Finite Group Databasebeta

← #14651445

Subgroups — #14651445

Order 2816.

424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 99 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#13077701C211yesmaximal, characteristic
2#13073803C211yesmaximal, characteristic
3#13067242C212yesmaximal
4#13066473C212yesmaximal
5C11×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66923C2211yescharacteristic
8C11×#432C2212yes—
9#10622843C411yescharacteristic
10#10622843C411yescharacteristic
11#10622637—24no—
12#10622597—21no—
13#10622597—21no—
14#10622590C411yescharacteristic
15#10622589C411yescharacteristic
16C4×C4⋊Dic11C2211yescharacteristic
17#10622546—21no—
18#10622546—21no—
19#10622539—21no—
20#10622539C2212yes—
21#10622538—21no—
22C11×#324—21no—
23C11×#324—21no—
24#10622103—24no—
25C22×Q8×C11C2×C411yescharacteristic
26C4×Q8×C11—22no—
27C4×Q8×C11—22no—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11C2×C411yescharacteristic
43#66923—22no—
44#66923—22no—
45C11×C4⋊C8—22no—
46C11×C22⋊C8—22no—
47C11×#97—22no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59#66867—22no—
60#66867D414yes—
61C4×C11⋊C8—22no—
62#9450—111nomaximal, Sylow
63C2×Q8×C11—22no—
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C2×C8×C11—42no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11C2×D412yes—
86C42×C11#4112yes—
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89C4⋊Dic11—42no—
90Dic11⋊C4—42no—
91Dic11⋊C4—42no—
92Dic11⋊C4—41no—
93Dic11⋊C4—42no—
94Dic11⋊C4—41no—
95C4×Dic11—41no—
96C4×Dic11—41no—
97C2×C11⋊C8—24no—
98#2983—111no—
99#2565—111no—
100#1534—112no—
101#1467D1111yescharacteristic
102#1285—112no—
103C23×C11C2×C22⋊C411yescharacteristic
104Q8×C11—44no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11#10112yes—
119C2×C4×C11C4×D412yes—
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12112yes—
122C2×C4×C11#12311yescharacteristic
123C2×Dic11—22no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—42no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C8×C11—82no—
135C11⋊C8—44no—
136C2×#125—111no—
137C2×C4×Q8C2×D1111yescharacteristic
138#446—224no—
139#432—112no—
140#432—221no—
141#432C2×D1112yes—
142#431—221no—
143#398—221no—
144#398—221no—
145#391—111no—
146#391—111no—
147#387—221no—
148#387—221no—
149#384—111no—
150#382—111no—
151C4×C4⋊C4—111no—
152#330—224no—
153#324—21no—
154#324—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11#38611yescharacteristic
158C22×C11C2×#10111yescharacteristic
159C22×C11#41311yescharacteristic
160C4×C11—22no—
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168Dic11—42no—
169Dic11—81no—
170Dic11—81no—
171Dic11—81no—
172C22×Q8C4×D1111yescharacteristic
173#125—222no—
174#125—222no—
175C4×Q8—22no—
176C4×Q8—22no—
177C2×C4⋊C4—111no—
178C2×C4⋊C4—111no—
179C2×C4⋊C4—221no—
180C2×C4⋊C4—221no—
181C2×C4⋊C4—221no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4C4×D1111yescharacteristic
185C2×C4⋊C4C22⋊D1111yescharacteristic
186C2×C4⋊C4C22⋊D1111yescharacteristic
187C2×C42—111no—
188C2×C42—111no—
189C2×C42D4411yescharacteristic
190C2×C42D4411yescharacteristic
191C2×C42C22×D1111yescharacteristic
192C4⋊C8—22no—
193C4⋊C8—222no—
194C4⋊C8—222no—
195C4⋊C8—222no—
196C22⋊C8—22no—
197C22⋊C8—222no—
198#97—22no—
199#97—114no—
200#97—222no—
201C4×C8—222no—
202#95—221no—
203#95—221no—
204#95—221no—
205#95—221no—
206#95—221no—
207#95—221no—
208#95—221no—
209C2×C11—21no—
210C2×C11—21no—
211C2×C11#188411yescharacteristic
212C2×C11#190111yescharacteristic
213C2×C11#191211yescharacteristic
214C2×Q8—22no—
215C2×Q8—22no—
216C2×Q8—41no—
217C22×C4—221no—
218C22×C4—221no—
219C22×C4—221no—
220C22×C4—221no—
221C22×C4(C2×D11)⋊C411yescharacteristic
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4C2×C4×D1111yescharacteristic
226C22×C4C2×D4411yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228C2×C8—42no—
229C2×C8—224no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—222no—
234C4⋊C4—222no—
235C4⋊C4—442no—
236C4⋊C4—442no—
237C4⋊C4—442no—
238C4⋊C4—441no—
239C4⋊C4—441no—
240C4⋊C4—442no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—441no—
246C42—441no—
247C42D4×D1112yes—
248C42#434112yes—
249C11#945011yescharacteristic, complemented, Sylow
250C23C2×(C2×D11)⋊C411yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—222no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4—441no—
269C2×C4—441no—
270C2×C4—441no—
271C2×C4—441no—
272C2×C4—442no—
273C2×C4—441no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4#6688812yes—
277C2×C4(C22⋊D11)⋊C412yes—
278C2×C4#6693511yescharacteristic
279C2×C4#6693911yescharacteristic
280C2×C4#6699212yes—
281C8—82no—
282C8—444no—
283C22—21no—
284C22—21no—
285C22#1062257111yescharacteristic
286C22#1062274511yescharacteristic
287C22C2×#6688811yescharacteristic
288C4—22no—
289C4—22no—
290C4—21no—
291C4—21no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—442no—
297C4—881no—
298C4—881no—
299C4—881no—
300C2—21no—
301C2—21no—
302C2#1306899711yescharacteristic
303C2#1306908211yescharacteristic
304C2#1306915111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1467C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1467D11
hypocenterC11#9450
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
249. C11#9450semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130738032
#130672422
#130664732
C11×#14672
#945011