Finite Group Databasebeta

← #14653260

Subgroups — #14653260

Order 2816.

390 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 127 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#13068754C211yesmaximal, characteristic
2#13067301C212yesmaximal
3#13067297C212yesmaximal
4#13066908C211yesmaximal, characteristic
5C2×C11×#498C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2212yes—
7C11×#498—22no—
8C11×#498C414yes—
9C2×C11×#106—22no—
10C2×C4×C8×C11C2211yescharacteristic
11#10622538C2212yes—
12#10622537C2211yescharacteristic
13#10622537C2211yescharacteristic
14#10622190—22no—
15#10622185—24no—
16#10622184—24no—
17#10622092—22no—
18C22×Q8×C11—22no—
19C22×C8×C11D412yes—
20C11×C4⋊Q8—22no—
21C11×C4⋊Q8—22no—
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8C2×C414yes—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—22no—
26C2×C42×C11C2311yescharacteristic
27C2×#4318—21no—
28C2×#4318—21no—
29C11×#106—28no—
30C4×C8×C11C2×C412yes—
31C4×C8×C11D412yes—
32C22⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—22no—
34C4⋊(C11⋊C8)—22no—
35C4⋊(C11⋊C8)D414yes—
36C4×C11⋊C8—22no—
37#9776—111nomaximal, Sylow
38C2×Q8×C11—24no—
39C2×Q8×C11—42no—
40C2×Q8×C11—84no—
41C22×C4×C11—42no—
42C22×C4×C11C2×D411yescharacteristic
43C22×C4×C11#4112yes—
44C2×C8×C11—22no—
45C2×C8×C11—22no—
46C2×C8×C11C22⋊C414yes—
47C11×C4⋊C4—24no—
48C11×C4⋊C4—24no—
49C11×C4⋊C4—42no—
50C11×C4⋊C4—42no—
51C42×C11C22×C411yescharacteristic
52C42×C11C2×D411yescharacteristic
53C42×C11C2×D412yes—
54#4318—42no—
55#4318—42no—
56C2×C11⋊C8—24no—
57C2×C11⋊C8—41no—
58C2×C11⋊C8—41no—
59C2×#498D1111yescharacteristic
60#1837—111no—
61#1549—112no—
62#1548—112no—
63#1452—111no—
64C23×C11#12411yescharacteristic
65Q8×C11—84no—
66Q8×C11—84no—
67C2×C4×C11—24no—
68C2×C4×C11—44no—
69C2×C4×C11—84no—
70C2×C4×C11C2×C22⋊C411yescharacteristic
71C2×C4×C11C4×D412yes—
72C2×C4×C11#12112yes—
73C2×C4×C11#12711yescharacteristic
74C2×C4×C11#13712yes—
75C2×C4×C11#13712yes—
76C8×C11—24no—
77C11⋊C8—44no—
78C11⋊C8—81no—
79C11⋊C8—81no—
80C2×C4⋊Q8C2×D1112yes—
81#498—22no—
82#498Dic1114yes—
83#431—112no—
84C2×#106—22no—
85#423—111no—
86#423—111no—
87C2×C4×C8C2×D1111yescharacteristic
88#341—222no—
89#333—224no—
90#332—224no—
91#322—222no—
92C22×C11—22no—
93C22×C11#39011yescharacteristic
94C22×C11#49112yes—
95C4×C11—22no—
96C4×C11—84no—
97C4×C11#41912yes—
98C4×C11#47114yes—
99C4×C11#49711yescharacteristic
100C4×C11#49711yescharacteristic
101C22×Q8—22no—
102C2×M16—221no—
103C2×M16—221no—
104C22×C8C22⋊D1112yes—
105C4⋊Q8—22no—
106C4⋊Q8—22no—
107C4⋊Q8—22no—
108C4⋊Q8C2×Dic1114yes—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C42C22×D1111yescharacteristic
112#106—28no—
113C4⋊C8—114no—
114C4⋊C8—222no—
115C4⋊C8—222no—
116C22⋊C8—222no—
117C4×C8—222no—
118C4×C8C2×Dic1112yes—
119C4×C8C22⋊D1112yes—
120C2×C11—22no—
121C2×C11#196011yescharacteristic
122C2×C11#197712yes—
123C2×Q8—24no—
124C2×Q8—42no—
125C2×Q8—84no—
126C22×C4—42no—
127C22×C4#434112yes—
128C22×C4C2×C22⋊D1111yescharacteristic
129M16—442no—
130M16—442no—
131C2×C8—22no—
132C2×C8—22no—
133C2×C8—224no—
134C2×C8—441no—
135C2×C8—441no—
136C2×C8C22⋊Dic1114yes—
137C4⋊C4—24no—
138C4⋊C4—24no—
139C4⋊C4—42no—
140C4⋊C4—42no—
141C42D4×D1112yes—
142C42C22×Dic1111yescharacteristic
143C42C2×C22⋊D1111yescharacteristic
144C11#977611yescharacteristic, complemented, Sylow
145C23#6698911yescharacteristic
146Q8—84no—
147Q8—84no—
148C2×C4—24no—
149C2×C4—44no—
150C2×C4—84no—
151C2×C4D4×Dic1112yes—
152C2×C4#6699112yes—
153C2×C4#6699311yescharacteristic
154C2×C4#6699512yes—
155C2×C4#6699512yes—
156C2×C4C2×C22⋊Dic1111yescharacteristic
157C8—24no—
158C8—444no—
159C8—881no—
160C8—881no—
161C22—22no—
162C22#1062269512yes—
163C22#1062283411yescharacteristic
164C4—22no—
165C4—84no—
166C4#1062269911yescharacteristic
167C4#1062269911yescharacteristic
168C4#1062279014yes—
169C4#1062283812yes—
170C2—22no—
171C2#1306943711yescharacteristic
172C2#1306952112yes—
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#498C2
socleC22×C11#390
prime radicalC23×C11#124
cosocleC2×C42×C11C23
hypercenterC2×#498D11
hypocenterC11#9776
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
144. C11#9776semidirect

Maximal subgroups

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

subgroupindex
#130687542
#130673012
#130672972
#130669082
C2×C11×#4982
#977611