Finite Group Databasebeta

← #13066639

Subgroups — #13066639

Order 1408.

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

normal subgroups only

This group has 154 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#10622562C211yesmaximal, characteristic
2C11×#342C211yesmaximal, characteristic
3#10622163C211yesmaximal, characteristic
4C2×C11×C22⋊C4—21no—
5C2×C11×C22⋊C4C2211yescharacteristic
6C2×C22⋊Dic11—21no—
7C2×C4⋊Dic11C411yescharacteristic, complemented
8C2×Dic11⋊C4—21no—
9C11⋊#95C411yescharacteristic, complemented
10C22⋊(C11⋊C8)—21no—
11C24×C11D411yescharacteristic
12C22×C4×C11—41no—
13C22×C4×C11C2×C411yescharacteristic
14C22×C4×C11D411yescharacteristic
15C22×Dic11—21no—
16C22×Dic11—21no—
17C11×C22⋊C4—22no—
18C11×C22⋊C4—41no—
19C11×C22⋊C4—41no—
20C22⋊Dic11—42no—
21C4⋊Dic11—41no—
22Dic11⋊C4—42no—
23C2×C11⋊C8—41no—
24#1352—111nomaximal, Sylow
25C23×C11—21no—
26C23×C11—21no—
27C23×C11—41no—
28C23×C11—41no—
29C23×C11C22⋊C411yescharacteristic
30C23×C11SD1611yescharacteristic
31C23×C11Q1611yescharacteristic
32C2×C4×C11—21no—
33C2×C4×C11—21no—
34C2×C4×C11—41no—
35C2×C4×C11—41no—
36C2×C4×C11—42no—
37C2×C4×C11—81no—
38C2×C4×C11—81no—
39C2×Dic11—22no—
40C2×Dic11—41no—
41C2×Dic11—41no—
42C2×Dic11—41no—
43C2×Dic11—41no—
44C2×Dic11—41no—
45C11⋊C8—81no—
46#399—111no—
47#342D1111yescharacteristic
48#323—111no—
49C22×C11—21no—
50C22×C11—21no—
51C22×C11—21no—
52C22×C11—21no—
53C22×C11—41no—
54C22×C11—41no—
55C22×C11—41no—
56C22×C11—41no—
57C22×C11—81no—
58C22×C11#9911yescharacteristic
59C22×C11#10311yescharacteristic
60C22×C11#10411yescharacteristic
61C4×C11—41no—
62C4×C11—41no—
63C4×C11—82no—
64Dic11—42no—
65Dic11—81no—
66C2×C4⋊C4—111no—
67C2×C4⋊C4—221no—
68C2×C22⋊C4—21no—
69C2×C22⋊C4—221no—
70C2×C22⋊C4C2×D1111yescharacteristic
71C22⋊C8—221no—
72#95—111no—
73C2×C11—21no—
74C2×C11—21no—
75C2×C11—41no—
76C2×C11—41no—
77C2×C11#32811yescharacteristic
78C2×C11#35211yescharacteristic
79C2×C11#35311yescharacteristic
80C24C22⋊D1111yescharacteristic
81C22×C4—41no—
82C22×C4—221no—
83C22×C4—221no—
84C22×C4C4×D1111yescharacteristic
85C22×C4D4411yescharacteristic
86C2×C8—441no—
87C4⋊C4—441no—
88C4⋊C4—442no—
89C22⋊C4—22no—
90C22⋊C4—41no—
91C22⋊C4—41no—
92C22⋊C4—442no—
93C11#135211yescharacteristic, complemented, Sylow
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23(C2×D11)⋊C411yescharacteristic
99C23#432411yescharacteristic
100C23#432611yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—42no—
106C2×C4—81no—
107C2×C4—81no—
108C2×C4—222no—
109C2×C4—441no—
110C2×C4—441no—
111C2×C4—441no—
112C2×C4—441no—
113C2×C4—441no—
114C8—881no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#6686911yescharacteristic
125C22#6687011yescharacteristic
126C22#6687411yescharacteristic
127C4—41no—
128C4—41no—
129C4—82no—
130C4—442no—
131C4—881no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#1062209011yescharacteristic
137C2#1062211011yescharacteristic
138C2#1062211211yescharacteristic
subgroupG/H
centerC22#66870
commutatorC22×C4×C11C2×C4
FrattiniC2×C22⋊C4C2×D11
FittingC11×#342C2
socleC22×C11#99
prime radicalC24×C11D4
cosocleC2×C11×C22⋊C4C22
hypercenter#342D11
hypocenterC11#1352
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
7. C2×C4⋊Dic11C4semidirect
9. C11⋊#95C4semidirect
93. C11#1352semidirect

Maximal subgroups

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

subgroupindex
#106225622
C11×#3422
#106221632
#135211