Finite Group Databasebeta

← C2×C32×C11×D91 #49115013

Subgroups — C2×C32×C11×D91 #49115013

Order 36036.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C11×D91C212yesmaximal, direct product factor
2C2×C32×C7×C11×C13C211yesmaximal, characteristic, complemented
3C2×C3×C11×D91C314yesmaximal, direct product factor
4C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
5C3×C11×D91C2×C318yesdirect product factor
6C2×C3×C7×C11×C13C2×C314yescomplemented
7C2×C32×C11×D13—71nomaximal, Hall
8C2×C11×D91C3211yescharacteristic, direct product factor, Hall
9C2×C32×D91C1111yesmaximal, characteristic, direct product factor, Hall
10C3×C7×C11×C13C22×C314yescomplemented
11C2×C32×C11×D7—131nomaximal, Hall
12C32×C11×D13—72no—
13C2×C32×C11×C13D711yescharacteristic, complemented
14C11×D91C2×C3212yesdirect product factor
15C2×C7×C11×C13C2×C3211yescharacteristic, complemented
16C2×C3×C11×D13—74no—
17C2×C32×C7×C13C2×C1111yescharacteristic, complemented
18C32×D91C2×C1112yesdirect product factor
19C2×C32×C7×C11D1311yescharacteristic, complemented
20C32×C11×D7—132no—
21C32×C11×C13C2×D711yescharacteristic, complemented, Hall
22C2×C3×D91C3×C1114yesdirect product factor
23C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
24C2×C3×C11×D7—134no—
25C2×C3×C11×C13C3×D714yescomplemented
26C3×C11×D13—78no—
27C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
28C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
29C2×C11×D13—71noHall
30C2×C3×C7×C13C2×C3×C1114yescomplemented
31C3×D91C2×C3×C1118yesdirect product factor
32C2×C32×D13—71noHall
33C2×C3×C7×C11C3×D1314yescomplemented
34C3×C11×D7—138no—
35C3×C11×C13C2×C3×D714yescomplemented
36C22×C32×C11—911noHall
37C2×D91C32×C1111yescharacteristic, direct product factor, Hall
38C2×C11×D7—131noHall
39C2×C11×C13C32×D711yescharacteristic, complemented
40C11×D13—72no—
41C3×C7×C13C22×C3×C1114yescomplemented
42C2×C32×D7—131noHall
43C2×C32×C13C11×D711yescharacteristic, complemented
44C32×D13—72no—
45C3×C7×C11C2×C3×D1314yescomplemented
46C2×C32×C11—912no—
47C2×C32×C11D9111yescharacteristic, direct product factor
48C2×C7×C13C2×C32×C1111yescharacteristic, complemented
49D91C2×C32×C1112yesdirect product factor
50C2×C3×D13—74no—
51C2×C7×C11C32×D1311yescharacteristic, complemented
52C11×D7—132no—
53C11×C13C2×C32×D711yescharacteristic, complemented, Hall
54C22×C3×C11—914no—
55C2×C32×C7C11×D1311yescharacteristic, complemented
56C32×D7—132no—
57C32×C13C2×C11×D711yescharacteristic, complemented, Hall
58C32×C11C2×D9111yescharacteristic, direct product factor, Hall
59C7×C13C22×C32×C1111yescharacteristic, complemented, Hall
60C2×C3×D7—134no—
61C2×C3×C13C3×C11×D714yescomplemented
62C3×D13—78no—
63C7×C11C2×C32×D1311yescharacteristic, complemented, Hall
64C2×C3×C11—918no—
65C2×C3×C11C3×D9114yesdirect product factor
66C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
67C2×D13—71noHall
68C22×C11—911noHall
69C2×C3×C7C3×C11×D1314yescomplemented
70C3×D7—138no—
71C3×C13C2×C3×C11×D714yescomplemented
72C22×C32—911noHall
73C3×C11C2×C3×D9114yesdirect product factor
