Finite Group Databasebeta

← C2×C32×C11×D85 #46778198

Subgroups — C2×C32×C11×D85 #46778198

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C11×D85C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C3×C11×D85C314yesmaximal, direct product factor
4C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
5C2×C32×C11×D17—51nomaximal, Hall
6C3×C11×D85C2×C318yesdirect product factor
7C2×C3×C5×C11×C17C2×C314yescomplemented
8C2×C11×D85C3211yescharacteristic, direct product factor, Hall
9C32×C11×D17—52no—
10C2×C32×C11×C17D511yescharacteristic, complemented
11C2×C32×D85C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C5×C11×C17C22×C314yescomplemented
13C2×C3×C11×D17—54no—
14C2×C32×D5×C11—171nomaximal, Hall
15C2×C5×C11×C17C2×C3211yescharacteristic, complemented
16C11×D85C2×C3212yesdirect product factor
17C32×C11×C17C2×D511yescharacteristic, complemented, Hall
18C2×C32×C5×C17C2×C1111yescharacteristic, complemented
19C32×D85C2×C1112yesdirect product factor
20C2×C3×C11×C17C3×D514yescomplemented
21C3×C11×D17—58no—
22C2×C3×D85C3×C1114yesdirect product factor
23C2×C32×C5×C11D1711yescharacteristic, complemented
24C32×D5×C11—172no—
25C5×C11×C17C22×C3211yescharacteristic, complemented, Hall
26C32×C5×C17C22×C1111yescharacteristic, complemented, Hall
27C2×C11×D17—51noHall
28C2×C3×D5×C11—174no—
29C2×C32×D17—51noHall
30C3×C11×C17C2×C3×D514yescomplemented
31C2×C3×C5×C17C2×C3×C1114yescomplemented
32C3×D85C2×C3×C1118yesdirect product factor
33C32×C5×C11C2×D1711yescharacteristic, complemented, Hall
34C22×C32×C11—851noHall
35C2×C11×C17C32×D511yescharacteristic, complemented
36C11×D17—52no—
37C2×D85C32×C1111yescharacteristic, direct product factor, Hall
38C2×C3×C5×C11C3×D1714yescomplemented
39C3×D5×C11—178no—
40C2×C32×C17D5×C1111yescharacteristic, complemented
41C32×D17—52no—
42C3×C5×C17C22×C3×C1114yescomplemented
43C2×D5×C11—171noHall
44C2×C3×D17—54no—
45C2×C32×C11—852no—
46C2×C32×C11D8511yescharacteristic, direct product factor
47C11×C17C2×C32×D511yescharacteristic, complemented, Hall
48C2×C32×D5—171noHall
49C2×C5×C17C2×C32×C1111yescharacteristic, complemented
50D85C2×C32×C1112yesdirect product factor
51C3×C5×C11C2×C3×D1714yescomplemented
52C32×C17C2×D5×C1111yescharacteristic, complemented, Hall
53C22×C3×C11—854no—
54C2×C5×C11C32×D1711yescharacteristic, complemented
55D5×C11—172no—
56C2×C3×C17C3×D5×C1114yescomplemented
57C3×D17—58no—
58C32×C11C2×D8511yescharacteristic, direct product factor, Hall
59C2×C32×C5C11×D1711yescharacteristic, complemented
60C32×D5—172no—
61C5×C17C22×C32×C1111yescharacteristic, complemented, Hall
62C2×D17—51noHall
63C2×C3×C11—858no—
64C2×C3×C11C3×D8514yesdirect product factor
65C2×C3×D5—174no—
66C5×C11C2×C32×D1711yescharacteristic, complemented, Hall
67C3×C17C2×C3×D5×C1114yescomplemented
68C32×C5C2×C11×D1711yescharacteristic, complemented, Hall
69C22×C11—851noHall
70C22×C32—851noHall
71C2×C17C32×D5×C1111yescharacteristic, complemented
72D17—52no—
73C3×C11C2×C3×D8514yesdirect product factor
