Finite Group Databasebeta

← D11×#2568 #14925743

Subgroups — D11×#2568 #14925743

Order 2816.

2614 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic
3#13073833C212yesmaximal, complemented
4#13073832C211yesmaximal, characteristic, complemented
5#13073831C211yesmaximal, characteristic, complemented
6#13073830C214yesmaximal, complemented
7#13073829C212yesmaximal, complemented
8#13073828C211yesmaximal, characteristic, complemented
9#13073827C214yesmaximal, complemented
10D11×#400C214yesmaximal
11D11×#391C212yesmaximal
12D11×#391C214yesmaximal
13D11×#382C212yesmaximal
14C4×C4⋊C4×D11C211yesmaximal, characteristic
15C11×#2568C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2212yes—
17C22×Q8×D11C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66997C2212yes—
22D11×C4⋊Q8—28no—
23C4×Q8×D11—28no—
24C2×C4⋊C4×D11C2212yes—
25C2×C4⋊C4×D11C2212yes—
26C2×C4⋊C4×D11C2212yes—
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×C4⋊C4×D11C2212yes—
29C2×#66941C2212yes—
30C2×#66941C2212yes—
31C2×#66940C2212yes—
32C2×#66940C2211yescharacteristic
33C2×C42×D11C2212yes—
34C2×C42×D11C2212yes—
35C2×C42×D11C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C2×C4×Dic22C2212yes—
38C2×C4×Dic22C2211yescharacteristic
39C11×#400C2214yes—
40C11×#391C2214yes—
41C11×#391C2212yes—
42C11×#382C2212yes—
43C4×C11×C4⋊C4C2211yescharacteristic
44#10622843C2212yes—
45#10622843C2214yes—
46#10622599C2214yes—
47#10622595C2214yes—
48#10622590C2212yes—
49#10622590C2212yes—
50C4⋊C4×Dic11C2212yes—
51#10622587C2212yes—
52#10622587C2214yes—
53#10622549C2212yes—
54C4×C4⋊Dic11C2211yescharacteristic
55C4×Dic11⋊C4C2212yes—
56#10622542C2214yes—
57#10622542C2212yes—
58D11×#95C2212yes—
59D11×#95C2218yes—
60D11×#95C2218yes—
61#10622273C2218yes—
62#10622272C2214yes—
63#10622271C2218yes—
64#10622263C2218yes—
65#10622262C2212yes—
66#10622259C2218yes—
67#10622259C2218yes—
68#10622259C2218yes—
69C22×Q8×C11C2312yes—
70C22×Q8×C11C2311yescharacteristic
71C2×Q8×D11—24no—
72C2×Q8×D11—28no—
73C2×Q8×D11—24no—
74C2×Q8×D11—216no—
75C2×Q8×D11Q818yescomplemented
76C22×C4×D11C2312yes—
77C22×C4×D11C2314yes—
78C22×C4×D11C2314yes—
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2312yes—
81C22×C4×D11C2311yescharacteristic
82C22×C4×D11C2311yescharacteristic
83C22×Dic22C2312yes—
84C22×Dic22C2314yes—
85C22×Dic22C2312yes—
86C22×Dic22C2311yescharacteristic
87C11×C4⋊Q8—24no—
88C4×Q8×C11—24no—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C42×C11C2312yes—
95C2×C42×C11C2312yes—
96C2×C42×C11C2311yescharacteristic
97Q8×Dic11—24no—
98#66997—28no—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2312yes—
104C2×Dic11⋊C4C2312yes—
105C2×Dic11⋊C4C2312yes—
106C2×Dic11⋊C4C2312yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2312yes—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C4⋊C4×D11—28no—
119C4⋊C4×D11—28no—
120C4⋊C4×D11—24no—
121C4⋊C4×D11—28no—
122C4⋊C4×D11—28no—
123#66941—28no—
124#66941—28no—
125#66940—24no—
126#66940—28no—
127C42×D11—28no—
128C42×D11—28no—
129C42×D11D418yes—
130#66922—24no—
131C4×Dic22—24no—
132C4×Dic22—28no—
133C11×#95C2318yes—
134C11×#95C2318yes—
