Finite Group Databasebeta

← C11×C5⋊(D67⋊C3) #36348644

Subgroups — C11×C5⋊(D67⋊C3) #36348644

Order 22110.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×C67⋊C3C211yesmaximal, characteristic, complemented, Hall
2C11×D335C311yesmaximal, characteristic, complemented, Hall
3C11×D67⋊C3—51nomaximal, Hall
4C5×C11×C67C2×C311yescharacteristic, complemented, Hall
5C11×C67⋊C3D511yescharacteristic, complemented, Hall
6C5⋊(D67⋊C3)C1111yesmaximal, characteristic, direct product factor, Hall
7C11×D67—51noHall
8C5×C67⋊C3C2×C1111yescharacteristic, complemented, Hall
9C11×C67C3×D511yescharacteristic, complemented, Hall
10D335C3×C1111yescharacteristic, complemented, Hall
11D67⋊C3—51noHall
12C5×C67C2×C3×C1111yescharacteristic, complemented, Hall
13C3×D5×C11—671nomaximal, Hall
14C67⋊C3D5×C1111yescharacteristic, complemented, Hall
15C3×C5×C11—671noHall
16D67—51noHall
17D5×C11—671noHall
18C67C3×D5×C1111yescharacteristic, complemented, Sylow
19C2×C3×C11—3351noHall
20C5×C11D67⋊C311yescharacteristic, complemented, Hall
21C3×C11—671noHall
22C3×D5—671noHall
23C2×C11—3351noHall
24C3×C5—671noHall
25C11C5⋊(D67⋊C3)11yescharacteristic, direct product factor, Sylow
26D5—671noHall
27C2×C3—3351noHall
28C5C11×D67⋊C311yescharacteristic, complemented, Sylow
29C3—671noSylow
30C2—3351noSylow
subgroupG/H
center, hypercenterC11C5⋊(D67⋊C3)
commutator, cosocle, hypocenterC5×C67C2×C3×C11
FrattiniC1G
Fitting, socleC5×C11×C67C2×C3
LCSG ▷ C5×C67
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C5×C11×C67⋊C3C2semidirect
2. C11×D335C3semidirect
4. C5×C11×C67C2×C3semidirect
5. C11×C67⋊C3D5semidirect
6. C5⋊(D67⋊C3)C11direct (N × H)
8. C5×C67⋊C3C2×C11semidirect
9. C11×C67C3×D5semidirect
10. D335C3×C11semidirect
12. C5×C67C2×C3×C11semidirect
14. C67⋊C3D5×C11semidirect
18. C67C3×D5×C11semidirect
20. C5×C11D67⋊C3semidirect
25. C11C5⋊(D67⋊C3)direct (N × H)
28. C5C11×D67⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5×C11×C67⋊C32
C11×D3353
C11×D67⋊C35
C5⋊(D67⋊C3)11
C3×D5×C1167