Finite Group Databasebeta

← D11×C23×C11⋊C5 #42123715

Subgroups — D11×C23×C11⋊C5 #42123715

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
4C5×D11×C23—111nomaximal
5C2×C23×C11⋊C5—111nomaximal
6C5×C11×C23—111no—
7C23×C11⋊C5D1111yescharacteristic, direct product factor
8D11×C11⋊C5C2311yesmaximal, characteristic, direct product factor, Hall
9C11×C11⋊C5C2×C2311yescharacteristic, complemented, Hall
10C2×C11×C23—111no—
11D11×C23C11⋊C511yescharacteristic, direct product factor
12C11×C23—101no—
13C11×C23C2×C11⋊C511yescharacteristic, complemented
14C11×C23C5×D1111yescharacteristic, complemented
15C11×D11C5×C2311yescharacteristic, complemented, Hall
16C2×C5×C23—1211noHall
17C112C2×C5×C2311yescharacteristic, complemented, Sylow
18C5×C23—111noHall
19C5×D11—111no—
20C2×C11⋊C5—111no—
21C5×C11—111no—
22C11⋊C5D11×C2311yescharacteristic, direct product factor
23C2×C23—111noHall
24C23D11×C11⋊C511yescharacteristic, direct product factor, Sylow
25C2×C11—111no—
26D11C23×C11⋊C511yescharacteristic, direct product factor
27C11—101no—
28C11C2×C23×C11⋊C511yescharacteristic, complemented
29C11C5×D11×C2311yescharacteristic, complemented
30C2×C5—1211noHall
31C5—111noSylow
32C2—111noSylow
subgroupG/H
center, hypercenterC23D11×C11⋊C5
commutator, cosocle, hypocenterC112C2×C5×C23
FrattiniC1G
Fitting, socleC112×C23C2×C5
LCSG ▷ C112
UCSC1 ◁ 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
7. C23×C11⋊C5D11direct (N × H)
8. D11×C11⋊C5C23direct (N × H)
9. C11×C11⋊C5C2×C23semidirect
11. D11×C23C11⋊C5direct (N × H)
13. C11×C23C2×C11⋊C5semidirect
14. C11×C23C5×D11semidirect
15. C11×D11C5×C23semidirect
17. C112C2×C5×C23semidirect
22. C11⋊C5D11×C23direct (N × H)
24. C23D11×C11⋊C5direct (N × H)
26. D11C23×C11⋊C5direct (N × H)
28. C11C2×C23×C11⋊C5semidirect
29. C11C5×D11×C23semidirect

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
C5×D11×C2311
C2×C23×C11⋊C511
D11×C11⋊C523