Finite Group Databasebeta

← C22×C3×C7×C11×C13⋊C3 #49115005

Subgroups — C22×C3×C7×C11×C13⋊C3 #49115005

Order 36036.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C7×C11×C13⋊C3C213yesmaximal, direct product factor
2C22×C7×C11×C13⋊C3C313yesmaximal, direct product factor
3C22×C3×C7×C11×C13C311yesmaximal, characteristic, complemented
4C3×C7×C11×C13⋊C3C2211yescharacteristic, direct product factor, Hall
5C2×C7×C11×C13⋊C3C2×C319yesdirect product factor
6C2×C3×C7×C11×C13C2×C313yescomplemented
7C22×C3×C11×C13⋊C3C711yesmaximal, characteristic, direct product factor, Hall
8C22×C7×C11×C13C3211yescharacteristic, complemented, Hall
9C22×C3×C7×C13⋊C3C1111yesmaximal, characteristic, direct product factor, Hall
10C7×C11×C13⋊C3C22×C313yesdirect product factor
11C3×C7×C11×C13C22×C311yescharacteristic, complemented
12C22×C32×C7×C11—131nomaximal, Hall
13C2×C3×C11×C13⋊C3C2×C713yesdirect product factor
14C2×C7×C11×C13C2×C3213yescomplemented
15C22×C3×C11×C13C3×C711yescharacteristic, complemented
16C22×C11×C13⋊C3C3×C713yesdirect product factor
17C2×C3×C7×C13⋊C3C2×C1113yesdirect product factor
18C2×C32×C7×C11—133no—
19C3×C11×C13⋊C3C22×C711yescharacteristic, direct product factor, Hall
20C22×C3×C7×C13C3×C1111yescharacteristic, complemented
21C22×C7×C13⋊C3C3×C1113yesdirect product factor
22C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
23C22×C3×C7×C11—133no—
24C22×C3×C7×C11C13⋊C311yescharacteristic, direct product factor
25C2×C3×C11×C13C2×C3×C713yescomplemented
26C2×C11×C13⋊C3C2×C3×C719yesdirect product factor
27C3×C7×C13⋊C3C22×C1111yescharacteristic, direct product factor, Hall
28C32×C7×C11—131noHall
29C22×C11×C13C32×C711yescharacteristic, complemented, Hall
30C2×C3×C7×C13C2×C3×C1113yescomplemented
31C2×C7×C13⋊C3C2×C3×C1119yesdirect product factor
32C22×C3×C13⋊C3C7×C1111yescharacteristic, direct product factor, Hall
33C2×C3×C7×C11—139no—
34C2×C3×C7×C11C2×C13⋊C313yesdirect product factor
35C3×C11×C13C22×C3×C711yescharacteristic, complemented
36C11×C13⋊C3C22×C3×C713yesdirect product factor
37C22×C32×C11—131noHall
38C22×C7×C13C32×C1111yescharacteristic, complemented, Hall
39C22×C7×C11C3×C13⋊C311yescharacteristic, direct product factor, Hall
40C2×C11×C13C2×C32×C713yescomplemented
41C3×C7×C13C22×C3×C1111yescharacteristic, complemented
42C7×C13⋊C3C22×C3×C1113yesdirect product factor
43C22×C32×C7—131noHall
44C2×C3×C13⋊C3C2×C7×C1113yesdirect product factor
