Finite Group Databasebeta

← D11×#2971 #15618270

Subgroups — D11×#2971 #15618270

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D11C211yesmaximal, characteristic
2#13077636C211yesmaximal, characteristic, complemented
3#13077635C212yesmaximal, complemented
4#13077634C213yesmaximal, complemented
5#13077633C213yesmaximal, complemented
6#13077632C216yesmaximal, complemented
7C8×Q8×D11C212yesmaximal, complemented
8D11×#436C216yesmaximal, complemented
9D11×#432C213yesmaximal, complemented
10C4×M16×D11C213yesmaximal, complemented
11C11×#2971C211yesmaximal, characteristic, complemented
12C2×#41×D11C411yescharacteristic
13C4×C11×#41C2211yescharacteristic
14#41×Dic11C411yescharacteristic
15C2×M16×D11C2216yes—
16C4×#4343C411yescharacteristic
17C4×#4343C2211yescharacteristic
18C4×Q8×D11C411yescharacteristic
19C4×Q8×D11C2211yescharacteristic
20C4×D4×D11C413yes—
21C4×D4×D11C2213yes—
22C4×#4341C413yes—
23C4×#4341C2213yes—
24#10623053C413yes—
25D11×#117C413yes—
26C4×#4339C2213yes—
27C2×C42×D11C2213yes—
28C8×Q8×C11C2212yescomplemented
29C11×#436C2216yescomplemented
30C11×#432C2213yescomplemented
31C4×C11×M16C2213yescomplemented
32#10622741C22112yescomplemented
33M16×Dic11C2216yescomplemented
34Q8×C11⋊C8C2212yescomplemented
35#10622625C2216yescomplemented
36#10622539C2213yescomplemented
37C4×#4318C2213yescomplemented
38#10622451C2216yescomplemented
39#10622448C2216yescomplemented
40D11×C4⋊C8C2216yes—
41#10622443C2216yescomplemented
42#10622342C22112yescomplemented
43D11×C22⋊C8C2216yes—
44#10622332C2216yescomplemented
45#10622320C2213yescomplemented
46#10622320C2213yescomplemented
47#10622318C2216yescomplemented
48D11×#97C2211yescharacteristic
49D11×#97C2213yes—
50#10622301C2216yescomplemented
51C4×#4313C2216yescomplemented
52C4×C8×D11C2216yes—
53C8×Dic22C2216yescomplemented
54C2×C11×#41C2×C411yescharacteristic
55#41×D11—28no—
56C2×#4343C2×C411yescharacteristic
57C2×Q8×D11C2×C411yescharacteristic
58C2×#4341C2×C413yes—
59C2×D4×D11C2×C413yes—
60C2×#4339C2×C413yes—
61C22×C4×D11C2×C413yes—
62C22×C4×D11C2×C413yes—
63C22×C4×D11C2313yes—
64C2×C11×M16C2316yes—
65C4×Q8×C11C2×C411yescharacteristic
66C4×Q8×C11C2311yescharacteristic
67C4×D4×C11C2×C413yes—
68C4×D4×C11C2313yes—
69C11×#117C2×C413yes—
70C2×C42×C11C2313yes—
71Q8×Dic11C2×C411yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73D4×Dic11C2×C413yes—
74D4×Dic11C2×C413yes—
75C4×C22⋊D11C2×C416yes—
76C4×C22⋊D11C2316yes—
77#66979C2×C413yes—
78C2×C4×Dic11C2×C413yes—
79C2×C4×Dic11C2×C413yes—
80C2×C4×Dic11C2313yes—
81C2×#4318C2316yes—
82M16×D11—224no—
83C2×#4313C2316yes—
84C2×#4313C2316yes—
85C2×C8×D11C2316yes—
86C2×C8×D11C2312yes—
87#66946C2×C413yes—
88#66946C2×C413yes—
89#66945C2×C413yes—
