Finite Group Databasebeta

← D11×#2054 #14781698

Subgroups — D11×#2054 #14781698

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D8×D11C211yesmaximal, characteristic
2C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
3C2×D11×#102C212yesmaximal, complemented
4D11×#390C212yesmaximal, complemented
5#13069928C211yesmaximal, characteristic, complemented
6#13069927C211yesmaximal, characteristic, complemented
7#13069926C212yesmaximal, complemented
8#13069925C212yesmaximal, complemented
9#13069924C211yesmaximal, characteristic, complemented
10D11×#340C211yesmaximal, characteristic, complemented
11C11×#2054C211yesmaximal, characteristic, complemented
12C22×D4×D11C2212yes—
13C22×C11×D8C2211yescharacteristic
14C22×#4323C2212yes—
15C2×D8×D11—28no—
16C2×D8×D11—24no—
17C22×D88C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2212yes—
21C2×C22⋊C4×D11—22no—
22C2×C22⋊C4×D11—22no—
23C2×C42×D11C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic, complemented
25C2×C11×#102C2212yescomplemented
26C11×#390C2212yescomplemented
27#10622834C2212yescomplemented
28C2×#66896C2212yescomplemented
29C2×#66885C2212yescomplemented
30C2×Dic11⋊C8C2211yescharacteristic, complemented
31C2×Dic11⋊C8C2211yescharacteristic, complemented
32#10622601C2212yescomplemented
33C2×#66873C2212yescomplemented
34#10622570—22no—
35#10622570—22no—
36#10622552C2212yescomplemented
37C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
38D11×C4⋊C8—24no—
39D11×#102—28no—
40C11×#340C2211yescharacteristic, complemented
41#10622189C2211yescharacteristic, complemented
42#10622167C2212yescomplemented
43C24×D11—22no—
44C22×D4×C11C2312yes—
45C22×C22⋊D11—22no—
46C2×D4×D11—24no—
47C2×D4×D11—24no—
48C2×D4×D11—24no—
49C2×D4×D11—24no—
50C2×D4×D11—24no—
51C2×D4×D11D418yes—
52C22×D44C2312yes—
53C22×C4×D11—22no—
54C22×C4×D11D411yescharacteristic
55C22×C4×D11D411yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C2×C11×D8—24no—
58C2×C11×D8—22no—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×#4323—24no—
68C2×#4323—24no—
69C2×#4323—24no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4⋊Dic11C2312yes—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81D8×D11—232no—
82C2×D88—24no—
83C2×D88—22no—
84C2×C8×D11—24no—
85C2×C8×D11—24no—
86C2×C8×D11—22no—
87C2×C8×D11D414yes—
88C4⋊C4×D11—24no—
89C4⋊C4×D11—24no—
90C22⋊C4×D11—48no—
91C22⋊C4×D11—48no—
92C42×D11—22no—
93C42×D11—22no—
94C11×C4⋊C8—22no—
95C11×#102—24no—
96#66896—24no—
97#66885—24no—
98Dic11⋊C8—22no—
99Dic11⋊C8—22no—
100#66873—24no—
101C4⋊(C11⋊C8)—22no—
102C2×#2054—111nomaximal, Sylow
103C24×C11—22no—
104C23×D11—22no—
105C23×D11—28no—
106C23×D11—44no—
107C23×D11—44no—
108C23×D11—44no—
109C23×D11—44no—
110C23×D11—44no—
111C23×D11—44no—
112C23×D11C2×D411yescharacteristic
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11C2×D414yes—
119C22×C4×C11—22no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—28no—
124C2×C22⋊D11—44no—
125C2×C22⋊D11—44no—
126C22×Dic11—22no—
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130D4×D11—216no—
131D4×D11—216no—
132D4×D11—48no—
133D4×D11—48no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44C2×D414yes—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—24no—
144C2×C4×D11—44no—
145C2×C4×D11—44no—
146C2×C4×D11—44no—
147C2×C4×D11D814yescomplemented
148C2×C4×D11C2×D414yes—
149C2×C4×D11C2×D412yes—
150C2×C4×D11#4112yes—
151C2×C4×D11#4114yes—
152C11×D8—28no—
153C2×C8×C11—22no—
154C2×C8×C11—21no—
155C2×C8×C11—22no—
156C2×C8×C11C2×D412yes—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C22⋊C4—44no—
160C11×C22⋊C4—44no—
161C42×C11—21no—
162C42×C11—21no—
163C22⋊Dic11—44no—
164C22⋊Dic11—44no—
165#4323—216no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—44no—
168(C2×D11)⋊C4—44no—
169(C2×D11)⋊C4—44no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172Dic11⋊C4—44no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8C2×D412yes—
181D88—28no—
182C8×D11—28no—
183C8×D11—44no—
184C23×D8—111no—
185C22×C4⋊C8—111no—
186C22×#102—112no—
187C2×#390—112no—
188#2054—111no—
189#2054—112no—
190#2054—112no—
191#2054—111no—
192#2054—111no—
193#2054D1111yescharacteristic, direct product factor
194C2×#340—111no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11C22×D411yescharacteristic
203C22×D11—24no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—416no—
211C22×D11—416no—
212C22×D11—416no—
213C22×D11—88no—
214C22×D11—88no—
215C22×D11—88no—
216C22×D11—88no—
217C22×D11#12114yes—
218C22×D11#12112yes—
219C22×D11C2×D812yes—
220C22×D11#13512yes—
221C22×D11AGL(1,ℤ/8)14yes—
222D4×C11—24no—
223D4×C11—24no—
224D4×C11—42no—
225D4×C11—42no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11C2×D812yescomplemented
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4112yes—
238C22⋊D11—416no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—22no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11#12112yes—
247C2×Dic11#12114yes—
248C2×Dic11C2×D812yescomplemented
249D44—24no—
250D44—24no—
251D44—42no—
252D44—42no—
253C4×D11—28no—
254C4×D11—44no—
255C4×D11—88no—
256C4×D11#12014yes—
257C4×D11#12318yes—
258C4×D11#12414yes—
259C8×C11—22no—
260C8×C11—41no—
261C11⋊C8—22no—
262C11⋊C8—41no—
263C23×D4—112no—
264C22×D8—112no—
265C22×D8—111no—
266C22×D8—224no—
267C22×D8—228no—
268C22×D8C2×D1111yescharacteristic
269C23×C8—111no—
270C23×C8—111no—
271C22×C4⋊C4—112no—
272C22×C22⋊C4—222no—
273C22×C22⋊C4—222no—
