Finite Group Databasebeta

← C2×C32×D5×C11×C17 #46778197

Subgroups — C2×C32×D5×C11×C17 #46778197

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D5×C11×C17C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C3×D5×C11×C17C314yesmaximal, direct product factor
4C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
5C22×C32×C11×C17—51nomaximal, Hall
6C3×D5×C11×C17C2×C318yesdirect product factor
7C2×C3×C5×C11×C17C2×C314yescomplemented
8C2×D5×C11×C17C3211yescharacteristic, direct product factor, Hall
9C2×C32×C11×C17—52no—
10C2×C32×C11×C17D511yescharacteristic, direct product factor
11C2×C32×D5×C17C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C5×C11×C17C22×C314yescomplemented
13C22×C3×C11×C17—54no—
14C2×C32×D5×C11C1711yesmaximal, characteristic, direct product factor, Hall
15C2×C5×C11×C17C2×C3211yescharacteristic, complemented
16D5×C11×C17C2×C3212yesdirect product factor
17C32×C11×C17C2×D511yescharacteristic, direct product factor, Hall
18C2×C32×C5×C17C2×C1111yescharacteristic, complemented
19C32×D5×C17C2×C1112yesdirect product factor
20C2×C3×C11×C17—58no—
21C2×C3×C11×C17C3×D514yesdirect product factor
22C2×C3×D5×C17C3×C1114yesdirect product factor
23C2×C32×C5×C11C2×C1711yescharacteristic, complemented
24C32×D5×C11C2×C1712yesdirect product factor
25C5×C11×C17C22×C3211yescharacteristic, complemented, Hall
26C32×C5×C17C22×C1111yescharacteristic, complemented, Hall
27C22×C11×C17—51noHall
28C2×C3×D5×C11C3×C1714yesdirect product factor
29C22×C32×C17—51noHall
30C3×C11×C17C2×C3×D514yesdirect product factor
31C2×C3×C5×C17C2×C3×C1114yescomplemented
32C3×D5×C17C2×C3×C1118yesdirect product factor
33C32×C5×C11C22×C1711yescharacteristic, complemented, Hall
34C22×C32×C11—51noHall
35C2×C11×C17—52no—
36C2×C11×C17C32×D511yescharacteristic, direct product factor
37C2×D5×C17C32×C1111yescharacteristic, direct product factor, Hall
38C2×C3×C5×C11C2×C3×C1714yescomplemented
39C3×D5×C11C2×C3×C1718yesdirect product factor
40C2×C32×C17—52no—
41C2×C32×C17D5×C1111yescharacteristic, direct product factor
42C3×C5×C17C22×C3×C1114yescomplemented
43C2×D5×C11C32×C1711yescharacteristic, direct product factor, Hall
44C22×C3×C17—54no—
45C2×C32×C11—52no—
46C2×C32×C11D5×C1711yescharacteristic, direct product factor
47C11×C17C2×C32×D511yescharacteristic, direct product factor, Hall
48C2×C32×D5C11×C1711yescharacteristic, direct product factor, Hall
49C2×C5×C17C2×C32×C1111yescharacteristic, complemented
50D5×C17C2×C32×C1112yesdirect product factor
51C3×C5×C11C22×C3×C1714yescomplemented
52C32×C17C2×D5×C1111yescharacteristic, direct product factor, Hall
53C22×C3×C11—54no—
54C2×C5×C11C2×C32×C1711yescharacteristic, complemented
55D5×C11C2×C32×C1712yesdirect product factor
56C2×C3×C17—58no—
57C2×C3×C17C3×D5×C1114yesdirect product factor
58C32×C11C2×D5×C1711yescharacteristic, direct product factor, Hall
59C2×C32×C5C2×C11×C1711yescharacteristic, complemented
60C32×D5C2×C11×C1712yesdirect product factor
61C5×C17C22×C32×C1111yescharacteristic, complemented, Hall
62C22×C17—51noHall
63C2×C3×C11—58no—
64C2×C3×C11C3×D5×C1714yesdirect product factor
65C2×C3×D5C3×C11×C1714yesdirect product factor
66C5×C11C22×C32×C1711yescharacteristic, complemented, Hall
67C3×C17C2×C3×D5×C1114yesdirect product factor
68C32×C5C22×C11×C1711yescharacteristic, complemented, Hall
69C22×C11—51noHall
70C22×C32—51noHall
71C2×C17—52no—
72C2×C17C32×D5×C1111yescharacteristic, direct product factor
73C3×C11C2×C3×D5×C1714yesdirect product factor
74C2×C3×C5C2×C3×C11×C1714yescomplemented
75C3×D5C2×C3×C11×C1718yesdirect product factor
76C2×C11—52no—
77C2×C11C32×D5×C1711yescharacteristic, direct product factor
78C2×D5C32×C11×C1711yescharacteristic, direct product factor, Hall
79C2×C32—52no—
80C2×C32D5×C11×C1711yescharacteristic, direct product factor
81C17C2×C32×D5×C1111yescharacteristic, direct product factor, Sylow
82C3×C5C22×C3×C11×C1714yescomplemented
83C22×C3—54no—
84C11C2×C32×D5×C1711yescharacteristic, direct product factor, Sylow
85C2×C5C2×C32×C11×C1711yescharacteristic, complemented
86D5C2×C32×C11×C1712yesdirect product factor
87C32C2×D5×C11×C1711yescharacteristic, direct product factor, Sylow
88C2×C3—58no—
89C2×C3C3×D5×C11×C1714yesdirect product factor
90C5C22×C32×C11×C1711yescharacteristic, complemented, Sylow
91C22—51noSylow
92C3C2×C3×D5×C11×C1714yesdirect product factor
93C2—52no—
94C2C32×D5×C11×C1711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C11×C17D5
commutator, cosocle, hypocenterC5C22×C32×C11×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C5
UCSC1 ◁ C2×C32×C11×C17