74C2×D7—131noHall
75C2×C13C32×C11×D711yescharacteristic, complemented
76D13—72no—
77C2×C11—912no—
78C2×C11C32×D9111yescharacteristic, direct product factor
79C3×C7C2×C3×C11×D1314yescomplemented
80C2×C32—912no—
81C2×C32C11×D9111yescharacteristic, direct product factor
82C2×C7C32×C11×D1311yescharacteristic, complemented
83D7—132no—
84C13C2×C32×C11×D711yescharacteristic, complemented, Sylow
85C22×C3—914no—
86C11C2×C32×D9111yescharacteristic, direct product factor, Sylow
87C32C2×C11×D9111yescharacteristic, direct product factor, Sylow
88C7C2×C32×C11×D1311yescharacteristic, complemented, Sylow
89C2×C3—918no—
90C2×C3C3×C11×D9114yesdirect product factor
91C22—911noSylow
92C3C2×C3×C11×D9114yesdirect product factor
93C2—912no—
94C2C32×C11×D9111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C11D91
commutator, cosocle, hypocenterC7×C13C22×C32×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C7×C13
UCSC1 ◁ C2×C32×C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×D91C2direct (N × H)
2. C2×C32×C7×C11×C13C2semidirect
3. C2×C3×C11×D91C3direct (N × H)
4. C32×C7×C11×C13C22semidirect
5. C3×C11×D91C2×C3direct (N × H)
6. C2×C3×C7×C11×C13C2×C3semidirect
8. C2×C11×D91C32direct (N × H)
9. C2×C32×D91C11direct (N × H)
10. C3×C7×C11×C13C22×C3semidirect
13. C2×C32×C11×C13D7semidirect
14. C11×D91C2×C32direct (N × H)
15. C2×C7×C11×C13C2×C32semidirect
17. C2×C32×C7×C13C2×C11semidirect
18. C32×D91C2×C11direct (N × H)
19. C2×C32×C7×C11D13semidirect
21. C32×C11×C13C2×D7semidirect
22. C2×C3×D91C3×C11direct (N × H)
23. C7×C11×C13C22×C32semidirect
25. C2×C3×C11×C13C3×D7semidirect
27. C32×C7×C13C22×C11semidirect
28. C32×C7×C11C2×D13semidirect
30. C2×C3×C7×C13C2×C3×C11semidirect
31. C3×D91C2×C3×C11direct (N × H)
33. C2×C3×C7×C11C3×D13semidirect
35. C3×C11×C13C2×C3×D7semidirect
37. C2×D91C32×C11direct (N × H)
39. C2×C11×C13C32×D7semidirect
41. C3×C7×C13C22×C3×C11semidirect
43. C2×C32×C13C11×D7semidirect
45. C3×C7×C11C2×C3×D13semidirect
47. C2×C32×C11D91direct (N × H)
48. C2×C7×C13C2×C32×C11semidirect
49. D91C2×C32×C11direct (N × H)
51. C2×C7×C11C32×D13semidirect
53. C11×C13C2×C32×D7semidirect
55. C2×C32×C7C11×D13semidirect
57. C32×C13C2×C11×D7semidirect
58. C32×C11C2×D91direct (N × H)
59. C7×C13C22×C32×C11semidirect
61. C2×C3×C13C3×C11×D7semidirect
63. C7×C11C2×C32×D13semidirect
65. C2×C3×C11C3×D91direct (N × H)
66. C32×C7C2×C11×D13semidirect
69. C2×C3×C7C3×C11×D13semidirect
71. C3×C13C2×C3×C11×D7semidirect
73. C3×C11C2×C3×D91direct (N × H)
75. C2×C13C32×C11×D7semidirect
78. C2×C11C32×D91direct (N × H)
79. C3×C7C2×C3×C11×D13semidirect
81. C2×C32C11×D91direct (N × H)
82. C2×C7C32×C11×D13semidirect
84. C13C2×C32×C11×D7semidirect
86. C11C2×C32×D91direct (N × H)
87. C32C2×C11×D91direct (N × H)
88. C7C2×C32×C11×D13semidirect
90. C2×C3C3×C11×D91direct (N × H)
92. C3C2×C3×C11×D91direct (N × H)
94. C2C32×C11×D91direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×D912
C2×C32×C7×C11×C132
C2×C3×C11×D913
C2×C32×C11×D137
C2×C32×D9111
C2×C32×C11×D713