Finite Group Databasebeta

← #14641342

Subgroups — #14641342

Order 2816.

140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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#13070724C211yesmaximal, characteristic
2#13066756C211yesmaximal, characteristic
3C11×#1384C211yesmaximal, characteristic
4C2×C11×M32C2211yescharacteristic
5C11×#427—21no—
6#10622729—21no—
7C2×Dic88C411yescharacteristic, complemented
8#10622143C411yescharacteristic, complemented
9#10622141—21no—
10#10622137—21no—
11C22×C8×C11D411yescharacteristic
12C11×#117—41no—
13#66977—41no—
14C2×Dic44—21no—
15C11×M32—41no—
16C2×C11×C16C2×C411yescharacteristic
17C2×C11×C16D411yescharacteristic
18C11×#107—41no—
19C11×#106—22no—
20#66882—21no—
21#66880—41no—
22Dic88—41no—
23C11⋊C32—41no—
24#7423—111nomaximal, Sylow
25C22×C4×C11D811yescharacteristic
26C2×Dic22—41no—
27C2×C8×C11—21no—
28C2×C8×C11—21no—
29C2×C8×C11C22⋊C411yescharacteristic
30C2×C8×C11SD1611yescharacteristic
31C11×C4⋊C4—42no—
32C11×C22⋊C4—81no—
33C42×C11—81no—
34C22⋊Dic11—81no—
35C4⋊Dic11—41no—
36Dic11⋊C4—81no—
37Dic44—41no—
38Dic44—41no—
39C11×C16—21no—
40C11×C16—21no—
41#2219—111no—
42#1400—111no—
43#1384D1111yescharacteristic
44C23×C11D1611yescharacteristic
45C2×C4×C11—21no—
46C2×C4×C11—21no—
47C2×C4×C11—82no—
48C2×C4×C11#10211yescharacteristic
49C2×C4×C11SD3211yescharacteristic
50C2×Dic11—81no—
51C2×Dic11—81no—
52Dic22—81no—
53Dic22—81no—
54C8×C11—21no—
55C8×C11#9911yescharacteristic
56C8×C11#10411yescharacteristic
57C2×Q32—111no—
58C2×M32C2×D1111yescharacteristic
59#467—221no—
60#427—21no—
61M64—221no—
62#367—111no—
63#358—221no—
64C22×C11—21no—
65C22×C11—41no—
66C22×C11#35711yescharacteristic
67C4×C11—21no—
68C4×C11—162no—
69C4×C11#32711yescharacteristic
70C4×C11#36011yescharacteristic
71Dic11—161no—
72Dic11—161no—
73C2×Q16—221no—
74C22×C8C22⋊D1111yescharacteristic
75C22⋊Q8—441no—
76#117—41no—
77Q32—441no—
78M32—41no—
79C2×C16C4×D1111yescharacteristic
80C2×C16D4411yescharacteristic
81#107—41no—
82#107—221no—
83#106—22no—
84#103—441no—
85C32—441no—
86C2×C11—21no—
87C2×C11—41no—
88C2×C11#134711yescharacteristic
89C2×Q8—441no—
90C22×C4#432311yescharacteristic
91Q16—441no—
92Q16—441no—
93C2×C8—21no—
94C2×C8—21no—
95C2×C8(C2×D11)⋊C411yescharacteristic
96C2×C8#432511yescharacteristic
97C4⋊C4—42no—
98C4⋊C4—441no—
99C4⋊C4—881no—
100C22⋊C4—81no—
101C22⋊C4—881no—
102C42—81no—
103C16—21no—
104C16—21no—
105C11#742311yescharacteristic, complemented, Sylow
106C23#6689011yescharacteristic
107Q8—881no—
108Q8—881no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—82no—
112C2×C4—881no—
113C2×C4—881no—
114C2×C4#6687311yescharacteristic
115C2×C4#6689211yescharacteristic
116C8—21no—
117C8#6686911yescharacteristic
118C8#6687011yescharacteristic
119C22—21no—
120C22—41no—
121C22#1062212911yescharacteristic
122C4—21no—
123C4—162no—
124C4—1761no—
125C4—1761no—
126C4#1062208911yescharacteristic
127C4#1062212611yescharacteristic
128C2—21no—
129C2—41no—
130C2#1306662411yescharacteristic
subgroupG/H
centerC2#13066624
commutatorC2×C11×C16C2×C4
FrattiniC2×M32C2×D11
FittingC11×#1384C2
socleC2×C11#1347
prime radicalC23×C11D16
cosocleC2×C11×M32C22
hypercenter#1384D11
hypocenterC11#7423
LCSG ▷ C2×C11×C16 ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32 ◁ #1384

Complements

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

NH ≅ G/Ntype
7. C2×Dic88C4semidirect
8. #10622143C4semidirect
105. C11#7423semidirect

Maximal subgroups

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

subgroupindex
#130707242
#130667562
C11×#13842
#742311