Finite Group Databasebeta

← #14653159

Subgroups — #14653159

Order 2816.

408 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 111 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#13078939C211yesmaximal, characteristic
2#13067179C212yesmaximal, complemented
3#13067175C212yesmaximal
4#13066908C211yesmaximal, characteristic, complemented
5C11×#1846C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7#10623001C2211yescharacteristic
8C2×C11×#107—21no—
9C2×C11×#106—21no—
10C2×C4×C8×C11C2211yescharacteristic
11C11×#382C2212yes—
12#10622726—21no—
13#10622726—21no—
14#10622538C2212yes—
15#10622310—22no—
16#10622307C412yescomplemented
17#10622294C412yescomplemented
18#10622092—22no—
19#10622090—24no—
20#10622089—24no—
21C2×#4339—21no—
22C22×C8×C11D411yescharacteristic
23C22×C8×C11D411yescharacteristic
24C2×C11×C4⋊C4—22no—
25C2×C42×C11C2311yescharacteristic
26#66983—22no—
27#66979—21no—
28#66977—22no—
29#66928—21no—
30#66927C2×C411yescharacteristic
31C4×D44—22no—
32#66923—21no—
33#66922C2×C412yes—
34#66922C2×C411yescharacteristic
35C4×Dic22—22no—
36C11×#107—42no—
37C11×#106—42no—
38C4×C8×C11C2×C412yes—
39C4×C8×C11D412yes—
40C11×#95—22no—
41C11×#95—22no—
42C22⋊(C11⋊C8)D414yes—
43#66885—22no—
44#66885—22no—
45#66880—22no—
46#66880—22no—
47C4⋊(C11⋊C8)—22no—
48C4×C11⋊C8—22no—
49#9758—111nomaximal, Sylow
50C22×C4×C11—42no—
51C22×C4×C11C2×D412yes—
52C22×C4×C11C2×D411yescharacteristic
53C2×C22⋊D11—41no—
54#4339—41no—
55#4339—41no—
56#4339—41no—
57#4339—41no—
58C2×D44—21no—
59C2×D44—22no—
60C2×C4×D11—41no—
61C2×Dic22—21no—
62C2×Dic22—22no—
63C2×C8×C11—21no—
64C2×C8×C11—21no—
65C2×C8×C11—21no—
66C2×C8×C11—21no—
67C2×C8×C11C22⋊C412yes—
68C2×C8×C11C22⋊C412yes—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C42×C11C22×C411yescharacteristic
72C42×C11C2×D411yescharacteristic
73C42×C11#4112yes—
74C22⋊Dic11—41no—
75(C2×D11)⋊C4—42no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79Dic11⋊C4—42no—
80C4×Dic11—41no—
81C2×C11⋊C8—24no—
82#3131—111no—
83#1846D1111yescharacteristic, complemented
84#1518—112no—
85#1517—112no—
86#1452—111no—
87C23×C11#12711yescharacteristic
88C22×D11—41no—
89C2×C4×C11—42no—
90C2×C4×C11—84no—
91C2×C4×C11—82no—
92C2×C4×C11C2×C22⋊C411yescharacteristic
93C2×C4×C11C4×D412yes—
94C2×C4×C11#12112yes—
95C2×C4×C11#12411yescharacteristic
96C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
98C2×C4×C11#13711yescharacteristic
99C2×C4×C11#13711yescharacteristic
100C22⋊D11—81no—
101C22⋊D11—81no—
102C2×Dic11—42no—
103C2×Dic11—41no—
104D44—41no—
105D44—41no—
106D44—82no—
107C4×D11—81no—
108C4×D11—81no—
109Dic22—41no—
110Dic22—41no—
111Dic22—82no—
112C8×C11—22no—
113C8×C11—22no—
114C11⋊C8—44no—
115#533—111no—
116#532—111no—
117#488—222no—
118#487—112no—
119#486—112no—
120#431—112no—
121C2×#107—21no—
122C2×#106—21no—
123#416—221no—
124#416—221no—
125C2×C4×C8C2×D1111yescharacteristic
126#382C2×D1112yes—
127#328—224no—
128#327—224no—
129#322—222no—
130C22×C11—22no—
131C22×C11#39011yescharacteristic
132C22×C11#49611yescharacteristic
133C22×C11#49711yescharacteristic
134C2×D11—81no—
135C2×D11—82no—
