Finite Group Databasebeta

← C24×C7×C11 #11927770

Subgroups — C24×C7×C11 #11927770

Order 1232.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C11C2115yesmaximal, direct product factor
2C22×C7×C11C22135yesdirect product factor
3C24×C11C711yesmaximal, characteristic, direct product factor, Hall
4C2×C7×C11C23115yesdirect product factor
5C24×C7C1111yesmaximal, characteristic, direct product factor, Hall
6C23×C11C2×C7115yesdirect product factor
7C7×C11C2411yescharacteristic, direct product factor, Hall
8C23×C7C2×C11115yesdirect product factor
9C22×C11C22×C7135yesdirect product factor
10C22×C7C22×C11135yesdirect product factor
11C2×C11C23×C7115yesdirect product factor
12C24C7×C1111yescharacteristic, direct product factor, Sylow
13C2×C7C23×C11115yesdirect product factor
14C11C24×C711yescharacteristic, direct product factor, Sylow
15C23C2×C7×C11115yesdirect product factor
16C7C24×C1111yescharacteristic, direct product factor, Sylow
17C22C22×C7×C11135yesdirect product factor
18C2C23×C7×C11115yesdirect 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×C11C2direct (N × H)
2. C22×C7×C11C22direct (N × H)
3. C24×C11C7direct (N × H)
4. C2×C7×C11C23direct (N × H)
5. C24×C7C11direct (N × H)
6. C23×C11C2×C7direct (N × H)
7. C7×C11C24direct (N × H)
8. C23×C7C2×C11direct (N × H)
9. C22×C11C22×C7direct (N × H)
10. C22×C7C22×C11direct (N × H)
11. C2×C11C23×C7direct (N × H)
12. C24C7×C11direct (N × H)
13. C2×C7C23×C11direct (N × H)
14. C11C24×C7direct (N × H)
15. C23C2×C7×C11direct (N × H)
16. C7C24×C11direct (N × H)
17. C22C22×C7×C11direct (N × H)
18. C2C23×C7×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C112
C24×C117
C24×C711