Finite Group Databasebeta

← C3×C11×(C19⋊C3)⋊D7 #39911879

Subgroups — C3×C11×(C19⋊C3)⋊D7 #39911879

Order 26334.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C11×C19⋊C3C211yesmaximal, characteristic, complemented, Hall
2C11×(C19⋊C3)⋊D7C313yesmaximal, direct product factor
3C3×C11×D133C311yesmaximal, characteristic, complemented
4C7×C11×C19⋊C3C2×C313yescomplemented
5C3×C7×C11×C19C2×C311yescharacteristic, complemented
6C3×C11×D19⋊C3—71nomaximal, Hall
7C11×D133C3211yescharacteristic, complemented, Hall
8C3×(C19⋊C3)⋊D7C1111yesmaximal, characteristic, direct product factor, Hall
9C3×C11×C19⋊C3D711yescharacteristic, complemented, Hall
10C7×C11×C19C2×C3211yescharacteristic, complemented, Hall
11C32×C11×D7—191nomaximal, Hall
12C3×C11×D19—71no—
13C11×D19⋊C3—73no—
14C3×C7×C19⋊C3C2×C1111yescharacteristic, complemented, Hall
15C3×D133C3×C1111yescharacteristic, complemented
16(C19⋊C3)⋊D7C3×C1113yesdirect product factor
17C32×C7×C11—191noHall
18C3×C11×C19C3×D711yescharacteristic, complemented
19C11×C19⋊C3C3×D713yescomplemented
20C3×C11×D7—193no—
21C3×C11×D7—191no—
22C11×D19—71noHall
23C3×C7×C19C2×C3×C1111yescharacteristic, complemented
24C7×C19⋊C3C2×C3×C1113yescomplemented
25C3×D19⋊C3—71noHall
26D133C32×C1111yescharacteristic, complemented, Hall
27C3×C7×C11—193no—
28C3×C7×C11D19⋊C311yescharacteristic, complemented
29C11×C19C32×D711yescharacteristic, complemented, Hall
30C2×C32×C11—1331noHall
31C3×C19⋊C3C11×D711yescharacteristic, complemented, Hall
32C11×D7—191noHall
33C7×C19C2×C32×C1111yescharacteristic, complemented, Hall
34C32×D7—191noHall
35C3×D19—71no—
36D19⋊C3—73no—
37C32×C11—191noHall
38C7×C11C3×D19⋊C311yescharacteristic, complemented, Hall
39C2×C3×C11—1333no—
40C2×C3×C11—1331no—
41C32×C7—191noHall
42C3×C19C3×C11×D711yescharacteristic, complemented
43C19⋊C3C3×C11×D713yescomplemented
44C3×D7—193no—
45C3×D7—191no—
46D19—71noHall
47C3×C11—193no—
48C3×C11(C19⋊C3)⋊D711yescharacteristic, direct product factor
49C2×C11—1331noHall
50C3×C7—193no—
51C3×C7C11×D19⋊C311yescharacteristic, complemented
52C19C32×C11×D711yescharacteristic, complemented, Sylow
53C2×C32—1331noHall
54D7—191noHall
55C11C3×(C19⋊C3)⋊D711yescharacteristic, direct product factor, Sylow
56C32—191noSylow
57C7C3×C11×D19⋊C311yescharacteristic, complemented, Sylow
58C2×C3—1333no—
59C2×C3—1331no—
60C3—193no—
61C3C11×(C19⋊C3)⋊D711yescharacteristic, direct product factor
62C2—1331noSylow
subgroupG/H
center, hypercenterC3×C11(C19⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C19C2×C32×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×C19⋊C3C2semidirect
2. C11×(C19⋊C3)⋊D7C3direct (N × H)
3. C3×C11×D133C3semidirect
4. C7×C11×C19⋊C3C2×C3semidirect
5. C3×C7×C11×C19C2×C3semidirect
7. C11×D133C32semidirect
8. C3×(C19⋊C3)⋊D7C11direct (N × H)
9. C3×C11×C19⋊C3D7semidirect
10. C7×C11×C19C2×C32semidirect
14. C3×C7×C19⋊C3C2×C11semidirect
15. C3×D133C3×C11semidirect
16. (C19⋊C3)⋊D7C3×C11direct (N × H)
18. C3×C11×C19C3×D7semidirect
19. C11×C19⋊C3C3×D7semidirect
23. C3×C7×C19C2×C3×C11semidirect
24. C7×C19⋊C3C2×C3×C11semidirect
26. D133C32×C11semidirect
28. C3×C7×C11D19⋊C3semidirect
29. C11×C19C32×D7semidirect
31. C3×C19⋊C3C11×D7semidirect
33. C7×C19C2×C32×C11semidirect
38. C7×C11C3×D19⋊C3semidirect
42. C3×C19C3×C11×D7semidirect
43. C19⋊C3C3×C11×D7semidirect
48. C3×C11(C19⋊C3)⋊D7direct (N × H)
51. C3×C7C11×D19⋊C3semidirect
52. C19C32×C11×D7semidirect
55. C11C3×(C19⋊C3)⋊D7direct (N × H)
57. C7C3×C11×D19⋊C3semidirect
61. C3C11×(C19⋊C3)⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×C11×C19⋊C32
C11×(C19⋊C3)⋊D73
C3×C11×D1333
C3×C11×D19⋊C37
C3×(C19⋊C3)⋊D711
C32×C11×D719