90#66945C2×C413yes—
91C4⋊C4×D11C2×C413yes—
92C4⋊C4×D11C2×C413yes—
93#66940C2×C413yes—
94#66940C2×C413yes—
95(C22⋊D11)⋊C4C2×C416yes—
96(C22⋊D11)⋊C4C2×C416yes—
97C22⋊C4×D11C2×C416yes—
98#66930C2×C416yes—
99C4×D44C2×C413yes—
100C4×D44C2313yes—
101#66925C2×C416yes—
102C42×D11C2×C413yes—
103C42×D11C2×C413yes—
104C42×D11C2×C413yes—
105C42×D11C2×C413yes—
106C42×D11C2311yescharacteristic
107C42×D11C2313yes—
108C42×D11C2313yes—
109C42×D11C2313yes—
110C4×Dic22C2×C413yes—
111C4×Dic22C2313yes—
112C11×C4⋊C8C2316yes—
113C11×C22⋊C8C2316yes—
114C11×#97C2313yes—
115C11×#97C2311yescharacteristic
116C4×C8×C11C2316yes—
117C22⋊(C11⋊C8)C2316yes—
118(C2×D11)⋊C8C23112yes—
119#66879C2312yes—
120#66879C2316yes—
121Dic11⋊C8C23112yes—
122C8×Dic11C2316yes—
123C8×Dic11C2316yes—
124C4⋊(C11⋊C8)C2316yes—
125#66867C2311yescharacteristic
126#66867C2313yes—
127C4×C11⋊C8C2316yes—
128C2×#2971—111nomaximal, Sylow
129C23×D11C22×C413yes—
130C11×#41—24no—
131C2×Q8×C11C22×C411yescharacteristic
132C2×D4×C11C22×C413yes—
133C22×C4×C11C22×C413yes—
134C22×C4×C11C22×C413yes—
135C22×C4×C11C2413yes—
136C2×C22⋊D11C22×C416yes—
137C22×Dic11C22×C413yes—
138C22×Dic11C22×C413yes—
139C22×Dic11C22×C413yes—
140#4343—24no—
141Q8×D11M1618yescomplemented
142#4341—212no—
143D4×D11—212no—
144#4339—212no—
145C2×D44C22×C413yes—
146C2×C4×D11—212no—
147C2×C4×D11—212no—
148C2×C4×D11—46no—
149C2×C4×D11C22×C411yescharacteristic
150C2×C4×D11C22×C411yescharacteristic
151C2×C4×D11C22×C413yes—
152C2×C4×D11C22×C413yes—
153C2×C4×D11C22×C413yes—
154C2×C4×D11C22×C413yes—
155C2×C4×D11C22×C413yes—
156C2×C4×D11C22×C413yes—
157C2×C4×D11C22×C413yes—
158C2×C4×D11C22×C413yes—
159C2×C4×D11C2413yes—
160C2×C4×D11C2411yescharacteristic
161C2×Dic22C22×C413yes—
162C11×M16—212no—
163C2×C8×C11C2416yes—
164C2×C8×C11C2412yes—
165C11×C4⋊C4C22×C413yes—
166C11×C4⋊C4C22×C413yes—
167C11×C22⋊C4C22×C416yes—
168C42×C11C22×C413yes—
169C42×C11C22×C413yes—
170C42×C11C2413yes—
171C42×C11C2411yescharacteristic
172C22⋊Dic11C22×C416yes—
173(C2×D11)⋊C4C22×C416yes—
174(C2×D11)⋊C4C22×C416yes—
175C4⋊Dic11C22×C413yes—
176C4⋊Dic11C22×C413yes—
177Dic11⋊C4C22×C416yes—
178Dic11⋊C4C22×C416yes—
179C4×Dic11C22×C413yes—
180C4×Dic11C22×C411yescharacteristic
181C4×Dic11C22×C411yescharacteristic
182C4×Dic11C22×C413yes—
183C4×Dic11C22×C413yes—
184C4×Dic11C22×C413yes—
185C4×Dic11C22×C413yes—
186C4×Dic11C22×C413yes—
187C4×Dic11C22×C413yes—
188C4×Dic11C22×C413yes—
189C4×Dic11C2413yes—
190C4×Dic11C2411yescharacteristic
191#4318—212no—
192C2×C11⋊C8C2416yes—
193C2×C11⋊C8C2412yes—
194#4313—212no—
195#4313—212no—
196C8×D11—212no—
197C8×D11#4118yescomplemented
198C2×C4×#41—111no—
199#2971—112no—
200#2971—116no—
201#2971—113no—
202#2971—113no—
203#2971—111no—
