Finite Group Databasebeta

← C11×3−1+22 #22548421

Subgroups — C11×3−1+22 #22548421

Order 8019.

836 conjugacy classes of subgroups; only the 518 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 518 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
1C32×C11×3−1+2C312yesmaximal
2C11×#6900C319yesmaximal, complemented
3C11×#6896C319yesmaximal, complemented
4C11×#6894C3112yesmaximal, complemented
5C11×#6891C312yesmaximal
6C9×C11×3−1+2C316yesmaximal, complemented
7C34×C11C3211yescharacteristic
8C3×C11×3−1+2—318no—
9C3×C11×3−1+2C3214yes—
10C3×C11×3−1+2C3216yes—
11C3×C11×3−1+2C3216yes—
12C3×C11×3−1+2C3216yes—
13C3×C11×3−1+2C3212yes—
14C32×C9×C11C3216yes—
15C11×C9⋊C9C32136yescomplemented
16C11×C9⋊C9C32136yescomplemented
17C11×C32⋊C9C32112yes—
18C11×C32⋊C9C3216yes—
19C92×C11C3219yescomplemented
203−1+22C1111yesmaximal, characteristic, direct product factor, Sylow
21C33×C11—36no—
22C33×C11—92no—
23C33×C11C3311yescharacteristic
24C33×C11C3311yescharacteristic
25C33×C11C3312yes—
26C11×3−1+2—312no—
27C11×3−1+2—318no—
28C11×3−1+2—318no—
29C11×3−1+2—96no—
30C11×3−1+23−1+2118yesdirect product factor
31C3×C9×C11—318no—
32C3×C9×C11C33118yes—
33C3×C9×C11C33112yes—
34C3×C9×C11C3316yes—
35C32×3−1+2C3×C1112yes—
36#6900C3×C1119yescomplemented
37#6896C3×C1119yescomplemented
38#6894C3×C11112yescomplemented
39#6891C3×C1112yes—
40C9×3−1+2C3×C1116yescomplemented
41C32×C11—32no—
42C32×C11—34no—
43C32×C11—32no—
44C32×C11—32no—
45C32×C11—32no—
46C32×C11—32no—
47C32×C11—99no—
48C32×C11C3×3−1+216yes—
49C32×C11C3411yescharacteristic
50C9×C11—312no—
51C9×C11—318no—
52C9×C11C3×3−1+2118yescomplemented
53C34C32×C1111yescharacteristic
54C3×3−1+2—318no—
55C3×3−1+2C32×C1114yes—
56C3×3−1+2C32×C1116yes—
57C3×3−1+2C32×C1116yes—
58C3×3−1+2C32×C1116yes—
59C3×3−1+2C32×C1112yes—
60C32×C9C32×C1116yes—
61C9⋊C9C32×C11136yescomplemented
62C9⋊C9C32×C11136yescomplemented
63C32⋊C9C32×C11112yes—
64C32⋊C9C32×C1116yes—
65C92C32×C1119yescomplemented
66C3×C11—36no—
67C3×C11—91no—
68C3×C11—91no—
69C3×C11C32×3−1+212yes—
70C3×C113−1+412yes—
71C33—36no—
72C33—92no—
73C33C33×C1111yescharacteristic
74C33C33×C1111yescharacteristic
75C33C33×C1112yes—
763−1+2—312no—
773−1+2—318no—
783−1+2—318no—
793−1+2—96no—
803−1+2C11×3−1+2118yesdirect product factor
81C3×C9—318no—
82C3×C9C33×C11118yes—
83C3×C9C33×C11112yes—
84C3×C9C33×C1116yes—
85C113−1+2211yescharacteristic, direct product factor, Sylow
86C32—34no—
87C32—32no—
88C32—32no—
89C32—32no—
90C32—32no—
91C32—32no—
92C32—99no—
93C32C3×C11×3−1+216yes—
94C32C34×C1111yescharacteristic
95C9—318no—
96C9—312no—
97C9C3×C11×3−1+2118yescomplemented
98C3—36no—
99C3—91no—
100C3—91no—
101C3C32×C11×3−1+212yes—
102C3C11×3−1+412yes—
subgroupG/H
center, socleC32×C11C34
commutator, FrattiniC32C34×C11
LCSG ▷ C32 ▷ C1
UCSC1 ◁ C32×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#6900C3semidirect
3. C11×#6896C3semidirect
4. C11×#6894C3semidirect
6. C9×C11×3−1+2C3semidirect
15. C11×C9⋊C9C32semidirect
16. C11×C9⋊C9C32semidirect
19. C92×C11C32semidirect
20. 3−1+22C11direct (N × H)
30. C11×3−1+23−1+2direct (N × H)
36. #6900C3×C11semidirect
37. #6896C3×C11semidirect
38. #6894C3×C11semidirect
40. C9×3−1+2C3×C11semidirect
52. C9×C11C3×3−1+2semidirect
61. C9⋊C9C32×C11semidirect
62. C9⋊C9C32×C11semidirect
65. C92C32×C11semidirect
80. 3−1+2C11×3−1+2direct (N × H)
85. C113−1+22direct (N × H)
97. C9C3×C11×3−1+2semidirect