Finite Group Databasebeta

← #14641166

Subgroups — #14641166

Order 2816.

176 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 47 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
1#13066560C212yesmaximal
2C11×#1991C211yesmaximal, characteristic
3C2×C11×#125C411yescharacteristic
4C2×C4×C8×C11C411yescharacteristic
5C11×#382C2211yescharacteristic
6C11×#340—22no—
7#10622166—22no—
8C22×C8×C11—21no—
9C11×#125—21no—
10C11×#125—41no—
11C11×#125C812yescomplemented
12C2×C11×C4⋊C4—21no—
13C2×C11×C4⋊C4—41no—
14C2×C11×C4⋊C4D412yes—
15C2×C42×C11C2×C411yescharacteristic
16C4×C8×C11—41no—
17C11×#95—41no—
18C22⋊(C11⋊C8)—42no—
19#7359—111nomaximal, Sylow
20C22×C4×C11—21no—
21C22×C4×C11—22no—
22C22×C4×C11—41no—
23C22×C4×C11C22⋊C411yescharacteristic
24C2×C8×C11—22no—
25C2×C8×C11—41no—
26C2×C8×C11—41no—
27C11×C4⋊C4—22no—
28C11×C4⋊C4—42no—
29C11×C4⋊C4—42no—
30C11×C4⋊C4—42no—
31C11×C4⋊C4—41no—
32C42×C11—21no—
33C42×C11C2×C811yescharacteristic
34C42×C11M1611yescharacteristic
35C2×C11⋊C8—82no—
36#1991D1111yescharacteristic
37#1324—112no—
38C23×C11#9911yescharacteristic
39C2×C4×C11—21no—
40C2×C4×C11—21no—
41C2×C4×C11—21no—
42C2×C4×C11—21no—
43C2×C4×C11—42no—
44C2×C4×C11—42no—
45C2×C4×C11—42no—
46C2×C4×C11—82no—
47C2×C4×C11—82no—
48C2×C4×C11C22⋊C811yescharacteristic
49C2×C4×C11#10011yescharacteristic
50C8×C11—42no—
51C11⋊C8—162no—
52C2×#125Dic1111yescharacteristic
53C2×C4×C8Dic1111yescharacteristic
54#382C2×D1111yescharacteristic
55#340—22no—
56#324—222no—
57C22×C11—22no—
58C22×C11#32311yescharacteristic
59C22×C11#35411yescharacteristic
60C22×C11#35611yescharacteristic
61C4×C11—21no—
62C4×C11—21no—
63C4×C11—41no—
64C4×C11—41no—
65C4×C11—82no—
66C4×C11—82no—
67C22×C8—21no—
68#125—21no—
69#125—41no—
70#125C11⋊C812yescomplemented
71C2×C4⋊C4—21no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4C22⋊D1112yes—
74C2×C42C2×Dic1111yescharacteristic
75C22⋊C8—442no—
76C4×C8—41no—
77#95—41no—
78C2×C11—21no—
79C2×C11—21no—
80C2×C11#131911yescharacteristic
81C2×C11#141412yes—
82C22×C4—21no—
83C22×C4—22no—
84C22×C4—41no—
85C22×C4C22⋊Dic1111yescharacteristic
86C2×C8—22no—
87C2×C8—41no—
88C2×C8—41no—
89C2×C8—882no—
90C4⋊C4—22no—
91C4⋊C4—42no—
92C4⋊C4—42no—
93C4⋊C4—42no—
94C4⋊C4—41no—
95C42—21no—
96C42C2×C11⋊C811yescharacteristic
97C42#431811yescharacteristic
98C11#735911yescharacteristic, complemented, Sylow
99C23#6689811yescharacteristic
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—42no—
105C2×C4—42no—
106C2×C4—42no—
107C2×C4—82no—
108C2×C4—82no—
109C2×C4C22⋊(C11⋊C8)11yescharacteristic
110C2×C4#6689711yescharacteristic
111C8—42no—
112C8—1762no—
113C22—22no—
114C22#1062216311yescharacteristic
115C22#1062217911yescharacteristic
116C22#1062218611yescharacteristic
117C4—21no—
118C4—21no—
119C4—41no—
120C4—41no—
121C4—82no—
122C4—82no—
123C2—21no—
124C2—21no—
125C2#1306655011yescharacteristic
126C2#1306679112yes—
subgroupG/H
centerC22#10622179
commutatorC42×C11C2×C8
Frattini#382C2×D11
FittingC11×#1991C2
socleC22×C11#354
prime radicalC23×C11#99
cosocleC11×#382C22
hypercenter#1991D11
hypocenterC11#7359
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1991

Complements

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

NH ≅ G/Ntype
11. C11×#125C8semidirect
70. #125C11⋊C8semidirect
98. C11#7359semidirect

Maximal subgroups

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

subgroupindex
#130665602
C11×#19912
#735911