Finite Group Databasebeta

← C32×C7×C92 #19100264

Subgroups — C32×C7×C92 #19100264

Order 5103.

2132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×C7×C9C314yesmaximal
2C3×C7×C92C3136yesmaximal, direct product factor
3C32×C92C711yesmaximal, characteristic, direct product factor, Sylow
4C34×C7C3211yescharacteristic
5C32×C7×C9C91108yesdirect product factor
6C32×C7×C9C32148yes—
7C7×C92C32181yesdirect product factor
8C33×C9C3×C714yes—
9C3×C92C3×C7136yesdirect product factor
10C33×C7C3×C9136yes—
11C33×C7C3314yes—
12C3×C7×C9C3×C91432yesdirect product factor
13C3×C7×C9C33136yes—
14C34C32×C711yescharacteristic
15C32×C9C7×C91108yesdirect product factor
16C32×C9C32×C7148yes—
17C92C32×C7181yesdirect product factor
18C32×C7C92181yesdirect product factor
19C32×C7C32×C9148yes—
20C32×C7C3411yescharacteristic
21C7×C9C32×C91108yesdirect product factor
22C33C3×C7×C9136yes—
23C33C33×C714yes—
24C3×C9C3×C7×C91432yesdirect product factor
25C3×C9C33×C7136yes—
26C3×C7C3×C92136yesdirect product factor
27C3×C7C33×C914yes—
28C32C7×C92181yesdirect product factor
29C32C32×C7×C9148yes—
30C32C34×C711yescharacteristic
31C9C32×C7×C91108yesdirect product factor
32C7C32×C9211yescharacteristic, direct product factor, Sylow
33C3C3×C7×C92136yesdirect product factor
34C3C33×C7×C914yes—
subgroupG/H
centerGC1
commutatorC1G
FrattiniC32C34×C7
socleC34×C7C32
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C7×C92C3direct (N × H)
3. C32×C92C7direct (N × H)
5. C32×C7×C9C9direct (N × H)
7. C7×C92C32direct (N × H)
9. C3×C92C3×C7direct (N × H)
12. C3×C7×C9C3×C9direct (N × H)
15. C32×C9C7×C9direct (N × H)
17. C92C32×C7direct (N × H)
18. C32×C7C92direct (N × H)
21. C7×C9C32×C9direct (N × H)
24. C3×C9C3×C7×C9direct (N × H)
26. C3×C7C3×C92direct (N × H)
28. C32C7×C92direct (N × H)
31. C9C32×C7×C9direct (N × H)
32. C7C32×C92direct (N × H)
33. C3C3×C7×C92direct (N × H)