Finite Group Databasebeta

← #14641395

Subgroups — #14641395

Order 2816.

144 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 37 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#13070191C211yesmaximal, characteristic
2C11⋊#1309C211yesmaximal, characteristic
3C11×#1327C211yesmaximal, characteristic
4C11×#423C2211yescharacteristic
5#10622738C411yescharacteristic
6#10622537—21no—
7C11×#349—21no—
8#10622197—21no—
9#10622195C411yescharacteristic
10#10622161—21no—
11C2×C11×M16C2×C411yescharacteristic
12C2×C11×M16D411yescharacteristic
13C2×C42×C11D411yescharacteristic
14#66979—21no—
15C2×#4318—21no—
16C2×#4318—22no—
17C11×M32—41no—
18C11×C4⋊C8—41no—
19#66883—41no—
20C4⋊(C11⋊C8)—41no—
21C4⋊(C11⋊C8)—41no—
22#7440—111nomaximal, Sylow
23C22×C4×C11—21no—
24C22×C4×C11C22⋊C411yescharacteristic
25C11×M16—41no—
26C11×M16—41no—
27C2×C8×C11—21no—
28C2×C8×C11—21no—
29C42×C11—21no—
30C42×C11SD1611yescharacteristic
31C42×C11Q1611yescharacteristic
32C22⋊Dic11—41no—
33C4⋊Dic11—41no—
34C4×Dic11—41no—
35#4318—41no—
36#4318—41no—
37#4318—82no—
38C2×C11⋊C8—42no—
39C2×C11⋊C8—41no—
40C11×C16—81no—
41#2102—111no—
42#1327D1111yescharacteristic
43#1309—111no—
44C23×C11#10411yescharacteristic
45C2×C4×C11—21no—
46C2×C4×C11—21no—
47C2×C4×C11—21no—
48C2×C4×C11—21no—
49C2×C4×C11—41no—
50C2×C4×C11—41no—
51C2×C4×C11#9911yescharacteristic
52C2×C4×C11#10311yescharacteristic
53C2×Dic11—81no—
54C8×C11—41no—
55C8×C11—41no—
56C11⋊C8—82no—
57C11⋊C8—81no—
58#430—111no—
59#423—221no—
60#423C2×D1111yescharacteristic
61#349—21no—
62#344—221no—
63#339—221no—
64H(3,ℤ/4)—111no—
65C22×C11—21no—
66C22×C11—41no—
67C22×C11#32811yescharacteristic
68C4×C11—21no—
69C4×C11—21no—
70C4×C11—21no—
71C4×C11—41no—
72C4×C11#35211yescharacteristic
73C4×C11#35511yescharacteristic
74Dic11—161no—
75C2×M16—221no—
76C2×M16—222no—
77C2×M16C4×D1111yescharacteristic
78C2×M16C22⋊D1111yescharacteristic
79#117—221no—
80C2×C42D4411yescharacteristic
81M32—41no—
82#108—441no—
83C4⋊C8—41no—
84C4⋊C8—441no—
85C4⋊C8—441no—
86C2×C11—21no—
87C2×C11—41no—
88C2×C11#135311yescharacteristic
89C22×C4—21no—
90C22×C4(C2×D11)⋊C411yescharacteristic
91M16—41no—
92M16—41no—
93M16—441no—
94M16—441no—
95M16—882no—
96C2×C8—21no—
97C2×C8—21no—
98C2×C8—442no—
99C2×C8—441no—
100C4⋊C4—441no—
101C22⋊C4—441no—
102C42—21no—
103C42—441no—
104C42#431411yescharacteristic
105C42Dic4411yescharacteristic
106C16—81no—
107C11#744011yescharacteristic, complemented, Sylow
108C23#6688911yescharacteristic
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—881no—
116C2×C4#6687011yescharacteristic
117C2×C4#6688011yescharacteristic
118C8—41no—
119C8—41no—
120C8—882no—
121C8—881no—
122C22—21no—
123C22—41no—
124C22#1062210511yescharacteristic
125C4—21no—
126C4—21no—
127C4—21no—
128C4—41no—
129C4—1761no—
130C4#1062211011yescharacteristic
131C4#1062211511yescharacteristic
132C2—21no—
133C2—41no—
134C2#1306664411yescharacteristic
subgroupG/H
centerC2#13066644
commutatorC2×C11×M16C2×C4
Frattini#423C2×D11
FittingC11×#1327C2
socleC2×C11#1353
prime radicalC23×C11#104
cosocleC11×#423C22
hypercenter#1327D11
hypocenterC11#7440
LCSG ▷ C2×C11×M16 ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1327

Complements

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

NH ≅ G/Ntype
107. C11#7440semidirect

Maximal subgroups

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

subgroupindex
#130701912
C11⋊#13092
C11×#13272
#744011