136C4×C11—22no—
137C4×C11—22no—
138C4×C11—162no—
139C4×C11#41711yescharacteristic
140C4×C11#41711yescharacteristic
141C4×C11#48911yescharacteristic
142C4×C11#48911yescharacteristic
143Dic11—81no—
144Dic11—82no—
145C2×#41—221no—
146C22×C8C22⋊D1111yescharacteristic
147C22×C8C22⋊D1111yescharacteristic
148C4⋊Q8—111no—
149C4⋊Q8—112no—
150#127—111no—
151#125—221no—
152#124—221no—
153C22⋊Q8—222no—
154#121—222no—
155C4×Q8—222no—
156C4×D4—222no—
157#117—221no—
158C2×C4⋊C4—22no—
159C2×C42C22×D1111yescharacteristic
160#107—42no—
161#106—42no—
162C4⋊C8—222no—
163#103—222no—
164#103—222no—
165#102—222no—
166#102—222no—
167C22⋊C8—114no—
168C4×C8—222no—
169C4×C8C4×D1112yes—
170C4×C8D4412yes—
171#95—22no—
172#95—22no—
173C2×C11—21no—
174C2×C11—21no—
175C2×C11#195911yescharacteristic
176C2×C11#197612yes—
177D11—161no—
178#41—441no—
179#41—441no—
180#41—441no—
181#41—441no—
182C2×Q8—222no—
183C2×Q8—221no—
184C2×D4—222no—
185C2×D4—221no—
186C2×D4—441no—
187C22×C4—42no—
188C22×C4—441no—
189C22×C4D4×D1112yes—
190C22×C4C2×C22⋊D1111yescharacteristic
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—224no—
196C2×C8(C2×D11)⋊C412yes—
197C2×C8(C2×D11)⋊C412yes—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C4⋊C4—222no—
203C4⋊C4—442no—
204C22⋊C4—441no—
205C22⋊C4—442no—
206C42—441no—
207C42C2×C4×D1111yescharacteristic
208C42C2×D4411yescharacteristic
209C42#434312yes—
210C11#975811yescharacteristic, complemented, Sylow
211C23—441no—
212C23#6699311yescharacteristic
213Q8—441no—
214Q8—441no—
215Q8—882no—
216D4—441no—
217D4—441no—
218D4—882no—
219D4—881no—
220D4—881no—
221C2×C4—42no—
222C2×C4—84no—
223C2×C4—82no—
224C2×C4—442no—
225C2×C4—441no—
226C2×C4—881no—
227C2×C4—881no—
228C2×C4#6694612yes—
229C2×C4#6694812yes—
230C2×C4C2×(C2×D11)⋊C411yescharacteristic
231C2×C4#6698511yescharacteristic
232C2×C4#6698511yescharacteristic
233C2×C4#6699511yescharacteristic
234C2×C4#6699511yescharacteristic
235C2×C4#6700011yescharacteristic
236C8—22no—
237C8—22no—
238C8—444no—
239C22—22no—
240C22—881no—
241C22—882no—
242C22#1062260111yescharacteristic
243C22#1062268711yescharacteristic
244C22#1062269911yescharacteristic
245C4—22no—
246C4—22no—
247C4—162no—
248C4—881no—
249C4—882no—
250C4#1062257911yescharacteristic
251C4#1062257911yescharacteristic
252C4#1062270211yescharacteristic
253C4#1062270211yescharacteristic
254C2—21no—
255C2—21no—
256C2—1761no—
257C2#1306943011yescharacteristic
258C2#1306951212yes—
subgroupG/H
centerC22#10622601
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1846C2
socleC22×C11#390
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1846D11
hypocenterC11#9758
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1846

Complements

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

NH ≅ G/Ntype
2. #13067179C2semidirect
4. #13066908C2semidirect
5. C11×#1846C2semidirect
16. #10622307C4semidirect
17. #10622294C4semidirect
83. #1846D11semidirect
210. C11#9758semidirect

Maximal subgroups

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

subgroupindex
#130789392
#130671792
#130671752
#130669082
C11×#18462
#975811