274C22×C42—111no—
275C2×C4⋊C8—111no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—224no—
279C2×C4⋊C8C2×D1111yescharacteristic, complemented
280C2×#102—112no—
281C2×#102—112no—
282C2×#102—112no—
283C2×#102—228no—
284C2×#102C2×D1112yescomplemented
285#390—112no—
286#390—112no—
287#390—112no—
288#390—222no—
289#390—222no—
290#390C2×D1112yescomplemented
291#340—111no—
292#340—112no—
293#340C2×D1111yescharacteristic, complemented
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11C2×#12112yes—
302C22×C11C2×#12111yescharacteristic
303C22×C11C22×D811yescharacteristic
304C22×C11C2×#13511yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)12yes—
306C2×D11—44no—
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—82no—
310C2×D11—82no—
311C2×D11—82no—
312C2×D11—82no—
313C2×D11—832no—
314C2×D11#39414yes—
315C2×D11#45918yes—
316C2×D11#46318yes—
317C2×D11#46614yes—
318C2×D11#46914yes—
319C4×C11—22no—
320C4×C11—41no—
321C4×C11—82no—
322C4×C11C2×#12011yescharacteristic
323C4×C11C2×#12312yes—
324C4×C11C2×#12411yescharacteristic
325Dic11—22no—
326Dic11—41no—
327Dic11—82no—
328Dic11#39414yes—
329C25—222no—
330C22×D4—118no—
331C22×D4—112no—
332C22×D4—224no—
333C22×D4—224no—
334C22×D4—224no—
335C22×D4—224no—
336C22×D4—224no—
337C22×D4—222no—
338C22×D4C22×D1112yes—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—222no—
343C2×D8—24no—
344C2×D8—22no—
345C2×D8—224no—
346C2×D8—224no—
347C2×D8—2232no—
348C2×D8—224no—
349C2×D8—224no—
350C2×D8—222no—
351C22×C8—111no—
352C22×C8—114no—
353C22×C8—111no—
354C22×C8—224no—
355C22×C8—224no—
356C22×C8—222no—
357C22×C8C22×D1111yescharacteristic
358C22×C8C22×D1111yescharacteristic
359C2×C4⋊C4—112no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—448no—
373C2×C22⋊C4—448no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—222no—
378C2×C42—222no—
379C2×C42C22×D1111yescharacteristic
380C4⋊C8—22no—
381C4⋊C8—222no—
382C4⋊C8—222no—
383C4⋊C8—222no—
384#102—24no—
385#102—224no—
386#102—224no—
387#102—224no—
388C2×C11—84no—
389C2×C11C2×#39411yescharacteristic
390C2×C11C2×#45912yes—
391C2×C11C2×#46312yes—
392C2×C11C2×#46611yescharacteristic
393C2×C11C2×#46911yescharacteristic
394D11—84no—
395D11#205418yesdirect product factor
396C24—22no—
397C24—111no—
398C24—228no—
399C24—222no—
400C24—444no—
401C24—444no—
402C24—444no—
403C24—444no—
404C24—444no—
405C24—444no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—114no—
412C2×D4—2216no—
413C2×D4—2216no—
414C2×D4—228no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—222no—
418C2×D4—222no—
419C2×D4—222no—
420C2×D4—448no—
421C2×D4—448no—
422C2×D4—444no—
423C2×D4—444no—
424C2×D4D4×D1114yes—
425C22×C4—22no—
426C22×C4—111no—
427C22×C4—112no—
428C22×C4—114no—
429C22×C4—112no—
430C22×C4—114no—
431C22×C4—111no—
432C22×C4—114no—
433C22×C4—111no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—444no—
440C22×C4—444no—
441C22×C4—444no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445D8—28no—
446D8—228no—
447D8—2216no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—21no—
451C2×C8—112no—
452C2×C8—228no—
453C2×C8—222no—
454C2×C8—222no—
455C2×C8—221no—
456C2×C8—444no—
457C2×C8D4×D1112yes—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—444no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C22⋊C4—444no—
466C22⋊C4—444no—
467C22⋊C4—444no—
468C22⋊C4—444no—
469C22⋊C4—444no—
470C22⋊C4—444no—
471C42—21no—
472C42—21no—
473C42—222no—
474C42—222no—
475C42—221no—
476C42—221no—
477C11C2×#205411yescharacteristic, complemented, Sylow
478C23—24no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—112no—
486C23—112no—
487C23—114no—
488C23—112no—
489C23—114no—
490C23—224no—
491C23—4416no—
492C23—4416no—
493C23—4416no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23—442no—
500C23—888no—
501C23—888no—
502C23—888no—
503C23—888no—
504C23C2×D4×D1111yescharacteristic
505D4—24no—
506D4—24no—
507D4—42no—
508D4—42no—
509D4—224no—
510D4—224no—
511D4—4416no—
512D4—442no—
513D4—442no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—112no—
522C2×C4—114no—
523C2×C4—114no—
524C2×C4—118no—
525C2×C4—114no—
526C2×C4—112no—
527C2×C4—228no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—222no—
531C2×C4—221no—
532C2×C4—444no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—888no—
537C2×C4D8×D1112yescomplemented
538C2×C4C2×D4×D1112yes—
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#41×D1112yes—
542C8—22no—
543C8—41no—
544C8—222no—
545C8—441no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22—118no—
554C22—118no—
555C22—114no—
556C22—114no—
557C22—114no—
558C22—444no—
559C22—444no—
560C22—444no—
561C22—8832no—
562C22—882no—
563C22—882no—
564C22—882no—
565C22—882no—
566C22D11×#12112yes—
567C22D11×#12111yescharacteristic
568C22C2×D8×D1111yescharacteristic
569C22D11×#13511yescharacteristic
570C22D11×AGL(1,ℤ/8)12yes—
571C4—22no—
572C4—41no—
573C4—82no—
574C4—114no—
575C4—222no—
576C4—441no—
577C4—882no—
578C4D11×#12011yescharacteristic
579C4D11×#12312yes—
580C4D11×#12411yescharacteristic
581C2—84no—
582C2—118no—
583C2—884no—
584C2D11×#39411yescharacteristic
585C2D11×#45912yes—
586C2D11×#46312yes—
587C2D11×#46611yescharacteristic
588C2D11×#46911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2054C2
socleC23×C11C22×D4
prime radicalC22×D8×D11C2
hypercenter#2054D11
hypocenterC11C2×#2054
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2054