74C2×C3×C5C3×C11×D1714yescomplemented
75C3×D5—178no—
76C2×C11—852no—
77C2×C11C32×D8511yescharacteristic, direct product factor
78C2×D5—171noHall
79C2×C32—852no—
80C2×C32C11×D8511yescharacteristic, direct product factor
81C17C2×C32×D5×C1111yescharacteristic, complemented, Sylow
82C3×C5C2×C3×C11×D1714yescomplemented
83C22×C3—854no—
84C11C2×C32×D8511yescharacteristic, direct product factor, Sylow
85C2×C5C32×C11×D1711yescharacteristic, complemented
86D5—172no—
87C32C2×C11×D8511yescharacteristic, direct product factor, Sylow
88C2×C3—858no—
89C2×C3C3×C11×D8514yesdirect product factor
90C5C2×C32×C11×D1711yescharacteristic, complemented, Sylow
91C22—851noSylow
92C3C2×C3×C11×D8514yesdirect product factor
93C2—852no—
94C2C32×C11×D8511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C11D85
commutator, cosocle, hypocenterC5×C17C22×C32×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C5×C17
UCSC1 ◁ C2×C32×C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×D85C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
3. C2×C3×C11×D85C3direct (N × H)
4. C32×C5×C11×C17C22semidirect
6. C3×C11×D85C2×C3direct (N × H)
7. C2×C3×C5×C11×C17C2×C3semidirect
8. C2×C11×D85C32direct (N × H)
10. C2×C32×C11×C17D5semidirect
11. C2×C32×D85C11direct (N × H)
12. C3×C5×C11×C17C22×C3semidirect
15. C2×C5×C11×C17C2×C32semidirect
16. C11×D85C2×C32direct (N × H)
17. C32×C11×C17C2×D5semidirect
18. C2×C32×C5×C17C2×C11semidirect
19. C32×D85C2×C11direct (N × H)
20. C2×C3×C11×C17C3×D5semidirect
22. C2×C3×D85C3×C11direct (N × H)
23. C2×C32×C5×C11D17semidirect
25. C5×C11×C17C22×C32semidirect
26. C32×C5×C17C22×C11semidirect
30. C3×C11×C17C2×C3×D5semidirect
31. C2×C3×C5×C17C2×C3×C11semidirect
32. C3×D85C2×C3×C11direct (N × H)
33. C32×C5×C11C2×D17semidirect
35. C2×C11×C17C32×D5semidirect
37. C2×D85C32×C11direct (N × H)
38. C2×C3×C5×C11C3×D17semidirect
40. C2×C32×C17D5×C11semidirect
42. C3×C5×C17C22×C3×C11semidirect
46. C2×C32×C11D85direct (N × H)
47. C11×C17C2×C32×D5semidirect
49. C2×C5×C17C2×C32×C11semidirect
50. D85C2×C32×C11direct (N × H)
51. C3×C5×C11C2×C3×D17semidirect
52. C32×C17C2×D5×C11semidirect
54. C2×C5×C11C32×D17semidirect
56. C2×C3×C17C3×D5×C11semidirect
58. C32×C11C2×D85direct (N × H)
59. C2×C32×C5C11×D17semidirect
61. C5×C17C22×C32×C11semidirect
64. C2×C3×C11C3×D85direct (N × H)
66. C5×C11C2×C32×D17semidirect
67. C3×C17C2×C3×D5×C11semidirect
68. C32×C5C2×C11×D17semidirect
71. C2×C17C32×D5×C11semidirect
73. C3×C11C2×C3×D85direct (N × H)
74. C2×C3×C5C3×C11×D17semidirect
77. C2×C11C32×D85direct (N × H)
80. C2×C32C11×D85direct (N × H)
81. C17C2×C32×D5×C11semidirect
82. C3×C5C2×C3×C11×D17semidirect
84. C11C2×C32×D85direct (N × H)
85. C2×C5C32×C11×D17semidirect
87. C32C2×C11×D85direct (N × H)
89. C2×C3C3×C11×D85direct (N × H)
90. C5C2×C32×C11×D17semidirect
92. C3C2×C3×C11×D85direct (N × H)
94. C2C32×C11×D85direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×D852
C2×C32×C5×C11×C172
C2×C3×C11×D853
C2×C32×C11×D175
C2×C32×D8511
C2×C32×D5×C1117