Finite Group Databasebeta

← C23×C72×C43 #72194792

Subgroups — C23×C72×C43 #72194792

Order 16856.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C43C718yesmaximal, direct product factor
2C22×C72×C43C217yesmaximal, direct product factor
3C2×C72×C43C2217yesdirect product factor
4C72×C43C2311yescharacteristic, direct product factor, Hall
5C22×C7×C43C2×C7156yesdirect product factor
6C2×C7×C43C22×C7156yesdirect product factor
7C23×C72C4311yesmaximal, characteristic, direct product factor, Hall
8C23×C43C7211yescharacteristic, direct product factor, Hall
9C7×C43C23×C718yesdirect product factor
10C22×C72C2×C4317yesdirect product factor
11C22×C43C2×C7217yesdirect product factor
12C2×C72C22×C4317yesdirect product factor
13C2×C43C22×C7217yesdirect product factor
14C23×C7C7×C4318yesdirect product factor
15C72C23×C4311yescharacteristic, direct product factor, Sylow
16C43C23×C7211yescharacteristic, direct product factor, Sylow
17C22×C7C2×C7×C43156yesdirect product factor
18C2×C7C22×C7×C43156yesdirect product factor
19C23C72×C4311yescharacteristic, direct product factor, Sylow
20C7C23×C7×C4318yesdirect product factor
21C22C2×C72×C4317yesdirect product factor
22C2C22×C72×C4317yesdirect 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×C43C7direct (N × H)
2. C22×C72×C43C2direct (N × H)
3. C2×C72×C43C22direct (N × H)
4. C72×C43C23direct (N × H)
5. C22×C7×C43C2×C7direct (N × H)
6. C2×C7×C43C22×C7direct (N × H)
7. C23×C72C43direct (N × H)
8. C23×C43C72direct (N × H)
9. C7×C43C23×C7direct (N × H)
10. C22×C72C2×C43direct (N × H)
11. C22×C43C2×C72direct (N × H)
12. C2×C72C22×C43direct (N × H)
13. C2×C43C22×C72direct (N × H)
14. C23×C7C7×C43direct (N × H)
15. C72C23×C43direct (N × H)
16. C43C23×C72direct (N × H)
17. C22×C7C2×C7×C43direct (N × H)
18. C2×C7C22×C7×C43direct (N × H)
19. C23C72×C43direct (N × H)
20. C7C23×C7×C43direct (N × H)
21. C22C2×C72×C43direct (N × H)
22. C2C22×C72×C43direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C437
C22×C72×C432
C23×C7243