Finite Group Databasebeta

← C3×C11⋊C5×D43 #28382003

Subgroups — C3×C11⋊C5×D43 #28382003

Order 14190.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C43×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C11⋊C5×D43C311yesmaximal, characteristic, direct product factor, Hall
3C3×C11×D43C511yesmaximal, characteristic, complemented, Hall
4C43×C11⋊C5C2×C311yescharacteristic, complemented, Hall
5C3×C11×C43C2×C511yescharacteristic, complemented, Hall
6C3×C5×D43—111nomaximal, Hall
7C11×D43C3×C511yescharacteristic, complemented, Hall
8C3×C5×C43—111noHall
9C11×C43C2×C3×C511yescharacteristic, complemented, Hall
10C5×D43—111noHall
11C2×C3×C11⋊C5—431nomaximal, Hall
12C3×D43C11⋊C511yescharacteristic, direct product factor, Hall
13C5×C43—111noHall
14C3×C11⋊C5D4311yescharacteristic, direct product factor, Hall
15C3×C43C2×C11⋊C511yescharacteristic, complemented, Hall
16C2×C11⋊C5—431noHall
17D43C3×C11⋊C511yescharacteristic, direct product factor, Hall
18C2×C3×C11—431noHall
19C11⋊C5C3×D4311yescharacteristic, direct product factor, Hall
20C43C2×C3×C11⋊C511yescharacteristic, complemented, Sylow
21C3×C11C5×D4311yescharacteristic, complemented, Hall
22C2×C3×C5—4731noHall
23C2×C11—431noHall
24C3×C5—111noHall
25C11C3×C5×D4311yescharacteristic, complemented, Sylow
26C2×C5—4731noHall
27C2×C3—431noHall
28C5—111noSylow
29C3C11⋊C5×D4311yescharacteristic, direct product factor, Sylow
30C2—431noSylow
subgroupG/H
center, hypercenterC3C11⋊C5×D43
commutator, cosocle, hypocenterC11×C43C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C43C2×C5
LCSG ▷ C11×C43
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C43×C11⋊C5C2semidirect
2. C11⋊C5×D43C3direct (N × H)
3. C3×C11×D43C5semidirect
4. C43×C11⋊C5C2×C3semidirect
5. C3×C11×C43C2×C5semidirect
7. C11×D43C3×C5semidirect
9. C11×C43C2×C3×C5semidirect
12. C3×D43C11⋊C5direct (N × H)
14. C3×C11⋊C5D43direct (N × H)
15. C3×C43C2×C11⋊C5semidirect
17. D43C3×C11⋊C5direct (N × H)
19. C11⋊C5C3×D43direct (N × H)
20. C43C2×C3×C11⋊C5semidirect
21. C3×C11C5×D43semidirect
25. C11C3×C5×D43semidirect
29. C3C11⋊C5×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C43×C11⋊C52
C11⋊C5×D433
C3×C11×D435
C3×C5×D4311
C2×C3×C11⋊C543