Finite Group Databasebeta

← C2×C7×C11×C3⋊D39 #49115025

Subgroups — C2×C7×C11×C3⋊D39 #49115025

Order 36036.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×C3⋊D39C212yesmaximal, direct product factor
2C2×C32×C7×C11×C13C211yesmaximal, characteristic, complemented
3C2×C7×C11×D39—34nomaximal
4C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
5C7×C11×D39—38no—
6C2×C3×C7×C11×C13D314yescomplemented
7C2×C11×C3⋊D39C711yesmaximal, characteristic, direct product factor, Hall
8C2×C7×C11×D13—91noHall
9C2×C7×C3⋊D39C1111yesmaximal, characteristic, direct product factor, Hall
10C3×C7×C11×C13C2×D314yescomplemented
11C2×C7×C11×C3⋊D3—131nomaximal, Hall
12C11×C3⋊D39C2×C712yesdirect product factor
13C2×C32×C11×C13C2×C711yescharacteristic, complemented
14C7×C11×D13—92no—
15C2×C7×C11×C13C3⋊D311yescharacteristic, complemented
16C2×C11×D39—34no—
17C2×C32×C7×C13C2×C1111yescharacteristic, complemented
18C7×C3⋊D39C2×C1112yesdirect product factor
19C2×C32×C7×C11D1311yescharacteristic, complemented
20C7×C11×C3⋊D3—132no—
21C32×C11×C13C22×C711yescharacteristic, complemented, Hall
22C2×C7×D39—34no—
23C7×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
24C2×D3×C7×C11—394no—
25C2×C3×C11×C13D3×C714yescomplemented
26C11×D39—38no—
27C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
28C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
29C2×C11×D13—91noHall
30C2×C3×C7×C13D3×C1114yescomplemented
31C7×D39—38no—
32C2×C3⋊D39C7×C1111yescharacteristic, direct product factor, Hall
33C2×C3×C7×C11D3914yescomplemented
34D3×C7×C11—398no—
35C3×C11×C13C2×D3×C714yescomplemented
36C2×C11×C3⋊D3—131noHall
37C2×C7×D13—91noHall
38C22×C7×C11—1171noHall
39C2×C11×C13C7×C3⋊D311yescharacteristic, complemented
40C11×D13—92no—
41C3×C7×C13C2×D3×C1114yescomplemented
42C2×C7×C3⋊D3—131noHall
43C2×C32×C13C2×C7×C1111yescharacteristic, complemented
44C3⋊D39C2×C7×C1112yesdirect product factor
45C3×C7×C11C2×D3914yescomplemented
46C2×C32×C11C7×D1311yescharacteristic, complemented
47C11×C3⋊D3—132no—
48C2×C7×C13C11×C3⋊D311yescharacteristic, complemented
49C7×D13—92no—
50C2×D39—34no—
51C2×C7×C11—1172no—
52C2×C7×C11C3⋊D3911yescharacteristic, direct product factor
53C11×C13C2×C7×C3⋊D311yescharacteristic, complemented, Hall
54C2×D3×C11—394no—
55C2×C32×C7C11×D1311yescharacteristic, complemented
56C7×C3⋊D3—132no—
57C32×C13C22×C7×C1111yescharacteristic, complemented, Hall
58C32×C11C2×C7×D1311yescharacteristic, complemented, Hall
59C7×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
60C2×D3×C7—394no—
61C2×C3×C13D3×C7×C1114yescomplemented
62D39—38no—
63C7×C11C2×C3⋊D3911yescharacteristic, direct product factor, Hall
64C2×C3×C11C7×D3914yescomplemented
65D3×C11—398no—
66C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
67C2×D13—91noHall
68C22×C11—1171noHall
69C2×C3×C7C11×D3914yescomplemented
70D3×C7—398no—
71C3×C13C2×D3×C7×C1114yescomplemented
72C2×C3⋊D3—131noHall
73C3×C11C2×C7×D3914yescomplemented
74C22×C7—1171noHall
75C2×C13C7×C11×C3⋊D311yescharacteristic, complemented
76D13—92no—
77C2×C11—1172no—
78C2×C11C7×C3⋊D3911yescharacteristic, direct product factor
79C3×C7C2×C11×D3914yescomplemented
80C2×C32C7×C11×D1311yescharacteristic, complemented
81C3⋊D3—132no—
82C2×C7—1172no—
83C2×C7C11×C3⋊D3911yescharacteristic, direct product factor
84C13C2×C7×C11×C3⋊D311yescharacteristic, complemented, Sylow
85C2×D3—394no—
86C11C2×C7×C3⋊D3911yescharacteristic, direct product factor, Sylow
87C32C2×C7×C11×D1311yescharacteristic, complemented, Sylow
88C7C2×C11×C3⋊D3911yescharacteristic, direct product factor, Sylow
89C2×C3C7×C11×D3914yescomplemented
90D3—398no—
91C22—1171noSylow
92C3C2×C7×C11×D3914yescomplemented
93C2—1172no—
94C2C7×C11×C3⋊D3911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7×C11C3⋊D39
commutator, cosocle, hypocenterC32×C13C22×C7×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32×C13
UCSC1 ◁ C2×C7×C11

