Finite Group Databasebeta

← D11×#2092 #14783526

Subgroups — D11×#2092 #14783526

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#107C211yesmaximal, characteristic, complemented
2C2×D11×#106C211yesmaximal, characteristic, complemented
3C2×D11×#102C211yesmaximal, characteristic
4C2×D11×#102C211yesmaximal, characteristic
5D11×#390C211yesmaximal, characteristic
6D11×#382C211yesmaximal, characteristic, complemented
7#13070140C211yesmaximal, characteristic, complemented
8#13070139C211yesmaximal, characteristic, complemented
9#13070138C211yesmaximal, characteristic, complemented
10#13070137C211yesmaximal, characteristic, complemented
11#13070136C211yesmaximal, characteristic, complemented
12#13070135C211yesmaximal, characteristic, complemented
13#13070134C211yesmaximal, characteristic, complemented
14D11×#336C211yesmaximal, characteristic, complemented
15C11×#2092C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C22⋊C4×D11—22no—
23C2×C42×D11C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic, complemented
25C2×C11×#106C2211yescharacteristic, complemented
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#382C2211yescharacteristic, complemented
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66882C2211yescharacteristic, complemented
36C2×#66881C2211yescharacteristic, complemented
37#10622601C2211yescharacteristic
38#10622590C2211yescharacteristic, complemented
39#10622590C2211yescharacteristic, complemented
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic, complemented
43C2×#66872C2211yescharacteristic, complemented
44C2×#66871C2211yescharacteristic, complemented
45C2×#66871C2211yescharacteristic, complemented
46#10622570—22no—
47#10622552C2211yescharacteristic
48#10622549C2211yescharacteristic, complemented
49D11×#107—24no—
50D11×#106—24no—
51D11×#102—24no—
52D11×#102—24no—
53D11×#95—22no—
54#10622263—22no—
55C11×#336C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622162C2211yescharacteristic, complemented
59C24×D11—21no—
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C2×D4×D11—22no—
63C2×D4×D11—22no—
64C2×D4×D11—22no—
65C2×D4×D11—22no—
66C2×D4×D11—22no—
67C2×D4×D11Q814yes—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11D412yes—
73C22×C4×D11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—22no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11D412yes—
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×C8×D11—22no—
95C2×C8×D11—22no—
96C2×C8×D11—22no—
97C2×C8×D11—22no—
98C2×C8×D11D414yes—
99C2×C8×D11D414yes—
100C4⋊C4×D11—22no—
101C4⋊C4×D11—22no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—22no—
106C22⋊C4×D11—48no—
107C42×D11—22no—
108C42×D11—22no—
109C11×#107—22no—
110C11×#106—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#95—22no—
114#66896—22no—
115#66896—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119#66885—22no—
120#66885—22no—
121#66882—22no—
122#66881—22no—
123#66873—22no—
124#66873—22no—
125#66872—22no—
126#66872—22no—
127#66871—22no—
128#66871—22no—
129C2×#2092—111nomaximal, Sylow
130C24×C11—21no—
131C23×D11—21no—
132C23×D11—24no—
133C23×D11—42no—
134C23×D11—42no—
135C23×D11—44no—
136C23×D11—44no—
137C23×D11C2×D411yescharacteristic
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—24no—
150C2×C22⋊D11—42no—
151C2×C22⋊D11—42no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11C2×D412yes—
156C22×Dic11C2×D411yescharacteristic
157D4×D11—28no—
158D4×D11—28no—
159D4×D11—44no—
160D4×D11—44no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44C2×Q812yes—
167C2×C4×D11—24no—
168C2×C4×D11—24no—
169C2×C4×D11—24no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—44no—
174C2×C4×D11—44no—
175C2×C4×D11—44no—
176C2×C4×D11C2×D412yes—
177C2×C4×D11C2×D412yes—
178C2×C4×D11C2×Q812yes—
179C2×C4×D11#4112yes—
180C2×C4×D11#4112yes—
181C2×C4×D11#4112yes—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C2×D412yes—
187C2×C8×C11C2×D412yes—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C22⋊C4—44no—
195C42×C11—21no—
196C42×C11—21no—
197C22⋊Dic11—44no—
198(C2×D11)⋊C4—44no—
199(C2×D11)⋊C4—44no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209C4×Dic11—24no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8C2×D412yes—
218C8×D11—28no—
219C8×D11—28no—
