Finite Group Databasebeta

← C32×#11925898 #24926147

Subgroups — C32×#11925898 #24926147

Order 10890.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#10597244C211yesmaximal, characteristic, complemented, Hall
2C3×#11925898C314yesmaximal, direct product factor
3C32×C11×D11C511yesmaximal, characteristic, complemented, Hall
4C3×#10597244C2×C314yescomplemented
5#11925898C3211yescharacteristic, direct product factor, Hall
6C32×C112C2×C511yescharacteristic, complemented, Hall
7C2×C32×C11⋊C5—111nomaximal
8C32×AGL(1,𝔽11)—111nomaximal
9C3×C11×D11C3×C514yescomplemented
10#10597244C2×C3211yescharacteristic, complemented, Hall
11C32×C11⋊C5—111no—
12C32×C11⋊C5—111no—
13C3×C112C2×C3×C514yescomplemented
14C2×C3×C11⋊C5—114no—
15C3×AGL(1,𝔽11)—114no—
16C11×D11C32×C511yescharacteristic, complemented, Hall
17C2×C32×C11—111no—
18C32×D11C11⋊C511yescharacteristic, complemented
19C3×C11⋊C5—114no—
20C3×C11⋊C5—114no—
21C112C2×C32×C511yescharacteristic, complemented, Sylow
22C2×C11⋊C5—111no—
23AGL(1,𝔽11)—111no—
24C32×C11—101no—
25C32×C11AGL(1,𝔽11)11yescharacteristic, complemented
26C32×C11C2×C11⋊C511yescharacteristic, complemented
27C2×C32×C5—1211noHall
28C2×C3×C11—114no—
29C3×D11C3×C11⋊C514yescomplemented
30C11⋊C5—111no—
31C11⋊C5—111no—
32C32×C5—1211noHall
33C3×C11—104no—
34C3×C11C3×AGL(1,𝔽11)14yescomplemented
35C3×C11C2×C3×C11⋊C514yescomplemented
36C2×C3×C5—1214no—
37C2×C11—111no—
38D11C32×C11⋊C511yescharacteristic, complemented
39C2×C32—111noHall
40C3×C5—1214no—
41C11—101no—
42C11C32×AGL(1,𝔽11)11yescharacteristic, complemented
43C11C2×C32×C11⋊C511yescharacteristic, complemented
44C2×C5—1211noHall
45C32#1192589811yescharacteristic, direct product factor, Sylow
46C2×C3—114no—
47C5—1211noSylow
48C3C3×#1192589814yesdirect product factor
49C2—111noSylow
subgroupG/H
center, hypercenterC32#11925898
commutator, cosocle, hypocenterC112C2×C32×C5
FrattiniC1G
Fitting, socleC32×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×#10597244C2semidirect
2. C3×#11925898C3direct (N × H)
3. C32×C11×D11C5semidirect
4. C3×#10597244C2×C3semidirect
5. #11925898C32direct (N × H)
6. C32×C112C2×C5semidirect
9. C3×C11×D11C3×C5semidirect
10. #10597244C2×C32semidirect
13. C3×C112C2×C3×C5semidirect
16. C11×D11C32×C5semidirect
18. C32×D11C11⋊C5semidirect
21. C112C2×C32×C5semidirect
25. C32×C11AGL(1,𝔽11)semidirect
26. C32×C11C2×C11⋊C5semidirect
29. C3×D11C3×C11⋊C5semidirect
34. C3×C11C3×AGL(1,𝔽11)semidirect
35. C3×C11C2×C3×C11⋊C5semidirect
38. D11C32×C11⋊C5semidirect
42. C11C32×AGL(1,𝔽11)semidirect
43. C11C2×C32×C11⋊C5semidirect
45. C32#11925898direct (N × H)
48. C3C3×#11925898direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#105972442
C3×#119258983
C32×C11×D115
C2×C32×C11⋊C511
C32×AGL(1,𝔽11)11