Finite Group Databasebeta

← C2×C3×AGL(1,𝔽43) #24925549

Subgroups — C2×C3×AGL(1,𝔽43) #24925549

Order 10836.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×(C43⋊C3)⋊C7C211yesmaximal, characteristic, complemented
2C3×AGL(1,𝔽43)C212yesmaximal, direct product factor
3C2×C3×D43⋊C7C311yesmaximal, characteristic, complemented
4C2×AGL(1,𝔽43)C313yesmaximal, direct product factor
5C3×(C43⋊C3)⋊C7C2211yescharacteristic, complemented, Hall
6C2×C3×C43⋊C7C2×C311yescharacteristic, complemented
7C3×D43⋊C7C2×C312yescomplemented
8C2×(C43⋊C3)⋊C7C2×C313yescomplemented
9AGL(1,𝔽43)C2×C316yesdirect product factor
10C2×C3×D43⋊C3C711yesmaximal, characteristic, complemented, Hall
11C2×D43⋊C7C3211yescharacteristic, complemented, Hall
12C3×C43⋊C7C22×C311yescharacteristic, complemented
13(C43⋊C3)⋊C7C22×C313yescomplemented
14C2×C3×C43⋊C3C2×C711yescharacteristic, complemented
15C3×D43⋊C3C2×C712yescomplemented
16C2×C43⋊C7C2×C3211yescharacteristic, complemented
17D43⋊C7C2×C3212yescomplemented
18C2×C3×D43C3×C711yescharacteristic, complemented
19C2×D43⋊C3C3×C713yescomplemented
20C3×C43⋊C3C22×C711yescharacteristic, complemented, Hall
21C43⋊C7C22×C3211yescharacteristic, complemented, Hall
22C2×C3×C43C2×C3×C711yescharacteristic, complemented
23C3×D43C2×C3×C712yescomplemented
24C2×C43⋊C3C2×C3×C713yescomplemented
25D43⋊C3C2×C3×C716yescomplemented
26C22×C32×C7—431nomaximal, Hall
27C2×D43C32×C711yescharacteristic, complemented, Hall
28C3×C43C22×C3×C711yescharacteristic, complemented
29C43⋊C3C22×C3×C713yescomplemented
30C2×C32×C7—432no—
31C2×C32×C7—431no—
32C2×C43C2×C32×C711yescharacteristic, complemented
33D43C2×C32×C712yescomplemented
34C22×C3×C7—433no—
35C22×C3×C7—431no—
36C32×C7—431noHall
37C43C22×C32×C711yescharacteristic, complemented, Sylow
38C2×C3×C7—436no—
39C2×C3×C7—433no—
40C2×C3×C7—432no—
41C2×C3×C7—431no—
42C22×C32—431noHall
43C22×C7—431noHall
44C3×C7—433no—
45C3×C7—431no—
46C2×C32—432no—
47C2×C32—431no—
48C2×C7—432no—
49C2×C7—431no—
50C22×C3—433no—
51C22×C3—431no—
52C32—431noSylow
53C7—431noSylow
54C2×C3—436no—
55C2×C3—432no—
56C2×C3—433no—
57C2×C3AGL(1,𝔽43)11yescharacteristic, direct product factor
58C22—431noSylow
59C3—433no—
60C3C2×AGL(1,𝔽43)11yescharacteristic, direct product factor
61C2—432no—
62C2C3×AGL(1,𝔽43)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽43)
commutator, cosocle, hypocenterC43C22×C32×C7
FrattiniC1G
Fitting, socleC2×C3×C43C2×C3×C7
LCSG ▷ C43
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×(C43⋊C3)⋊C7C2semidirect
2. C3×AGL(1,𝔽43)C2direct (N × H)
3. C2×C3×D43⋊C7C3semidirect
4. C2×AGL(1,𝔽43)C3direct (N × H)
5. C3×(C43⋊C3)⋊C7C22semidirect
6. C2×C3×C43⋊C7C2×C3semidirect
7. C3×D43⋊C7C2×C3semidirect
8. C2×(C43⋊C3)⋊C7C2×C3semidirect
9. AGL(1,𝔽43)C2×C3direct (N × H)
10. C2×C3×D43⋊C3C7semidirect
11. C2×D43⋊C7C32semidirect
12. C3×C43⋊C7C22×C3semidirect
13. (C43⋊C3)⋊C7C22×C3semidirect
14. C2×C3×C43⋊C3C2×C7semidirect
15. C3×D43⋊C3C2×C7semidirect
16. C2×C43⋊C7C2×C32semidirect
17. D43⋊C7C2×C32semidirect
18. C2×C3×D43C3×C7semidirect
19. C2×D43⋊C3C3×C7semidirect
20. C3×C43⋊C3C22×C7semidirect
21. C43⋊C7C22×C32semidirect
22. C2×C3×C43C2×C3×C7semidirect
23. C3×D43C2×C3×C7semidirect
24. C2×C43⋊C3C2×C3×C7semidirect
25. D43⋊C3C2×C3×C7semidirect
27. C2×D43C32×C7semidirect
28. C3×C43C22×C3×C7semidirect
29. C43⋊C3C22×C3×C7semidirect
32. C2×C43C2×C32×C7semidirect
33. D43C2×C32×C7semidirect
37. C43C22×C32×C7semidirect
57. C2×C3AGL(1,𝔽43)direct (N × H)
60. C3C2×AGL(1,𝔽43)direct (N × H)
62. C2C3×AGL(1,𝔽43)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×(C43⋊C3)⋊C72
C3×AGL(1,𝔽43)2
C2×C3×D43⋊C73
C2×AGL(1,𝔽43)3
C2×C3×D43⋊C37
C22×C32×C743