Finite Group Databasebeta

← C22×C7×C31×C13⋊C3 #46799619

Subgroups — C22×C7×C31×C13⋊C3 #46799619

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×C31×C13⋊C3C213yesmaximal, direct product factor
2C22×C7×C13×C31C311yesmaximal, characteristic, complemented, Hall
3C7×C31×C13⋊C3C2211yescharacteristic, direct product factor, Hall
4C2×C7×C13×C31C2×C313yescomplemented
5C22×C31×C13⋊C3C711yesmaximal, characteristic, direct product factor, Hall
6C7×C13×C31C22×C311yescharacteristic, complemented, Hall
7C22×C3×C7×C31—131nomaximal, Hall
8C2×C31×C13⋊C3C2×C713yesdirect product factor
9C22×C13×C31C3×C711yescharacteristic, complemented, Hall
10C2×C3×C7×C31—133no—
11C31×C13⋊C3C22×C711yescharacteristic, direct product factor, Hall
12C22×C7×C13⋊C3C3111yesmaximal, characteristic, direct product factor, Hall
13C22×C7×C31C13⋊C311yescharacteristic, direct product factor, Hall
14C2×C13×C31C2×C3×C713yescomplemented
15C3×C7×C31—131noHall
16C2×C7×C13⋊C3C2×C3113yesdirect product factor
17C2×C7×C31C2×C13⋊C313yesdirect product factor
18C13×C31C22×C3×C711yescharacteristic, complemented, Hall
19C22×C3×C31—131noHall
20C22×C7×C13C3×C3111yescharacteristic, complemented, Hall
21C7×C13⋊C3C22×C3111yescharacteristic, direct product factor, Hall
22C7×C31C22×C13⋊C311yescharacteristic, direct product factor, Hall
23C2×C3×C31—133no—
24C2×C7×C13C2×C3×C3113yescomplemented
25C22×C13⋊C3C7×C3111yescharacteristic, direct product factor, Hall
26C22×C31C7×C13⋊C311yescharacteristic, direct product factor, Hall
27C3×C31—131noHall
28C7×C13C22×C3×C3111yescharacteristic, complemented, Hall
29C22×C3×C7—131noHall
30C2×C13⋊C3C2×C7×C3113yesdirect product factor
31C2×C31C2×C7×C13⋊C313yesdirect product factor
32C22×C13C3×C7×C3111yescharacteristic, complemented, Hall
33C2×C3×C7—133no—
34C13⋊C3C22×C7×C3111yescharacteristic, direct product factor, Hall
35C31C22×C7×C13⋊C311yescharacteristic, direct product factor, Sylow
36C22×C7C31×C13⋊C311yescharacteristic, direct product factor, Hall
37C2×C13C2×C3×C7×C3113yescomplemented
38C3×C7—131noHall
39C2×C7C2×C31×C13⋊C313yesdirect product factor
40C13C22×C3×C7×C3111yescharacteristic, complemented, Sylow
41C22×C3—131noHall
42C7C22×C31×C13⋊C311yescharacteristic, direct product factor, Sylow
43C2×C3—133no—
44C22C7×C31×C13⋊C311yescharacteristic, direct product factor, Sylow
45C3—131noSylow
46C2C2×C7×C31×C13⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C7×C31C13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C7×C31
FrattiniC1G
Fitting, socleC22×C7×C13×C31C3
LCSG ▷ C13
UCSC1 ◁ C22×C7×C31

Complements

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

NH ≅ G/Ntype
1. C2×C7×C31×C13⋊C3C2direct (N × H)
2. C22×C7×C13×C31C3semidirect
3. C7×C31×C13⋊C3C22direct (N × H)
4. C2×C7×C13×C31C2×C3semidirect
5. C22×C31×C13⋊C3C7direct (N × H)
6. C7×C13×C31C22×C3semidirect
8. C2×C31×C13⋊C3C2×C7direct (N × H)
9. C22×C13×C31C3×C7semidirect
11. C31×C13⋊C3C22×C7direct (N × H)
12. C22×C7×C13⋊C3C31direct (N × H)
13. C22×C7×C31C13⋊C3direct (N × H)
14. C2×C13×C31C2×C3×C7semidirect
16. C2×C7×C13⋊C3C2×C31direct (N × H)
17. C2×C7×C31C2×C13⋊C3direct (N × H)
18. C13×C31C22×C3×C7semidirect
20. C22×C7×C13C3×C31semidirect
21. C7×C13⋊C3C22×C31direct (N × H)
22. C7×C31C22×C13⋊C3direct (N × H)
24. C2×C7×C13C2×C3×C31semidirect
25. C22×C13⋊C3C7×C31direct (N × H)
26. C22×C31C7×C13⋊C3direct (N × H)
28. C7×C13C22×C3×C31semidirect
30. C2×C13⋊C3C2×C7×C31direct (N × H)
31. C2×C31C2×C7×C13⋊C3direct (N × H)
32. C22×C13C3×C7×C31semidirect
34. C13⋊C3C22×C7×C31direct (N × H)
35. C31C22×C7×C13⋊C3direct (N × H)
36. C22×C7C31×C13⋊C3direct (N × H)
37. C2×C13C2×C3×C7×C31semidirect
39. C2×C7C2×C31×C13⋊C3direct (N × H)
40. C13C22×C3×C7×C31semidirect
42. C7C22×C31×C13⋊C3direct (N × H)
44. C22C7×C31×C13⋊C3direct (N × H)
46. C2C2×C7×C31×C13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×C31×C13⋊C32
C22×C7×C13×C313
C22×C31×C13⋊C37
C22×C3×C7×C3113
C22×C7×C13⋊C331