Finite Group Databasebeta

← C3×#16812513 #23782869

Subgroups — C3×#16812513 #23782869

Order 10449.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C32⋊(C43⋊C3)C313yesmaximal, complemented
2#16812513C319yesmaximal, direct product factor
3C32×C9×C43C311yesmaximal, characteristic, complemented
4C32×C43⋊C3—33no—
5C32⋊(C43⋊C3)—36no—
6C32⋊(C43⋊C3)C3219yescomplemented
7C33×C43C3211yescharacteristic
8C3×C9×C43—32no—
9C3×C9×C43—31no—
10C3×C9×C43C3213yescomplemented
11C32×C43—33no—
12C32×C43H(3,𝔽3)12yes—
13C32×C43H(3,𝔽3)11yescharacteristic
14C32×C43C3311yescharacteristic
15C3×C43⋊C3—39no—
16C3×C43⋊C3—99no—
17C9×C43—33no—
18C3×#732—431nomaximal, Sylow
19C3×C43—32no—
20C3×C43—31no—
21C3×C43#73213yescomplemented
22C3×C43C3×H(3,𝔽3)11yescharacteristic
23C43⋊C3—99no—
24C3×H(3,𝔽3)—433no—
25C32×C9C43⋊C311yescharacteristic, complemented
26#732—439no—
27C43C3×#73211yescharacteristic, complemented, Sylow
28C33—1293no—
29C33C3×C43⋊C311yescharacteristic
30H(3,𝔽3)—439no—
31H(3,𝔽3)—1296no—
32C3×C9—32no—
33C3×C9—31no—
34C3×C9C3×C43⋊C313yescomplemented
35C32—33no—
36C32—1299no—
37C32—3879no—
38C32C32⋊(C43⋊C3)12yes—
39C32C32⋊(C43⋊C3)11yescharacteristic
40C32C32×C43⋊C311yescharacteristic
41C9—33no—
42C3—32no—
43C3—31no—
44C3—3879no—
45C3#1681251313yesdirect product factor
46C3C3×C32⋊(C43⋊C3)11yescharacteristic
subgroupG/H
centerC32C32⋊(C43⋊C3)
commutator, cosocleC32×C43C33
FrattiniC32C32×C43⋊C3
FittingC32×C9×C43C3
socleC32×C43H(3,𝔽3)
hypercenterC32×C9C43⋊C3
hypocenterC43C3×#732
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9

Complements

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

NH ≅ G/Ntype
1. C3×C32⋊(C43⋊C3)C3semidirect
2. #16812513C3direct (N × H)
3. C32×C9×C43C3semidirect
6. C32⋊(C43⋊C3)C32semidirect
10. C3×C9×C43C32semidirect
21. C3×C43#732semidirect
25. C32×C9C43⋊C3semidirect
27. C43C3×#732semidirect
34. C3×C9C3×C43⋊C3semidirect
45. C3#16812513direct (N × H)