Finite Group Databasebeta

← #13068291

Subgroups — #13068291

Order 1408.

176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C11×#494C211yesmaximal, characteristic
2#10622706C211yesmaximal, characteristic
3#10622692C211yesmaximal, characteristic
4#10622691C211yesmaximal, characteristic
5#10622691C211yesmaximal, characteristic
6#10622294C211yesmaximal, characteristic
7#10622092C211yesmaximal, characteristic
8C2×C11×Q16—22no—
9C11×C4⋊Q8C2211yescharacteristic
10C11×C4⋊Q8C2211yescharacteristic
11#66922C2211yescharacteristic
12#66922C2211yescharacteristic
13C4×C8×C11C2211yescharacteristic
14#66880—22no—
15#66874—22no—
16#66872—22no—
17#66871—22no—
18#66871—22no—
19C4×C11⋊C8C2211yescharacteristic
20C4×C11⋊C8C2211yescharacteristic
21C2×Q8×C11—21no—
22C2×Q8×C11—21no—
23C2×Dic22—21no—
24C2×Dic22—21no—
25C11×Q16—44no—
26C2×C8×C11D412yes—
27C11×C4⋊C4—21no—
28C11×C4⋊C4—21no—
29C11×C4⋊C4—21no—
30C11×C4⋊C4—21no—
31C42×C11C2311yescharacteristic
32C4⋊Dic11—21no—
33C4⋊Dic11—21no—
34C4⋊Dic11—21no—
35C4⋊Dic11—21no—
36C2×C11⋊C8D412yes—
37C2×C11⋊C8D412yes—
38#1723—111nomaximal, Sylow
39Q8×C11—42no—
40Q8×C11—42no—
41C2×C4×C11—41no—
42C2×C4×C11—41no—
43C2×C4×C11C2×D411yescharacteristic
44C2×C4×C11C2×D411yescharacteristic
45C2×C4×C11C2×D411yescharacteristic
46C2×Dic11—41no—
47C2×Dic11—41no—
48Dic22—42no—
49Dic22—42no—
50C8×C11—22no—
51C11⋊C8—22no—
52C11⋊C8Q1614yescomplemented
53#500—111no—
54#500—111no—
55#498—111no—
56#494D1111yescharacteristic
57#487—111no—
58#487—111no—
59#322—111no—
60C22×C11#12711yescharacteristic
61C4×C11—81no—
62C4×C11—81no—
63C4×C11C2×Q1612yes—
64C4×C11AGL(1,ℤ/8)12yes—
65C4×C11#13712yes—
66Dic11—81no—
67Dic11—81no—
68C2×Q16—22no—
69C4⋊Q8—111no—
70C4⋊Q8—111no—
71C4⋊Q8C2×D1111yescharacteristic
72C4⋊Q8C2×D1111yescharacteristic
73#107—222no—
74#107—222no—
75#106—222no—
76#103—222no—
77#103—222no—
78C4×C8—111no—
79C4×C8—111no—
80C4×C8C2×D1111yescharacteristic
81C2×C11#49411yescharacteristic
82C2×C11#49611yescharacteristic
83C2×C11#49711yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—221no—
87C2×Q8—221no—
88Q16—44no—
89C2×C8—112no—
90C2×C8—112no—
91C2×C8C22⋊D1112yes—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—221no—
97C4⋊C4—221no—
98C4⋊C4—221no—
99C4⋊C4—221no—
100C42C22×D1111yescharacteristic
101C11#172311yescharacteristic, complemented, Sylow
102Q8—42no—
103Q8—42no—
104Q8—442no—
105Q8—442no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—441no—
109C2×C4—441no—
110C2×C4D4×D1111yescharacteristic
111C2×C4D4×D1111yescharacteristic
112C2×C4C2×C22⋊D1111yescharacteristic
113C8—22no—
114C8—114no—
115C8—222no—
116C22#6699311yescharacteristic
117C4—81no—
118C4—81no—
119C4—881no—
120C4—881no—
121C4Q16×D1112yes—
122C4#6697112yes—
123C4#6698512yes—
124C2#1062268711yescharacteristic
125C2#1062279411yescharacteristic
126C2#1062280311yescharacteristic
subgroupG/H
centerC22#66993
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#494C2
socle, prime radicalC22×C11#127
hypercenter#494D11
hypocenterC11#1723
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
52. C11⋊C8Q16semidirect
101. C11#1723semidirect

Maximal subgroups

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

subgroupindex
C11×#4942
#106227062
#106226922
#106226912
#106222942
#106220922
#172311