Finite Group Databasebeta

← #14722350

Subgroups — #14722350

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077248C212yesmaximal
3#13067354C211yesmaximal, characteristic, complemented
4#13067353C212yesmaximal, complemented
5#13067331C214yesmaximal, complemented
6#13067279C214yesmaximal, complemented
7C11×#1561C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623259C2212yes—
10D11×C4⋊Q8C2212yes—
11#10623219C412yes—
12D11×#125C412yes—
13D11×C22⋊Q8—22no—
14#10623153—22no—
15#10623109—22no—
16C4×Q8×D11—22no—
17D11×#117C412yes—
18#10623048C412yes—
19C2×C42×D11C2211yescharacteristic
20#10623001C2211yescharacteristic
21C11×#423C2212yes—
22#10622739—22no—
23M16×Dic11—22no—
24#10622537C2212yes—
25#10622448—22no—
26#10622448C2214yes—
27#10622446—22no—
28#10622446C2214yes—
29C11×#332C2214yescomplemented
30#10622185C2214yescomplemented
31#10622124C2214yescomplemented
32#10622120C2214yescomplemented
33C2×Q8×D11—22no—
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11D412yes—
36C2×C11×M16—22no—
37C11×C4⋊Q8C2312yes—
38C11×#125C2×C412yes—
39C11×C22⋊Q8—22no—
40C4×Q8×C11—22no—
41C11×#117C2×C412yes—
42C2×C42×C11C2311yescharacteristic
43#66999—22no—
44Q8×Dic11—22no—
45#66997—22no—
46#66979C2×C412yes—
47#66977—22no—
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11D412yes—
50C2×#4318—22no—
51#66950—22no—
52#66949—24no—
53#66945C2×C414yes—
54C4⋊C4×D11—24no—
55C4⋊C4×D11—22no—
56C4⋊C4×D11C2×C414yes—
57#66943C2×C414yes—
58#66942—24no—
59#66941—22no—
60#66941C2×C414yes—
61#66940—24no—
62#66940—22no—
63C22⋊C4×D11—22no—
64#66931—24no—
65#66930—22no—
66#66925—22no—
67C42×D11—22no—
68C42×D11C2×C411yescharacteristic
69C42×D11C2×C411yescharacteristic
70C42×D11D412yes—
71C42×D11D412yes—
72C42×D11C2311yescharacteristic
73C42×D11C2311yescharacteristic
74#66923C2×C412yes—
75#66922C2312yes—
76C4×Dic22—22no—
77C4×Dic22—24no—
78C11×C4⋊C8—22no—
79C11×C4⋊C8C2314yes—
80(C2×D11)⋊C8—24no—
81(C2×D11)⋊C8—24no—
82#66879—24no—
83C8×Dic11—24no—
84C4⋊(C11⋊C8)—22no—
85C4⋊(C11⋊C8)C2314yes—
86#17739—111nomaximal, Sylow
87C23×D11C22⋊C411yescharacteristic
88C2×Q8×C11—22no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D412yes—
91C22×Dic11C22⋊C411yescharacteristic
92C22×Dic11C22⋊C412yes—
93Q8×D11—44no—
94Q8×D11—44no—
95C2×C4×D11—24no—
96C2×C4×D11—24no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×C4×D11C22⋊C411yescharacteristic
100C2×C4×D11C22⋊C412yes—
101C2×C4×D11C22⋊C412yes—
102C2×C4×D11C22⋊C411yescharacteristic
103C2×C4×D11C22×C411yescharacteristic
104C2×C4×D11C22×C411yescharacteristic
105C2×C4×D11C2×D412yes—
106C2×C4×D11C2×D412yes—
107C2×Dic22—24no—
108C2×Dic22—22no—
109C11×M16—44no—
110C2×C8×C11—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4C22×C414yes—
114C11×C22⋊C4—22no—
115C42×C11—22no—
116C42×C11C22×C411yescharacteristic
117C42×C11C2×D412yes—
118C42×C11C2411yescharacteristic
119C22⋊Dic11—22no—
120(C2×D11)⋊C4—24no—
