Finite Group Databasebeta

← #13066642

Subgroups — #13066642

Order 1408.

116 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 35 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#10622599C211yesmaximal, characteristic
2C11×#343C211yesmaximal, characteristic
3#10622166C211yesmaximal, characteristic
4C2×C11×M16—21no—
5C2×C11×C4⋊C4C2211yescharacteristic
6C2×C4⋊Dic11C411yescharacteristic
7C11⋊#95—21no—
8C11⋊#95—21no—
9C11⋊#95C411yescharacteristic
10C22⋊(C11⋊C8)—21no—
11C22×C4×C11C2×C411yescharacteristic
12C22×C4×C11D411yescharacteristic
13C22×C4×C11D411yescharacteristic
14C22×Dic11—21no—
15C22×Dic11—21no—
16C11×M16—22no—
17C11×M16—41no—
18C2×C8×C11—41no—
19C11×C4⋊C4—41no—
20C4⋊Dic11—41no—
21C2×C11⋊C8—41no—
22#1353—111nomaximal, Sylow
23C23×C11C22⋊C411yescharacteristic
24C2×C4×C11—21no—
25C2×C4×C11—21no—
26C2×C4×C11—21no—
27C2×C4×C11—21no—
28C2×C4×C11—41no—
29C2×C4×C11—41no—
30C2×C4×C11SD1611yescharacteristic
31C2×C4×C11Q1611yescharacteristic
32C2×Dic11—41no—
33C2×Dic11—41no—
34C2×Dic11—42no—
35C2×Dic11—41no—
36C2×Dic11—41no—
37C8×C11—42no—
38C11⋊C8—81no—
39#400—111no—
40#343D1111yescharacteristic
41#324—111no—
42C22×C11—21no—
43C22×C11—21no—
44C22×C11#9911yescharacteristic
45C22×C11#10311yescharacteristic
46C22×C11#10411yescharacteristic
47C4×C11—21no—
48C4×C11—21no—
49C4×C11—41no—
50C4×C11—41no—
51Dic11—81no—
52Dic11—81no—
53C2×M16—21no—
54C2×C4⋊C4—111no—
55C2×C4⋊C4C2×D1111yescharacteristic
56C22⋊C8—221no—
57#95—111no—
58#95—221no—
59#95—221no—
60C2×C11—21no—
61C2×C11—21no—
62C2×C11#32811yescharacteristic
63C2×C11#35211yescharacteristic
64C2×C11#35511yescharacteristic
65C22×C4—221no—
66C22×C4—221no—
67C22×C4C4×D1111yescharacteristic
68C22×C4D4411yescharacteristic
69C22×C4C22⋊D1111yescharacteristic
70M16—22no—
71M16—41no—
72C2×C8—41no—
73C2×C8—441no—
74C4⋊C4—41no—
75C4⋊C4—441no—
76C11#135311yescharacteristic, complemented, Sylow
77C23(C2×D11)⋊C411yescharacteristic
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—41no—
83C2×C4—41no—
84C2×C4—441no—
85C2×C4—441no—
86C2×C4—442no—
87C2×C4—441no—
88C2×C4—441no—
89C2×C4#432411yescharacteristic
90C2×C4#432611yescharacteristic
91C8—42no—
92C8—881no—
93C22—21no—
94C22—21no—
95C22#6686911yescharacteristic
96C22#6687011yescharacteristic
97C22#6687411yescharacteristic
98C4—21no—
99C4—21no—
100C4—41no—
101C4—41no—
102C4—881no—
103C4—881no—
104C2—21no—
105C2—21no—
106C2#1062209011yescharacteristic
107C2#1062211411yescharacteristic
108C2#1062211511yescharacteristic
subgroupG/H
centerC22#66870
commutatorC22×C4×C11C2×C4
FrattiniC2×C4⋊C4C2×D11
FittingC11×#343C2
socleC22×C11#99
prime radicalC23×C11C22⋊C4
cosocleC2×C11×C4⋊C4C22
hypercenter#343D11
hypocenterC11#1353
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
76. C11#1353semidirect

Maximal subgroups

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

subgroupindex
#106225992
C11×#3432
#106221662
#135311