Finite Group Databasebeta

← C9×C13×#737 #23745012

Subgroups — C9×C13×#737 #23745012

Order 9477.

986 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C13×#737C311yesmaximal, characteristic
2C9×C13×3−1+2C3124yesmaximal, complemented
3C9×C13×H(3,𝔽3)C313yesmaximal
4C13×#6887C318yesmaximal, complemented
5C3×C92×C13C314yesmaximal, complemented
6C13×#737C9127yesdirect product factor
7C3×C13×3−1+2C3218yes—
8C3×C13×H(3,𝔽3)C3211yescharacteristic
9C32×C9×C13C32112yes—
10C32×C9×C13C3214yes—
11C13×C9⋊C9C32148yes—
12C13×C32⋊C9C32124yes—
13C92×C13C3218yes—
14C92×C13C32124yes—
15C92×C13C3211yescharacteristic
16C9×#737C1311yesmaximal, characteristic, direct product factor, Sylow
17C33×C13C3314yes—
18C13×3−1+2C3×C9172yescomplemented
19C13×H(3,𝔽3)C3×C919yes—
20C3×C9×C13—336no—
21C3×C9×C13C3×C9136yescomplemented
22C3×C9×C13C33124yes—
23C3×C9×C13C3311yescharacteristic
24C3×C9×C13C3318yes—
25C3×C9×C13C3313yes—
26C3×#737C3×C1311yescharacteristic
27C9×3−1+2C3×C13124yescomplemented
28C9×H(3,𝔽3)C3×C1313yes—
29#6887C3×C1318yescomplemented
30C3×C92C3×C1314yescomplemented
31C32×C13—312no—
32C32×C13C32×C9112yes—
33C32×C13C3411yescharacteristic
34C9×C13—324no—
35C9×C13C32×C913yes—
36C9×C13C32×C9124yes—
37C9×C13#73719yesdirect product factor
38#737C9×C13127yesdirect product factor
39C3×3−1+2C32×C1318yes—
40C3×H(3,𝔽3)C32×C1311yescharacteristic
41C32×C9C32×C13112yes—
42C32×C9C32×C1314yes—
43C9⋊C9C32×C13148yes—
44C32⋊C9C32×C13124yes—
45C92C32×C1318yes—
46C92C32×C13124yes—
47C92C32×C1311yescharacteristic
48C3×C13—312no—
49C3×C13C33×C911yescharacteristic
50C3×C13C3×#73713yes—
51C33C33×C1314yes—
523−1+2C3×C9×C13172yescomplemented
53H(3,𝔽3)C3×C9×C1319yes—
54C3×C9—336no—
55C3×C9C3×C9×C13136yescomplemented
56C3×C9C33×C13124yes—
57C3×C9C33×C1311yescharacteristic
58C3×C9C33×C1318yes—
59C3×C9C33×C1313yes—
60C13C9×#73711yescharacteristic, direct product factor, Sylow
61C32—312no—
62C32C32×C9×C13112yes—
63C32C34×C1311yescharacteristic
64C9—324no—
65C9C32×C9×C1313yes—
66C9C32×C9×C13124yes—
67C9C13×#73719yesdirect product factor
68C3—312no—
69C3C33×C9×C1311yescharacteristic
70C3C3×C13×#73713yes—
subgroupG/H
centerC92×C13C32
commutatorC3C33×C9×C13
Frattini, cosocleC32C34×C13
socleC32×C13C34
prime radicalC3×C13×H(3,𝔽3)C32
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C92×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C9×C13×3−1+2C3semidirect
4. C13×#6887C3semidirect
5. C3×C92×C13C3semidirect
6. C13×#737C9direct (N × H)
16. C9×#737C13direct (N × H)
18. C13×3−1+2C3×C9semidirect
21. C3×C9×C13C3×C9semidirect
27. C9×3−1+2C3×C13semidirect
29. #6887C3×C13semidirect
30. C3×C92C3×C13semidirect
37. C9×C13#737direct (N × H)
38. #737C9×C13direct (N × H)
52. 3−1+2C3×C9×C13semidirect
55. C3×C9C3×C9×C13semidirect
60. C13C9×#737direct (N × H)
67. C9C13×#737direct (N × H)