Finite Group Databasebeta

← C2×C9×#11925898 #36344886

Subgroups — C2×C9×#11925898 #36344886

Order 21780.

126 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#10597244C211yesmaximal, characteristic, complemented
2C9×#11925898C212yesmaximal, direct product factor
3C2×C3×#11925898C311yesmaximal, characteristic
4C9×#10597244C2211yescharacteristic, complemented, Hall
5C2×C9×C11×D11C511yesmaximal, characteristic, complemented, Hall
6C2×C3×#10597244C2×C311yescharacteristic
7C3×#11925898C2×C312yes—
8C2×#11925898C911yescharacteristic, direct product factor, Hall
9C9×C11×D11C2×C512yescomplemented
10C2×C9×C112C2×C511yescharacteristic, complemented
11C22×C9×C11⋊C5—111nomaximal
12C2×C9×AGL(1,𝔽11)—111nomaximal
13C3×#10597244C22×C311yescharacteristic
14C2×C3×C11×D11C3×C511yescharacteristic
15C2×#10597244C2×C911yescharacteristic, complemented
16#11925898C2×C912yesdirect product factor
17C9×C112C22×C511yescharacteristic, complemented, Hall
18C2×C9×C11⋊C5—112no—
19C2×C9×C11⋊C5—111no—
20C2×C9×C11⋊C5—111no—
21C9×AGL(1,𝔽11)—112no—
22C2×C3×C112C2×C3×C511yescharacteristic
23C3×C11×D11C2×C3×C512yes—
24C22×C3×C11⋊C5—111no—
25C2×C3×AGL(1,𝔽11)—111no—
26#10597244C22×C911yescharacteristic, complemented, Hall
27C9×C11⋊C5—111no—
28C9×C11⋊C5—111no—
29C2×C11×D11C5×C911yescharacteristic, complemented, Hall
30C22×C9×C11—111no—
31C2×C9×D11C11⋊C511yescharacteristic, complemented
32C3×C112C22×C3×C511yescharacteristic
33C2×C3×C11⋊C5—112no—
34C2×C3×C11⋊C5—111no—
35C2×C3×C11⋊C5—111no—
36C3×AGL(1,𝔽11)—112no—
37C2×C112C2×C5×C911yescharacteristic, complemented
38C11×D11C2×C5×C912yescomplemented
39C22×C11⋊C5—111no—
40C2×AGL(1,𝔽11)—111no—
41C2×C9×C11—101no—
42C2×C9×C11—112no—
43C2×C9×C11AGL(1,𝔽11)11yescharacteristic, complemented
44C2×C9×C11C2×C11⋊C511yescharacteristic, complemented
45C9×D11C2×C11⋊C512yescomplemented
46C22×C5×C9—1211noHall
47C3×C11⋊C5—111no—
48C3×C11⋊C5—111no—
49C22×C3×C11—111no—
50C2×C3×D11C3×C11⋊C511yescharacteristic
51C112C22×C5×C911yescharacteristic, complemented, Sylow
52C2×C11⋊C5—112no—
53C2×C11⋊C5—111no—
54C2×C11⋊C5—111no—
55AGL(1,𝔽11)—112no—
56C9×C11—101no—
57C9×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
58C9×C11C22×C11⋊C511yescharacteristic, complemented
59C2×C5×C9—1212no—
60C2×C5×C9—1211no—
61C2×C3×C11—101no—
62C2×C3×C11—112no—
63C2×C3×C11C3×AGL(1,𝔽11)11yescharacteristic
64C2×C3×C11C2×C3×C11⋊C511yescharacteristic
65C3×D11C2×C3×C11⋊C512yes—
66C22×C3×C5—1211no—
67C11⋊C5—111no—
68C11⋊C5—111no—
69C5×C9—1211noHall
70C22×C11—111no—
71C2×D11C9×C11⋊C511yescharacteristic, complemented
72C22×C9—111noHall
73C3×C11—101no—
74C3×C11C2×C3×AGL(1,𝔽11)11yescharacteristic
75C3×C11C22×C3×C11⋊C511yescharacteristic
76C2×C3×C5—1212no—
77C2×C3×C5—1211no—
78C2×C11—101no—
79C2×C11—112no—
80C2×C11C9×AGL(1,𝔽11)11yescharacteristic, complemented
81C2×C11C2×C9×C11⋊C511yescharacteristic, complemented
82D11C2×C9×C11⋊C512yescomplemented
83C22×C5—1211noHall
84C2×C9—112no—
85C2×C9#1192589811yescharacteristic, direct product factor
86C3×C5—1211no—
87C22×C3—111no—
88C11—101no—
89C11C2×C9×AGL(1,𝔽11)11yescharacteristic, complemented
90C11C22×C9×C11⋊C511yescharacteristic, complemented
91C2×C5—1212no—
92C2×C5—1211no—
93C9C2×#1192589811yescharacteristic, direct product factor, Sylow
94C2×C3—112no—
95C2×C3C3×#1192589811yescharacteristic
96C5—1211noSylow
97C22—111noSylow
98C3C2×C3×#1192589811yescharacteristic
99C2—112no—
100C2C9×#1192589811yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C9#11925898
commutator, hypocenterC112C22×C5×C9
FrattiniC3C2×C3×#11925898
FittingC2×C9×C112C2×C5
socleC2×C3×C112C2×C3×C5
prime radicalC2×C3×#11925898C3
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×#10597244C2semidirect
2. C9×#11925898C2direct (N × H)
4. C9×#10597244C22semidirect
5. C2×C9×C11×D11C5semidirect
8. C2×#11925898C9direct (N × H)
9. C9×C11×D11C2×C5semidirect
10. C2×C9×C112C2×C5semidirect
15. C2×#10597244C2×C9semidirect
16. #11925898C2×C9direct (N × H)
17. C9×C112C22×C5semidirect
26. #10597244C22×C9semidirect
29. C2×C11×D11C5×C9semidirect
31. C2×C9×D11C11⋊C5semidirect
37. C2×C112C2×C5×C9semidirect
38. C11×D11C2×C5×C9semidirect
43. C2×C9×C11AGL(1,𝔽11)semidirect
44. C2×C9×C11C2×C11⋊C5semidirect
45. C9×D11C2×C11⋊C5semidirect
51. C112C22×C5×C9semidirect
57. C9×C11C2×AGL(1,𝔽11)semidirect
58. C9×C11C22×C11⋊C5semidirect
71. C2×D11C9×C11⋊C5semidirect
80. C2×C11C9×AGL(1,𝔽11)semidirect
81. C2×C11C2×C9×C11⋊C5semidirect
82. D11C2×C9×C11⋊C5semidirect
85. C2×C9#11925898direct (N × H)
89. C11C2×C9×AGL(1,𝔽11)semidirect
90. C11C22×C9×C11⋊C5semidirect
93. C9C2×#11925898direct (N × H)
100. C2C9×#11925898direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#105972442
C9×#119258982
C2×C3×#119258983
C2×C9×C11×D115
C22×C9×C11⋊C511
C2×C9×AGL(1,𝔽11)11