Finite Group Databasebeta

← C3×C43⋊H(5,𝔽3) #44535401

Subgroups — C3×C43⋊H(5,𝔽3) #44535401

Order 31347.

6776 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43⋊H(5,𝔽3)C3181yesmaximal, direct product factor
2C32×C32⋊(C43⋊C3)C3112yesmaximal, complemented
3C3×H(3,𝔽3)×C43⋊C3C3127yesmaximal, complemented
4C32×H(3,𝔽3)×C43C311yesmaximal, characteristic, complemented
5C33×C43⋊C3C32136yescomplemented
6C3×C32⋊(C43⋊C3)C32172yescomplemented
7C3×C32⋊(C43⋊C3)C3219yescomplemented
8C3×C32⋊(C43⋊C3)C321324yescomplemented
9H(3,𝔽3)×C43⋊C3C321729yescomplemented
10C34×C43C3214yescomplemented
11C3×H(3,𝔽3)×C43C3219yescomplemented
12C3×H(3,𝔽3)×C43C32127yescomplemented
13C32×C43⋊C3—9108no—
14C32×C43⋊C3C33127yes—
15C32×C43⋊C3C331324yescomplemented
16C32⋊(C43⋊C3)C331648yescomplemented
17C32⋊(C43⋊C3)C33181yescomplemented
18C33×C43—912no—
19C33×C43C33112yes—
20C33×C43C3311yescharacteristic
21C33×C43C33136yescomplemented
22H(3,𝔽3)×C43C33181yescomplemented
23C3×H(5,𝔽3)—431nomaximal, Sylow
24C32×C43—33no—
25C32×C43—336no—
26C32×C43—936no—
27C32×C43C34136yes—
28C32×C43C3413yes—
29C32×C43C3411yescharacteristic
30C3×C43⋊C3—381no—
31C3×C43⋊C3—9324no—
32C3×C43⋊C3C34181yes—
33H(5,𝔽3)—4381no—
34C32×H(3,𝔽3)—4312no—
35C32×H(3,𝔽3)—4327no—
36C32×H(3,𝔽3)C43⋊C311yescharacteristic, complemented
37C3×C43—336no—
38C3×C43—33no—
39C3×C43H(5,𝔽3)13yescomplemented
40C3×C43C3511yescharacteristic
41C43⋊C3—381no—
42C34—4336no—
43C34C3×C43⋊C314yescomplemented
44C3×H(3,𝔽3)—439no—
45C3×H(3,𝔽3)—4372no—
46C3×H(3,𝔽3)—43324no—
47C3×H(3,𝔽3)—43729no—
48C3×H(3,𝔽3)C3×C43⋊C319yescomplemented
49C3×H(3,𝔽3)C3×C43⋊C3127yescomplemented
50C43C3×H(5,𝔽3)11yescharacteristic, complemented, Sylow
51C33—912no—
52C33—4327no—
53C33—43324no—
54C33—387108no—
55C33C32×C43⋊C311yescharacteristic
56C33C32×C43⋊C3112yes—
57C33C32×C43⋊C3136yescomplemented
58H(3,𝔽3)—4381no—
59H(3,𝔽3)—43648no—
60H(3,𝔽3)C32×C43⋊C3181yescomplemented
61C32—33no—
62C32—336no—
63C32—936no—
64C32—4381no—
65C32—12981no—
66C32—387324no—
67C32C33×C43⋊C313yes—
68C32C33×C43⋊C3136yes—
69C32C33×C43⋊C311yescharacteristic
70C3—33no—
71C3—336no—
72C3—12981no—
73C3C43⋊H(5,𝔽3)13yesdirect product factor
74C3C34×C43⋊C311yescharacteristic
subgroupG/H
centerC32C33×C43⋊C3
commutator, cosocleC3×C43C35
FrattiniC3C34×C43⋊C3
FittingC32×H(3,𝔽3)×C43C3
socleC32×C43C34
hypercenterC32×H(3,𝔽3)C43⋊C3
hypocenterC43C3×H(5,𝔽3)
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C32×H(3,𝔽3)

Complements

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

NH ≅ G/Ntype
1. C43⋊H(5,𝔽3)C3direct (N × H)
2. C32×C32⋊(C43⋊C3)C3semidirect
3. C3×H(3,𝔽3)×C43⋊C3C3semidirect
4. C32×H(3,𝔽3)×C43C3semidirect
5. C33×C43⋊C3C32semidirect
6. C3×C32⋊(C43⋊C3)C32semidirect
7. C3×C32⋊(C43⋊C3)C32semidirect
8. C3×C32⋊(C43⋊C3)C32semidirect
9. H(3,𝔽3)×C43⋊C3C32semidirect
10. C34×C43C32semidirect
11. C3×H(3,𝔽3)×C43C32semidirect
12. C3×H(3,𝔽3)×C43C32semidirect
15. C32×C43⋊C3C33semidirect
16. C32⋊(C43⋊C3)C33semidirect
17. C32⋊(C43⋊C3)C33semidirect
21. C33×C43C33semidirect
22. H(3,𝔽3)×C43C33semidirect
36. C32×H(3,𝔽3)C43⋊C3semidirect
39. C3×C43H(5,𝔽3)semidirect
43. C34C3×C43⋊C3semidirect
48. C3×H(3,𝔽3)C3×C43⋊C3semidirect
49. C3×H(3,𝔽3)C3×C43⋊C3semidirect
50. C43C3×H(5,𝔽3)semidirect
57. C33C32×C43⋊C3semidirect
60. H(3,𝔽3)C32×C43⋊C3semidirect
73. C3C43⋊H(5,𝔽3)direct (N × H)

Maximal subgroups

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

subgroupindex
C43⋊H(5,𝔽3)3
C32×C32⋊(C43⋊C3)3
C3×H(3,𝔽3)×C43⋊C33
C32×H(3,𝔽3)×C433
C3×H(5,𝔽3)43