204#2971D1111yescharacteristic, direct product factor
205C2×C8×Q8—112no—
206C2×#436—116no—
207C2×#432—113no—
208C2×C4×M16—113no—
209C23×C11C23×C413yes—
210C22×D11—26no—
211C22×D11—26no—
212C22×D11—26no—
213C22×D11C23×C413yes—
214C22×D11C23×C411yescharacteristic
215Q8×C11C2×M1614yescomplemented
216D4×C11—26no—
217C2×C4×C11—26no—
218C2×C4×C11—26no—
219C2×C4×C11—43no—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C23×C413yes—
223C2×C4×C11C23×C413yes—
224C2×C4×C11C23×C413yes—
225C2×C4×C11C2511yescharacteristic
226C22⋊D11—212no—
227C2×Dic11—26no—
228C2×Dic11—26no—
229C2×Dic11—43no—
230C2×Dic11C23×C411yescharacteristic
231C2×Dic11C23×C411yescharacteristic
232C2×Dic11C23×C413yes—
233C2×Dic11C23×C413yes—
234C2×Dic11C23×C411yescharacteristic
235C2×Dic11C23×C413yes—
236D44—26no—
237C4×D11—26no—
238C4×D11—22no—
239C4×D11—22no—
240C4×D11—26no—
241C4×D11—26no—
242C4×D11—26no—
243C4×D11—26no—
244C4×D11—26no—
245C4×D11—43no—
246C4×D11—43no—
247C4×D11C2×M16112yes—
248C4×D11C2×#4114yes—
249Dic22C2×M16112yescomplemented
250C8×C11—26no—
251C8×C11C2×#4114yescomplemented
252C11⋊C8—26no—
253C11⋊C8C2×#4114yescomplemented
254C22×#41—111no—
255C22×M16—116no—
256C4×#41—111no—
257C4×#41—111no—
258C4×#41—111no—
259C4×#41—113no—
260C4×#41—113no—
261C4×#41—113no—
262C4×#41—113no—
263C4×#41C2×D1111yescharacteristic
264C2×C4×Q8—111no—
265C2×C4×Q8—111no—
266C2×C4×D4—113no—
267C2×C4×D4—113no—
268C2×#117—113no—
269C22×C42—113no—
270C8×Q8—112no—
271C8×Q8—116no—
272C8×Q8—116no—
273C8×Q8C2×D1112yescomplemented
274#436—1112no—
275#436—116no—
276#436—116no—
277#436—1112no—
278#436—116no—
279#436C2×D1116yescomplemented
280#432—113no—
281#432—116no—
282#432—116no—
283#432—116no—
284#432C2×D1113yescomplemented
285C2×C4⋊C8—116no—
286C2×C22⋊C8—116no—
287C4×M16—116no—
288C4×M16—113no—
289C4×M16—113no—
290C4×M16—113no—
291C4×M16—116no—
292C4×M16C2×D1113yescomplemented
293C2×#97—111no—
294C2×#97—113no—
295C2×C4×C8—116no—
296C22×C11—23no—
297C22×C11—23no—
298C22×C11—23no—
299C22×C11C24×C411yescharacteristic
300C2×D11—23no—
301C2×D11—23no—
302C2×D11—23no—
303C2×D11—412no—
304C2×D11C4×#4112yes—
305C2×D11C22×M1612yes—
306C2×D11#56812yes—
307C4×C11—23no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—23no—
311C4×C11C22×M1616yes—
312C4×C11C22×#4112yes—
313Dic11—23no—
314Dic11—21no—
315Dic11—21no—
316Dic11—23no—
317Dic11C4×#4112yes—
318Dic11C22×M1616yes—
319C2×#41—111no—
320C2×#41—113no—
321C2×#41—113no—
322C2×#41—228no—
323C2×#41C4×D1111yescharacteristic
324C22×Q8—111no—
325C22×D4—113no—
326C23×C4—113no—
327C23×C4—113no—
328C23×C4—113no—
329C2×M16—116no—
330C2×M16—116no—
331C2×M16—116no—
332C2×M16—2224no—
333C2×M16C22×D1116yes—
334C22×C8—112no—
335C22×C8—116no—
