Finite Group Databasebeta

← C22×C11×C23×C31 #44535876

Subgroups — C22×C11×C23×C31 #44535876

Order 31372.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C23×C31C213yesmaximal, direct product factor
2C11×C23×C31C2211yescharacteristic, direct product factor, Hall
3C22×C23×C31C1111yesmaximal, characteristic, direct product factor, Hall
4C2×C23×C31C2×C1113yesdirect product factor
5C22×C11×C31C2311yesmaximal, characteristic, direct product factor, Hall
6C22×C11×C23C3111yesmaximal, characteristic, direct product factor, Hall
7C23×C31C22×C1111yescharacteristic, direct product factor, Hall
8C2×C11×C31C2×C2313yesdirect product factor
9C2×C11×C23C2×C3113yesdirect product factor
10C11×C31C22×C2311yescharacteristic, direct product factor, Hall
11C11×C23C22×C3111yescharacteristic, direct product factor, Hall
12C22×C31C11×C2311yescharacteristic, direct product factor, Hall
13C22×C23C11×C3111yescharacteristic, direct product factor, Hall
14C2×C31C2×C11×C2313yesdirect product factor
15C2×C23C2×C11×C3113yesdirect product factor
16C22×C11C23×C3111yescharacteristic, direct product factor, Hall
17C31C22×C11×C2311yescharacteristic, direct product factor, Sylow
18C23C22×C11×C3111yescharacteristic, direct product factor, Sylow
19C2×C11C2×C23×C3113yesdirect product factor
20C11C22×C23×C3111yescharacteristic, direct product factor, Sylow
21C22C11×C23×C3111yescharacteristic, direct product factor, Sylow
22C2C2×C11×C23×C3113yesdirect 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. C2×C11×C23×C31C2direct (N × H)
2. C11×C23×C31C22direct (N × H)
3. C22×C23×C31C11direct (N × H)
4. C2×C23×C31C2×C11direct (N × H)
5. C22×C11×C31C23direct (N × H)
6. C22×C11×C23C31direct (N × H)
7. C23×C31C22×C11direct (N × H)
8. C2×C11×C31C2×C23direct (N × H)
9. C2×C11×C23C2×C31direct (N × H)
10. C11×C31C22×C23direct (N × H)
11. C11×C23C22×C31direct (N × H)
12. C22×C31C11×C23direct (N × H)
13. C22×C23C11×C31direct (N × H)
14. C2×C31C2×C11×C23direct (N × H)
15. C2×C23C2×C11×C31direct (N × H)
16. C22×C11C23×C31direct (N × H)
17. C31C22×C11×C23direct (N × H)
18. C23C22×C11×C31direct (N × H)
19. C2×C11C2×C23×C31direct (N × H)
20. C11C22×C23×C31direct (N × H)
21. C22C11×C23×C31direct (N × H)
22. C2C2×C11×C23×C31direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×C23×C312
C22×C23×C3111
C22×C11×C3123
C22×C11×C2331