Finite Group Databasebeta

← #13068271

Subgroups — #13068271

Order 1408.

186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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×#487C211yesmaximal, characteristic, complemented
2#10622701C211yesmaximal, characteristic
3#10622701C211yesmaximal, characteristic
4#10622694C211yesmaximal, characteristic, complemented
5#10622691C211yesmaximal, characteristic, complemented
6#10622306C211yesmaximal, characteristic
7#10622092C211yesmaximal, characteristic, complemented
8C11×C4⋊Q8C2211yescharacteristic
9C11×C4⋊Q8C2211yescharacteristic
10C2×#4314—22no—
11#66927C2211yescharacteristic
12#66922C2211yescharacteristic
13C11×#103—22no—
14C4×C8×C11C2211yescharacteristic
15#66899—22no—
16#66873—22no—
17#66873—22no—
18#66871—22no—
19C4×C11⋊C8C2211yescharacteristic
20C4×C11⋊C8C2211yescharacteristic
21C2×Q8×C11—21no—
22C2×Q8×C11—21no—
23C2×D44—21no—
24C2×D44—21no—
25C2×D44—21no—
26C2×Dic22—21no—
27C2×C8×C11D412yes—
28C11×C4⋊C4—21no—
29C11×C4⋊C4—21no—
30C11×C4⋊C4—21no—
31C11×C4⋊C4—21no—
32C42×C11C2311yescharacteristic
33C4⋊Dic11—21no—
34C4⋊Dic11—21no—
35C2×C11⋊C8D412yes—
36C2×C11⋊C8D412yes—
37#4314—44no—
38#1719—111nomaximal, Sylow
39C22×D11—41no—
40Q8×C11—42no—
41Q8×C11—42no—
42C2×C4×C11—41no—
43C2×C4×C11—41no—
44C2×C4×C11C2×D411yescharacteristic
45C2×C4×C11C2×D411yescharacteristic
46C2×C4×C11C2×D411yescharacteristic
47C2×Dic11—41no—
48D44—42no—
49D44—42no—
50D44—42no—
51Dic22—42no—
52C8×C11—22no—
53C11⋊C8—22no—
54C11⋊C8—22no—
55#500—111no—
56#492—111no—
57#487—111no—
58#487D1111yescharacteristic, complemented
59#486—111no—
60#486—111no—
61#322—111no—
62C22×C11#12711yescharacteristic
63C2×D11—81no—
64C2×D11—81no—
65C2×D11—81no—
66C4×C11—81no—
67C4×C11—81no—
68C4×C11#13512yes—
69C4×C11AGL(1,ℤ/8)12yes—
70C4×C11#13712yes—
71Dic11—81no—
72C2×SD16—222no—
73C4⋊Q8—111no—
74C4⋊Q8C2×D1111yescharacteristic
75C4⋊Q8C2×D1111yescharacteristic
76#127—111no—
77#107—222no—
78#103—22no—
79#103—222no—
80#102—222no—
81#102—222no—
82C4×C8—111no—
83C4×C8—111no—
84C4×C8C2×D1111yescharacteristic
85C2×C11#49511yescharacteristic
86C2×C11#49611yescharacteristic
87C2×C11#49711yescharacteristic
88D11—161no—
89C2×Q8—21no—
90C2×Q8—21no—
91C2×Q8—221no—
92C2×D4—221no—
93C2×D4—221no—
94C2×D4—221no—
95SD16—444no—
96C2×C8—112no—
97C2×C8—112no—
98C2×C8C22⋊D1112yes—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—221no—
104C4⋊C4—221no—
105C42C22×D1111yescharacteristic
106C11#171911yescharacteristic, complemented, Sylow
107C23—441no—
108Q8—42no—
109Q8—42no—
110Q8—442no—
111D4—442no—
112D4—442no—
113D4—442no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—441no—
117C2×C4D4×D1111yescharacteristic
118C2×C4D4×D1111yescharacteristic
119C2×C4C2×C22⋊D1111yescharacteristic
120C8—22no—
121C8—222no—
122C8—222no—
123C22—881no—
124C22—881no—
125C22—881no—
126C22#6699311yescharacteristic
127C4—81no—
128C4—81no—
129C4—881no—
130C4#6696912yes—
131C4#6697112yes—
132C4#6700212yes—
133C2—1761no—
134C2#1062267111yescharacteristic
135C2#1062278111yescharacteristic
136C2#1062280311yescharacteristic
subgroupG/H
centerC22#66993
commutator, cosocleC42×C11C23
FrattiniC42C22×D11
FittingC11×#487C2
socleC22×C11#127
prime radical#66927C22
hypercenter#487D11
hypocenterC11#1719
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. C11×#487C2semidirect
4. #10622694C2semidirect
5. #10622691C2semidirect
7. #10622092C2semidirect
58. #487D11semidirect
106. C11#1719semidirect

Maximal subgroups

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

subgroupindex
C11×#4872
#106227012
#106226942
#106226912
#106223062
#106220922
#171911