135C11×#95C2312yes—
136C11⋊#95C2318yes—
137C11⋊#95C2318yes—
138C11⋊#95C2318yes—
139C11⋊#95C2318yes—
140C11⋊#95C2318yes—
141C11⋊#95C2318yes—
142C11⋊#95C2312yes—
143C11⋊#95C2314yes—
144C2×#2568—111nomaximal, Sylow
145C23×D11C2411yescharacteristic
146C2×Q8×C11—22no—
147C2×Q8×C11—24no—
148C2×Q8×C11—22no—
149C2×Q8×C11—28no—
150C2×Q8×C11C2×Q814yescomplemented
151C22×C4×C11C2414yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2411yescharacteristic
155C22×C4×C11C2412yes—
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2411yescharacteristic
162C22×Dic11C2412yes—
163C22×Dic11C2411yescharacteristic
164C22×Dic11C2411yescharacteristic
165Q8×D11—232no—
166Q8×D11—432no—
167C2×C4×D11—24no—
168C2×C4×D11—24no—
169C2×C4×D11—28no—
170C2×C4×D11—24no—
171C2×C4×D11—28no—
172C2×C4×D11—28no—
173C2×C4×D11—216no—
174C2×C4×D11—24no—
175C2×C4×D11—28no—
176C2×C4×D11—28no—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2×D414yes—
179C2×C4×D11C2×D414yes—
180C2×C4×D11C2×Q818yes—
181C2×C4×D11C2×Q814yes—
182C2×C4×D11#4114yes—
183C2×C4×D11#4118yes—
184C2×Dic22—24no—
185C2×Dic22—24no—
186C2×Dic22—28no—
187C2×Dic22—216no—
188C2×Dic22—22no—
189C2×Dic22—24no—
190C2×Dic22—22no—
191C2×Dic22—28no—
192C2×Dic22C2×Q818yescomplemented
193C2×Dic22C2×Q814yescomplemented
194C11×C4⋊C4—24no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C42×C11—24no—
200C42×C11—24no—
201C42×C11C2×D414yes—
202C4⋊Dic11—24no—
203C4⋊Dic11—22no—
204C4⋊Dic11—24no—
205C4⋊Dic11—24no—
206C4⋊Dic11—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—28no—
210Dic11⋊C4—28no—
211Dic11⋊C4—28no—
212Dic11⋊C4—24no—
213C4×Dic11—24no—
214C4×Dic11—24no—
215C4×Dic11—28no—
216C4×Dic11—24no—
217C4×Dic11—24no—
218C4×Dic11C2×D414yes—
219C4×Dic11C2×D414yes—
220C4×Dic11C2×D414yes—
221C22×C4⋊Q8—111no—
222C22×C4×Q8—111no—
223#2568—114no—
224#2568—114no—
225#2568—112no—
226#2568—112no—
227#2568—111no—
228#2568—111no—
229#2568—111no—
230#2568D1111yescharacteristic, direct product factor
231C2×#400—114no—
232C2×#391—112no—
233C2×#391—114no—
234C2×#382—112no—
235C2×C4×C4⋊C4—111no—
236C23×C11C2511yescharacteristic
237C22×D11C22×D412yes—
238C22×D11C22×Q812yes—
239C22×D11C2×#4112yes—
240C22×D11C2×#4114yes—
241C22×D112−1+414yes—
242Q8×C11—28no—
243Q8×C11—48no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—28no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×Q814yes—
258C2×C4×C11C22×Q812yes—
259C2×C4×C11C2×#4112yes—
260C2×C4×C11C2×#4114yes—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—28no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11C22×D412yes—
272C2×Dic11C22×D412yes—
273C2×Dic11C22×D412yes—
274C2×Dic11C22×Q814yes—
275C2×Dic11C22×Q812yes—
276C2×Dic11C2×#4112yes—
277C2×Dic11C2×#4114yes—
278C4×D11—216no—
279C4×D11—28no—
280C4×D11—416no—
281C4×D11—48no—
282C4×D11—416no—
283C4×D11C22⋊Q8116yes—
284C4×D11#124116yes—
285Dic22—28no—
286Dic22—216no—
287Dic22—48no—
288Dic22—416no—
289C23×Q8—111no—
290C23×Q8—112no—
291C2×C4⋊Q8—112no—
292C2×C4⋊Q8—112no—
293C2×C4⋊Q8—112no—
294C2×C4⋊Q8—111no—
295C2×C4⋊Q8—228no—
296C2×C4⋊Q8C2×D1111yescharacteristic
297C2×C4×Q8—111no—
298C2×C4×Q8—112no—
