Finite Group Databasebeta

← C24×C7×C199 #72199735

Subgroups — C24×C7×C199 #72199735

Order 22288.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C199C2115yesmaximal, direct product factor
2C22×C7×C199C22135yesdirect product factor
3C24×C199C711yesmaximal, characteristic, direct product factor, Hall
4C2×C7×C199C23115yesdirect product factor
5C23×C199C2×C7115yesdirect product factor
6C7×C199C2411yescharacteristic, direct product factor, Hall
7C22×C199C22×C7135yesdirect product factor
8C2×C199C23×C7115yesdirect product factor
9C199C24×C711yescharacteristic, direct product factor, Sylow
10C24×C7C19911yesmaximal, characteristic, direct product factor, Hall
11C23×C7C2×C199115yesdirect product factor
12C22×C7C22×C199135yesdirect product factor
13C24C7×C19911yescharacteristic, direct product factor, Sylow
14C2×C7C23×C199115yesdirect product factor
15C23C2×C7×C199115yesdirect product factor
16C7C24×C19911yescharacteristic, direct product factor, Sylow
17C22C22×C7×C199135yesdirect product factor
18C2C23×C7×C199115yesdirect 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×C199C2direct (N × H)
2. C22×C7×C199C22direct (N × H)
3. C24×C199C7direct (N × H)
4. C2×C7×C199C23direct (N × H)
5. C23×C199C2×C7direct (N × H)
6. C7×C199C24direct (N × H)
7. C22×C199C22×C7direct (N × H)
8. C2×C199C23×C7direct (N × H)
9. C199C24×C7direct (N × H)
10. C24×C7C199direct (N × H)
11. C23×C7C2×C199direct (N × H)
12. C22×C7C22×C199direct (N × H)
13. C24C7×C199direct (N × H)
14. C2×C7C23×C199direct (N × H)
15. C23C2×C7×C199direct (N × H)
16. C7C24×C199direct (N × H)
17. C22C22×C7×C199direct (N × H)
18. C2C23×C7×C199direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×C1992
C24×C1997
C24×C7199