121C4⋊Dic11—24no—
122C4⋊Dic11—22no—
123C4⋊Dic11C22×C414yes—
124Dic11⋊C4—24no—
125Dic11⋊C4—24no—
126Dic11⋊C4—24no—
127Dic11⋊C4—24no—
128C4×Dic11—24no—
129C4×Dic11—22no—
130C4×Dic11C22⋊C412yes—
131C4×Dic11C22⋊C412yes—
132C4×Dic11C22⋊C412yes—
133C4×Dic11C22×C411yescharacteristic
134C4×Dic11C22×C411yescharacteristic
135C4×Dic11C2×D412yes—
136C4×Dic11C2×D412yes—
137#4318—44no—
138C2×C11⋊C8—24no—
139C2×#533—111no—
140#2920—112no—
141#1561—112no—
142#1561—111no—
143#1561D1111yescharacteristic, complemented
144#1556—114no—
145#1544—114no—
146C23×C11C2×C22⋊C411yescharacteristic
147C22×D11—22no—
148C22×D11—42no—
149C22×D11C2×C22⋊C411yescharacteristic
150C22×D11C2×C22⋊C411yescharacteristic
151Q8×C11—42no—
152Q8×C11—42no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11C2×C22⋊C412yes—
158C2×C4×C11C2×C22⋊C411yescharacteristic
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D412yes—
161C2×Dic11—22no—
162C2×Dic11—24no—
163C2×Dic11—42no—
164C2×Dic11C2×C22⋊C412yes—
165C2×Dic11C2×C22⋊C412yes—
166C2×Dic11C2×C22⋊C411yescharacteristic
167C2×Dic11C2×C22⋊C411yescharacteristic
168C4×D11—22no—
169C4×D11—22no—
170C4×D11—22no—
171C4×D11—22no—
172C4×D11—22no—
173C4×D11—22no—
174C4×D11—22no—
175C4×D11—42no—
176C4×D11—42no—
177C4×D11—48no—
178C4×D11#10114yes—
179Dic22—48no—
180Dic22—42no—
181Dic22—42no—
182C8×C11—44no—
183C11⋊C8—44no—
184#533—112no—
185#533—112no—
186#533—112no—
187#533—111no—
188#533—222no—
189#533—222no—
190#533C2×D1111yescharacteristic
191C2×C4⋊Q8—112no—
192C2×#125—112no—
193C2×C22⋊Q8—222no—
194C2×C4×Q8—222no—
195C2×#117—112no—
196C22×C42—111no—
197#432—114no—
198#432—222no—
199#431—114no—
200#431—222no—
201#423—112no—
202#423C2×D1112yes—
203#407—222no—
204C4×M16—222no—
205#332—114no—
206#332—114no—
207#332—114no—
208#332C2×D1114yescomplemented
209C22×C11—21no—
210C22×C11—22no—
211C22×C11C22×C22⋊C411yescharacteristic
212C2×D11—22no—
213C2×D11—21no—
214C2×D11—22no—
215C2×D11—44no—
216C2×D11C2×#10112yes—
217C4×C11—21no—
218C4×C11—22no—
219C4×C11—44no—
220C4×C11C2×#10112yes—
221C4×C11#57512yes—
222C4×C11#57512yes—
223Dic11—21no—
224Dic11—22no—
225Dic11—22no—
226Dic11—44no—
227Dic11C2×#10112yes—
228C22×Q8—222no—
229C23×C4—111no—
230C23×C4—112no—
231C2×M16—22no—
232C2×M16—222no—
233C4⋊Q8—114no—
234C4⋊Q8—112no—
235C4⋊Q8—222no—
236C4⋊Q8—222no—
237C4⋊Q8C22×D1112yes—
238#125—114no—
239#125—112no—
240#125—224no—
241#125C4×D1112yes—
242C22⋊Q8—22no—
243C22⋊Q8—224no—
244C22⋊Q8—224no—
245C22⋊Q8—222no—
246C22⋊Q8—222no—
247C22⋊Q8—222no—
248C4×Q8—22no—
249C4×Q8—224no—
250C4×Q8—224no—
251C4×Q8—222no—
252C4×Q8—222no—
253C4×Q8—222no—
254#117—112no—
255#117—114no—
256#117—222no—
257#117—222no—
258#117C4×D1112yes—
259C2×C4⋊C4—114no—
260C2×C4⋊C4—224no—
261C2×C4⋊C4—222no—
262C2×C22⋊C4—222no—
263C2×C42—111no—
264C2×C42—112no—
265C2×C42—111no—
266C2×C42—111no—
267C2×C42—112no—
268C2×C42—112no—
269C2×C42—111no—
270C2×C42—111no—
271C2×C42—222no—