299C2×C4×Q8—111no—
300C2×C4×Q8—112no—
301C2×C4×Q8—111no—
302C2×C4×Q8—228no—
303C2×C4×Q8C2×D1111yescharacteristic
304C22×C4⋊C4—112no—
305C22×C4⋊C4—112no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4—112no—
308C22×C4⋊C4—112no—
309C22×C42—111no—
310C22×C42—112no—
311C22×C42—112no—
312#400—114no—
313#400—114no—
314#400—118no—
315#400—114no—
316#400—118no—
317#400C2×D1114yes—
318#391—114no—
319#391—112no—
320#391—114no—
321#391—112no—
322#391—114no—
323#391—112no—
324#391—118no—
325#391—118no—
326#391—118no—
327#391C2×D1114yes—
328#391C2×D1112yes—
329#382—112no—
330#382—112no—
331#382—112no—
332#382—118no—
333#382C2×D1112yes—
334C4×C4⋊C4—112no—
335C4×C4⋊C4—112no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—112no—
338C4×C4⋊C4C2×D1111yescharacteristic
339C2×#95—112no—
340C2×#95—118no—
341C2×#95—118no—
342C22×C11C23×D411yescharacteristic
343C22×C11C23×Q811yescharacteristic
344C22×C11C22×#4111yescharacteristic
345C22×C11C22×#4112yes—
346C22×C11C2×2−1+412yes—
347C2×D11C2×C22⋊Q814yes—
348C2×D11C2×#12414yes—
349C2×D11#53614yes—
350C2×D11#55618yes—
351C2×D11#55718yes—
352C4×C11—24no—
353C4×C11—22no—
354C4×C11—44no—
355C4×C11—42no—
356C4×C11—44no—
357C4×C11C2×C22⋊Q814yes—
358C4×C11C2×#12414yes—
359Dic11—24no—
360Dic11—22no—
361Dic11—44no—
362Dic11—42no—
363Dic11—44no—
364Dic11C2×C22⋊Q814yes—
365Dic11C2×#12414yes—
366C22×Q8—118no—
367C22×Q8—112no—
368C22×Q8—111no—
369C22×Q8—114no—
370C22×Q8—112no—
371C22×Q8—224no—
372C22×Q8—224no—
373C22×Q8—228no—
374C22×Q8—2216no—
375C22×Q8C22×D1112yes—
376C22×Q8C22×D1111yescharacteristic
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4—112no—
381C23×C4—114no—
382C23×C4—112no—
383C23×C4—114no—
384C4⋊Q8—24no—
385C4⋊Q8—228no—
386C4⋊Q8—228no—
387C4⋊Q8—228no—
388C4⋊Q8—224no—
389C4×Q8—24no—
390C4×Q8—228no—
391C4×Q8—224no—
392C4×Q8—228no—
393C4×Q8—224no—
394C4×Q8—224no—
395C2×C4⋊C4—112no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—228no—
408C2×C4⋊C4—228no—
409C2×C4⋊C4—228no—
410C2×C4⋊C4—228no—
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1112yes—
415C2×C4⋊C4C22×D1112yes—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—118no—
420C2×C42—112no—
421C2×C42—112no—
422C2×C42—112no—
423C2×C42—114no—
424C2×C42—112no—
425C2×C42—228no—
426C2×C42—228no—
427C2×C42C22×D1112yes—
428C2×C42C22×D1112yes—
429C2×C42C22×D1111yescharacteristic
430#95—114no—
431#95—112no—
432#95—118no—
433#95—118no—
434#95—118no—
435#95—118no—
436#95—118no—
437#95—118no—
438#95C22×D1112yes—
439#95C22×D1118yes—
440#95C22×D1118yes—
441C2×C11C22×C22⋊Q811yescharacteristic
442C2×C11C22×#12411yescharacteristic
443C2×C11C2×#53611yescharacteristic
444C2×C11C2×#55612yes—
445C2×C11C2×#55712yes—
446D11#256818yesdirect product factor
447C24—111no—
448C2×Q8—22no—
449C2×Q8—24no—
450C2×Q8—22no—
451C2×Q8—28no—
452C2×Q8—118no—
453C2×Q8—114no—
454C2×Q8—224no—
455C2×Q8—224no—
456C2×Q8—228no—
457C2×Q8—2216no—
458C2×Q8—2232no—
459C2×Q8—222no—
460C2×Q8—224no—
461C2×Q8—222no—
462C2×Q8—228no—
463C2×Q8—4432no—
464C2×Q8Q8×D1114yescomplemented
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—114no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—118no—