Complements

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

NH ≅ G/Ntype
1. C7×C11×C3⋊D39C2direct (N × H)
2. C2×C32×C7×C11×C13C2semidirect
4. C32×C7×C11×C13C22semidirect
6. C2×C3×C7×C11×C13D3semidirect
7. C2×C11×C3⋊D39C7direct (N × H)
9. C2×C7×C3⋊D39C11direct (N × H)
10. C3×C7×C11×C13C2×D3semidirect
12. C11×C3⋊D39C2×C7direct (N × H)
13. C2×C32×C11×C13C2×C7semidirect
15. C2×C7×C11×C13C3⋊D3semidirect
17. C2×C32×C7×C13C2×C11semidirect
18. C7×C3⋊D39C2×C11direct (N × H)
19. C2×C32×C7×C11D13semidirect
21. C32×C11×C13C22×C7semidirect
23. C7×C11×C13C2×C3⋊D3semidirect
25. C2×C3×C11×C13D3×C7semidirect
27. C32×C7×C13C22×C11semidirect
28. C32×C7×C11C2×D13semidirect
30. C2×C3×C7×C13D3×C11semidirect
32. C2×C3⋊D39C7×C11direct (N × H)
33. C2×C3×C7×C11D39semidirect
35. C3×C11×C13C2×D3×C7semidirect
39. C2×C11×C13C7×C3⋊D3semidirect
41. C3×C7×C13C2×D3×C11semidirect
43. C2×C32×C13C2×C7×C11semidirect
44. C3⋊D39C2×C7×C11direct (N × H)
45. C3×C7×C11C2×D39semidirect
46. C2×C32×C11C7×D13semidirect
48. C2×C7×C13C11×C3⋊D3semidirect
52. C2×C7×C11C3⋊D39direct (N × H)
53. C11×C13C2×C7×C3⋊D3semidirect
55. C2×C32×C7C11×D13semidirect
57. C32×C13C22×C7×C11semidirect
58. C32×C11C2×C7×D13semidirect
59. C7×C13C2×C11×C3⋊D3semidirect
61. C2×C3×C13D3×C7×C11semidirect
63. C7×C11C2×C3⋊D39direct (N × H)
64. C2×C3×C11C7×D39semidirect
66. C32×C7C2×C11×D13semidirect
69. C2×C3×C7C11×D39semidirect
71. C3×C13C2×D3×C7×C11semidirect
73. C3×C11C2×C7×D39semidirect
75. C2×C13C7×C11×C3⋊D3semidirect
78. C2×C11C7×C3⋊D39direct (N × H)
79. C3×C7C2×C11×D39semidirect
80. C2×C32C7×C11×D13semidirect
83. C2×C7C11×C3⋊D39direct (N × H)
84. C13C2×C7×C11×C3⋊D3semidirect
86. C11C2×C7×C3⋊D39direct (N × H)
87. C32C2×C7×C11×D13semidirect
88. C7C2×C11×C3⋊D39direct (N × H)
89. C2×C3C7×C11×D39semidirect
92. C3C2×C7×C11×D39semidirect
94. C2C7×C11×C3⋊D39direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C11×C3⋊D392
C2×C32×C7×C11×C132
C2×C7×C11×D393
C2×C11×C3⋊D397
C2×C7×C3⋊D3911
C2×C7×C11×C3⋊D313