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊C8C2semidirect
3. C2×D11×#102C2semidirect
4. D11×#390C2semidirect
5. #13069928C2semidirect
6. #13069927C2semidirect
7. #13069926C2semidirect
8. #13069925C2semidirect
9. #13069924C2semidirect
10. D11×#340C2semidirect
11. C11×#2054C2semidirect
24. C2×C11×C4⋊C8C22semidirect
25. C2×C11×#102C22semidirect
26. C11×#390C22semidirect
27. #10622834C22semidirect
28. C2×#66896C22semidirect
29. C2×#66885C22semidirect
30. C2×Dic11⋊C8C22semidirect
31. C2×Dic11⋊C8C22semidirect
32. #10622601C22semidirect
33. C2×#66873C22semidirect
36. #10622552C22semidirect
37. C2×C4⋊(C11⋊C8)C22semidirect
40. C11×#340C22semidirect
41. #10622189C22semidirect
42. #10622167C22semidirect
147. C2×C4×D11D8semidirect
193. #2054D11direct (N × H)
233. C2×C4×C11C2×D8semidirect
248. C2×Dic11C2×D8semidirect
279. C2×C4⋊C8C2×D11semidirect
284. C2×#102C2×D11semidirect
290. #390C2×D11semidirect
293. #340C2×D11semidirect
395. D11#2054direct (N × H)
477. C11C2×#2054semidirect
537. C2×C4D8×D11semidirect

Maximal subgroups

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

subgroupindex
C22×D8×D112
C2×D11×C4⋊C82
C2×D11×#1022
D11×#3902
#130699282
#130699272
#130699262
#130699252
#130699242
D11×#3402
C11×#20542
C2×#205411