Finite Group Databasebeta

← C22×C11⋊C5×C43⋊C3 #43248804

Subgroups — C22×C11⋊C5×C43⋊C3 #43248804

Order 28380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11⋊C5×C43⋊C3C213yesmaximal, direct product factor
2C22×C43×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
3C11⋊C5×C43⋊C3C2211yescharacteristic, direct product factor, Hall
4C22×C11×C43⋊C3C511yesmaximal, characteristic, complemented, Hall
5C2×C43×C11⋊C5C2×C313yescomplemented
6C2×C11×C43⋊C3C2×C513yescomplemented
7C22×C5×C43⋊C3—111nomaximal, Hall
8C43×C11⋊C5C22×C311yescharacteristic, complemented, Hall
9C22×C11×C43C3×C511yescharacteristic, complemented, Hall
10C11×C43⋊C3C22×C511yescharacteristic, complemented, Hall
11C2×C5×C43⋊C3—113no—
12C2×C11×C43C2×C3×C513yescomplemented
13C22×C5×C43—111noHall
14C22×C3×C11⋊C5—431nomaximal, Hall
15C5×C43⋊C3—111noHall
16C22×C43⋊C3C11⋊C511yescharacteristic, direct product factor, Hall
17C11×C43C22×C3×C511yescharacteristic, complemented, Hall
18C2×C5×C43—113no—
19C2×C3×C11⋊C5—433no—
20C2×C43⋊C3C2×C11⋊C513yesdirect product factor
21C22×C11⋊C5C43⋊C311yescharacteristic, direct product factor, Hall
22C5×C43—111noHall
23C22×C43C3×C11⋊C511yescharacteristic, complemented, Hall
24C3×C11⋊C5—431noHall
25C22×C3×C11—431noHall
26C43⋊C3C22×C11⋊C511yescharacteristic, direct product factor, Hall
27C2×C11⋊C5C2×C43⋊C313yesdirect product factor
28C2×C43C2×C3×C11⋊C513yescomplemented
29C2×C3×C11—433no—
30C22×C3×C5—4731noHall
31C11⋊C5C22×C43⋊C311yescharacteristic, direct product factor, Hall
32C22×C11C5×C43⋊C311yescharacteristic, complemented, Hall
33C43C22×C3×C11⋊C511yescharacteristic, complemented, Sylow
34C3×C11—431noHall
35C2×C3×C5—4733no—
36C2×C11C2×C5×C43⋊C313yescomplemented
37C22×C5—111noHall
38C3×C5—4731noHall
39C22×C3—431noHall
40C11C22×C5×C43⋊C311yescharacteristic, complemented, Sylow
41C2×C5—113no—
42C2×C3—433no—
43C5—111noSylow
44C22C11⋊C5×C43⋊C311yescharacteristic, direct product factor, Sylow
45C3—431noSylow
46C2C2×C11⋊C5×C43⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22C11⋊C5×C43⋊C3
commutator, cosocle, hypocenterC11×C43C22×C3×C5
FrattiniC1G
Fitting, socleC22×C11×C43C3×C5
LCSG ▷ C11×C43
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×C11⋊C5×C43⋊C3C2direct (N × H)
2. C22×C43×C11⋊C5C3semidirect
3. C11⋊C5×C43⋊C3C22direct (N × H)
4. C22×C11×C43⋊C3C5semidirect
5. C2×C43×C11⋊C5C2×C3semidirect
6. C2×C11×C43⋊C3C2×C5semidirect
8. C43×C11⋊C5C22×C3semidirect
9. C22×C11×C43C3×C5semidirect
10. C11×C43⋊C3C22×C5semidirect
12. C2×C11×C43C2×C3×C5semidirect
16. C22×C43⋊C3C11⋊C5direct (N × H)
17. C11×C43C22×C3×C5semidirect
20. C2×C43⋊C3C2×C11⋊C5direct (N × H)
21. C22×C11⋊C5C43⋊C3direct (N × H)
23. C22×C43C3×C11⋊C5semidirect
26. C43⋊C3C22×C11⋊C5direct (N × H)
27. C2×C11⋊C5C2×C43⋊C3direct (N × H)
28. C2×C43C2×C3×C11⋊C5semidirect
31. C11⋊C5C22×C43⋊C3direct (N × H)
32. C22×C11C5×C43⋊C3semidirect
33. C43C22×C3×C11⋊C5semidirect
36. C2×C11C2×C5×C43⋊C3semidirect
40. C11C22×C5×C43⋊C3semidirect
44. C22C11⋊C5×C43⋊C3direct (N × H)
46. C2C2×C11⋊C5×C43⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11⋊C5×C43⋊C32
C22×C43×C11⋊C53
C22×C11×C43⋊C35
C22×C5×C43⋊C311
C22×C3×C11⋊C543