Finite Group Databasebeta

← C32×C7×#737 #19100349

Subgroups — C32×C7×#737 #19100349

Order 5103.

5804 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×#737C31108yesmaximal, direct product factor
2C32×C7×3−1+2C318yesmaximal, complemented
3C32×C7×H(3,𝔽3)C311yesmaximal, characteristic
4C33×C7×C9C314yesmaximal, complemented
5C32×#737C711yesmaximal, characteristic, direct product factor, Sylow
6C34×C7C3214yes—
7C7×#737C321729yesdirect product factor
8C3×C7×3−1+2C321288yescomplemented
9C3×C7×H(3,𝔽3)C32136yes—
10C32×C7×C9C3218yes—
11C32×C7×C9C3211yescharacteristic
12C32×C7×C9C321144yescomplemented
13C3×#737C3×C71108yesdirect product factor
14C32×3−1+2C3×C718yescomplemented
15C32×H(3,𝔽3)C3×C711yescharacteristic
16C33×C9C3×C714yescomplemented
17C33×C7—336no—
18C33×C7C33148yes—
19C33×C7C3311yescharacteristic
20C7×3−1+2C331648yescomplemented
21C7×H(3,𝔽3)C33181yes—
22C3×C7×C9C33196yes—
23C3×C7×C9C33112yes—
24C3×C7×C9C331324yescomplemented
25C34C32×C714yes—
26#737C32×C71729yesdirect product factor
27C3×3−1+2C32×C71288yescomplemented
28C3×H(3,𝔽3)C32×C7136yes—
29C32×C9C32×C711yescharacteristic
30C32×C9C32×C718yes—
31C32×C9C32×C71144yescomplemented
32C32×C7—3144no—
33C32×C7#73719yesdirect product factor
34C32×C7C34136yes—
35C32×C7C3414yes—
36C7×C9C3419yes—
37C7×C9C34172yes—
38C33—336no—
39C33C33×C7148yes—
40C33C33×C711yescharacteristic
413−1+2C33×C71648yescomplemented
42H(3,𝔽3)C33×C7181yes—
43C3×C9C33×C7112yes—
44C3×C9C33×C7196yes—
45C3×C9C33×C71324yescomplemented
46C3×C7—336no—
47C3×C7C3×#737112yesdirect product factor
48C3×C7C3511yescharacteristic
49C32—3144no—
50C32C7×#73719yesdirect product factor
51C32C34×C7136yes—
52C32C34×C714yes—
53C9C34×C719yes—
54C9C34×C7172yes—
55C7C32×#73711yescharacteristic, direct product factor, Sylow
56C3—336no—
57C3C3×C7×#737112yesdirect product factor
58C3C35×C711yescharacteristic
subgroupG/H
centerC32×C7×C9C32
commutator, FrattiniC3C35×C7
socleC33×C7C33
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C32×C7×C9 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C7×#737C3direct (N × H)
2. C32×C7×3−1+2C3semidirect
4. C33×C7×C9C3semidirect
5. C32×#737C7direct (N × H)
7. C7×#737C32direct (N × H)
8. C3×C7×3−1+2C32semidirect
12. C32×C7×C9C32semidirect
13. C3×#737C3×C7direct (N × H)
14. C32×3−1+2C3×C7semidirect
16. C33×C9C3×C7semidirect
20. C7×3−1+2C33semidirect
24. C3×C7×C9C33semidirect
26. #737C32×C7direct (N × H)
27. C3×3−1+2C32×C7semidirect
31. C32×C9C32×C7semidirect
33. C32×C7#737direct (N × H)
41. 3−1+2C33×C7semidirect
45. C3×C9C33×C7semidirect
47. C3×C7C3×#737direct (N × H)
50. C32C7×#737direct (N × H)
55. C7C32×#737direct (N × H)
57. C3C3×C7×#737direct (N × H)