336C4×Q8—111no—
337C4×Q8—111no—
338C4×Q8—113no—
339C4×Q8—113no—
340C4×Q8—113no—
341C4×Q8—113no—
342C4×Q8C4×D1111yescharacteristic
343C4×Q8C22×D1111yescharacteristic
344C4×D4—113no—
345C4×D4—113no—
346C4×D4—116no—
347C4×D4—116no—
348C4×D4—113no—
349C4×D4—113no—
350C4×D4—116no—
351C4×D4—116no—
352C4×D4—113no—
353C4×D4—113no—
354C4×D4C4×D1113yes—
355C4×D4C22×D1113yes—
356#117—113no—
357#117—113no—
358#117—113no—
359#117—116no—
360#117—116no—
361#117C4×D1113yes—
362C2×C4⋊C4—113no—
363C2×C4⋊C4—113no—
364C2×C22⋊C4—116no—
365C2×C42—113no—
366C2×C42—113no—
367C2×C42—113no—
368C2×C42—113no—
369C2×C42—113no—
370C2×C42—113no—
371C2×C42—113no—
372C2×C42—113no—
373C2×C42—113no—
374C2×C42—113no—
375C2×C42—111no—
376C2×C42C22×D1113yes—
377C4⋊C8—1112no—
378C4⋊C8—116no—
379C4⋊C8C22×D1116yes—
380C22⋊C8—116no—
381C22⋊C8—1112no—
382C22⋊C8C22×D1116yes—
383#97—112no—
384#97—116no—
385#97—111no—
386#97—113no—
387#97C22×D1111yescharacteristic
388#97C22×D1113yes—
389C4×C8—116no—
390C4×C8—116no—
391C4×C8—116no—
392C4×C8C22×D1116yes—
393C2×C11—43no—
394C2×C11C2×C4×#4111yescharacteristic
395C2×C11C23×M1611yescharacteristic
396C2×C11C2×#56811yescharacteristic
397D11—43no—
398D11#297114yesdirect product factor
399C24—113no—
400#41—24no—
401#41—2212no—
402#41—2212no—
403#41—224no—
404C2×Q8—118no—
405C2×Q8—113no—
406C2×Q8C2×C4×D1111yescharacteristic
407C2×D4—116no—
408C2×D4—113no—
409C2×D4—2212no—
410C2×D4C2×C4×D1113yes—
411C22×C4—113no—
412C22×C4—111no—
413C22×C4—113no—
414C22×C4—113no—
415C22×C4—113no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—113no—
419C22×C4—113no—
420C22×C4—113no—
421C22×C4—113no—
422C22×C4—113no—
423C22×C4—113no—
424C22×C4—113no—
425C22×C4—113no—
426C22×C4—2212no—
427C22×C4—2212no—
428C22×C4—446no—
429C22×C4C2×C4×D1113yes—
430C22×C4C2×C4×D1113yes—
431C22×C4C23×D1113yes—
432M16—212no—
433M16—2212no—
434M16—2212no—
435M16—2212no—
436C2×C8—112no—
437C2×C8—118no—
438C2×C8—116no—
439C2×C8—2212no—
440C2×C8C23×D1116yes—
441C2×C8C23×D1112yes—
442C4⋊C4—116no—
443C4⋊C4—116no—
444C4⋊C4—113no—
445C4⋊C4—113no—
446C4⋊C4C2×C4×D1113yes—
447C4⋊C4C2×C4×D1113yes—
448C22⋊C4—116no—
449C22⋊C4—116no—
450C22⋊C4—116no—
451C22⋊C4C2×C4×D1116yes—
452C42—111no—
453C42—111no—
454C42—113no—
455C42—113no—
456C42—113no—
457C42—113no—
458C42—113no—
459C42—113no—
460C42—113no—
461C42—113no—
462C42—113no—
463C42—111no—
464C42C2×C4×D1113yes—
465C42C2×C4×D1113yes—
466C42C23×D1113yes—
467C42C23×D1111yescharacteristic
468C11C2×#297111yescharacteristic, complemented, Sylow
469C23—111no—
470C23—113no—
471C23—226no—
472C23—226no—
473C23—226no—
474C23C22×C4×D1113yes—
475Q8—1112no—
476Q8M16×D1114yescomplemented
477D4—26no—
478D4—2212no—
479D4—226no—
480C2×C4—26no—
