Finite Group Databasebeta

← C34×C7×C43 #72201673

Subgroups — C34×C7×C43 #72201673

Order 24381.

848 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×C7×C43C3140yesmaximal, direct product factor
2C34×C43C711yesmaximal, characteristic, direct product factor, Hall
3C32×C7×C43C321130yesdirect product factor
4C33×C43C3×C7140yesdirect product factor
5C3×C7×C43C33140yesdirect product factor
6C34×C7C4311yesmaximal, characteristic, direct product factor, Hall
7C32×C43C32×C71130yesdirect product factor
8C7×C43C3411yescharacteristic, direct product factor, Hall
9C33×C7C3×C43140yesdirect product factor
10C3×C43C33×C7140yesdirect product factor
11C34C7×C4311yescharacteristic, direct product factor, Sylow
12C32×C7C32×C431130yesdirect product factor
13C43C34×C711yescharacteristic, direct product factor, Sylow
14C33C3×C7×C43140yesdirect product factor
15C3×C7C33×C43140yesdirect product factor
16C32C32×C7×C431130yesdirect product factor
17C7C34×C4311yescharacteristic, direct product factor, Sylow
18C3C33×C7×C43140yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C33×C7×C43C3direct (N × H)
2. C34×C43C7direct (N × H)
3. C32×C7×C43C32direct (N × H)
4. C33×C43C3×C7direct (N × H)
5. C3×C7×C43C33direct (N × H)
6. C34×C7C43direct (N × H)
7. C32×C43C32×C7direct (N × H)
8. C7×C43C34direct (N × H)
9. C33×C7C3×C43direct (N × H)
10. C3×C43C33×C7direct (N × H)
11. C34C7×C43direct (N × H)
12. C32×C7C32×C43direct (N × H)
13. C43C34×C7direct (N × H)
14. C33C3×C7×C43direct (N × H)
15. C3×C7C33×C43direct (N × H)
16. C32C32×C7×C43direct (N × H)
17. C7C34×C43direct (N × H)
18. C3C33×C7×C43direct (N × H)

Maximal subgroups

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

subgroupindex
C33×C7×C433
C34×C437
C34×C743