Finite Group Databasebeta

← C2×C3×C31×AGL(1,𝔽11) #35205774

Subgroups — C2×C3×C31×AGL(1,𝔽11) #35205774

Order 20460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C31×AGL(1,𝔽11)C212yesmaximal, direct product factor
2C2×C3×C31×C11⋊C5C211yesmaximal, characteristic, complemented
3C2×C31×AGL(1,𝔽11)C311yesmaximal, characteristic, direct product factor, Hall
4C3×C31×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×C3×D11×C31C511yesmaximal, characteristic, complemented, Hall
6C31×AGL(1,𝔽11)C2×C312yesdirect product factor
7C2×C31×C11⋊C5C2×C311yescharacteristic, complemented
8C3×D11×C31C2×C512yescomplemented
9C2×C3×C11×C31C2×C511yescharacteristic, complemented
10C22×C3×C5×C31—111nomaximal, Hall
11C31×C11⋊C5C22×C311yescharacteristic, complemented, Hall
12C2×D11×C31C3×C511yescharacteristic, complemented, Hall
13C3×C11×C31C22×C511yescharacteristic, complemented, Hall
14C2×C3×C5×C31—112no—
15C2×C3×C5×C31—111no—
16C2×C11×C31C2×C3×C511yescharacteristic, complemented
17D11×C31C2×C3×C512yescomplemented
18C2×C3×AGL(1,𝔽11)C3111yesmaximal, characteristic, direct product factor, Hall
19C22×C5×C31—111noHall
20C3×C5×C31—111noHall
21C22×C3×C31—111noHall
22C11×C31C22×C3×C511yescharacteristic, complemented, Hall
23C2×C3×C11⋊C5C2×C3111yescharacteristic, complemented
24C3×AGL(1,𝔽11)C2×C3112yesdirect product factor
25C2×C5×C31—112no—
26C2×C5×C31—111no—
27C2×AGL(1,𝔽11)C3×C3111yescharacteristic, direct product factor, Hall
28C2×C3×C31—112no—
29C2×C3×C31AGL(1,𝔽11)11yescharacteristic, direct product factor
30C3×C11⋊C5C22×C3111yescharacteristic, complemented, Hall
31C5×C31—111noHall
32C2×C3×D11C5×C3111yescharacteristic, complemented, Hall
33C22×C31—111noHall
34C2×C11⋊C5C2×C3×C3111yescharacteristic, complemented
35AGL(1,𝔽11)C2×C3×C3112yesdirect product factor
36C3×C31C2×AGL(1,𝔽11)11yescharacteristic, direct product factor, Hall
37C2×C3×C11C2×C5×C3111yescharacteristic, complemented
38C3×D11C2×C5×C3112yescomplemented
39C2×C31—112no—
40C2×C31C3×AGL(1,𝔽11)11yescharacteristic, direct product factor
41C22×C3×C5—111noHall
42C11⋊C5C22×C3×C3111yescharacteristic, complemented, Hall
43C2×D11C3×C5×C3111yescharacteristic, complemented, Hall
44C3×C11C22×C5×C3111yescharacteristic, complemented, Hall
45C31C2×C3×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
46C2×C3×C5—112no—
47C2×C3×C5—111no—
48C2×C11C2×C3×C5×C3111yescharacteristic, complemented
49D11C2×C3×C5×C3112yescomplemented
50C22×C5—111noHall
51C3×C5—111noHall
52C22×C3—111noHall
53C11C22×C3×C5×C3111yescharacteristic, complemented, Sylow
54C2×C5—112no—
55C2×C5—111no—
56C2×C3—112no—
57C2×C3C31×AGL(1,𝔽11)11yescharacteristic, direct product factor
58C5—111noSylow
59C22—111noSylow
60C3C2×C31×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
61C2—112no—
62C2C3×C31×AGL(1,𝔽11)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C31AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C3×C5×C31
FrattiniC1G
Fitting, socleC2×C3×C11×C31C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C31

Complements

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

NH ≅ G/Ntype
1. C3×C31×AGL(1,𝔽11)C2direct (N × H)
2. C2×C3×C31×C11⋊C5C2semidirect
3. C2×C31×AGL(1,𝔽11)C3direct (N × H)
4. C3×C31×C11⋊C5C22semidirect
5. C2×C3×D11×C31C5semidirect
6. C31×AGL(1,𝔽11)C2×C3direct (N × H)
7. C2×C31×C11⋊C5C2×C3semidirect
8. C3×D11×C31C2×C5semidirect
9. C2×C3×C11×C31C2×C5semidirect
11. C31×C11⋊C5C22×C3semidirect
12. C2×D11×C31C3×C5semidirect
13. C3×C11×C31C22×C5semidirect
16. C2×C11×C31C2×C3×C5semidirect
17. D11×C31C2×C3×C5semidirect
18. C2×C3×AGL(1,𝔽11)C31direct (N × H)
22. C11×C31C22×C3×C5semidirect
23. C2×C3×C11⋊C5C2×C31semidirect
24. C3×AGL(1,𝔽11)C2×C31direct (N × H)
27. C2×AGL(1,𝔽11)C3×C31direct (N × H)
29. C2×C3×C31AGL(1,𝔽11)direct (N × H)
30. C3×C11⋊C5C22×C31semidirect
32. C2×C3×D11C5×C31semidirect
34. C2×C11⋊C5C2×C3×C31semidirect
35. AGL(1,𝔽11)C2×C3×C31direct (N × H)
36. C3×C31C2×AGL(1,𝔽11)direct (N × H)
37. C2×C3×C11C2×C5×C31semidirect
38. C3×D11C2×C5×C31semidirect
40. C2×C31C3×AGL(1,𝔽11)direct (N × H)
42. C11⋊C5C22×C3×C31semidirect
43. C2×D11C3×C5×C31semidirect
44. C3×C11C22×C5×C31semidirect
45. C31C2×C3×AGL(1,𝔽11)direct (N × H)
48. C2×C11C2×C3×C5×C31semidirect
49. D11C2×C3×C5×C31semidirect
53. C11C22×C3×C5×C31semidirect
57. C2×C3C31×AGL(1,𝔽11)direct (N × H)
60. C3C2×C31×AGL(1,𝔽11)direct (N × H)
62. C2C3×C31×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
C3×C31×AGL(1,𝔽11)2
C2×C3×C31×C11⋊C52
C2×C31×AGL(1,𝔽11)3
C2×C3×D11×C315
C22×C3×C5×C3111
C2×C3×AGL(1,𝔽11)31