Finite Group Databasebeta

← C11×C23×AGL(1,𝔽11) #42123711

Subgroups — C11×C23×AGL(1,𝔽11) #42123711

Order 27830.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C23×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C11×D11×C23C511yesmaximal, characteristic, complemented, Hall
3C112×C23C2×C511yescharacteristic, complemented, Hall
4C23×AGL(1,𝔽11)C1111yesmaximal, characteristic, direct product factor
5C2×C5×C11×C23—111nomaximal
6C5×C11×C23—111no—
7C23×C11⋊C5C2×C1111yescharacteristic, complemented
8C11×AGL(1,𝔽11)C2311yesmaximal, characteristic, direct product factor, Hall
9C11×C11⋊C5C2×C2311yescharacteristic, complemented, Hall
10C2×C11×C23—111no—
11D11×C23C5×C1111yescharacteristic, complemented
12C11×C23—101no—
13C11×C23AGL(1,𝔽11)11yescharacteristic, direct product factor
14C11×C23C2×C5×C1111yescharacteristic, complemented
15C11×D11C5×C2311yescharacteristic, complemented, Hall
16C2×C5×C23—111noHall
17C112C2×C5×C2311yescharacteristic, complemented, Sylow
18C5×C23—111noHall
19C2×C5×C11—111no—
20AGL(1,𝔽11)C11×C2311yescharacteristic, direct product factor
21C5×C11—111no—
22C11⋊C5C2×C11×C2311yescharacteristic, complemented
23C2×C23—111noHall
24C23C11×AGL(1,𝔽11)11yescharacteristic, direct product factor, Sylow
25C2×C11—111no—
26D11C5×C11×C2311yescharacteristic, complemented
27C11—101no—
28C11C2×C5×C11×C2311yescharacteristic, complemented
29C11C23×AGL(1,𝔽11)11yescharacteristic, direct product factor
30C2×C5—111noHall
31C5—111noSylow
32C2—111noSylow
subgroupG/H
center, hypercenterC11×C23AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C5×C11×C23
FrattiniC1G
Fitting, socleC112×C23C2×C5
LCSG ▷ C11
UCSC1 ◁ C11×C23

Complements

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

NH ≅ G/Ntype
1. C11×C23×C11⋊C5C2semidirect
2. C11×D11×C23C5semidirect
3. C112×C23C2×C5semidirect
4. C23×AGL(1,𝔽11)C11direct (N × H)
7. C23×C11⋊C5C2×C11semidirect
8. C11×AGL(1,𝔽11)C23direct (N × H)
9. C11×C11⋊C5C2×C23semidirect
11. D11×C23C5×C11semidirect
13. C11×C23AGL(1,𝔽11)direct (N × H)
14. C11×C23C2×C5×C11semidirect
15. C11×D11C5×C23semidirect
17. C112C2×C5×C23semidirect
20. AGL(1,𝔽11)C11×C23direct (N × H)
22. C11⋊C5C2×C11×C23semidirect
24. C23C11×AGL(1,𝔽11)direct (N × H)
26. D11C5×C11×C23semidirect
28. C11C2×C5×C11×C23semidirect
29. C11C23×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
C11×C23×C11⋊C52
C11×D11×C235
C23×AGL(1,𝔽11)11
C2×C5×C11×C2311
C11×AGL(1,𝔽11)23