Finite Group Databasebeta

← C22×C3×C11×C127 #30660921

Subgroups — C22×C3×C11×C127 #30660921

Order 16764.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C11×C127C213yesmaximal, direct product factor
2C22×C11×C127C311yesmaximal, characteristic, direct product factor, Hall
3C3×C11×C127C2211yescharacteristic, direct product factor, Hall
4C2×C11×C127C2×C313yesdirect product factor
5C22×C3×C127C1111yesmaximal, characteristic, direct product factor, Hall
6C11×C127C22×C311yescharacteristic, direct product factor, Hall
7C2×C3×C127C2×C1113yesdirect product factor
8C22×C127C3×C1111yescharacteristic, direct product factor, Hall
9C3×C127C22×C1111yescharacteristic, direct product factor, Hall
10C2×C127C2×C3×C1113yesdirect product factor
11C22×C3×C11C12711yesmaximal, characteristic, direct product factor, Hall
12C127C22×C3×C1111yescharacteristic, direct product factor, Sylow
13C2×C3×C11C2×C12713yesdirect product factor
14C22×C11C3×C12711yescharacteristic, direct product factor, Hall
15C3×C11C22×C12711yescharacteristic, direct product factor, Hall
16C2×C11C2×C3×C12713yesdirect product factor
17C22×C3C11×C12711yescharacteristic, direct product factor, Hall
18C11C22×C3×C12711yescharacteristic, direct product factor, Sylow
19C2×C3C2×C11×C12713yesdirect product factor
20C22C3×C11×C12711yescharacteristic, direct product factor, Sylow
21C3C22×C11×C12711yescharacteristic, direct product factor, Sylow
22C2C2×C3×C11×C12713yesdirect 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. C2×C3×C11×C127C2direct (N × H)
2. C22×C11×C127C3direct (N × H)
3. C3×C11×C127C22direct (N × H)
4. C2×C11×C127C2×C3direct (N × H)
5. C22×C3×C127C11direct (N × H)
6. C11×C127C22×C3direct (N × H)
7. C2×C3×C127C2×C11direct (N × H)
8. C22×C127C3×C11direct (N × H)
9. C3×C127C22×C11direct (N × H)
10. C2×C127C2×C3×C11direct (N × H)
11. C22×C3×C11C127direct (N × H)
12. C127C22×C3×C11direct (N × H)
13. C2×C3×C11C2×C127direct (N × H)
14. C22×C11C3×C127direct (N × H)
15. C3×C11C22×C127direct (N × H)
16. C2×C11C2×C3×C127direct (N × H)
17. C22×C3C11×C127direct (N × H)
18. C11C22×C3×C127direct (N × H)
19. C2×C3C2×C11×C127direct (N × H)
20. C22C3×C11×C127direct (N × H)
21. C3C22×C11×C127direct (N × H)
22. C2C2×C3×C11×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C11×C1272
C22×C11×C1273
C22×C3×C12711
C22×C3×C11127