Finite Group Databasebeta

← #13066561

Subgroups — #13066561

Order 1408.

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

normal subgroups only

This group has 134 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#10622589C211yesmaximal, characteristic
2C11×#324C211yesmaximal, characteristic
3#10622166C211yesmaximal, characteristic
4C2×C11×C4⋊C4C2211yescharacteristic
5C2×C4⋊Dic11C411yescharacteristic
6C2×Dic11⋊C4—21no—
7C2×Dic11⋊C4—21no—
8C2×C4×Dic11C411yescharacteristic
9C11×C22⋊C8—21no—
10C22⋊(C11⋊C8)—21no—
11C22×C4×C11C2×C411yescharacteristic
12C22×C4×C11D411yescharacteristic
13C22×C4×C11D411yescharacteristic
14C22×Dic11—21no—
15C22×Dic11—21no—
16C2×C8×C11—41no—
17C11×C4⋊C4—41no—
18C4⋊Dic11—41no—
19Dic11⋊C4—42no—
20Dic11⋊C4—42no—
21C4×Dic11—21no—
22C4×Dic11C812yescomplemented
23C2×C11⋊C8—41no—
24#1325—111nomaximal, Sylow
25C23×C11C22⋊C411yescharacteristic
26C2×C4×C11—21no—
27C2×C4×C11—21no—
28C2×C4×C11—21no—
29C2×C4×C11—21no—
30C2×C4×C11—41no—
31C2×C4×C11—41no—
32C2×C4×C11C2×C811yescharacteristic
33C2×C4×C11M1611yescharacteristic
34C2×Dic11—22no—
35C2×Dic11—22no—
36C2×Dic11—22no—
37C2×Dic11—41no—
38C2×Dic11—41no—
39C2×Dic11—41no—
40C8×C11—81no—
41C11⋊C8—81no—
42#384—111no—
43#324—111no—
44#324D1111yescharacteristic
45C22×C11—21no—
46C22×C11—21no—
47C22×C11C22⋊C811yescharacteristic
48C22×C11#9911yescharacteristic
49C22×C11#10111yescharacteristic
50C4×C11—21no—
51C4×C11—21no—
52C4×C11—41no—
53C4×C11—41no—
54Dic11—24no—
55Dic11—81no—
56C2×C4⋊C4—111no—
57C2×C4⋊C4—221no—
58C2×C4⋊C4—221no—
59C2×C4⋊C4C2×D1111yescharacteristic
60C2×C42—111no—
61C22⋊C8—21no—
62C22⋊C8—221no—
63C2×C11—21no—
64C2×C11—21no—
65C2×C11#32411yescharacteristic
66C2×C11#35311yescharacteristic
67C2×C11#35611yescharacteristic
68C22×C4—221no—
69C22×C4—221no—
70C22×C4C4×D1111yescharacteristic
71C22×C4D4411yescharacteristic
72C22×C4C22⋊D1111yescharacteristic
73C2×C8—41no—
74C2×C8—441no—
75C4⋊C4—41no—
76C4⋊C4—441no—
77C4⋊C4—442no—
78C4⋊C4—442no—
79C42—112no—
80C42—221no—
81C11#132511yescharacteristic, complemented, Sylow
82C23(C2×D11)⋊C411yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—222no—
90C2×C4—222no—
91C2×C4—222no—
92C2×C4—441no—
93C2×C4—441no—
94C2×C4—441no—
95C2×C4C8×D1111yescharacteristic
96C2×C4#431311yescharacteristic
97C8—81no—
98C8—881no—
99C22—21no—
100C22—21no—
101C22#6687011yescharacteristic
102C22(C2×D11)⋊C811yescharacteristic
103C22#6688811yescharacteristic
104C4—21no—
105C4—21no—
106C4—41no—
107C4—41no—
108C4—224no—
109C4—881no—
110C2—21no—
111C2—21no—
112C2#1062210711yescharacteristic
113C2#1062211211yescharacteristic
114C2#1062211611yescharacteristic
subgroupG/H
centerC22#66870
commutatorC2×C4×C11C2×C8
FrattiniC2×C4⋊C4C2×D11
FittingC11×#324C2
socleC22×C11#99
prime radicalC23×C11C22⋊C4
cosocleC2×C11×C4⋊C4C22
hypercenter#324D11
hypocenterC11#1325
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
22. C4×Dic11C8semidirect
81. C11#1325semidirect

Maximal subgroups

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

subgroupindex
#106225892
C11×#3242
#106221662
#132511