Finite Group Databasebeta

← C2×C9×(C11⋊C5)⋊D11 #36344887

Subgroups — C2×C9×(C11⋊C5)⋊D11 #36344887

Order 21780.

150 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 54 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×C11×C11⋊C5C211yesmaximal, characteristic, complemented
2C9×(C11⋊C5)⋊D11C212yesmaximal, direct product factor
3C2×C3×(C11⋊C5)⋊D11C311yesmaximal, characteristic
4C9×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×C9×C11⋊D11C511yesmaximal, characteristic, complemented, Hall
6C2×C3×C11×C11⋊C5C2×C311yescharacteristic
7C3×(C11⋊C5)⋊D11C2×C312yes—
8C2×(C11⋊C5)⋊D11C911yescharacteristic, direct product factor, Hall
9C9×C11⋊D11C2×C512yescomplemented
10C2×C9×C112C2×C511yescharacteristic, complemented
11C2×C5×C9×D11—111nomaximal
12C2×C9×AGL(1,𝔽11)—111nomaximal
13C3×C11×C11⋊C5C22×C311yescharacteristic
14C2×C3×C11⋊D11C3×C511yescharacteristic
15C2×C11×C11⋊C5C2×C911yescharacteristic, complemented
16(C11⋊C5)⋊D11C2×C912yesdirect product factor
17C9×C112C22×C511yescharacteristic, complemented, Hall
18C2×C5×C9×C11—111no—
19C5×C9×D11—112no—
20C2×C9×C11⋊C5D1111yescharacteristic, complemented
21C9×AGL(1,𝔽11)—112no—
22C2×C3×C112C2×C3×C511yescharacteristic
23C3×C11⋊D11C2×C3×C512yes—
24C2×C3×C5×D11—111no—
25C2×C3×AGL(1,𝔽11)—111no—
26C11×C11⋊C5C22×C911yescharacteristic, complemented, Hall
27C5×C9×C11—111no—
28C9×C11⋊C5C2×D1111yescharacteristic, complemented
29C2×C11⋊D11C5×C911yescharacteristic, complemented, Hall
30C2×C9×D11—111no—
31C2×C9×D11—111no—
32C2×C9×D11—552no—
33C3×C112C22×C3×C511yescharacteristic
34C2×C3×C5×C11—111no—
35C3×C5×D11—112no—
36C2×C3×C11⋊C5C3×D1111yescharacteristic
37C3×AGL(1,𝔽11)—112no—
38C2×C112C2×C5×C911yescharacteristic, complemented
39C11⋊D11C2×C5×C912yescomplemented
40C2×C5×D11—111no—
41C2×AGL(1,𝔽11)—111no—
42C2×C9×C11—52no—
43C2×C9×C11AGL(1,𝔽11)11yescharacteristic, complemented
44C2×C9×C11C5×D1111yescharacteristic, complemented
45C9×D11—112no—
46C9×D11—112no—
47C9×D11—554no—
48C22×C5×C9—1211noHall
49C3×C5×C11—111no—
50C3×C11⋊C5C2×C3×D1111yescharacteristic
51C2×C3×D11—111no—
52C2×C3×D11—111no—
53C2×C3×D11—552no—
54C112C22×C5×C911yescharacteristic, complemented, Sylow
55C2×C5×C11—111no—
56C5×D11—112no—
57C2×C11⋊C5C9×D1111yescharacteristic, complemented
58AGL(1,𝔽11)—112no—
59C9×C11—52no—
60C9×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
61C9×C11C2×C5×D1111yescharacteristic, complemented
62C2×C5×C9—111no—
63C2×C5×C9—1212no—
64C2×C3×C11—52no—
65C2×C3×C11C3×AGL(1,𝔽11)11yescharacteristic