45C3×C7×C11—133no—
46C3×C7×C11C22×C13⋊C311yescharacteristic, direct product factor
47C2×C32×C11—133no—
48C2×C7×C13C2×C32×C1113yescomplemented
49C22×C3×C13C3×C7×C1111yescharacteristic, complemented
50C22×C13⋊C3C3×C7×C1113yesdirect product factor
51C2×C7×C11C2×C3×C13⋊C313yesdirect product factor
52C11×C13C22×C32×C711yescharacteristic, complemented, Hall
53C22×C3×C11—133no—
54C22×C3×C11C7×C13⋊C311yescharacteristic, direct product factor
55C2×C32×C7—133no—
56C3×C13⋊C3C22×C7×C1111yescharacteristic, direct product factor, Hall
57C32×C11—131noHall
58C7×C13C22×C32×C1111yescharacteristic, complemented, Hall
59C22×C3×C7—133no—
60C22×C3×C7C11×C13⋊C311yescharacteristic, direct product factor
61C2×C3×C13C2×C3×C7×C1113yescomplemented
62C2×C13⋊C3C2×C3×C7×C1119yesdirect product factor
63C7×C11C22×C3×C13⋊C311yescharacteristic, direct product factor, Hall
64C2×C3×C11—139no—
65C2×C3×C11C2×C7×C13⋊C313yesdirect product factor
66C32×C7—131noHall
67C22×C13C32×C7×C1111yescharacteristic, complemented, Hall
68C22×C11C3×C7×C13⋊C311yescharacteristic, direct product factor, Hall
69C2×C3×C7—139no—
70C2×C3×C7C2×C11×C13⋊C313yesdirect product factor
71C3×C13C22×C3×C7×C1111yescharacteristic, complemented
72C13⋊C3C22×C3×C7×C1113yesdirect product factor
73C22×C32—131noHall
74C3×C11—133no—
75C3×C11C22×C7×C13⋊C311yescharacteristic, direct product factor
76C22×C7C3×C11×C13⋊C311yescharacteristic, direct product factor, Hall
77C2×C13C2×C32×C7×C1113yescomplemented
78C2×C11C2×C3×C7×C13⋊C313yesdirect product factor
79C3×C7—133no—
80C3×C7C22×C11×C13⋊C311yescharacteristic, direct product factor
81C2×C32—133no—
82C2×C7C2×C3×C11×C13⋊C313yesdirect product factor
83C13C22×C32×C7×C1111yescharacteristic, complemented, Sylow
84C22×C3—133no—
85C22×C3C7×C11×C13⋊C311yescharacteristic, direct product factor
86C11C22×C3×C7×C13⋊C311yescharacteristic, direct product factor, Sylow
87C32—131noSylow
88C7C22×C3×C11×C13⋊C311yescharacteristic, direct product factor, Sylow
89C2×C3—139no—
90C2×C3C2×C7×C11×C13⋊C313yesdirect product factor
91C22C3×C7×C11×C13⋊C311yescharacteristic, direct product factor, Sylow
92C3—133no—
93C3C22×C7×C11×C13⋊C311yescharacteristic, direct product factor
94C2C2×C3×C7×C11×C13⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C3×C7×C11C13⋊C3
commutator, cosocle, hypocenterC13C22×C32×C7×C11
FrattiniC1G
Fitting, socleC22×C3×C7×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C3×C7×C11

