Finite Group Databasebeta

← C2×C7×C11×C13×C3⋊D3 #49115024

Subgroups — C2×C7×C11×C13×C3⋊D3 #49115024

Order 36036.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×C13×C3⋊D3C212yesmaximal, direct product factor
2C2×C32×C7×C11×C13C211yesmaximal, characteristic, complemented
3C2×D3×C7×C11×C13—34nomaximal
4C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
5D3×C7×C11×C13—38no—
6C2×C3×C7×C11×C13D314yescomplemented
7C2×C11×C13×C3⋊D3C711yesmaximal, characteristic, direct product factor, Hall
8C22×C7×C11×C13—91noHall
9C2×C7×C13×C3⋊D3C1111yesmaximal, characteristic, direct product factor, Hall
10C3×C7×C11×C13C2×D314yescomplemented
11C2×C7×C11×C3⋊D3C1311yesmaximal, characteristic, direct product factor, Hall
12C11×C13×C3⋊D3C2×C712yesdirect product factor
13C2×C32×C11×C13C2×C711yescharacteristic, complemented
14C2×C7×C11×C13—92no—
15C2×C7×C11×C13C3⋊D311yescharacteristic, direct product factor
16C2×D3×C11×C13—34no—
17C2×C32×C7×C13C2×C1111yescharacteristic, complemented
18C7×C13×C3⋊D3C2×C1112yesdirect product factor
19C2×C32×C7×C11C2×C1311yescharacteristic, complemented
20C7×C11×C3⋊D3C2×C1312yesdirect product factor
21C32×C11×C13C22×C711yescharacteristic, complemented, Hall
22C2×D3×C7×C13—34no—
23C7×C11×C13C2×C3⋊D311yescharacteristic, direct product factor, Hall
24C2×D3×C7×C11—34no—
25C2×C3×C11×C13D3×C714yescomplemented
26D3×C11×C13—38no—
27C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
28C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
29C22×C11×C13—91noHall
30C2×C3×C7×C13D3×C1114yescomplemented
31D3×C7×C13—38no—
32C2×C13×C3⋊D3C7×C1111yescharacteristic, direct product factor, Hall
33C2×C3×C7×C11D3×C1314yescomplemented
34D3×C7×C11—38no—
35C3×C11×C13C2×D3×C714yescomplemented
36C2×C11×C3⋊D3C7×C1311yescharacteristic, direct product factor, Hall
37C22×C7×C13—91noHall
38C22×C7×C11—91noHall
39C2×C11×C13—92no—
40C2×C11×C13C7×C3⋊D311yescharacteristic, direct product factor
41C3×C7×C13C2×D3×C1114yescomplemented
42C2×C7×C3⋊D3C11×C1311yescharacteristic, direct product factor, Hall
43C2×C32×C13C2×C7×C1111yescharacteristic, complemented
44C13×C3⋊D3C2×C7×C1112yesdirect product factor
45C3×C7×C11C2×D3×C1314yescomplemented
46C2×C32×C11C2×C7×C1311yescharacteristic, complemented
47C11×C3⋊D3C2×C7×C1312yesdirect product factor
48C2×C7×C13—92no—
49C2×C7×C13C11×C3⋊D311yescharacteristic, direct product factor
50C2×D3×C13—34no—
51C2×C7×C11—92no—
52C2×C7×C11C13×C3⋊D311yescharacteristic, direct product factor
53C11×C13C2×C7×C3⋊D311yescharacteristic, direct product factor, Hall
54C2×D3×C11—34no—
55C2×C32×C7C2×C11×C1311yescharacteristic, complemented
56C7×C3⋊D3C2×C11×C1312yesdirect product factor
57C32×C13C22×C7×C1111yescharacteristic, complemented, Hall
58C32×C11C22×C7×C1311yescharacteristic, complemented, Hall
59C7×C13C2×C11×C3⋊D311yescharacteristic, direct product factor, Hall
60C2×D3×C7—34no—
61C2×C3×C13D3×C7×C1114yescomplemented
62D3×C13—38no—
63C7×C11C2×C13×C3⋊D311yescharacteristic, direct product factor, Hall
64C2×C3×C11D3×C7×C1314yescomplemented
65D3×C11—38no—
66C32×C7C22×C11×C1311yescharacteristic, complemented, Hall
67C22×C13—91noHall
68C22×C11—91noHall
69C2×C3×C7D3×C11×C1314yescomplemented
70D3×C7—38no—
71C3×C13C2×D3×C7×C1114yescomplemented
72C2×C3⋊D3C7×C11×C1311yescharacteristic, direct product factor, Hall
73C3×C11C2×D3×C7×C1314yescomplemented
74C22×C7—91noHall
75C2×C13—92no—
76C2×C13C7×C11×C3⋊D311yescharacteristic, direct product factor
77C2×C11—92no—
78C2×C11C7×C13×C3⋊D311yescharacteristic, direct product factor
79C3×C7C2×D3×C11×C1314yescomplemented
80C2×C32C2×C7×C11×C1311yescharacteristic, complemented
81C3⋊D3C2×C7×C11×C1312yesdirect product factor
82C2×C7—92no—
83C2×C7C11×C13×C3⋊D311yescharacteristic, direct product factor
84C13C2×C7×C11×C3⋊D311yescharacteristic, direct product factor, Sylow
85C2×D3—34no—
86C11C2×C7×C13×C3⋊D311yescharacteristic, direct product factor, Sylow
87C32C22×C7×C11×C1311yescharacteristic, complemented, Sylow
88C7C2×C11×C13×C3⋊D311yescharacteristic, direct product factor, Sylow
89C2×C3D3×C7×C11×C1314yescomplemented
90D3—38no—
91C22—91noSylow
92C3C2×D3×C7×C11×C1314yescomplemented
93C2—92no—
94C2C7×C11×C13×C3⋊D311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7×C11×C13C3⋊D3
commutator, cosocle, hypocenterC32C22×C7×C11×C13
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32
UCSC1 ◁ C2×C7×C11×C13

