Finite Group Databasebeta

← C26×C3×D3 #11919300

Subgroups — C26×C3×D3 #11919300

Order 1152.

119673 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C26×C32C211yesmaximal, characteristic, complemented
2C25×C3×D3C21126yesmaximal, direct product factor
3C27×C3—31nomaximal
4C26×D3C311yesmaximal, characteristic, direct product factor
5C25×C32C22163yescomplemented
6C24×C3×D3C2212604yesdirect product factor
7C26×C3—21no—
8C26×C3—3126no—
9C26×C3D311yescharacteristic, direct product factor
10C26×C3C2×C311yescharacteristic, complemented
11C25×D3C2×C31126yesdirect product factor
12C24×C32C231651yescomplemented
13C23×C3×D3C23111160yesdirect product factor
14C27—31noSylow
15C25×C3—263no—
16C25×C3—32604no—
17C25×C3C2×D3163yesdirect product factor
18C25×C3C22×C3163yescomplemented
19C24×D3C22×C312604yesdirect product factor
20C23×C32C2411395yescomplemented
21C22×C3×D3C24110416yesdirect product factor
22C26—3126no—
23C26C3×D311yescharacteristic, direct product factor
24C24×C3—2651no—
25C24×C3—311160no—
26C24×C3C22×D31651yesdirect product factor
27C24×C3C23×C31651yescomplemented
28C23×D3C23×C3111160yesdirect product factor
29C22×C32C251651yescomplemented
30C2×C3×D3C2512016yesdirect product factor
31C25—32604no—
32C25C2×C3×D3163yesdirect product factor
33C23×C3—21395no—
34C23×C3—310416no—
35C23×C3C23×D311395yesdirect product factor
36C23×C3C24×C311395yescomplemented
37C22×D3C24×C3110416yesdirect product factor
38C2×C32C26163yescomplemented
39C3×D3C26164yesdirect product factor
40C24—311160no—
41C24C22×C3×D31651yesdirect product factor
42C22×C3—2651no—
43C22×C3—32016no—
44C22×C3C24×D31651yesdirect product factor
45C22×C3C25×C31651yescomplemented
46C2×D3C25×C312016yesdirect product factor
47C32C2711yescharacteristic, complemented, Sylow
48C23—310416no—
49C23C23×C3×D311395yesdirect product factor
50C2×C3—263no—
51C2×C3—364no—
52C2×C3C25×D3163yesdirect product factor
53C2×C3C26×C3163yescomplemented
54D3C26×C3164yesdirect product factor
55C22—32016no—
56C22C24×C3×D31651yesdirect product factor
57C3—21no—
58C3C26×D311yescharacteristic, direct product factor
59C3C27×C311yescharacteristic, complemented
60C2—364no—
61C2C25×C3×D3163yesdirect product factor
subgroupG/H
center, hypercenterC26×C3D3
commutator, cosocle, hypocenterC3C27×C3
FrattiniC1G
Fitting, socleC26×C32C2
LCSG ▷ C3
UCSC1 ◁ C26×C3

Complements

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

NH ≅ G/Ntype
1. C26×C32C2semidirect
2. C25×C3×D3C2direct (N × H)
4. C26×D3C3direct (N × H)
5. C25×C32C22semidirect
6. C24×C3×D3C22direct (N × H)
9. C26×C3D3direct (N × H)
10. C26×C3C2×C3semidirect
11. C25×D3C2×C3direct (N × H)
12. C24×C32C23semidirect
13. C23×C3×D3C23direct (N × H)
17. C25×C3C2×D3direct (N × H)
18. C25×C3C22×C3semidirect
19. C24×D3C22×C3direct (N × H)
20. C23×C32C24semidirect
21. C22×C3×D3C24direct (N × H)
23. C26C3×D3direct (N × H)
26. C24×C3C22×D3direct (N × H)
27. C24×C3C23×C3semidirect
28. C23×D3C23×C3direct (N × H)
29. C22×C32C25semidirect
30. C2×C3×D3C25direct (N × H)
32. C25C2×C3×D3direct (N × H)
35. C23×C3C23×D3direct (N × H)
36. C23×C3C24×C3semidirect
37. C22×D3C24×C3direct (N × H)
38. C2×C32C26semidirect
39. C3×D3C26direct (N × H)
41. C24C22×C3×D3direct (N × H)
44. C22×C3C24×D3direct (N × H)
45. C22×C3C25×C3semidirect
46. C2×D3C25×C3direct (N × H)
47. C32C27semidirect
49. C23C23×C3×D3direct (N × H)
52. C2×C3C25×D3direct (N × H)
53. C2×C3C26×C3semidirect
54. D3C26×C3direct (N × H)
56. C22C24×C3×D3direct (N × H)
58. C3C26×D3direct (N × H)
59. C3C27×C3semidirect
61. C2C25×C3×D3direct (N × H)

Maximal subgroups

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

subgroupindex
C26×C322
C25×C3×D32
C27×C33
C26×D33