Complements

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

NH ≅ G/Ntype
1. C2×C3×C7×C11×C13⋊C3C2direct (N × H)
2. C22×C7×C11×C13⋊C3C3direct (N × H)
3. C22×C3×C7×C11×C13C3semidirect
4. C3×C7×C11×C13⋊C3C22direct (N × H)
5. C2×C7×C11×C13⋊C3C2×C3direct (N × H)
6. C2×C3×C7×C11×C13C2×C3semidirect
7. C22×C3×C11×C13⋊C3C7direct (N × H)
8. C22×C7×C11×C13C32semidirect
9. C22×C3×C7×C13⋊C3C11direct (N × H)
10. C7×C11×C13⋊C3C22×C3direct (N × H)
11. C3×C7×C11×C13C22×C3semidirect
13. C2×C3×C11×C13⋊C3C2×C7direct (N × H)
14. C2×C7×C11×C13C2×C32semidirect
15. C22×C3×C11×C13C3×C7semidirect
16. C22×C11×C13⋊C3C3×C7direct (N × H)
17. C2×C3×C7×C13⋊C3C2×C11direct (N × H)
19. C3×C11×C13⋊C3C22×C7direct (N × H)
20. C22×C3×C7×C13C3×C11semidirect
21. C22×C7×C13⋊C3C3×C11direct (N × H)
22. C7×C11×C13C22×C32semidirect
24. C22×C3×C7×C11C13⋊C3direct (N × H)
25. C2×C3×C11×C13C2×C3×C7semidirect
26. C2×C11×C13⋊C3C2×C3×C7direct (N × H)
27. C3×C7×C13⋊C3C22×C11direct (N × H)
29. C22×C11×C13C32×C7semidirect
30. C2×C3×C7×C13C2×C3×C11semidirect
31. C2×C7×C13⋊C3C2×C3×C11direct (N × H)
32. C22×C3×C13⋊C3C7×C11direct (N × H)
34. C2×C3×C7×C11C2×C13⋊C3direct (N × H)
35. C3×C11×C13C22×C3×C7semidirect
36. C11×C13⋊C3C22×C3×C7direct (N × H)
38. C22×C7×C13C32×C11semidirect
39. C22×C7×C11C3×C13⋊C3direct (N × H)
40. C2×C11×C13C2×C32×C7semidirect
41. C3×C7×C13C22×C3×C11semidirect
42. C7×C13⋊C3C22×C3×C11direct (N × H)
44. C2×C3×C13⋊C3C2×C7×C11direct (N × H)
46. C3×C7×C11C22×C13⋊C3direct (N × H)
48. C2×C7×C13C2×C32×C11semidirect
49. C22×C3×C13C3×C7×C11semidirect
50. C22×C13⋊C3C3×C7×C11direct (N × H)
51. C2×C7×C11C2×C3×C13⋊C3direct (N × H)
52. C11×C13C22×C32×C7semidirect
54. C22×C3×C11C7×C13⋊C3direct (N × H)
56. C3×C13⋊C3C22×C7×C11direct (N × H)
58. C7×C13C22×C32×C11semidirect
60. C22×C3×C7C11×C13⋊C3direct (N × H)
61. C2×C3×C13C2×C3×C7×C11semidirect
62. C2×C13⋊C3C2×C3×C7×C11direct (N × H)
63. C7×C11C22×C3×C13⋊C3direct (N × H)
65. C2×C3×C11C2×C7×C13⋊C3direct (N × H)
67. C22×C13C32×C7×C11semidirect
68. C22×C11C3×C7×C13⋊C3direct (N × H)
70. C2×C3×C7C2×C11×C13⋊C3direct (N × H)
71. C3×C13C22×C3×C7×C11semidirect
72. C13⋊C3C22×C3×C7×C11direct (N × H)
75. C3×C11C22×C7×C13⋊C3direct (N × H)
76. C22×C7C3×C11×C13⋊C3direct (N × H)
77. C2×C13C2×C32×C7×C11semidirect
78. C2×C11C2×C3×C7×C13⋊C3direct (N × H)
80. C3×C7C22×C11×C13⋊C3direct (N × H)
82. C2×C7C2×C3×C11×C13⋊C3direct (N × H)
83. C13C22×C32×C7×C11semidirect
85. C22×C3C7×C11×C13⋊C3direct (N × H)
86. C11C22×C3×C7×C13⋊C3direct (N × H)
88. C7C22×C3×C11×C13⋊C3direct (N × H)
90. C2×C3C2×C7×C11×C13⋊C3direct (N × H)
91. C22C3×C7×C11×C13⋊C3direct (N × H)
93. C3C22×C7×C11×C13⋊C3direct (N × H)
94. C2C2×C3×C7×C11×C13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C7×C11×C13⋊C32
C22×C7×C11×C13⋊C33
C22×C3×C7×C11×C133
C22×C3×C11×C13⋊C37
C22×C3×C7×C13⋊C311
C22×C32×C7×C1113