Finite Group Databasebeta

← C24×C11×C71 #72190837

Subgroups — C24×C11×C71 #72190837

Order 12496.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×C71C2115yesmaximal, direct product factor
2C22×C11×C71C22135yesdirect product factor
3C2×C11×C71C23115yesdirect product factor
4C24×C71C1111yesmaximal, characteristic, direct product factor, Hall
5C11×C71C2411yescharacteristic, direct product factor, Hall
6C23×C71C2×C11115yesdirect product factor
7C22×C71C22×C11135yesdirect product factor
8C24×C11C7111yesmaximal, characteristic, direct product factor, Hall
9C2×C71C23×C11115yesdirect product factor
10C23×C11C2×C71115yesdirect product factor
11C71C24×C1111yescharacteristic, direct product factor, Sylow
12C22×C11C22×C71135yesdirect product factor
13C2×C11C23×C71115yesdirect product factor
14C24C11×C7111yescharacteristic, direct product factor, Sylow
15C11C24×C7111yescharacteristic, direct product factor, Sylow
16C23C2×C11×C71115yesdirect product factor
17C22C22×C11×C71135yesdirect product factor
18C2C23×C11×C71115yesdirect 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×C11×C71C2direct (N × H)
2. C22×C11×C71C22direct (N × H)
3. C2×C11×C71C23direct (N × H)
4. C24×C71C11direct (N × H)
5. C11×C71C24direct (N × H)
6. C23×C71C2×C11direct (N × H)
7. C22×C71C22×C11direct (N × H)
8. C24×C11C71direct (N × H)
9. C2×C71C23×C11direct (N × H)
10. C23×C11C2×C71direct (N × H)
11. C71C24×C11direct (N × H)
12. C22×C11C22×C71direct (N × H)
13. C2×C11C23×C71direct (N × H)
14. C24C11×C71direct (N × H)
15. C11C24×C71direct (N × H)
16. C23C2×C11×C71direct (N × H)
17. C22C22×C11×C71direct (N × H)
18. C2C23×C11×C71direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×C712
C24×C7111
C24×C1171