C2×C32×C5×C11×D17 #46778194

Subgroups — C2×C32×C5×C11×D17 #46778194

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×D17C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C3×C5×C11×D17C314yesmaximal, direct product factor
4C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
5C2×C32×C11×D17C511yesmaximal, characteristic, direct product factor, Hall
6C3×C5×C11×D17C2×C318yesdirect product factor
7C2×C3×C5×C11×C17C2×C314yescomplemented
8C2×C5×C11×D17C3211yescharacteristic, direct product factor, Hall
9C32×C11×D17C2×C512yesdirect product factor
10C2×C32×C11×C17C2×C511yescharacteristic, complemented
11C2×C32×C5×D17C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C5×C11×C17C22×C314yescomplemented
13C2×C3×C11×D17C3×C514yesdirect product factor
14C22×C32×C5×C11—171nomaximal, Hall
15C2×C5×C11×C17C2×C3211yescharacteristic, complemented
16C5×C11×D17C2×C3212yesdirect product factor
17C32×C11×C17C22×C511yescharacteristic, complemented, Hall
18C2×C32×C5×C17C2×C1111yescharacteristic, complemented
19C32×C5×D17C2×C1112yesdirect product factor
20C2×C3×C11×C17C2×C3×C514yescomplemented
21C3×C11×D17C2×C3×C518yesdirect product factor
22C2×C3×C5×D17C3×C1114yesdirect product factor
23C2×C32×C5×C11—172no—
24C2×C32×C5×C11D1711yescharacteristic, direct product factor
25C5×C11×C17C22×C3211yescharacteristic, complemented, Hall
26C32×C5×C17C22×C1111yescharacteristic, complemented, Hall
27C2×C11×D17C32×C511yescharacteristic, direct product factor, Hall
28C22×C3×C5×C11—174no—
29C2×C32×D17C5×C1111yescharacteristic, direct product factor, Hall
30C3×C11×C17C22×C3×C514yescomplemented
31C2×C3×C5×C17C2×C3×C1114yescomplemented
32C3×C5×D17C2×C3×C1118yesdirect product factor
33C32×C5×C11C2×D1711yescharacteristic, direct product factor, Hall
34C22×C32×C11—171noHall
35C2×C11×C17C2×C32×C511yescharacteristic, complemented
36C11×D17C2×C32×C512yesdirect product factor
37C2×C5×D17C32×C1111yescharacteristic, direct product factor, Hall
38C2×C3×C5×C11—178no—
39C2×C3×C5×C11C3×D1714yesdirect product factor
40C2×C32×C17C2×C5×C1111yescharacteristic, complemented
41C32×D17C2×C5×C1112yesdirect product factor
42C3×C5×C17C22×C3×C1114yescomplemented
43C22×C5×C11—171noHall
44C2×C3×D17C3×C5×C1114yesdirect product factor
45C2×C32×C11—172no—
46C2×C32×C11C5×D1711yescharacteristic, direct product factor
47C11×C17C22×C32×C511yescharacteristic, complemented, Hall
48C22×C32×C5—171noHall
49C2×C5×C17C2×C32×C1111yescharacteristic, complemented
50C5×D17C2×C32×C1112yesdirect product factor
51C3×C5×C11C2×C3×D1714yesdirect product factor
52C32×C17C22×C5×C1111yescharacteristic, complemented, Hall
53C22×C3×C11—174no—
54C2×C5×C11—172no—
55C2×C5×C11C32×D1711yescharacteristic, direct product factor
56C2×C3×C17C2×C3×C5×C1114yescomplemented
57C3×D17C2×C3×C5×C1118yesdirect product factor
58C32×C11C2×C5×D1711yescharacteristic, direct product factor, Hall
59C2×C32×C5—172no—
60C2×C32×C5C11×D1711yescharacteristic, direct product factor
61C5×C17C22×C32×C1111yescharacteristic, complemented, Hall
62C2×D17C32×C5×C1111yescharacteristic, direct product factor, Hall
63C2×C3×C11—178no—
64C2×C3×C11C3×C5×D1714yesdirect product factor
65C22×C3×C5—174no—
66C5×C11C2×C32×D1711yescharacteristic, direct product factor, Hall
67C3×C17C22×C3×C5×C1114yescomplemented
68C32×C5C2×C11×D1711yescharacteristic, direct product factor, Hall
69C22×C11—171noHall
70C22×C32—171noHall
71C2×C17C2×C32×C5×C1111yescharacteristic, complemented
72D17C2×C32×C5×C1112yesdirect product factor
73C3×C11C2×C3×C5×D1714yesdirect product factor
74C2×C3×C5—178no—
75C2×C3×C5C3×C11×D1714yesdirect product factor
76C2×C11—172no—
77C2×C11C32×C5×D1711yescharacteristic, direct product factor
78C22×C5—171noHall
79C2×C32—172no—
80C2×C32C5×C11×D1711yescharacteristic, direct product factor
81C17C22×C32×C5×C1111yescharacteristic, complemented, Sylow
82C3×C5C2×C3×C11×D1714yesdirect product factor
83C22×C3—174no—
84C11C2×C32×C5×D1711yescharacteristic, direct product factor, Sylow
85C2×C5—172no—
86C2×C5C32×C11×D1711yescharacteristic, direct product factor
87C32C2×C5×C11×D1711yescharacteristic, direct product factor, Sylow
88C2×C3—178no—
89C2×C3C3×C5×C11×D1714yesdirect product factor
90C5C2×C32×C11×D1711yescharacteristic, direct product factor, Sylow
91C22—171noSylow
92C3C2×C3×C5×C11×D1714yesdirect product factor
93C2—172no—
94C2C32×C5×C11×D1711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C5×C11D17
commutator, cosocle, hypocenterC17C22×C32×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C17
UCSC1 ◁ C2×C32×C5×C11

