Finite Group Databasebeta

← C7×#10624864 #19100273

Subgroups — C7×#10624864 #19100273

Order 5103.

926 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×C9⋊C9C314yesmaximal, complemented
6#10624864C711yesmaximal, characteristic, direct product factor, Sylow
7C7×#737C9127yescomplemented
8C3×C7×3−1+2C3218yes—
9C3×C7×H(3,𝔽3)C3211yescharacteristic
10C32×C7×C9C32112yes—
11C32×C7×C9C3214yes—
12C7×C9⋊C9C3211yescharacteristic
13C7×C9⋊C9C3218yes—
14C7×C9⋊C9C32124yes—
15C7×C9⋊C9C32124yes—
16C7×C32⋊C9C32124yes—
17C7×C92C32124yes—
18C3×#737C3×C711yescharacteristic
19C9×3−1+2C3×C7124yescomplemented
20C9×H(3,𝔽3)C3×C713yes—
21#6887C3×C718yescomplemented
22C3×C9⋊C9C3×C714yescomplemented
23C33×C7C3314yes—
24C7×3−1+2C3×C9172yescomplemented
25C7×H(3,𝔽3)C3×C919yes—
26C3×C7×C9—912no—
27C3×C7×C9C3×C9136yescomplemented
28C3×C7×C9C33124yes—
29C3×C7×C9C3313yes—
30C3×C7×C9C3318yes—
31C3×C7×C9C3311yescharacteristic
32#737C7×C9127yescomplemented
33C3×3−1+2C32×C718yes—
34C3×H(3,𝔽3)C32×C711yescharacteristic
35C32×C9C32×C7112yes—
36C32×C9C32×C714yes—
37C9⋊C9C32×C711yescharacteristic
38C9⋊C9C32×C718yes—
39C9⋊C9C32×C7124yes—
40C9⋊C9C32×C7124yes—
41C32⋊C9C32×C7124yes—
42C92C32×C7124yes—
43C32×C7—312no—
44C32×C7C32×C9112yes—
45C32×C7C3411yescharacteristic
46C7×C9—33no—
47C7×C9—324no—
48C7×C9C32×C913yes—
49C7×C9C32×C9124yes—
50C33C33×C714yes—
513−1+2C3×C7×C9172yescomplemented
52H(3,𝔽3)C3×C7×C919yes—
53C3×C9—912no—
54C3×C9C3×C7×C9136yescomplemented
55C3×C9C33×C7124yes—
56C3×C9C33×C713yes—
57C3×C9C33×C718yes—
58C3×C9C33×C711yescharacteristic
59C3×C7—312no—
60C3×C7C33×C911yescharacteristic
61C3×C73−1+413yes—
62C32—312no—
63C32C32×C7×C9112yes—
64C32C34×C711yescharacteristic
65C9—33no—
66C9—324no—
67C9C32×C7×C913yes—
68C9C32×C7×C9124yes—
69C7#1062486411yescharacteristic, direct product factor, Sylow
70C3—312no—
71C3C33×C7×C911yescharacteristic
72C3C7×3−1+413yes—
subgroupG/H
center, socleC32×C7C34
commutatorC3C33×C7×C9
FrattiniC32C34×C7
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C32×C7 ◁ 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×C9⋊C9C3semidirect
6. #10624864C7direct (N × H)
7. C7×#737C9semidirect
19. C9×3−1+2C3×C7semidirect
21. #6887C3×C7semidirect
22. C3×C9⋊C9C3×C7semidirect
24. C7×3−1+2C3×C9semidirect
27. C3×C7×C9C3×C9semidirect
32. #737C7×C9semidirect
51. 3−1+2C3×C7×C9semidirect
54. C3×C9C3×C7×C9semidirect
69. C7#10624864direct (N × H)