Finite Group Databasebeta

← C11×#10624890 #22548413

Subgroups — C11×#10624890 #22548413

Order 8019.

620 conjugacy classes of subgroups; only the 440 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 440 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
1C11×#6899C3118yesmaximal, complemented
2C11×#6898C319yesmaximal, complemented
3C11×#6894C316yesmaximal, complemented
4C11×#6891C312yesmaximal
5C11×#6891C311yesmaximal, characteristic
6C9×C11×3−1+2C313yesmaximal, complemented
7C3×C11×C32⋊C9C311yesmaximal, characteristic
8C34×C11C3211yescharacteristic
9C3×C11×3−1+2C3213yes—
10C3×C11×3−1+2C3216yes—
11C32×C9×C11C3211yescharacteristic
12C32×C9×C11C3212yes—
13C11×C9⋊C9C32118yescomplemented
14C11×C9⋊C9C32154yescomplemented
15C11×C32⋊C9C3213yes—
16C11×C32⋊C9C3216yes—
17C11×C32⋊C9C3216yes—
18C11×C32⋊C9C3213yes—
19C11×C32⋊C9C3216yes—
20C11×C32⋊C9C3216yes—
21C11×C32⋊C9C3216yes—
22C92×C11C3219yescomplemented
23#10624890C1111yesmaximal, characteristic, direct product factor, Sylow
24C33×C11—33no—
25C33×C11—91no—
26C33×C11—92no—
27C33×C11C3311yescharacteristic
28C33×C11C3312yes—
29C33×C11C3311yescharacteristic
30C11×3−1+2—39no—
31C11×3−1+2—96no—
32C3×C9×C11—91no—
33C3×C9×C11—92no—
34C3×C9×C11C3313yes—
35C3×C9×C11C3319yes—
36C3×C9×C11C33118yes—
37C3×C9×C11C3316yes—
38#6899C3×C11118yescomplemented
39#6898C3×C1119yescomplemented
40#6894C3×C1116yescomplemented
41#6891C3×C1112yes—
42#6891C3×C1111yescharacteristic
43C9×3−1+2C3×C1113yescomplemented
44C3×C32⋊C9C3×C1111yescharacteristic
45C32×C11—31no—
46C32×C11—32no—
47C32×C11—31no—
48C32×C11—32no—
49C32×C11—32no—
50C32×C11—31no—
51C32×C11—32no—
52C32×C11—32no—
53C32×C11—32no—
54C32×C11—99no—
55C32×C11#73713yes—
56C32×C11C3411yescharacteristic
57C9×C11—39no—
58C9×C11—33no—
59C9×C11—36no—
60C9×C11—318no—
61C34C32×C1111yescharacteristic
62C3×3−1+2C32×C1113yes—
63C3×3−1+2C32×C1116yes—
64C32×C9C32×C1111yescharacteristic
65C32×C9C32×C1112yes—
66C9⋊C9C32×C11118yescomplemented
67C9⋊C9C32×C11154yescomplemented
68C32⋊C9C32×C1113yes—
69C32⋊C9C32×C1116yes—
70C32⋊C9C32×C1116yes—
71C32⋊C9C32×C1113yes—
72C32⋊C9C32×C1116yes—
73C32⋊C9C32×C1116yes—
74C32⋊C9C32×C1116yes—
75C92C32×C1119yescomplemented
76C3×C11—33no—
77C3×C11—92no—
78C3×C11—91no—
79C3×C11C3×#73711yescharacteristic
80C3×C113−1+411yescharacteristic
81C3×C113−1+412yes—
82C33—33no—
83C33—91no—
84C33—92no—
85C33C33×C1111yescharacteristic
86C33C33×C1112yes—
87C33C33×C1111yescharacteristic
883−1+2—39no—
893−1+2—96no—
90C3×C9—91no—
91C3×C9—92no—
92C3×C9C33×C1113yes—
93C3×C9C33×C1119yes—
94C3×C9C33×C11118yes—
95C3×C9C33×C1116yes—
96C11#1062489011yescharacteristic, direct product factor, Sylow
97C32—31no—
98C32—32no—
99C32—31no—
100C32—32no—
101C32—32no—
102C32—31no—
103C32—32no—
104C32—32no—
105C32—32no—
106C32—99no—
107C32C11×#73713yes—
108C32C34×C1111yescharacteristic
109C9—39no—
110C9—33no—
111C9—36no—
112C9—318no—
113C3—33no—
114C3—92no—
115C3—91no—
116C3C3×C11×#73711yescharacteristic
117C3C11×3−1+411yescharacteristic
118C3C11×3−1+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
1. C11×#6899C3semidirect
2. C11×#6898C3semidirect
3. C11×#6894C3semidirect
6. C9×C11×3−1+2C3semidirect
13. C11×C9⋊C9C32semidirect
14. C11×C9⋊C9C32semidirect
22. C92×C11C32semidirect
23. #10624890C11direct (N × H)
38. #6899C3×C11semidirect
39. #6898C3×C11semidirect
40. #6894C3×C11semidirect
43. C9×3−1+2C3×C11semidirect
66. C9⋊C9C32×C11semidirect
67. C9⋊C9C32×C11semidirect
75. C92C32×C11semidirect
96. C11#10624890direct (N × H)