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×D17C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
3. C2×C3×C5×C11×D17C3direct (N × H)
4. C32×C5×C11×C17C22semidirect
5. C2×C32×C11×D17C5direct (N × H)
6. C3×C5×C11×D17C2×C3direct (N × H)
7. C2×C3×C5×C11×C17C2×C3semidirect
8. C2×C5×C11×D17C32direct (N × H)
9. C32×C11×D17C2×C5direct (N × H)
10. C2×C32×C11×C17C2×C5semidirect
11. C2×C32×C5×D17C11direct (N × H)
12. C3×C5×C11×C17C22×C3semidirect
13. C2×C3×C11×D17C3×C5direct (N × H)
15. C2×C5×C11×C17C2×C32semidirect
16. C5×C11×D17C2×C32direct (N × H)
17. C32×C11×C17C22×C5semidirect
18. C2×C32×C5×C17C2×C11semidirect
19. C32×C5×D17C2×C11direct (N × H)
20. C2×C3×C11×C17C2×C3×C5semidirect
21. C3×C11×D17C2×C3×C5direct (N × H)
22. C2×C3×C5×D17C3×C11direct (N × H)
24. C2×C32×C5×C11D17direct (N × H)
25. C5×C11×C17C22×C32semidirect
26. C32×C5×C17C22×C11semidirect
27. C2×C11×D17C32×C5direct (N × H)
29. C2×C32×D17C5×C11direct (N × H)
30. C3×C11×C17C22×C3×C5semidirect
31. C2×C3×C5×C17C2×C3×C11semidirect
32. C3×C5×D17C2×C3×C11direct (N × H)
33. C32×C5×C11C2×D17direct (N × H)
35. C2×C11×C17C2×C32×C5semidirect
36. C11×D17C2×C32×C5direct (N × H)
37. C2×C5×D17C32×C11direct (N × H)
39. C2×C3×C5×C11C3×D17direct (N × H)
40. C2×C32×C17C2×C5×C11semidirect
41. C32×D17C2×C5×C11direct (N × H)
42. C3×C5×C17C22×C3×C11semidirect
44. C2×C3×D17C3×C5×C11direct (N × H)
46. C2×C32×C11C5×D17direct (N × H)
47. C11×C17C22×C32×C5semidirect
49. C2×C5×C17C2×C32×C11semidirect
50. C5×D17C2×C32×C11direct (N × H)
51. C3×C5×C11C2×C3×D17direct (N × H)
52. C32×C17C22×C5×C11semidirect
55. C2×C5×C11C32×D17direct (N × H)
56. C2×C3×C17C2×C3×C5×C11semidirect
57. C3×D17C2×C3×C5×C11direct (N × H)
58. C32×C11C2×C5×D17direct (N × H)
60. C2×C32×C5C11×D17direct (N × H)
61. C5×C17C22×C32×C11semidirect
62. C2×D17C32×C5×C11direct (N × H)
64. C2×C3×C11C3×C5×D17direct (N × H)
66. C5×C11C2×C32×D17direct (N × H)
67. C3×C17C22×C3×C5×C11semidirect
68. C32×C5C2×C11×D17direct (N × H)
71. C2×C17C2×C32×C5×C11semidirect
72. D17C2×C32×C5×C11direct (N × H)
73. C3×C11C2×C3×C5×D17direct (N × H)
75. C2×C3×C5C3×C11×D17direct (N × H)
77. C2×C11C32×C5×D17direct (N × H)
80. C2×C32C5×C11×D17direct (N × H)
81. C17C22×C32×C5×C11semidirect
82. C3×C5C2×C3×C11×D17direct (N × H)
84. C11C2×C32×C5×D17direct (N × H)
86. C2×C5C32×C11×D17direct (N × H)
87. C32C2×C5×C11×D17direct (N × H)
89. C2×C3C3×C5×C11×D17direct (N × H)
90. C5C2×C32×C11×D17direct (N × H)
92. C3C2×C3×C5×C11×D17direct (N × H)
94. C2C32×C5×C11×D17direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C11×D172
C2×C32×C5×C11×C172
C2×C3×C5×C11×D173
C2×C32×C11×D175
C2×C32×C5×D1711
C22×C32×C5×C1117