Finite Group Databasebeta

← C7×C11×C22⋊(C37⋊C3) #46803294

Subgroups — C7×C11×C22⋊(C37⋊C3) #46803294

Order 34188.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C11×C37C311yesmaximal, characteristic, complemented, Hall
2C7×C11×C37⋊C3—41nomaximal, Hall
3C2×C7×C11×C37—31no—
4C11×C22⋊(C37⋊C3)C711yesmaximal, characteristic, direct product factor, Hall
5C7×C22⋊(C37⋊C3)C1111yesmaximal, characteristic, direct product factor, Hall
6C7×C11×C37A411yescharacteristic, complemented, Hall
7C22×C11×C37C3×C711yescharacteristic, complemented, Hall
8C11×C37⋊C3—41noHall
9C22×C7×C37C3×C1111yescharacteristic, complemented, Hall
10C7×C11×A4—371nomaximal, Hall
11C2×C11×C37—31no—
12C7×C37⋊C3—41noHall
13C2×C7×C37—31no—
14C22⋊(C37⋊C3)C7×C1111yescharacteristic, direct product factor, Hall
15C11×C37C7×A411yescharacteristic, complemented, Hall
16C22×C7×C11C37⋊C311yescharacteristic, complemented, Hall
17C7×C37C11×A411yescharacteristic, complemented, Hall
18C3×C7×C11—1481noHall
19C2×C7×C11—31no—
20C22×C37C3×C7×C1111yescharacteristic, complemented, Hall
21C11×A4—371noHall
22C37⋊C3—41noHall
23C7×A4—371noHall
24C7×C11C22⋊(C37⋊C3)11yescharacteristic, direct product factor, Hall
25C2×C37—31no—
26C22×C11C7×C37⋊C311yescharacteristic, complemented, Hall
27C37C7×C11×A411yescharacteristic, complemented, Sylow
28C3×C11—1481noHall
29C22×C7C11×C37⋊C311yescharacteristic, complemented, Hall
30C2×C11—31no—
31C3×C7—1481noHall
32C2×C7—31no—
33A4—371noHall
34C11C7×C22⋊(C37⋊C3)11yescharacteristic, direct product factor, Sylow
35C7C11×C22⋊(C37⋊C3)11yescharacteristic, direct product factor, Sylow
36C22C7×C11×C37⋊C311yescharacteristic, complemented, Sylow
37C3—1481noSylow
38C2—31no—
subgroupG/H
center, hypercenterC7×C11C22⋊(C37⋊C3)
commutator, cosocle, hypocenterC22×C37C3×C7×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C37C3
LCSG ▷ C22×C37
UCSC1 ◁ C7×C11

Complements

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

NH ≅ G/Ntype
1. C22×C7×C11×C37C3semidirect
4. C11×C22⋊(C37⋊C3)C7direct (N × H)
5. C7×C22⋊(C37⋊C3)C11direct (N × H)
6. C7×C11×C37A4semidirect
7. C22×C11×C37C3×C7semidirect
9. C22×C7×C37C3×C11semidirect
14. C22⋊(C37⋊C3)C7×C11direct (N × H)
15. C11×C37C7×A4semidirect
16. C22×C7×C11C37⋊C3semidirect
17. C7×C37C11×A4semidirect
20. C22×C37C3×C7×C11semidirect
24. C7×C11C22⋊(C37⋊C3)direct (N × H)
26. C22×C11C7×C37⋊C3semidirect
27. C37C7×C11×A4semidirect
29. C22×C7C11×C37⋊C3semidirect
34. C11C7×C22⋊(C37⋊C3)direct (N × H)
35. C7C11×C22⋊(C37⋊C3)direct (N × H)
36. C22C7×C11×C37⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C7×C11×C373
C7×C11×C37⋊C34
C11×C22⋊(C37⋊C3)7
C7×C22⋊(C37⋊C3)11
C7×C11×A437