Finite Group Databasebeta

← #14649283

Subgroups — #14649283

Order 2816.

546 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 139 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#13071323C211yesmaximal, characteristic
2#13067008C212yesmaximal
3#13066940C211yesmaximal, characteristic, complemented
4#13066444C212yesmaximal, complemented
5C11×#2982C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#67000C411yescharacteristic
8C2×C4×D44C2211yescharacteristic
9C8×Q8×C11—24no—
10C11×#431—22no—
11C11×#431C2212yes—
12#10622843C411yescharacteristic
13#10622602—22no—
14#10622601C411yescharacteristic
15#10622589C411yescharacteristic
16#10622553—22no—
17#10622545C2211yescharacteristic
18#10622538C2212yes—
19#10622166—22no—
20#10622097—24no—
21C22×Q8×C11C2×C411yescharacteristic
22C22×D44C2×C411yescharacteristic
23C22×C4×D11—21no—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C2×C11×C4⋊C4C2×C411yescharacteristic
27C2×C11×C4⋊C4D412yes—
28C2×C42×C11D412yes—
29C2×C42×C11C2311yescharacteristic
30#67000—22no—
31#67000C814yescomplemented
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—22no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—22no—
37C2×C4×Dic11C2×C411yescharacteristic
38C2×C4×Dic11C2×C411yescharacteristic
39C4×D44—22no—
40C4×D44—22no—
41C11×C4⋊C8—24no—
42C11×C4⋊C8—22no—
43C11×C22⋊C8—22no—
44C4×C8×C11—24no—
45C4×C8×C11D414yes—
46C11⋊#95—22no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C22⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51C4×C11⋊C8—22no—
52#9102—111nomaximal, Sylow
53C23×D11—21no—
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C2×Q8×C11C2×C812yes—
57C2×Q8×C11M1612yes—
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×D44—22no—
67C2×D44—21no—
68C2×D44—22no—
69C2×D44C2×C812yes—
70C2×C4×D11—42no—
71C2×C4×D11—82no—
72C2×C8×C11—24no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—24no—
75C42×C11—22no—
76C42×C11—22no—
77C42×C11C2×D412yes—
78C42×C11#4112yes—
79(C2×D11)⋊C4—28no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82(C2×D11)⋊C4—82no—
83C4⋊Dic11—22no—
84Dic11⋊C4—82no—
85C4×Dic11—21no—
86C4×Dic11—22no—
87C4×Dic11C2×C812yes—
88C2×C11⋊C8—42no—
89#2982D1111yescharacteristic, complemented
90#2326—111no—
91#1478—112no—
92#1461—111no—
93#1274—112no—
94C23×C11C2×C22⋊C411yescharacteristic
95C22×D11—22no—
96C22×D11—42no—
97C22×D11—42no—
98C22×D11—41no—
99C22×D11—41no—
100Q8×C11—24no—
101Q8×C11—24no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—42no—
108C2×C4×C11C22⋊C814yes—
109C2×C4×C11C4×D412yes—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11#12112yes—
112C2×C4×C11#12311yescharacteristic
113C2×C4×C11C22×C811yescharacteristic
114C2×C4×C11C2×M1611yescharacteristic
115C2×C4×C11#13112yes—
116C2×Dic11—22no—
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—42no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—41no—
124D44—24no—
125D44—42no—
126C4×D11—84no—
127C8×C11—44no—
128C11⋊C8—82no—
129C2×#124—111no—
130C2×C4×Q8C2×D1111yescharacteristic
131C2×C4×D4—111no—
132C8×Q8—24no—
133#431—22no—
134#431—112no—
135#431C2×D1112yes—
136#391—111no—
137#390—111no—
138#388—222no—
139#385—222no—
140#384—111no—
141#376—111no—
142D4⋊C8—224no—
143#324—222no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11#38611yescharacteristic
147C22×C11C2×C22⋊C811yescharacteristic
