Finite Group Databasebeta

← C2×C9×#11925893 #36344881

Subgroups — C2×C9×#11925893 #36344881

Order 21780.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#10597245C211yesmaximal, characteristic, complemented
2C9×#11925893C212yesmaximal, direct product factor
3C2×C3×#11925893C311yesmaximal, characteristic
4C9×#10597245C2211yescharacteristic, complemented, Hall
5C2×C9×C11⋊D11C511yesmaximal, characteristic, complemented, Hall
6C2×C3×#10597245C2×C311yescharacteristic
7C3×#11925893C2×C312yes—
8C2×#11925893C911yescharacteristic, direct product factor, Hall
9C9×C11⋊D11C2×C512yescomplemented
10C2×C9×C112C2×C511yescharacteristic, complemented
11C2×C9×AGL(1,𝔽11)—112nomaximal
12C3×#10597245C22×C311yescharacteristic
13C2×C3×C11⋊D11C3×C511yescharacteristic
14C2×#10597245C2×C911yescharacteristic, complemented
15#11925893C2×C912yesdirect product factor
16C9×C112C22×C511yescharacteristic, complemented, Hall
17C2×C9×C11⋊C5—112no—
18C9×AGL(1,𝔽11)—114no—
19C2×C3×C112C2×C3×C511yescharacteristic
20C3×C11⋊D11C2×C3×C512yes—
21C2×C3×AGL(1,𝔽11)—112no—
22#10597245C22×C911yescharacteristic, complemented, Hall
23C9×C11⋊C5—112no—
24C2×C11⋊D11C5×C911yescharacteristic, complemented, Hall
25C2×C9×D11—112no—
26C2×C9×D11—552no—
27C3×C112C22×C3×C511yescharacteristic
28C2×C3×C11⋊C5—112no—
29C3×AGL(1,𝔽11)—114no—
30C2×C112C2×C5×C911yescharacteristic, complemented
31C11⋊D11C2×C5×C912yescomplemented
32C2×AGL(1,𝔽11)—112no—
33C2×C9×C11—52no—
34C2×C9×C11AGL(1,𝔽11)12yescomplemented
35C9×D11—114no—
36C9×D11—554no—
37C22×C5×C9—1211noHall
38C3×C11⋊C5—112no—
39C2×C3×D11—112no—
40C2×C3×D11—552no—
41C112C22×C5×C911yescharacteristic, complemented, Sylow
42C2×C11⋊C5—112no—
43AGL(1,𝔽11)—114no—
44C9×C11—52no—
45C9×C11C2×AGL(1,𝔽11)12yescomplemented
46C2×C5×C9—1212no—
47C2×C5×C9—1211no—
48C2×C3×C11—52no—
49C2×C3×C11C3×AGL(1,𝔽11)12yes—
50C3×D11—114no—
51C3×D11—554no—
52C22×C3×C5—1211no—
53C11⋊C5—112no—
54C5×C9—1211noHall
55C2×D11—112no—
56C2×D11—552no—
57C22×C9—1211noHall
58C3×C11—52no—
59C3×C11C2×C3×AGL(1,𝔽11)12yes—
60C2×C3×C5—1212no—
61C2×C3×C5—1211no—
62C2×C11—52no—
63C2×C11C9×AGL(1,𝔽11)12yescomplemented
64D11—114no—
65D11—554no—
66C22×C5—1211noHall
67C2×C9—1212no—
68C2×C9#1192589311yescharacteristic, direct product factor
69C3×C5—1211no—
70C22×C3—1211no—
71C11—52no—
72C11C2×C9×AGL(1,𝔽11)12yescomplemented
73C2×C5—1212no—
74C2×C5—1211no—
75C9C2×#1192589311yescharacteristic, direct product factor, Sylow
76C2×C3—1212no—
77C2×C3C3×#1192589311yescharacteristic
78C5—1211noSylow
79C22—1211noSylow
80C3C2×C3×#1192589311yescharacteristic
81C2—1212no—
82C2C9×#1192589311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C9#11925893
commutator, hypocenterC112C22×C5×C9
FrattiniC3C2×C3×#11925893
FittingC2×C9×C112C2×C5
socleC2×C3×C112C2×C3×C5
prime radicalC2×C3×#11925893C3
cosocleC3×C112C22×C3×C5
LCSG ▷ C112
UCSC1 ◁ C2×C9

Complements

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

NH ≅ G/Ntype
1. C2×C9×#10597245C2semidirect
2. C9×#11925893C2direct (N × H)
4. C9×#10597245C22semidirect
5. C2×C9×C11⋊D11C5semidirect
8. C2×#11925893C9direct (N × H)
9. C9×C11⋊D11C2×C5semidirect
10. C2×C9×C112C2×C5semidirect
14. C2×#10597245C2×C9semidirect
15. #11925893C2×C9direct (N × H)
16. C9×C112C22×C5semidirect
22. #10597245C22×C9semidirect
24. C2×C11⋊D11C5×C9semidirect
30. C2×C112C2×C5×C9semidirect
31. C11⋊D11C2×C5×C9semidirect
34. C2×C9×C11AGL(1,𝔽11)semidirect
41. C112C22×C5×C9semidirect
45. C9×C11C2×AGL(1,𝔽11)semidirect
63. C2×C11C9×AGL(1,𝔽11)semidirect
68. C2×C9#11925893direct (N × H)
72. C11C2×C9×AGL(1,𝔽11)semidirect
75. C9C2×#11925893direct (N × H)
82. C2C9×#11925893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#105972452
C9×#119258932
C2×C3×#119258933
C2×C9×C11⋊D115
C2×C9×AGL(1,𝔽11)11