481C2×C4—26no—
482C2×C4—43no—
483C2×C4—111no—
484C2×C4—113no—
485C2×C4—1112no—
486C2×C4—114no—
487C2×C4—111no—
488C2×C4—111no—
489C2×C4—113no—
490C2×C4—113no—
491C2×C4—226no—
492C2×C4—226no—
493C2×C4—222no—
494C2×C4—226no—
495C2×C4—222no—
496C2×C4—226no—
497C2×C4—226no—
498C2×C4—226no—
499C2×C4—226no—
500C2×C4—226no—
501C2×C4—443no—
502C2×C4—443no—
503C2×C4—443no—
504C2×C4C22×C4×D1111yescharacteristic
505C2×C4C22×C4×D1111yescharacteristic
506C2×C4C22×C4×D1113yes—
507C2×C4C22×C4×D1113yes—
508C2×C4C22×C4×D1113yes—
509C2×C4C24×D1111yescharacteristic
510C8—26no—
511C8—114no—
512C8—226no—
513C8#41×D1114yescomplemented
514C22—23no—
515C22—23no—
516C22—23no—
517C22—112no—
518C22—112no—
519C22—112no—
520C22—223no—
521C22—223no—
522C22—223no—
523C22—4412no—
524C22C23×C4×D1111yescharacteristic
525C4—21no—
526C4—21no—
527C4—23no—
528C4—23no—
529C4—116no—
530C4—112no—
531C4—221no—
532C4—221no—
533C4—223no—
534C4—223no—
535C4C2×M16×D1116yes—
536C4C2×#41×D1112yes—
537C2—43no—
538C2—114no—
539C2—443no—
540C2C4×#41×D1111yescharacteristic
541C2C22×M16×D1111yescharacteristic
542C2D11×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2971C2
prime radicalC2×#41×D11C4
cosocleC2×C4×C11C25
hypercenter#2971D11
hypocenterC11C2×#2971
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #13077636C2semidirect
3. #13077635C2semidirect
4. #13077634C2semidirect
5. #13077633C2semidirect
6. #13077632C2semidirect
7. C8×Q8×D11C2semidirect
8. D11×#436C2semidirect
9. D11×#432C2semidirect
10. C4×M16×D11C2semidirect
11. C11×#2971C2semidirect
28. C8×Q8×C11C22semidirect
29. C11×#436C22semidirect
30. C11×#432C22semidirect
31. C4×C11×M16C22semidirect
32. #10622741C22semidirect
33. M16×Dic11C22semidirect
34. Q8×C11⋊C8C22semidirect
35. #10622625C22semidirect
36. #10622539C22semidirect
37. C4×#4318C22semidirect
38. #10622451C22semidirect
39. #10622448C22semidirect
41. #10622443C22semidirect
42. #10622342C22semidirect
44. #10622332C22semidirect
45. #10622320C22semidirect
46. #10622320C22semidirect
47. #10622318C22semidirect
50. #10622301C22semidirect
51. C4×#4313C22semidirect
53. C8×Dic22C22semidirect
141. Q8×D11M16semidirect
197. C8×D11#41semidirect
204. #2971D11direct (N × H)
215. Q8×C11C2×M16semidirect
249. Dic22C2×M16semidirect
251. C8×C11C2×#41semidirect
253. C11⋊C8C2×#41semidirect
273. C8×Q8C2×D11semidirect
279. #436C2×D11semidirect
284. #432C2×D11semidirect
292. C4×M16C2×D11semidirect
398. D11#2971direct (N × H)
468. C11C2×#2971semidirect
476. Q8M16×D11semidirect
513. C8#41×D11semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D112
#130776362
#130776352
#130776342
#130776332
#130776322
C8×Q8×D112
D11×#4362
D11×#4322
C4×M16×D112
C11×#29712
C2×#297111