148C22×C11#40811yescharacteristic
149C2×D11—44no—
150C2×D11—42no—
151C2×D11—82no—
152C2×D11—81no—
153C2×D11—81no—
154C4×C11—24no—
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—42no—
159C4×C11C8×D412yes—
160C4×C11#43512yes—
161Dic11—42no—
162Dic11—81no—
163Dic11—81no—
164C22×Q8C4×D1111yescharacteristic
165C22×D4—111no—
166C23×C4—221no—
167#124—114no—
168#124—222no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×D4—222no—
172C4×D4—222no—
173C2×C4⋊C4—111no—
174C2×C4⋊C4—222no—
175C2×C4⋊C4C4×D1111yescharacteristic
176C2×C4⋊C4D4412yes—
177C2×C22⋊C4—222no—
178C2×C22⋊C4—221no—
179C2×C22⋊C4—222no—
180C2×C42—111no—
181C2×C42—111no—
182C2×C42C22⋊D1112yes—
183C2×C42C22×D1111yescharacteristic
184C4⋊C8—24no—
185C4⋊C8—22no—
186C4⋊C8—222no—
187C22⋊C8—22no—
188C22⋊C8—222no—
189C4×C8—24no—
190C4×C8—222no—
191C4×C8C22⋊D1114yes—
192#95—222no—
193#95—221no—
194#95—221no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11#186911yescharacteristic
198C2×C11#191011yescharacteristic
199C2×C11#191211yescharacteristic
200D11—82no—
201C24—221no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8C8×D1112yes—
205C2×Q8#431312yes—
206C2×D4—112no—
207C2×D4—221no—
208C2×D4—222no—
209C2×D4—222no—
210C22×C4—221no—
211C22×C4—221no—
212C22×C4—221no—
213C22×C4—442no—
214C22×C4—882no—
215C22×C4(C2×D11)⋊C412yes—
216C22×C4(C2×D11)⋊C412yes—
217C22×C4C2×C4×D1111yescharacteristic
218C22×C4C2×D4411yescharacteristic
219C22×C4C2×C22⋊D1111yescharacteristic
220C2×C8—24no—
221C2×C8—442no—
222C4⋊C4—22no—
223C4⋊C4—24no—
224C4⋊C4—222no—
225C4⋊C4—882no—
226C22⋊C4—228no—
227C22⋊C4—441no—
228C22⋊C4—441no—
229C22⋊C4—882no—
230C42—22no—
231C42—22no—
232C42—112no—
233C42—221no—
234C42—222no—
235C42#433912yes—
236C42C2×C22⋊D1112yes—
237C11#910211yescharacteristic, complemented, Sylow
238C23—222no—
239C23—442no—
240C23—442no—
241C23—441no—
242C23—441no—
243C23C2×(C2×D11)⋊C411yescharacteristic
244Q8—24no—
245Q8—24no—
246D4—224no—
247D4—442no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—222no—
255C2×C4—441no—
256C2×C4—441no—
257C2×C4—441no—
258C2×C4—442no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—884no—
263C2×C4(C2×D11)⋊C814yes—
264C2×C4C2×C8×D1111yescharacteristic
265C2×C4C2×#431311yescharacteristic
266C2×C4#6695412yes—
267C2×C4C4×C22⋊D1112yes—
268C2×C4#6698211yescharacteristic
269C2×C4#6698312yes—
270C2×C4#6700611yescharacteristic
271C8—44no—
272C8—882no—
273C22—21no—
274C22—21no—
275C22—444no—
276C22—442no—
277C22—882no—
278C22—881no—
279C22—881no—
280C22C2×(C2×D11)⋊C811yescharacteristic
281C22#1062272311yescharacteristic
282C22#1062282611yescharacteristic
283C4—22no—
284C4—21no—
285C4—21no—
286C4—24no—
287C4—42no—
288C4—442no—
289C4—881no—
290C4—881no—
291C4C8×C22⋊D1112yes—
292C4#1062272412yes—
293C2—21no—
294C2—21no—
295C2—882no—
296C2#1306890811yescharacteristic
297C2#1306914311yescharacteristic
298C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#2982C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#2982D11
hypocenterC11#9102
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
3. #13066940C2semidirect
4. #13066444C2semidirect
5. C11×#2982C2semidirect
31. #67000C8semidirect
89. #2982D11semidirect
237. C11#9102semidirect

Maximal subgroups

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

subgroupindex
#130713232
#130670082
#130669402
#130664442
C11×#29822
#910211