Finite Group Databasebeta

← C2×C3×C11×D183 #37563565

Subgroups — C2×C3×C11×D183 #37563565

Order 24156.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11×D183C212yesmaximal, direct product factor
2C2×C32×C11×C61C211yesmaximal, characteristic, complemented
3C2×C3×C11×D61—31nomaximal
4C2×C11×D183C311yesmaximal, characteristic, direct product factor
5C32×C11×C61C2211yescharacteristic, complemented, Hall
6C11×D183C2×C312yesdirect product factor
7C3×C11×D61—32no—
8C2×C3×C11×C61—21no—
9C2×C3×C11×C61D311yescharacteristic, complemented
10C2×C3×C11×C61C2×C311yescharacteristic, complemented
11C2×C11×D61—31noHall
12C2×C3×D183C1111yesmaximal, characteristic, direct product factor, Hall
13C3×C11×C61—21no—
14C3×C11×C61C2×D311yescharacteristic, complemented
15C3×C11×C61C22×C311yescharacteristic, complemented
16C2×C11×C61C3×D311yescharacteristic, complemented
17C11×D61—32no—
18C2×C32×C61C2×C1111yescharacteristic, complemented
19C3×D183C2×C1112yesdirect product factor
20C2×D183C3×C1111yescharacteristic, direct product factor
21C2×C3×D61—31no—
22C11×C61C2×C3×D311yescharacteristic, complemented, Hall
23C32×C61C22×C1111yescharacteristic, complemented, Hall
24C2×C3×D3×C11—611nomaximal, Hall
25C2×C3×C61—21no—
26C2×C3×C61D3×C1111yescharacteristic, complemented
27C2×C3×C61C2×C3×C1111yescharacteristic, complemented
28D183C2×C3×C1112yesdirect product factor
29C3×D61—32no—
30C2×D61—31noHall
31C2×C32×C11D6111yescharacteristic, complemented
32C3×D3×C11—612no—
33C3×C61—21no—
34C3×C61C2×D3×C1111yescharacteristic, complemented
35C3×C61C22×C3×C1111yescharacteristic, complemented
36C22×C3×C11—1831no—
37C2×D3×C11—611no—
38C2×C61C3×D3×C1111yescharacteristic, complemented
39D61—32no—
40C32×C11C2×D6111yescharacteristic, complemented, Hall
41C2×C3×C11—21no—
42C2×C3×C11—1832no—
43C2×C3×C11C3×D6111yescharacteristic, complemented
44C2×C3×C11D18311yescharacteristic, direct product factor
45D3×C11—612no—
46C61C2×C3×D3×C1111yescharacteristic, complemented, Sylow
47C22×C11—1831noHall
48C2×C3×D3—611noHall
49C3×C11—21no—
50C3×C11C2×C3×D6111yescharacteristic, complemented
51C3×C11C2×D18311yescharacteristic, direct product factor
52C2×C11—1832no—
53C2×C11C3×D18311yescharacteristic, direct product factor
54C2×C32C11×D6111yescharacteristic, complemented
55C3×D3—612no—
56C22×C3—1831no—
57C2×D3—611no—
58C11C2×C3×D18311yescharacteristic, direct product factor, Sylow
59C32C2×C11×D6111yescharacteristic, complemented, Sylow
60C2×C3—21no—
61C2×C3—1832no—
62C2×C3C3×C11×D6111yescharacteristic, complemented
63C2×C3C11×D18311yescharacteristic, direct product factor
64D3—612no—
65C22—1831noSylow
66C3—21no—
67C3C2×C11×D18311yescharacteristic, direct product factor
68C3C2×C3×C11×D6111yescharacteristic, complemented
69C2—1832no—
70C2C3×C11×D18311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C11D183
commutator, cosocle, hypocenterC3×C61C22×C3×C11
FrattiniC1G
Fitting, socleC2×C32×C11×C61C2
LCSG ▷ C3×C61
UCSC1 ◁ C2×C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C11×D183C2direct (N × H)
2. C2×C32×C11×C61C2semidirect
4. C2×C11×D183C3direct (N × H)
5. C32×C11×C61C22semidirect
6. C11×D183C2×C3direct (N × H)
9. C2×C3×C11×C61D3semidirect
10. C2×C3×C11×C61C2×C3semidirect
12. C2×C3×D183C11direct (N × H)
14. C3×C11×C61C2×D3semidirect
15. C3×C11×C61C22×C3semidirect
16. C2×C11×C61C3×D3semidirect
18. C2×C32×C61C2×C11semidirect
19. C3×D183C2×C11direct (N × H)
20. C2×D183C3×C11direct (N × H)
22. C11×C61C2×C3×D3semidirect
23. C32×C61C22×C11semidirect
26. C2×C3×C61D3×C11semidirect
27. C2×C3×C61C2×C3×C11semidirect
28. D183C2×C3×C11direct (N × H)
31. C2×C32×C11D61semidirect
34. C3×C61C2×D3×C11semidirect
35. C3×C61C22×C3×C11semidirect
38. C2×C61C3×D3×C11semidirect
40. C32×C11C2×D61semidirect
43. C2×C3×C11C3×D61semidirect
44. C2×C3×C11D183direct (N × H)
46. C61C2×C3×D3×C11semidirect
50. C3×C11C2×C3×D61semidirect
51. C3×C11C2×D183direct (N × H)
53. C2×C11C3×D183direct (N × H)
54. C2×C32C11×D61semidirect
58. C11C2×C3×D183direct (N × H)
59. C32C2×C11×D61semidirect
62. C2×C3C3×C11×D61semidirect
63. C2×C3C11×D183direct (N × H)
67. C3C2×C11×D183direct (N × H)
68. C3C2×C3×C11×D61semidirect
70. C2C3×C11×D183direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11×D1832
C2×C32×C11×C612
C2×C3×C11×D613
C2×C11×D1833
C2×C3×D18311
C2×C3×D3×C1161