Finite Group Databasebeta

← C23×C3×C7×C131 #72199488

Subgroups — C23×C3×C7×C131 #72199488

Order 22008.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C131C311yesmaximal, characteristic, direct product factor, Hall
2C23×C3×C131C711yesmaximal, characteristic, direct product factor, Hall
3C22×C3×C7×C131C217yesmaximal, direct product factor
4C2×C3×C7×C131C2217yesdirect product factor
5C22×C7×C131C2×C317yesdirect product factor
6C3×C7×C131C2311yescharacteristic, direct product factor, Hall
7C2×C7×C131C22×C317yesdirect product factor
8C22×C3×C131C2×C717yesdirect product factor
9C23×C131C3×C711yescharacteristic, direct product factor, Hall
10C7×C131C23×C311yescharacteristic, direct product factor, Hall
11C2×C3×C131C22×C717yesdirect product factor
12C22×C131C2×C3×C717yesdirect product factor
13C3×C131C23×C711yescharacteristic, direct product factor, Hall
14C2×C131C22×C3×C717yesdirect product factor
15C23×C3×C7C13111yesmaximal, characteristic, direct product factor, Hall
16C131C23×C3×C711yescharacteristic, direct product factor, Sylow
17C22×C3×C7C2×C13117yesdirect product factor
18C23×C7C3×C13111yescharacteristic, direct product factor, Hall
19C2×C3×C7C22×C13117yesdirect product factor
20C22×C7C2×C3×C13117yesdirect product factor
21C23×C3C7×C13111yescharacteristic, direct product factor, Hall
22C3×C7C23×C13111yescharacteristic, direct product factor, Hall
23C2×C7C22×C3×C13117yesdirect product factor
24C22×C3C2×C7×C13117yesdirect product factor
25C23C3×C7×C13111yescharacteristic, direct product factor, Sylow
26C7C23×C3×C13111yescharacteristic, direct product factor, Sylow
27C2×C3C22×C7×C13117yesdirect product factor
28C22C2×C3×C7×C13117yesdirect product factor
29C3C23×C7×C13111yescharacteristic, direct product factor, Sylow
30C2C22×C3×C7×C13117yesdirect 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. C23×C7×C131C3direct (N × H)
2. C23×C3×C131C7direct (N × H)
3. C22×C3×C7×C131C2direct (N × H)
4. C2×C3×C7×C131C22direct (N × H)
5. C22×C7×C131C2×C3direct (N × H)
6. C3×C7×C131C23direct (N × H)
7. C2×C7×C131C22×C3direct (N × H)
8. C22×C3×C131C2×C7direct (N × H)
9. C23×C131C3×C7direct (N × H)
10. C7×C131C23×C3direct (N × H)
11. C2×C3×C131C22×C7direct (N × H)
12. C22×C131C2×C3×C7direct (N × H)
13. C3×C131C23×C7direct (N × H)
14. C2×C131C22×C3×C7direct (N × H)
15. C23×C3×C7C131direct (N × H)
16. C131C23×C3×C7direct (N × H)
17. C22×C3×C7C2×C131direct (N × H)
18. C23×C7C3×C131direct (N × H)
19. C2×C3×C7C22×C131direct (N × H)
20. C22×C7C2×C3×C131direct (N × H)
21. C23×C3C7×C131direct (N × H)
22. C3×C7C23×C131direct (N × H)
23. C2×C7C22×C3×C131direct (N × H)
24. C22×C3C2×C7×C131direct (N × H)
25. C23C3×C7×C131direct (N × H)
26. C7C23×C3×C131direct (N × H)
27. C2×C3C22×C7×C131direct (N × H)
28. C22C2×C3×C7×C131direct (N × H)
29. C3C23×C7×C131direct (N × H)
30. C2C22×C3×C7×C131direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C1313
C23×C3×C1317
C22×C3×C7×C1312
C23×C3×C7131