Complements

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

NH ≅ G/Ntype
1. C7×C11×C13×C3⋊D3C2direct (N × H)
2. C2×C32×C7×C11×C13C2semidirect
4. C32×C7×C11×C13C22semidirect
6. C2×C3×C7×C11×C13D3semidirect
7. C2×C11×C13×C3⋊D3C7direct (N × H)
9. C2×C7×C13×C3⋊D3C11direct (N × H)
10. C3×C7×C11×C13C2×D3semidirect
11. C2×C7×C11×C3⋊D3C13direct (N × H)
12. C11×C13×C3⋊D3C2×C7direct (N × H)
13. C2×C32×C11×C13C2×C7semidirect
15. C2×C7×C11×C13C3⋊D3direct (N × H)
17. C2×C32×C7×C13C2×C11semidirect
18. C7×C13×C3⋊D3C2×C11direct (N × H)
19. C2×C32×C7×C11C2×C13semidirect
20. C7×C11×C3⋊D3C2×C13direct (N × H)
21. C32×C11×C13C22×C7semidirect
23. C7×C11×C13C2×C3⋊D3direct (N × H)
25. C2×C3×C11×C13D3×C7semidirect
27. C32×C7×C13C22×C11semidirect
28. C32×C7×C11C22×C13semidirect
30. C2×C3×C7×C13D3×C11semidirect
32. C2×C13×C3⋊D3C7×C11direct (N × H)
33. C2×C3×C7×C11D3×C13semidirect
35. C3×C11×C13C2×D3×C7semidirect
36. C2×C11×C3⋊D3C7×C13direct (N × H)
40. C2×C11×C13C7×C3⋊D3direct (N × H)
41. C3×C7×C13C2×D3×C11semidirect
42. C2×C7×C3⋊D3C11×C13direct (N × H)
43. C2×C32×C13C2×C7×C11semidirect
44. C13×C3⋊D3C2×C7×C11direct (N × H)
45. C3×C7×C11C2×D3×C13semidirect
46. C2×C32×C11C2×C7×C13semidirect
47. C11×C3⋊D3C2×C7×C13direct (N × H)
49. C2×C7×C13C11×C3⋊D3direct (N × H)
52. C2×C7×C11C13×C3⋊D3direct (N × H)
53. C11×C13C2×C7×C3⋊D3direct (N × H)
55. C2×C32×C7C2×C11×C13semidirect
56. C7×C3⋊D3C2×C11×C13direct (N × H)
57. C32×C13C22×C7×C11semidirect
58. C32×C11C22×C7×C13semidirect
59. C7×C13C2×C11×C3⋊D3direct (N × H)
61. C2×C3×C13D3×C7×C11semidirect
63. C7×C11C2×C13×C3⋊D3direct (N × H)
64. C2×C3×C11D3×C7×C13semidirect
66. C32×C7C22×C11×C13semidirect
69. C2×C3×C7D3×C11×C13semidirect
71. C3×C13C2×D3×C7×C11semidirect
72. C2×C3⋊D3C7×C11×C13direct (N × H)
73. C3×C11C2×D3×C7×C13semidirect
76. C2×C13C7×C11×C3⋊D3direct (N × H)
78. C2×C11C7×C13×C3⋊D3direct (N × H)
79. C3×C7C2×D3×C11×C13semidirect
80. C2×C32C2×C7×C11×C13semidirect
81. C3⋊D3C2×C7×C11×C13direct (N × H)
83. C2×C7C11×C13×C3⋊D3direct (N × H)
84. C13C2×C7×C11×C3⋊D3direct (N × H)
86. C11C2×C7×C13×C3⋊D3direct (N × H)
87. C32C22×C7×C11×C13semidirect
88. C7C2×C11×C13×C3⋊D3direct (N × H)
89. C2×C3D3×C7×C11×C13semidirect
92. C3C2×D3×C7×C11×C13semidirect
94. C2C7×C11×C13×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C11×C13×C3⋊D32
C2×C32×C7×C11×C132
C2×D3×C7×C11×C133
C2×C11×C13×C3⋊D37
C2×C7×C13×C3⋊D311
C2×C7×C11×C3⋊D313