Finite Group Databasebeta

← C7×C9×#737 #19100270

Subgroups — C7×C9×#737 #19100270

Order 5103.

986 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×#737C311yesmaximal, characteristic
2C7×C9×3−1+2C3124yesmaximal, complemented
3C7×C9×H(3,𝔽3)C313yesmaximal
4C7×#6887C318yesmaximal, complemented
5C3×C7×C92C314yesmaximal, complemented
6C9×#737C711yesmaximal, characteristic, direct product factor, Sylow
7C7×#737C9127yesdirect product factor
8C3×C7×3−1+2C3218yes—
9C3×C7×H(3,𝔽3)C3211yescharacteristic
10C32×C7×C9C32112yes—
11C32×C7×C9C3214yes—
12C7×C9⋊C9C32148yes—
13C7×C32⋊C9C32124yes—
14C7×C92C3218yes—
15C7×C92C32124yes—
16C7×C92C3211yescharacteristic
17C3×#737C3×C711yescharacteristic
18C9×3−1+2C3×C7124yescomplemented
19C9×H(3,𝔽3)C3×C713yes—
20#6887C3×C718yescomplemented
21C3×C92C3×C714yescomplemented
22C33×C7C3314yes—
23C7×3−1+2C3×C9172yescomplemented
24C7×H(3,𝔽3)C3×C919yes—
25C3×C7×C9—336no—
26C3×C7×C9C3×C9136yescomplemented
27C3×C7×C9C33124yes—
28C3×C7×C9C3311yescharacteristic
29C3×C7×C9C3318yes—
30C3×C7×C9C3313yes—
31#737C7×C9127yesdirect product factor
32C3×3−1+2C32×C718yes—
33C3×H(3,𝔽3)C32×C711yescharacteristic
34C32×C9C32×C7112yes—
35C32×C9C32×C714yes—
36C9⋊C9C32×C7148yes—
37C32⋊C9C32×C7124yes—
38C92C32×C718yes—
39C92C32×C7124yes—
40C92C32×C711yescharacteristic
41C32×C7—312no—
42C32×C7C32×C9112yes—
43C32×C7C3411yescharacteristic
44C7×C9—324no—
45C7×C9C32×C913yes—
46C7×C9C32×C9124yes—
47C7×C9#73719yesdirect product factor
48C33C33×C714yes—
493−1+2C3×C7×C9172yescomplemented
50H(3,𝔽3)C3×C7×C919yes—
51C3×C9—336no—
52C3×C9C3×C7×C9136yescomplemented
53C3×C9C33×C7124yes—
54C3×C9C33×C711yescharacteristic
55C3×C9C33×C718yes—
56C3×C9C33×C713yes—
57C3×C7—312no—
58C3×C7C33×C911yescharacteristic
59C3×C7C3×#73713yes—
60C32—312no—
61C32C32×C7×C9112yes—
62C32C34×C711yescharacteristic
63C9—324no—
64C9C32×C7×C913yes—
65C9C32×C7×C9124yes—
66C9C7×#73719yesdirect product factor
67C7C9×#73711yescharacteristic, direct product factor, Sylow
68C3—312no—
69C3C33×C7×C911yescharacteristic
70C3C3×C7×#73713yes—
subgroupG/H
centerC7×C92C32
commutatorC3C33×C7×C9
FrattiniC32C34×C7
socleC32×C7C34
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C7×C92 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×C9×3−1+2C3semidirect
4. C7×#6887C3semidirect
5. C3×C7×C92C3semidirect
6. C9×#737C7direct (N × H)
7. C7×#737C9direct (N × H)
18. C9×3−1+2C3×C7semidirect
20. #6887C3×C7semidirect
21. C3×C92C3×C7semidirect
23. C7×3−1+2C3×C9semidirect
26. C3×C7×C9C3×C9semidirect
31. #737C7×C9direct (N × H)
47. C7×C9#737direct (N × H)
49. 3−1+2C3×C7×C9semidirect
52. C3×C9C3×C7×C9semidirect
66. C9C7×#737direct (N × H)
67. C7C9×#737direct (N × H)