Finite Group Databasebeta

← #14653170

Subgroups — #14653170

Order 2816.

478 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 119 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#13068747C211yesmaximal, characteristic, complemented
2#13067176C214yesmaximal, complemented
3#13066908C211yesmaximal, characteristic, complemented
4C11×#3147C211yesmaximal, characteristic
5C2×C11×#135—22no—
6C11×#532C2212yes—
7C11×#495—22no—
8C11×#494C411yescharacteristic, complemented
9C11×#493C411yescharacteristic, complemented
10C11×#492C412yescomplemented
11C2×C4×C8×C11C2211yescharacteristic
12#10622549C2212yes—
13#10622538C2212yes—
14#10622189—22no—
15#10622175—28no—
16#10622092—22no—
17C2×C11×#41—22no—
18C11×#135—48no—
19C2×C11×Q16—22no—
20C2×C11×SD16—24no—
21C2×C11×D8—22no—
22C22×C8×C11D412yes—
23C11×C4⋊Q8C2×C412yes—
24C11×#127C2×C412yes—
25C11×#124—22no—
26C11×#121—24no—
27C4×D4×C11—24no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—22no—
30C4×C8×C11C2×C411yescharacteristic
31C4×C8×C11C2×C411yescharacteristic
32C4×C8×C11D412yes—
33C11⋊#95—24no—
34C22⋊(C11⋊C8)D414yes—
35C4⋊(C11⋊C8)—22no—
36C4×C11⋊C8—22no—
37#9760—111nomaximal, Sylow
38C11×#41—48no—
39C2×Q8×C11—22no—
40C2×D4×C11—22no—
41C2×D4×C11—24no—
42C2×D4×C11—42no—
43C22×C4×C11—42no—
44C22×C4×C11C2×D412yes—
45C22×C4×C11C2×D411yescharacteristic
46C22×Dic11—42no—
47C11×Q16—44no—
48C11×SD16—48no—
49C11×D8—44no—
50C2×C8×C11—24no—
51C2×C8×C11C22⋊C412yes—
52C2×C8×C11C22⋊C412yes—
53C11×C4⋊C4—24no—
54C11×C22⋊C4—44no—
55C42×C11C22×C411yescharacteristic
56C42×C11C2×D411yescharacteristic
57C42×C11#4112yes—
58C4⋊Dic11—44no—
59C2×C11⋊C8—24no—
60#3147D1111yescharacteristic
61#1835—111no—
62#1517—114no—
63#1452—111no—
64C23×C11—42no—
65C23×C11#12711yescharacteristic
66Q8×C11—44no—
67D4×C11—44no—
68D4×C11—84no—
69D4×C11—84no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11—84no—
73C2×C4×C11C2×C22⋊C411yescharacteristic
74C2×C4×C11C4×D412yes—
75C2×C4×C11#12112yes—
76C2×C4×C11#12411yescharacteristic
77C2×C4×C11AGL(1,ℤ/8)14yes—
78C2×Dic11—84no—
79C2×Dic11—82no—
80C8×C11—22no—
81C8×C11—22no—
82C11⋊C8—44no—
83C2×#135—22no—
84#532C2×D1112yes—
85#495—22no—
86#494Dic1111yescharacteristic, complemented
87#493Dic1111yescharacteristic, complemented
88#492Dic1112yescomplemented
89#431—112no—
90C2×C4×C8C2×D1111yescharacteristic
91#382—112no—
92#340—222no—
93#327—228no—
94#322—222no—
95C22×C11—22no—
96C22×C11—82no—
97C22×C11—84no—
98C22×C11#39011yescharacteristic
99C22×C11#49612yes—
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—82no—
103C4×C11#41812yes—
104C4×C11#49012yes—
105Dic11—162no—
106C2×#41—22no—
107#135—48no—
108C2×Q16—22no—
109C2×SD16—24no—
110C2×D8—22no—
111C22×C8C22⋊D1112yes—
112C4⋊Q8C2×Dic1112yes—
113#127C2×Dic1112yes—
114#124—22no—
115#121—24no—
116C4×D4—24no—
117C2×C4⋊C4—222no—
118C2×C42C22×D1111yescharacteristic
119C4⋊C8—222no—
120C22⋊C8—114no—
121C4×C8—222no—
122C4×C8C2×Dic1111yescharacteristic
123C4×C8C2×Dic1111yescharacteristic
124C4×C8C22⋊D1112yes—
125#95—224no—
126C2×C11—22no—
127C2×C11—162no—
128C2×C11#196111yescharacteristic
129C2×C11#197612yes—
130#41—48no—
131C2×Q8—22no—
132C2×D4—24no—
133C2×D4—22no—
134C2×D4—42no—
135C22×C4—42no—
136C22×C4—442no—
137C22×C4D4×D1112yes—
138C22×C4C2×C22⋊D1111yescharacteristic
139Q16—44no—
140SD16—48no—
141D8—44no—
142C2×C8—24no—
143C2×C8—224no—
144C2×C8C22⋊Dic1112yes—
145C2×C8C22⋊Dic1112yes—
146C4⋊C4—24no—
147C4⋊C4—444no—
148C22⋊C4—44no—
149C42#434112yes—
150C42C22×Dic1111yescharacteristic
151C42C2×C22⋊D1111yescharacteristic
152C11#976011yescharacteristic, complemented, Sylow
153C23—42no—
154C23#6699311yescharacteristic
155Q8—44no—
156D4—44no—
157D4—84no—
158D4—84no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—84no—
162C2×C4—884no—
163C2×C4—882no—
164C2×C4#6698514yes—
165C2×C4D4×Dic1112yes—
166C2×C4#6698911yescharacteristic
167C2×C4#6699112yes—
168C2×C4C2×C22⋊Dic1111yescharacteristic
169C8—22no—
170C8—22no—
171C8—444no—
172C22—22no—
173C22—82no—
174C22—84no—
175C22#1062268712yes—
176C22#1062283411yescharacteristic
177C4—22no—
178C4—22no—
179C4—82no—
180C4—1762no—
181C4#1062268412yes—
182C4#1062282812yes—
183C2—22no—
184C2—162no—
185C2#1306944111yescharacteristic
186C2#1306951512yes—
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3147C2
socleC22×C11#390
cosocleC2×C42×C11C23
hypercenter#3147D11
hypocenterC11#9760
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #13068747C2semidirect
2. #13067176C2semidirect
3. #13066908C2semidirect
8. C11×#494C4semidirect
9. C11×#493C4semidirect
10. C11×#492C4semidirect
86. #494Dic11semidirect
87. #493Dic11semidirect
88. #492Dic11semidirect
152. C11#9760semidirect

Maximal subgroups

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

subgroupindex
#130687472
#130671762
#130669082
C11×#31472
#976011