472C22×C4—112no—
473C22×C4—111no—
474C22×C4—114no—
475C22×C4—118no—
476C22×C4—114no—
477C22×C4—112no—
478C22×C4—114no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—228no—
484C22×C4—228no—
485C22×C4—228no—
486C22×C4—2216no—
487C22×C4—228no—
488C22×C4—228no—
489C22×C4C23×D1114yes—
490C22×C4C23×D1112yes—
491C22×C4C23×D1114yes—
492C22×C4C23×D1111yescharacteristic
493C22×C4C23×D1112yes—
494C22×C4C23×D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—224no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—228no—
505C4⋊C4—228no—
506C4⋊C4—228no—
507C4⋊C4—224no—
508C4⋊C4—222no—
509C4⋊C4—224no—
510C4⋊C4—224no—
511C4⋊C4—224no—
512C42—24no—
513C42—24no—
514C42—114no—
515C42—114no—
516C42—114no—
517C42—224no—
518C42—224no—
519C42—228no—
520C42—224no—
521C42—224no—
522C42D4×D1114yes—
523C11C2×#256811yescharacteristic, complemented, Sylow
524C23—112no—
525C23—112no—
526C23—114no—
527C23—112no—
528C23—114no—
529C23C24×D1111yescharacteristic
530Q8—28no—
531Q8—48no—
532Q8—2216no—
533Q8—228no—
534Q8—4416no—
535Q8—448no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—28no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—112no—
550C2×C4—114no—
551C2×C4—1116no—
552C2×C4—1116no—
553C2×C4—112no—
554C2×C4—114no—
555C2×C4—2216no—
556C2×C4—228no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—228no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—4416no—
568C2×C4—4416no—
569C2×C4—448no—
570C2×C4C2×D4×D1112yes—
571C2×C4C2×D4×D1112yes—
572C2×C4C2×D4×D1112yes—
573C2×C4C2×Q8×D1114yes—
574C2×C4C2×Q8×D1112yes—
575C2×C4#41×D1112yes—
576C2×C4#41×D1114yes—
577C22—114no—
578C22—118no—
579C22—114no—
580C22—118no—
581C22—114no—
582C22C22×D4×D1111yescharacteristic
583C22C22×Q8×D1111yescharacteristic
584C22C2×#41×D1112yes—
585C22C2×#41×D1111yescharacteristic
586C22D11×2−1+412yes—
587C4—22no—
588C4—24no—
589C4—44no—
590C4—44no—
591C4—42no—
592C4—114no—
593C4—114no—
594C4—222no—
595C4—224no—
596C4—444no—
597C4—444no—
598C4—442no—
599C4D11×C22⋊Q814yes—
600C4D11×#12414yes—
601C2—118no—
602C2C2×D11×C22⋊Q811yescharacteristic
603C2C2×D11×#12411yescharacteristic
604C2D11×#53611yescharacteristic
605C2D11×#55612yes—
606C2D11×#55712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2568C2
prime radicalC23×D11C24
hypercenter#2568D11
hypocenterC11C2×#2568
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2568

Complements

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

NH ≅ G/Ntype
3. #13073833C2semidirect
4. #13073832C2semidirect
5. #13073831C2semidirect
6. #13073830C2semidirect
7. #13073829C2semidirect
8. #13073828C2semidirect
9. #13073827C2semidirect
15. C11×#2568C2semidirect
75. C2×Q8×D11Q8semidirect
150. C2×Q8×C11C2×Q8semidirect
192. C2×Dic22C2×Q8semidirect
193. C2×Dic22C2×Q8semidirect
230. #2568D11direct (N × H)
446. D11#2568direct (N × H)
464. C2×Q8Q8×D11semidirect
523. C11C2×#2568semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×C4×Q8×D112
#130738332
#130738322
#130738312
#130738302
#130738292
#130738282
#130738272
D11×#4002
D11×#3912
D11×#3822
C4×C4⋊C4×D112
C11×#25682
C2×#256811