Finite Group Databasebeta

← C2×C3×C11×D227 #44471979

Subgroups — C2×C3×C11×D227 #44471979

Order 29964.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×D227C212yesmaximal, direct product factor
2C2×C3×C11×C227C211yesmaximal, characteristic, complemented
3C2×C11×D227C311yesmaximal, characteristic, direct product factor, Hall
4C3×C11×C227C2211yescharacteristic, complemented, Hall
5C2×C11×C227C2×C311yescharacteristic, complemented
6C11×D227C2×C312yesdirect product factor
7C2×C3×D227C1111yesmaximal, characteristic, direct product factor, Hall
8C11×C227C22×C311yescharacteristic, complemented, Hall
9C2×C3×C227C2×C1111yescharacteristic, complemented
10C3×D227C2×C1112yesdirect product factor
11C2×D227C3×C1111yescharacteristic, direct product factor, Hall
12C3×C227C22×C1111yescharacteristic, complemented, Hall
13C2×C227C2×C3×C1111yescharacteristic, complemented
14D227C2×C3×C1112yesdirect product factor
15C227C22×C3×C1111yescharacteristic, complemented, Sylow
16C22×C3×C11—2271nomaximal, Hall
17C2×C3×C11—2272no—
18C2×C3×C11D22711yescharacteristic, direct product factor
19C22×C11—2271noHall
20C3×C11C2×D22711yescharacteristic, direct product factor, Hall
21C2×C11—2272no—
22C2×C11C3×D22711yescharacteristic, direct product factor
23C22×C3—2271noHall
24C11C2×C3×D22711yescharacteristic, direct product factor, Sylow
25C2×C3—2272no—
26C2×C3C11×D22711yescharacteristic, direct product factor
27C22—2271noSylow
28C3C2×C11×D22711yescharacteristic, direct product factor, Sylow
29C2—2272no—
30C2C3×C11×D22711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11D227
commutator, cosocle, hypocenterC227C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C227C2
LCSG ▷ C227
UCSC1 ◁ C2×C3×C11

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C11×D227C2direct (N × H)
2. C2×C3×C11×C227C2semidirect
3. C2×C11×D227C3direct (N × H)
4. C3×C11×C227C22semidirect
5. C2×C11×C227C2×C3semidirect
6. C11×D227C2×C3direct (N × H)
7. C2×C3×D227C11direct (N × H)
8. C11×C227C22×C3semidirect
9. C2×C3×C227C2×C11semidirect
10. C3×D227C2×C11direct (N × H)
11. C2×D227C3×C11direct (N × H)
12. C3×C227C22×C11semidirect
13. C2×C227C2×C3×C11semidirect
14. D227C2×C3×C11direct (N × H)
15. C227C22×C3×C11semidirect
18. C2×C3×C11D227direct (N × H)
20. C3×C11C2×D227direct (N × H)
22. C2×C11C3×D227direct (N × H)
24. C11C2×C3×D227direct (N × H)
26. C2×C3C11×D227direct (N × H)
28. C3C2×C11×D227direct (N × H)
30. C2C3×C11×D227direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×D2272
C2×C3×C11×C2272
C2×C11×D2273
C2×C3×D22711
C22×C3×C11227