Finite Group Databasebeta

← C2×C3×C72×AGL(1,𝔽11) #44568749

Subgroups — C2×C3×C72×AGL(1,𝔽11) #44568749

Order 32340.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C72×C11⋊C5C211yesmaximal, characteristic, complemented
2C3×C72×AGL(1,𝔽11)C212yesmaximal, direct product factor
3C2×C72×AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor, Hall
4C3×C72×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×C3×C72×D11C511yesmaximal, characteristic, complemented, Hall
6C2×C72×C11⋊C5C2×C311yescharacteristic, complemented
7C72×AGL(1,𝔽11)C2×C312yesdirect product factor
8C2×C3×C7×AGL(1,𝔽11)C718yesmaximal, direct product factor
9C3×C72×D11C2×C512yescomplemented
10C2×C3×C72×C11C2×C511yescharacteristic, complemented
11C22×C3×C5×C72—111nomaximal, Hall
12C72×C11⋊C5C22×C311yescharacteristic, complemented, Hall
13C3×C7×AGL(1,𝔽11)C2×C7116yesdirect product factor
14C2×C3×C7×C11⋊C5C2×C718yescomplemented
15C2×C72×D11C3×C511yescharacteristic, complemented, Hall
16C3×C72×C11C22×C511yescharacteristic, complemented, Hall
17C2×C7×AGL(1,𝔽11)C3×C718yesdirect product factor
18C2×C3×C5×C72—112no—
19C2×C3×C5×C72—111no—
20C3×C7×C11⋊C5C22×C718yescomplemented
21C2×C72×C11C2×C3×C511yescharacteristic, complemented
22C72×D11C2×C3×C512yescomplemented
23C22×C5×C72—111noHall
24C2×C3×C7×D11C5×C718yescomplemented
25C2×C7×C11⋊C5C2×C3×C718yescomplemented
26C7×AGL(1,𝔽11)C2×C3×C7116yesdirect product factor
27C3×C5×C72—111noHall
28C2×C3×AGL(1,𝔽11)C7211yescharacteristic, direct product factor, Hall
29C22×C3×C72—111noHall
30C72×C11C22×C3×C511yescharacteristic, complemented, Hall
31C2×C5×C72—112no—
32C2×C5×C72—111no—
33C2×C3×C7×C11C2×C5×C718yescomplemented
34C3×C7×D11C2×C5×C7116yescomplemented
35C22×C3×C5×C7—118no—
36C7×C11⋊C5C22×C3×C718yescomplemented
37C2×C3×C11⋊C5C2×C7211yescharacteristic, complemented
38C3×AGL(1,𝔽11)C2×C7212yesdirect product factor
39C2×C7×D11C3×C5×C718yescomplemented
40C2×C3×C72—112no—
41C2×C3×C72AGL(1,𝔽11)11yescharacteristic, direct product factor
42C5×C72—111noHall
43C3×C7×C11C22×C5×C718yescomplemented
44C2×AGL(1,𝔽11)C3×C7211yescharacteristic, direct product factor, Hall
45C2×C3×C5×C7—1116no—
46C2×C3×C5×C7—118no—
47C22×C72—111noHall
48C3×C11⋊C5C22×C7211yescharacteristic, complemented, Hall
49C2×C7×C11C2×C3×C5×C718yescomplemented
50C7×D11C2×C3×C5×C7116yescomplemented
51C3×C72C2×AGL(1,𝔽11)11yescharacteristic, direct product factor, Hall
52C22×C5×C7—118no—
53C2×C3×D11C5×C7211yescharacteristic, complemented, Hall
54C2×C11⋊C5C2×C3×C7211yescharacteristic, complemented
55AGL(1,𝔽11)C2×C3×C7212yesdirect product factor
56C3×C5×C7—118no—
57C2×C72—112no—
58C2×C72C3×AGL(1,𝔽11)11yescharacteristic, direct product factor
59C22×C3×C7—118no—
60C7×C11C22×C3×C5×C718yescomplemented
61C2×C5×C7—1116no—
62C2×C5×C7—118no—
63C2×C3×C11C2×C5×C7211yescharacteristic, complemented
64C3×D11C2×C5×C7212yescomplemented
65C22×C3×C5—111noHall
66C11⋊C5C22×C3×C7211yescharacteristic, complemented, Hall
67C72C2×C3×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
68C2×D11C3×C5×C7211yescharacteristic, complemented, Hall
69C2×C3×C7—1116no—
70C2×C3×C7C7×AGL(1,𝔽11)18yesdirect product factor
71C5×C7—118no—
72C3×C11C22×C5×C7211yescharacteristic, complemented, Hall
73C2×C3×C5—112no—
74C2×C3×C5—111no—
75C22×C7—118no—
76C2×C11C2×C3×C5×C7211yescharacteristic, complemented
77D11C2×C3×C5×C7212yescomplemented
78C3×C7C2×C7×AGL(1,𝔽11)18yesdirect product factor
79C22×C5—111noHall
80C3×C5—111noHall
81C2×C7—1116no—
82C2×C7C3×C7×AGL(1,𝔽11)18yesdirect product factor
83C22×C3—111noHall
84C11C22×C3×C5×C7211yescharacteristic, complemented, Sylow
85C2×C5—112no—
86C2×C5—111no—
87C7C2×C3×C7×AGL(1,𝔽11)18yesdirect product factor
88C2×C3—112no—
89C2×C3C72×AGL(1,𝔽11)11yescharacteristic, direct product factor
90C5—111noSylow
91C22—111noSylow
92C3C2×C72×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
93C2—112no—
94C2C3×C72×AGL(1,𝔽11)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C72AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C3×C5×C72
FrattiniC1G
Fitting, socleC2×C3×C72×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C72

