Finite Group Databasebeta

← #14641398

Subgroups — #14641398

Order 2816.

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

normal subgroups only

This group has 136 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
2#13066527C211yesmaximal, characteristic
3C11×#1327C211yesmaximal, characteristic
4C11×#423C2211yescharacteristic
5#10622738C411yescharacteristic
6#10622539—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—
16C11×M32—41no—
17C11×C4⋊C8—41no—
18C22⋊(C11⋊C8)—22no—
19#66883—41no—
20C4⋊(C11⋊C8)—41no—
21#66867—41no—
22#7441—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—
37C2×C11⋊C8—42no—
38C2×C11⋊C8—41no—
39C11×C16—81no—
40#2102—111no—
41#1327D1111yescharacteristic
42#1307—111no—
43C23×C11#10411yescharacteristic
44C2×C4×C11—21no—
45C2×C4×C11—21no—
46C2×C4×C11—21no—
47C2×C4×C11—21no—
48C2×C4×C11—81no—
49C2×C4×C11#9911yescharacteristic
50C2×C4×C11#10311yescharacteristic
51C2×Dic11—81no—
52C8×C11—41no—
53C8×C11—41no—
54C11⋊C8—82no—
55C11⋊C8—81no—
56#432—221no—
57#430—111no—
58#423C2×D1111yescharacteristic
59#349—21no—
60#344—221no—
61#339—221no—
62H(3,ℤ/4)—111no—
63C22×C11—21no—
64C22×C11—41no—
65C22×C11#32811yescharacteristic
66C4×C11—21no—
67C4×C11—41no—
68C4×C11—41no—
69C4×C11#35211yescharacteristic
70C4×C11#35511yescharacteristic
71Dic11—161no—
72C2×M16—221no—
73C2×M16C4×D1111yescharacteristic
74C2×M16C22⋊D1111yescharacteristic
75#117—221no—
76C2×C42D4411yescharacteristic
77M32—41no—
78#108—441no—
79C4⋊C8—41no—
80C4⋊C8—441no—
81C22⋊C8—222no—
82#97—441no—
83C2×C11—21no—
84C2×C11—41no—
85C2×C11#135311yescharacteristic
86C22×C4—21no—
87C22×C4(C2×D11)⋊C411yescharacteristic
88M16—41no—
89M16—41no—
90M16—441no—
91M16—441no—
92C2×C8—21no—
93C2×C8—21no—
94C2×C8—442no—
95C2×C8—441no—
96C4⋊C4—441no—
97C22⋊C4—441no—
98C42—21no—
99C42—441no—
100C42#431411yescharacteristic
101C42Dic4411yescharacteristic
102C16—81no—
103C11#744111yescharacteristic, complemented, Sylow
104C23#6688911yescharacteristic
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—81no—
110C2×C4—881no—
111C2×C4#6687011yescharacteristic
112C2×C4#6688011yescharacteristic
113C8—41no—
114C8—41no—
115C8—882no—
116C8—881no—
117C22—21no—
118C22—41no—
119C22#1062210511yescharacteristic
120C4—21no—
121C4—41no—
122C4—41no—
123C4—1761no—
124C4#1062211011yescharacteristic
125C4#1062211511yescharacteristic
126C2—21no—
127C2—41no—
128C2#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#7441
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
103. C11#7441semidirect

Maximal subgroups

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

subgroupindex
#130701912
#130665272
C11×#13272
#744111