Finite Group Databasebeta

← C2×C7×C11×D79 #37566653

Subgroups — C2×C7×C11×D79 #37566653

Order 24332.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×D79C212yesmaximal, direct product factor
2C2×C7×C11×C79C211yesmaximal, characteristic, complemented
3C7×C11×C79C2211yescharacteristic, complemented, Hall
4C2×C11×D79C711yesmaximal, characteristic, direct product factor, Hall
5C2×C7×D79C1111yesmaximal, characteristic, direct product factor, Hall
6C2×C11×C79C2×C711yescharacteristic, complemented
7C11×D79C2×C712yesdirect product factor
8C2×C7×C79C2×C1111yescharacteristic, complemented
9C7×D79C2×C1112yesdirect product factor
10C11×C79C22×C711yescharacteristic, complemented, Hall
11C7×C79C22×C1111yescharacteristic, complemented, Hall
12C2×D79C7×C1111yescharacteristic, direct product factor, Hall
13C22×C7×C11—791nomaximal, Hall
14C2×C79C2×C7×C1111yescharacteristic, complemented
15D79C2×C7×C1112yesdirect product factor
16C2×C7×C11—792no—
17C2×C7×C11D7911yescharacteristic, direct product factor
18C79C22×C7×C1111yescharacteristic, complemented, Sylow
19C7×C11C2×D7911yescharacteristic, direct product factor, Hall
20C22×C11—791noHall
21C22×C7—791noHall
22C2×C11—792no—
23C2×C11C7×D7911yescharacteristic, direct product factor
24C2×C7—792no—
25C2×C7C11×D7911yescharacteristic, direct product factor
26C11C2×C7×D7911yescharacteristic, direct product factor, Sylow
27C7C2×C11×D7911yescharacteristic, direct product factor, Sylow
28C22—791noSylow
29C2—792no—
30C2C7×C11×D7911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7×C11D79
commutator, cosocle, hypocenterC79C22×C7×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C79C2
LCSG ▷ C79
UCSC1 ◁ C2×C7×C11

Complements

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

NH ≅ G/Ntype
1. C7×C11×D79C2direct (N × H)
2. C2×C7×C11×C79C2semidirect
3. C7×C11×C79C22semidirect
4. C2×C11×D79C7direct (N × H)
5. C2×C7×D79C11direct (N × H)
6. C2×C11×C79C2×C7semidirect
7. C11×D79C2×C7direct (N × H)
8. C2×C7×C79C2×C11semidirect
9. C7×D79C2×C11direct (N × H)
10. C11×C79C22×C7semidirect
11. C7×C79C22×C11semidirect
12. C2×D79C7×C11direct (N × H)
14. C2×C79C2×C7×C11semidirect
15. D79C2×C7×C11direct (N × H)
17. C2×C7×C11D79direct (N × H)
18. C79C22×C7×C11semidirect
19. C7×C11C2×D79direct (N × H)
23. C2×C11C7×D79direct (N × H)
25. C2×C7C11×D79direct (N × H)
26. C11C2×C7×D79direct (N × H)
27. C7C2×C11×D79direct (N × H)
30. C2C7×C11×D79direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C11×D792
C2×C7×C11×C792
C2×C11×D797
C2×C7×D7911
C22×C7×C1179