66C2×C3×C11C3×C5×D1111yescharacteristic
67C3×D11—112no—
68C3×D11—112no—
69C3×D11—554no—
70C22×C3×C5—1211no—
71C5×C11—111no—
72C11⋊C5C2×C9×D1111yescharacteristic, complemented
73C5×C9—111noHall
74C2×D11—111no—
75C2×D11—111no—
76C2×D11—552no—
77C22×C9—1211noHall
78C3×C11—52no—
79C3×C11C2×C3×AGL(1,𝔽11)11yescharacteristic
80C3×C11C2×C3×C5×D1111yescharacteristic
81C2×C3×C5—111no—
82C2×C3×C5—1212no—
83C2×C11—52no—
84C2×C11C9×AGL(1,𝔽11)11yescharacteristic, complemented
85C2×C11C5×C9×D1111yescharacteristic, complemented
86D11—112no—
87D11—112no—
88D11—554no—
89C22×C5—1211noHall
90C2×C9—1212no—
91C2×C9(C11⋊C5)⋊D1111yescharacteristic, direct product factor
92C3×C5—111no—
93C22×C3—1211no—
94C11—52no—
95C11C2×C9×AGL(1,𝔽11)11yescharacteristic, complemented
96C11C2×C5×C9×D1111yescharacteristic, complemented
97C2×C5—111no—
98C2×C5—1212no—
99C9C2×(C11⋊C5)⋊D1111yescharacteristic, direct product factor, Sylow
100C2×C3—1212no—
101C2×C3C3×(C11⋊C5)⋊D1111yescharacteristic
102C5—111noSylow
103C22—1211noSylow
104C3C2×C3×(C11⋊C5)⋊D1111yescharacteristic
105C2—1212no—
106C2C9×(C11⋊C5)⋊D1111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C9(C11⋊C5)⋊D11
commutator, hypocenterC112C22×C5×C9
FrattiniC3C2×C3×(C11⋊C5)⋊D11
FittingC2×C9×C112C2×C5
socleC2×C3×C112C2×C3×C5
prime radicalC2×C3×(C11⋊C5)⋊D11C3
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×C11×C11⋊C5C2semidirect
2. C9×(C11⋊C5)⋊D11C2direct (N × H)
4. C9×C11×C11⋊C5C22semidirect
5. C2×C9×C11⋊D11C5semidirect
8. C2×(C11⋊C5)⋊D11C9direct (N × H)
9. C9×C11⋊D11C2×C5semidirect
10. C2×C9×C112C2×C5semidirect
15. C2×C11×C11⋊C5C2×C9semidirect
16. (C11⋊C5)⋊D11C2×C9direct (N × H)
17. C9×C112C22×C5semidirect
20. C2×C9×C11⋊C5D11semidirect
26. C11×C11⋊C5C22×C9semidirect
28. C9×C11⋊C5C2×D11semidirect
29. C2×C11⋊D11C5×C9semidirect
38. C2×C112C2×C5×C9semidirect
39. C11⋊D11C2×C5×C9semidirect
43. C2×C9×C11AGL(1,𝔽11)semidirect
44. C2×C9×C11C5×D11semidirect
54. C112C22×C5×C9semidirect
57. C2×C11⋊C5C9×D11semidirect
60. C9×C11C2×AGL(1,𝔽11)semidirect
61. C9×C11C2×C5×D11semidirect
72. C11⋊C5C2×C9×D11semidirect
84. C2×C11C9×AGL(1,𝔽11)semidirect
85. C2×C11C5×C9×D11semidirect
91. C2×C9(C11⋊C5)⋊D11direct (N × H)
95. C11C2×C9×AGL(1,𝔽11)semidirect
96. C11C2×C5×C9×D11semidirect
99. C9C2×(C11⋊C5)⋊D11direct (N × H)
106. C2C9×(C11⋊C5)⋊D11direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×C11×C11⋊C52
C9×(C11⋊C5)⋊D112
C2×C3×(C11⋊C5)⋊D113
C2×C9×C11⋊D115
C2×C5×C9×D1111
C2×C9×AGL(1,𝔽11)11