Finite Group Databasebeta

← C2×C9×#11925895 #36344883

Subgroups — C2×C9×#11925895 #36344883

Order 21780.

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

normal subgroups only

This group has 180 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×#10597243C211yesmaximal, characteristic, complemented
2C9×#11925895C212yesmaximal, direct product factor
3C2×C3×#11925895C311yesmaximal, characteristic
4C9×#10597243C2211yescharacteristic, complemented, Hall
5C2×C9×C11×D11C511yesmaximal, characteristic, complemented, Hall
6C2×C3×#10597243C2×C311yescharacteristic
7C3×#11925895C2×C312yes—
8C2×#11925895C911yescharacteristic, 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×#10597243C22×C311yescharacteristic
14C2×C3×C11×D11C3×C511yescharacteristic
15C2×#10597243C2×C911yescharacteristic, complemented
16#11925895C2×C912yesdirect product factor
17C9×C112C22×C511yescharacteristic, complemented, Hall
18C2×C9×C11⋊C5—112no—
19C2×C9×C11⋊C5—111no—
20C2×C9×C11⋊C5—111no—
21C2×C9×C11⋊C5—225no—
22C9×AGL(1,𝔽11)—112no—
23C2×C3×C112C2×C3×C511yescharacteristic
24C3×C11×D11C2×C3×C512yes—
25C22×C3×C11⋊C5—111no—
26C2×C3×AGL(1,𝔽11)—111no—
27#10597243C22×C911yescharacteristic, complemented, Hall
28C9×C11⋊C5—111no—
29C9×C11⋊C5—111no—
30C9×C11⋊C5—225no—
31C2×C11×D11C5×C911yescharacteristic, complemented, Hall
32C22×C9×C11—111no—
33C2×C9×D11C11⋊C511yescharacteristic, complemented
34C3×C112C22×C3×C511yescharacteristic
35C2×C3×C11⋊C5—112no—
36C2×C3×C11⋊C5—111no—
37C2×C3×C11⋊C5—111no—
38C2×C3×C11⋊C5—225no—
39C3×AGL(1,𝔽11)—112no—
40C2×C112C2×C5×C911yescharacteristic, complemented
41C11×D11C2×C5×C912yescomplemented
42C22×C11⋊C5—111no—
43C2×AGL(1,𝔽11)—111no—
44C2×C9×C11—25no—
45C2×C9×C11—112no—
46C2×C9×C11AGL(1,𝔽11)11yescharacteristic, complemented
47C2×C9×C11C2×C11⋊C511yescharacteristic, complemented
48C9×D11C2×C11⋊C512yescomplemented
49C22×C5×C9—1211noHall
50C3×C11⋊C5—111no—
51C3×C11⋊C5—111no—
52C3×C11⋊C5—225no—
53C22×C3×C11—111no—
54C2×C3×D11C3×C11⋊C511yescharacteristic
55C112C22×C5×C911yescharacteristic, complemented, Sylow
56C2×C11⋊C5—112no—
57C2×C11⋊C5—111no—
58C2×C11⋊C5—111no—
59C2×C11⋊C5—225no—
60AGL(1,𝔽11)—112no—
61C9×C11—25no—
62C9×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
63C9×C11C22×C11⋊C511yescharacteristic, complemented
64C2×C5×C9—1212no—
65C2×C5×C9—1211no—
66C2×C3×C11—25no—
67C2×C3×C11—112no—
68C2×C3×C11C3×AGL(1,𝔽11)11yescharacteristic
69C2×C3×C11C2×C3×C11⋊C511yescharacteristic
70C3×D11C2×C3×C11⋊C512yes—
71C22×C3×C5—1211no—
72C11⋊C5—111no—
73C11⋊C5—111no—
74C11⋊C5—225no—
75C5×C9—1211noHall
76C22×C11—111no—
77C2×D11C9×C11⋊C511yescharacteristic, complemented
78C22×C9—111noHall
79C3×C11—25no—
80C3×C11C2×C3×AGL(1,𝔽11)11yescharacteristic
81C3×C11C22×C3×C11⋊C511yescharacteristic
82C2×C3×C5—1212no—
83C2×C3×C5—1211no—
84C2×C11—25no—
85C2×C11—112no—
86C2×C11C9×AGL(1,𝔽11)11yescharacteristic, complemented
87C2×C11C2×C9×C11⋊C511yescharacteristic, complemented
88D11C2×C9×C11⋊C512yescomplemented
89C22×C5—1211noHall
90C2×C9—112no—
91C2×C9#1192589511yescharacteristic, direct product factor
92C3×C5—1211no—
93C22×C3—111no—
94C11—25no—
95C11C2×C9×AGL(1,𝔽11)11yescharacteristic, complemented
96C11C22×C9×C11⋊C511yescharacteristic, complemented
97C2×C5—1212no—
98C2×C5—1211no—
99C9C2×#1192589511yescharacteristic, direct product factor, Sylow
100C2×C3—112no—
101C2×C3C3×#1192589511yescharacteristic
102C5—1211noSylow
103C22—111noSylow
104C3C2×C3×#1192589511yescharacteristic
105C2—112no—
106C2C9×#1192589511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C9#11925895
commutator, hypocenterC112C22×C5×C9
FrattiniC3C2×C3×#11925895
FittingC2×C9×C112C2×C5
socleC2×C3×C112C2×C3×C5
prime radicalC2×C3×#11925895C3
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×#10597243C2semidirect
2. C9×#11925895C2direct (N × H)
4. C9×#10597243C22semidirect
5. C2×C9×C11×D11C5semidirect
8. C2×#11925895C9direct (N × H)
9. C9×C11×D11C2×C5semidirect
10. C2×C9×C112C2×C5semidirect
15. C2×#10597243C2×C9semidirect
16. #11925895C2×C9direct (N × H)
17. C9×C112C22×C5semidirect
27. #10597243C22×C9semidirect
31. C2×C11×D11C5×C9semidirect
33. C2×C9×D11C11⋊C5semidirect
40. C2×C112C2×C5×C9semidirect
41. C11×D11C2×C5×C9semidirect
46. C2×C9×C11AGL(1,𝔽11)semidirect
47. C2×C9×C11C2×C11⋊C5semidirect
48. C9×D11C2×C11⋊C5semidirect
55. C112C22×C5×C9semidirect
62. C9×C11C2×AGL(1,𝔽11)semidirect
63. C9×C11C22×C11⋊C5semidirect
77. C2×D11C9×C11⋊C5semidirect
86. C2×C11C9×AGL(1,𝔽11)semidirect
87. C2×C11C2×C9×C11⋊C5semidirect
88. D11C2×C9×C11⋊C5semidirect
91. C2×C9#11925895direct (N × H)
95. C11C2×C9×AGL(1,𝔽11)semidirect
96. C11C22×C9×C11⋊C5semidirect
99. C9C2×#11925895direct (N × H)
106. C2C9×#11925895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#105972432
C9×#119258952
C2×C3×#119258953
C2×C9×C11×D115
C22×C9×C11⋊C511
C2×C9×AGL(1,𝔽11)11