Finite Group Databasebeta

← C33×H(3,𝔽3)×C43 #44531875

Subgroups — C33×H(3,𝔽3)×C43 #44531875

Order 31347.

11744 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C35×C43C314yesmaximal, complemented
2C32×H(3,𝔽3)×C43C31117yesmaximal, direct product factor
3C34×C43—3108no—
4C34×C43C3211yescharacteristic
5C34×C43C321156yescomplemented
6C3×H(3,𝔽3)×C43C3211053yesdirect product factor
7C33×C43—31404no—
8C33×C43H(3,𝔽3)127yesdirect product factor
9C33×C43C33113yes—
10C33×C43C331468yescomplemented
11H(3,𝔽3)×C43C331729yesdirect product factor
12C33×H(3,𝔽3)C4311yesmaximal, characteristic, direct product factor, Sylow
13C32×C43—31404no—
14C32×C43C3×H(3,𝔽3)1117yesdirect product factor
15C32×C43C34113yes—
16C32×C43C341108yescomplemented
17C35C3×C4314yescomplemented
18C32×H(3,𝔽3)C3×C431117yesdirect product factor
19C3×C43—3108no—
20C3×C43C32×H(3,𝔽3)139yesdirect product factor
21C3×C43C3511yescharacteristic
22C34—3108no—
23C34C32×C4311yescharacteristic
24C34C32×C431156yescomplemented
25C3×H(3,𝔽3)C32×C4311053yesdirect product factor
26C43C33×H(3,𝔽3)11yescharacteristic, direct product factor, Sylow
27C33—31404no—
28C33H(3,𝔽3)×C43127yesdirect product factor
29C33C33×C43113yes—
30C33C33×C431468yescomplemented
31H(3,𝔽3)C33×C431729yesdirect product factor
32C32—31404no—
33C32C3×H(3,𝔽3)×C431117yesdirect product factor
34C32C34×C43113yes—
35C32C34×C431108yescomplemented
36C3—3108no—
37C3C32×H(3,𝔽3)×C43139yesdirect product factor
38C3C35×C4311yescharacteristic
subgroupG/H
center, socleC34×C43C32
commutator, Frattini, cosocleC3C35×C43
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C34×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C35×C43C3semidirect
2. C32×H(3,𝔽3)×C43C3direct (N × H)
5. C34×C43C32semidirect
6. C3×H(3,𝔽3)×C43C32direct (N × H)
8. C33×C43H(3,𝔽3)direct (N × H)
10. C33×C43C33semidirect
11. H(3,𝔽3)×C43C33direct (N × H)
12. C33×H(3,𝔽3)C43direct (N × H)
14. C32×C43C3×H(3,𝔽3)direct (N × H)
16. C32×C43C34semidirect
17. C35C3×C43semidirect
18. C32×H(3,𝔽3)C3×C43direct (N × H)
20. C3×C43C32×H(3,𝔽3)direct (N × H)
24. C34C32×C43semidirect
25. C3×H(3,𝔽3)C32×C43direct (N × H)
26. C43C33×H(3,𝔽3)direct (N × H)
28. C33H(3,𝔽3)×C43direct (N × H)
30. C33C33×C43semidirect
31. H(3,𝔽3)C33×C43direct (N × H)
33. C32C3×H(3,𝔽3)×C43direct (N × H)
35. C32C34×C43semidirect
37. C3C32×H(3,𝔽3)×C43direct (N × H)

Maximal subgroups

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

subgroupindex
C35×C433
C32×H(3,𝔽3)×C433
C33×H(3,𝔽3)43