Complements

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

NH ≅ G/Ntype
1. C2×C3×C72×C11⋊C5C2semidirect
2. C3×C72×AGL(1,𝔽11)C2direct (N × H)
3. C2×C72×AGL(1,𝔽11)C3direct (N × H)
4. C3×C72×C11⋊C5C22semidirect
5. C2×C3×C72×D11C5semidirect
6. C2×C72×C11⋊C5C2×C3semidirect
7. C72×AGL(1,𝔽11)C2×C3direct (N × H)
8. C2×C3×C7×AGL(1,𝔽11)C7direct (N × H)
9. C3×C72×D11C2×C5semidirect
10. C2×C3×C72×C11C2×C5semidirect
12. C72×C11⋊C5C22×C3semidirect
13. C3×C7×AGL(1,𝔽11)C2×C7direct (N × H)
14. C2×C3×C7×C11⋊C5C2×C7semidirect
15. C2×C72×D11C3×C5semidirect
16. C3×C72×C11C22×C5semidirect
17. C2×C7×AGL(1,𝔽11)C3×C7direct (N × H)
20. C3×C7×C11⋊C5C22×C7semidirect
21. C2×C72×C11C2×C3×C5semidirect
22. C72×D11C2×C3×C5semidirect
24. C2×C3×C7×D11C5×C7semidirect
25. C2×C7×C11⋊C5C2×C3×C7semidirect
26. C7×AGL(1,𝔽11)C2×C3×C7direct (N × H)
28. C2×C3×AGL(1,𝔽11)C72direct (N × H)
30. C72×C11C22×C3×C5semidirect
33. C2×C3×C7×C11C2×C5×C7semidirect
34. C3×C7×D11C2×C5×C7semidirect
36. C7×C11⋊C5C22×C3×C7semidirect
37. C2×C3×C11⋊C5C2×C72semidirect
38. C3×AGL(1,𝔽11)C2×C72direct (N × H)
39. C2×C7×D11C3×C5×C7semidirect
41. C2×C3×C72AGL(1,𝔽11)direct (N × H)
43. C3×C7×C11C22×C5×C7semidirect
44. C2×AGL(1,𝔽11)C3×C72direct (N × H)
48. C3×C11⋊C5C22×C72semidirect
49. C2×C7×C11C2×C3×C5×C7semidirect
50. C7×D11C2×C3×C5×C7semidirect
51. C3×C72C2×AGL(1,𝔽11)direct (N × H)
53. C2×C3×D11C5×C72semidirect
54. C2×C11⋊C5C2×C3×C72semidirect
55. AGL(1,𝔽11)C2×C3×C72direct (N × H)
58. C2×C72C3×AGL(1,𝔽11)direct (N × H)
60. C7×C11C22×C3×C5×C7semidirect
63. C2×C3×C11C2×C5×C72semidirect
64. C3×D11C2×C5×C72semidirect
66. C11⋊C5C22×C3×C72semidirect
67. C72C2×C3×AGL(1,𝔽11)direct (N × H)
68. C2×D11C3×C5×C72semidirect
70. C2×C3×C7C7×AGL(1,𝔽11)direct (N × H)
72. C3×C11C22×C5×C72semidirect
76. C2×C11C2×C3×C5×C72semidirect
77. D11C2×C3×C5×C72semidirect
78. C3×C7C2×C7×AGL(1,𝔽11)direct (N × H)
82. C2×C7C3×C7×AGL(1,𝔽11)direct (N × H)
84. C11C22×C3×C5×C72semidirect
87. C7C2×C3×C7×AGL(1,𝔽11)direct (N × H)
89. C2×C3C72×AGL(1,𝔽11)direct (N × H)
92. C3C2×C72×AGL(1,𝔽11)direct (N × H)
94. C2C3×C72×AGL(1,𝔽11)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C72×C11⋊C52
C3×C72×AGL(1,𝔽11)2
C2×C72×AGL(1,𝔽11)3
C2×C3×C72×D115
C2×C3×C7×AGL(1,𝔽11)7
C22×C3×C5×C7211