Finite Group Databasebeta

← C26×C3×C112 #72200569

Subgroups — C26×C3×C112 #72200569

Order 23232.

79100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C3×C112C2163yesmaximal, direct product factor
2C26×C112C311yesmaximal, characteristic, direct product factor, Hall
3C24×C3×C112C221651yesdirect product factor
4C25×C112C2×C3163yesdirect product factor
5C23×C3×C112C2311395yesdirect product factor
6C26×C3×C11C11112yesmaximal, direct product factor
7C24×C112C22×C31651yesdirect product factor
8C22×C3×C112C241651yesdirect product factor
9C25×C3×C11C2×C111756yesdirect product factor
10C23×C112C23×C311395yesdirect product factor
11C2×C3×C112C25163yesdirect product factor
12C26×C11C3×C11112yesdirect product factor
13C24×C3×C11C22×C1117812yesdirect product factor
14C22×C112C24×C31651yesdirect product factor
15C3×C112C2611yescharacteristic, direct product factor, Hall
16C25×C11C2×C3×C111756yesdirect product factor
17C23×C3×C11C23×C11116740yesdirect product factor
18C2×C112C25×C3163yesdirect product factor
19C26×C3C11211yescharacteristic, direct product factor, Hall
20C24×C11C22×C3×C1117812yesdirect product factor
21C22×C3×C11C24×C1117812yesdirect product factor
22C112C26×C311yescharacteristic, direct product factor, Sylow
23C25×C3C2×C112163yesdirect product factor
24C23×C11C23×C3×C11116740yesdirect product factor
25C2×C3×C11C25×C111756yesdirect product factor
26C26C3×C11211yescharacteristic, direct product factor, Sylow
27C24×C3C22×C1121651yesdirect product factor
28C22×C11C24×C3×C1117812yesdirect product factor
29C3×C11C26×C11112yesdirect product factor
30C25C2×C3×C112163yesdirect product factor
31C23×C3C23×C11211395yesdirect product factor
32C2×C11C25×C3×C111756yesdirect product factor
33C24C22×C3×C1121651yesdirect product factor
34C22×C3C24×C1121651yesdirect product factor
35C11C26×C3×C11112yesdirect product factor
36C23C23×C3×C11211395yesdirect product factor
37C2×C3C25×C112163yesdirect product factor
38C22C24×C3×C1121651yesdirect product factor
39C3C26×C11211yescharacteristic, direct product factor, Sylow
40C2C25×C3×C112163yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C25×C3×C112C2direct (N × H)
2. C26×C112C3direct (N × H)
3. C24×C3×C112C22direct (N × H)
4. C25×C112C2×C3direct (N × H)
5. C23×C3×C112C23direct (N × H)
6. C26×C3×C11C11direct (N × H)
7. C24×C112C22×C3direct (N × H)
8. C22×C3×C112C24direct (N × H)
9. C25×C3×C11C2×C11direct (N × H)
10. C23×C112C23×C3direct (N × H)
11. C2×C3×C112C25direct (N × H)
12. C26×C11C3×C11direct (N × H)
13. C24×C3×C11C22×C11direct (N × H)
14. C22×C112C24×C3direct (N × H)
15. C3×C112C26direct (N × H)
16. C25×C11C2×C3×C11direct (N × H)
17. C23×C3×C11C23×C11direct (N × H)
18. C2×C112C25×C3direct (N × H)
19. C26×C3C112direct (N × H)
20. C24×C11C22×C3×C11direct (N × H)
21. C22×C3×C11C24×C11direct (N × H)
22. C112C26×C3direct (N × H)
23. C25×C3C2×C112direct (N × H)
24. C23×C11C23×C3×C11direct (N × H)
25. C2×C3×C11C25×C11direct (N × H)
26. C26C3×C112direct (N × H)
27. C24×C3C22×C112direct (N × H)
28. C22×C11C24×C3×C11direct (N × H)
29. C3×C11C26×C11direct (N × H)
30. C25C2×C3×C112direct (N × H)
31. C23×C3C23×C112direct (N × H)
32. C2×C11C25×C3×C11direct (N × H)
33. C24C22×C3×C112direct (N × H)
34. C22×C3C24×C112direct (N × H)
35. C11C26×C3×C11direct (N × H)
36. C23C23×C3×C112direct (N × H)
37. C2×C3C25×C112direct (N × H)
38. C22C24×C3×C112direct (N × H)
39. C3C26×C112direct (N × H)
40. C2C25×C3×C112direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C3×C1122
C26×C1123
C26×C3×C1111