Finite Group Databasebeta

← C24×C3×C7 #66759

Subgroups — C24×C3×C7 #66759

Order 336.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C7C2115yesmaximal, direct product factor
2C24×C7C311yesmaximal, characteristic, direct product factor, Hall
3C22×C3×C7C22135yesdirect product factor
4C23×C7C2×C3115yesdirect product factor
5C24×C3C711yesmaximal, characteristic, direct product factor, Hall
6C2×C3×C7C23115yesdirect product factor
7C22×C7C22×C3135yesdirect product factor
8C23×C3C2×C7115yesdirect product factor
9C3×C7C2411yescharacteristic, direct product factor, Hall
10C24C3×C711yescharacteristic, direct product factor, Sylow
11C2×C7C23×C3115yesdirect product factor
12C22×C3C22×C7135yesdirect product factor
13C23C2×C3×C7115yesdirect product factor
14C7C24×C311yescharacteristic, direct product factor, Sylow
15C2×C3C23×C7115yesdirect product factor
16C22C22×C3×C7135yesdirect product factor
17C3C24×C711yescharacteristic, direct product factor, Sylow
18C2C23×C3×C7115yesdirect 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×C3×C7C2direct (N × H)
2. C24×C7C3direct (N × H)
3. C22×C3×C7C22direct (N × H)
4. C23×C7C2×C3direct (N × H)
5. C24×C3C7direct (N × H)
6. C2×C3×C7C23direct (N × H)
7. C22×C7C22×C3direct (N × H)
8. C23×C3C2×C7direct (N × H)
9. C3×C7C24direct (N × H)
10. C24C3×C7direct (N × H)
11. C2×C7C23×C3direct (N × H)
12. C22×C3C22×C7direct (N × H)
13. C23C2×C3×C7direct (N × H)
14. C7C24×C3direct (N × H)
15. C2×C3C23×C7direct (N × H)
16. C22C22×C3×C7direct (N × H)
17. C3C24×C7direct (N × H)
18. C2C23×C3×C7direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C72
C24×C73
C24×C37