272C2×C42C22×D1111yescharacteristic
273C4⋊C8—22no—
274C4⋊C8—114no—
275C4⋊C8—222no—
276C4⋊C8C22×D1114yes—
277C22⋊C8—224no—
278C22⋊C8—224no—
279#97—224no—
280C4×C8—224no—
281C2×C11—41no—
282C2×C11C22×#10111yescharacteristic
283C2×C11#289612yes—
284D11—22no—
285D11—41no—
286C24—111no—
287C2×Q8—22no—
288C2×Q8—224no—
289C2×Q8—222no—
290C2×Q8—444no—
291C2×Q8—444no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—112no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—112no—
299C22×C4—112no—
300C22×C4—112no—
301C22×C4—112no—
302C22×C4—224no—
303C22×C4—224no—
304C22×C4—442no—
305C22×C4—442no—
306C22×C4C2×C4×D1111yescharacteristic
307C22×C4D4×D1112yes—
308M16—44no—
309M16—444no—
310C2×C8—24no—
311C2×C8—224no—
312C4⋊C4—24no—
313C4⋊C4—22no—
314C4⋊C4—114no—
315C4⋊C4—224no—
316C4⋊C4—224no—
317C4⋊C4—224no—
318C4⋊C4—224no—
319C4⋊C4—224no—
320C4⋊C4—222no—
321C4⋊C4C2×C4×D1114yes—
322C22⋊C4—22no—
323C22⋊C4—224no—
324C22⋊C4—222no—
325C42—22no—
326C42—112no—
327C42—112no—
328C42—112no—
329C42—111no—
330C42—111no—
331C42—112no—
332C42—112no—
333C42—224no—
334C42—222no—
335C42C2×C4×D1111yescharacteristic
336C42D4×D1112yes—
337C42C23×D1111yescharacteristic
338C11#1773911yescharacteristic, complemented, Sylow
339C23—111no—
340C23—111no—
341C23—222no—
342C23—442no—
343C23C22⋊C4×D1111yescharacteristic
344Q8—42no—
345Q8—42no—
346Q8—448no—
347Q8—442no—
348Q8—442no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—111no—
354C2×C4—114no—
355C2×C4—111no—
356C2×C4—112no—
357C2×C4—112no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—224no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—448no—
370C2×C4—442no—
371C2×C4C22⋊C4×D1112yes—
372C2×C4C22⋊C4×D1111yescharacteristic
373C2×C4C22×C4×D1111yescharacteristic
374C2×C4C2×D4×D1112yes—
375C8—44no—
376C8—444no—
377C22—21no—
378C22—22no—
379C22—112no—
380C22—222no—
381C22—221no—
382C22—222no—
383C22—444no—
384C22C2×C22⋊C4×D1111yescharacteristic
385C4—21no—
386C4—22no—
387C4—44no—
388C4—112no—
389C4—221no—
390C4—222no—
391C4—222no—
392C4—444no—
393C4D11×#10112yes—
394C4#1062330412yes—
395C4#1062330812yes—
396C2—41no—
397C2—222no—
398C2—441no—
399C2C2×D11×#10111yescharacteristic
400C2#1307713212yes—
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1561C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1561D11
hypocenterC11#17739
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

Complements

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

NH ≅ G/Ntype
3. #13067354C2semidirect
4. #13067353C2semidirect
5. #13067331C2semidirect
6. #13067279C2semidirect
7. C11×#1561C2semidirect
29. C11×#332C22semidirect
30. #10622185C22semidirect
31. #10622124C22semidirect
32. #10622120C22semidirect
143. #1561D11semidirect
208. #332C2×D11semidirect
338. C11#17739semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130772482
#130673542
#130673532
#130673312
#130672792
C11×#15612
#1773911