Finite Group Databasebeta

← #14653161

Subgroups — #14653161

Order 2816.

408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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#13068780C211yesmaximal, characteristic, complemented
3#13067181C212yesmaximal, complemented
4#13067177C212yesmaximal
5C11×#1452C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7#10623001C2211yescharacteristic
8C11×#431C2212yes—
9C2×C4×C8×C11C2211yescharacteristic
10#10622726—21no—
11#10622726—21no—
12C2×#66882—21no—
13C2×#66881—21no—
14#10622549C2212yes—
15#10622310—22no—
16#10622307C412yescomplemented
17#10622294C412yescomplemented
18C11×#322—22no—
19#10622108—24no—
20#10622105—24no—
21C2×#4339—21no—
22C22×C8×C11D411yescharacteristic
23C22×C8×C11D411yescharacteristic
24C2×C42×C11C2311yescharacteristic
25#66983—22no—
26#66979—21no—
27C2×C4⋊Dic11—22no—
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×C4⋊C8—22no—
37C11×C22⋊C8D414yes—
38C4×C8×C11—22no—
39C4×C8×C11C2×C412yes—
40C4×C8×C11D412yes—
41C11⋊#95—22no—
42C11⋊#95—22no—
43#66885—22no—
44#66885—22no—
45#66882—42no—
46#66881—42no—
47#66880—22no—
48#66880—22no—
49#9758—111nomaximal, Sylow
50C22×C4×C11C2×D412yes—
51C22×C4×C11C2×D411yescharacteristic
52C2×C22⋊D11—41no—
53C22×Dic11—42no—
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—24no—
64C2×C8×C11—21no—
65C2×C8×C11—21no—
66C2×C8×C11—21no—
67C2×C8×C11—21no—
68C2×C8×C11C22⋊C412yes—
69C2×C8×C11C22⋊C412yes—
70C42×C11C22×C411yescharacteristic
71C42×C11C2×D411yescharacteristic
72C42×C11#4112yes—
73C22⋊Dic11—41no—
74(C2×D11)⋊C4—42no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—42no—
79C4⋊Dic11—42no—
80Dic11⋊C4—42no—
81C4×Dic11—41no—
82#3131—111no—
83#1846—111no—
84#1518—112no—
85#1517—112no—
86#1452D1111yescharacteristic, complemented
87C23×C11#12711yescharacteristic
88C22×D11—41no—
89C2×C4×C11—42no—
90C2×C4×C11C2×C22⋊C411yescharacteristic
91C2×C4×C11C4×D412yes—
92C2×C4×C11#12112yes—
93C2×C4×C11#12411yescharacteristic
94C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C11#13711yescharacteristic
97C2×C4×C11#13711yescharacteristic
98C22⋊D11—81no—
99C22⋊D11—81no—
100C2×Dic11—42no—
101C2×Dic11—41no—
102C2×Dic11—84no—
103C2×Dic11—82no—
104D44—41no—
105D44—41no—
106D44—82no—
107C4×D11—81no—
108C4×D11—81no—
109Dic22—41no—
110Dic22—41no—
111Dic22—82no—
112C8×C11—22no—
113C8×C11—22no—
114C8×C11—44no—
115#533—111no—
116#532—111no—
117#488—222no—
118#487—112no—
119#486—112no—
120#431C2×D1112yes—
121C2×#107—221no—
122C2×#106—221no—
123#416—221no—
124#416—221no—
125C2×C4×C8C2×D1111yescharacteristic
126#382—112no—
127#328—224no—
128#327—224no—
129#322—22no—
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#41711yescharacteristic
139C4×C11#41711yescharacteristic
140C4×C11#48911yescharacteristic
141C4×C11#48911yescharacteristic
142Dic11—81no—
143Dic11—82no—
144Dic11—162no—
145C2×#41—221no—
146C22×C8D4411yescharacteristic
147C22×C8D4411yescharacteristic
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—222no—
159C2×C42C22×D1111yescharacteristic
160#107—442no—
161#106—442no—
162C4⋊C8—22no—
163#103—222no—
164#103—222no—
165#102—222no—
166#102—222no—
167C22⋊C8D4414yes—
168C4×C8—22no—
169C4×C8C4×D1112yes—
170C4×C8C22⋊D1112yes—
171#95—222no—
172#95—222no—
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—441no—
188C22×C4—442no—
189C22×C4C2×D4412yes—
190C22×C4C2×D4411yescharacteristic
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—24no—
196C2×C8(C2×D11)⋊C412yes—
197C2×C8(C2×D11)⋊C412yes—
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—222no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C4⋊C4—442no—
204C22⋊C4—441no—
205C22⋊C4—442no—
206C42—441no—
207C42C2×C4×D1111yescharacteristic
208C42#433912yes—
209C42C2×C22⋊D1111yescharacteristic
210C11#975811yescharacteristic, complemented, Sylow
211C23—441no—
212C23#6692711yescharacteristic
213Q8—441no—
214Q8—441no—
215Q8—882no—
216D4—441no—
217D4—441no—
218D4—882no—
219D4—881no—
220D4—881no—
221C2×C4—42no—
222C2×C4—442no—
223C2×C4—441no—
224C2×C4—881no—
225C2×C4—881no—
226C2×C4—884no—
227C2×C4—882no—
228C2×C4C4×D4412yes—
229C2×C4#6692811yescharacteristic
230C2×C4#6696111yescharacteristic
231C2×C4#6696111yescharacteristic
232C2×C4#6696211yescharacteristic
233C2×C4#6696211yescharacteristic
234C2×C4C2×(C2×D11)⋊C411yescharacteristic
235C2×C4#6698312yes—
236C8—22no—
237C8—22no—
238C8—44no—
239C22—22no—
240C22—881no—
241C22—882no—
242C22#1062232511yescharacteristic
243C22#1062232811yescharacteristic
244C22#1062255211yescharacteristic
245C4—22no—
246C4—22no—
247C4—881no—
248C4—882no—
249C4—1762no—
250C4#1062232711yescharacteristic
251C4#1062232711yescharacteristic
252C4#1062274611yescharacteristic
253C4#1062274611yescharacteristic
254C2—21no—
255C2—21no—
256C2—1761no—
257C2#1306943211yescharacteristic
258C2#1306951412yes—
subgroupG/H
centerC22#10622552
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1452C2
socleC22×C11#390
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1452D11
hypocenterC11#9758
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1452

Complements

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

NH ≅ G/Ntype
2. #13068780C2semidirect
3. #13067181C2semidirect
5. C11×#1452C2semidirect
16. #10622307C4semidirect
17. #10622294C4semidirect
86. #1452D11semidirect
210. C11#9758semidirect

Maximal subgroups

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

subgroupindex
#130789392
#130687802
#130671812
#130671772
C11×#14522
#975811