Complements

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

NH ≅ G/Ntype
1. C32×D5×C11×C17C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
3. C2×C3×D5×C11×C17C3direct (N × H)
4. C32×C5×C11×C17C22semidirect
6. C3×D5×C11×C17C2×C3direct (N × H)
7. C2×C3×C5×C11×C17C2×C3semidirect
8. C2×D5×C11×C17C32direct (N × H)
10. C2×C32×C11×C17D5direct (N × H)
11. C2×C32×D5×C17C11direct (N × H)
12. C3×C5×C11×C17C22×C3semidirect
14. C2×C32×D5×C11C17direct (N × H)
15. C2×C5×C11×C17C2×C32semidirect
16. D5×C11×C17C2×C32direct (N × H)
17. C32×C11×C17C2×D5direct (N × H)
18. C2×C32×C5×C17C2×C11semidirect
19. C32×D5×C17C2×C11direct (N × H)
21. C2×C3×C11×C17C3×D5direct (N × H)
22. C2×C3×D5×C17C3×C11direct (N × H)
23. C2×C32×C5×C11C2×C17semidirect
24. C32×D5×C11C2×C17direct (N × H)
25. C5×C11×C17C22×C32semidirect
26. C32×C5×C17C22×C11semidirect
28. C2×C3×D5×C11C3×C17direct (N × H)
30. C3×C11×C17C2×C3×D5direct (N × H)
31. C2×C3×C5×C17C2×C3×C11semidirect
32. C3×D5×C17C2×C3×C11direct (N × H)
33. C32×C5×C11C22×C17semidirect
36. C2×C11×C17C32×D5direct (N × H)
37. C2×D5×C17C32×C11direct (N × H)
38. C2×C3×C5×C11C2×C3×C17semidirect
39. C3×D5×C11C2×C3×C17direct (N × H)
41. C2×C32×C17D5×C11direct (N × H)
42. C3×C5×C17C22×C3×C11semidirect
43. C2×D5×C11C32×C17direct (N × H)
46. C2×C32×C11D5×C17direct (N × H)
47. C11×C17C2×C32×D5direct (N × H)
48. C2×C32×D5C11×C17direct (N × H)
49. C2×C5×C17C2×C32×C11semidirect
50. D5×C17C2×C32×C11direct (N × H)
51. C3×C5×C11C22×C3×C17semidirect
52. C32×C17C2×D5×C11direct (N × H)
54. C2×C5×C11C2×C32×C17semidirect
55. D5×C11C2×C32×C17direct (N × H)
57. C2×C3×C17C3×D5×C11direct (N × H)
58. C32×C11C2×D5×C17direct (N × H)
59. C2×C32×C5C2×C11×C17semidirect
60. C32×D5C2×C11×C17direct (N × H)
61. C5×C17C22×C32×C11semidirect
64. C2×C3×C11C3×D5×C17direct (N × H)
65. C2×C3×D5C3×C11×C17direct (N × H)
66. C5×C11C22×C32×C17semidirect
67. C3×C17C2×C3×D5×C11direct (N × H)
68. C32×C5C22×C11×C17semidirect
72. C2×C17C32×D5×C11direct (N × H)
73. C3×C11C2×C3×D5×C17direct (N × H)
74. C2×C3×C5C2×C3×C11×C17semidirect
75. C3×D5C2×C3×C11×C17direct (N × H)
77. C2×C11C32×D5×C17direct (N × H)
78. C2×D5C32×C11×C17direct (N × H)
80. C2×C32D5×C11×C17direct (N × H)
81. C17C2×C32×D5×C11direct (N × H)
82. C3×C5C22×C3×C11×C17semidirect
84. C11C2×C32×D5×C17direct (N × H)
85. C2×C5C2×C32×C11×C17semidirect
86. D5C2×C32×C11×C17direct (N × H)
87. C32C2×D5×C11×C17direct (N × H)
89. C2×C3C3×D5×C11×C17direct (N × H)
90. C5C22×C32×C11×C17semidirect
92. C3C2×C3×D5×C11×C17direct (N × H)
94. C2C32×D5×C11×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C32×D5×C11×C172
C2×C32×C5×C11×C172
C2×C3×D5×C11×C173
C22×C32×C11×C175
C2×C32×D5×C1711
C2×C32×D5×C1117