220C22×#107—111no—
221C22×#106—111no—
222C22×#102—111no—
223C22×#102—111no—
224C2×#390—111no—
225C2×#382—111no—
226#2092—111no—
227#2092—111no—
228#2092—111no—
229#2092—111no—
230#2092—111no—
231#2092—111no—
232#2092—111no—
233#2092D1111yescharacteristic, direct product factor
234C2×#336—111no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—48no—
247C22×D11—416no—
248C22×D11—88no—
249C22×D11—84no—
250C22×D11—84no—
251C22×D11C22⋊Q812yes—
252C22×D11#12312yes—
253C22×D11#12712yes—
254C22×D11#13514yes—
255C22×D11AGL(1,ℤ/8)14yes—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—41no—
259D4×C11—41no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×Q811yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C22⋊D11—48no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11C22⋊Q812yes—
286C2×Dic11#12312yes—
287C2×Dic11#12712yes—
288D44—22no—
289D44—22no—
290D44—41no—
291D44—41no—
292C4×D11—48no—
293C4×D11—84no—
294C4×D11—84no—
295C4×D11—84no—
296C4×D11C22⋊Q814yes—
297C4×D11C22⋊Q814yes—
298C4×D11#12314yes—
299C4×D11#12314yes—
300C8×C11—22no—
301C8×C11—22no—
302C11⋊C8—22no—
303C11⋊C8—22no—
304C23×D4—111no—
305C23×C8—111no—
306C23×C8—111no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—111no—
310C22×C22⋊C4—222no—
311C22×C42—111no—
312C2×#107—111no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#107—224no—
316C2×#107C2×D1111yescharacteristic, complemented
317C2×#106—111no—
318C2×#106—111no—
319C2×#106—111no—
320C2×#106—224no—
321C2×#106C2×D1111yescharacteristic, complemented
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—224no—
329C2×#102—224no—
330C2×#102C2×D1111yescharacteristic
331C2×#102C2×D1111yescharacteristic
332#390—111no—
333#390—111no—
334#390—111no—
335#390—222no—
336#390C2×D1111yescharacteristic
337#382—111no—
338#382—111no—
339#382—111no—
340#382—222no—
341#382C2×D1111yescharacteristic, complemented
342C2×#95—222no—
343#336—111no—
344#336—111no—
345#336—111no—
346#336C2×D1111yescharacteristic, complemented
347C22×C11—44no—
348C22×C11—42no—
349C22×C11—82no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11C2×C22⋊Q811yescharacteristic
353C22×C11C2×#12311yescharacteristic
354C22×C11C2×#12711yescharacteristic
355C22×C11C2×#13512yes—
356C22×C11C2×AGL(1,ℤ/8)12yes—
357C2×D11—44no—
358C2×D11—42no—
359C2×D11—82no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—816no—
363C2×D11#39914yes—
364C2×D11#47818yes—
365C2×D11#48218yes—
366C2×D11#49514yes—
367C2×D11#49614yes—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11C2×C22⋊Q811yescharacteristic
373C4×C11C2×C22⋊Q811yescharacteristic
374C4×C11C2×#12311yescharacteristic
375C4×C11C2×#12311yescharacteristic
376Dic11—42no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380Dic11#39914yes—
381C25—221no—
382C22×D4—114no—
383C22×D4—111no—
384C22×D4—222no—
385C22×D4—222no—
386C22×D4—222no—
387C22×D4—222no—
388C22×D4—222no—
389C22×D4—221no—
390C22×D4C22×D1111yescharacteristic
391C23×C4—111no—
392C23×C4—112no—
393C23×C4—221no—
394C23×C4—221no—
395C23×C4—221no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8—114no—
399C22×C8—114no—
400C22×C8—222no—
401C22×C8—222no—
402C22×C8—222no—
403C22×C8—222no—
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—22no—
422C2×C22⋊C4—222no—
423C2×C22⋊C4—222no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—448no—
426C2×C42—112no—
427C2×C42—111no—
428C2×C42—222no—
429C2×C42—222no—
430C2×C42C22×D1111yescharacteristic
431#107—22no—
432#107—222no—
433#107—222no—
434#107—222no—
435#106—22no—
436#106—222no—
437#106—222no—
438#106—222no—
439#102—22no—
440#102—22no—
441#102—222no—
442#102—222no—
443#102—222no—
444#102—222no—
445#102—222no—
446#102—222no—
447#95—22no—
448#95—222no—
449#95—222no—
450#95—222no—
451C2×C11—82no—
452C2×C11C2×#39911yescharacteristic
453C2×C11C2×#47812yes—
454C2×C11C2×#48212yes—
455C2×C11C2×#49511yescharacteristic
456C2×C11C2×#49611yescharacteristic
457D11—82no—
458D11#209218yesdirect product factor
459C24—21no—
460C24—111no—
461C24—224no—
462C24—221no—
463C24—444no—
464C24—442no—
465C24—442no—
466C24—444no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—112no—
473C2×D4—228no—
474C2×D4—228no—
475C2×D4—224no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—444no—
482C2×D4—444no—
483C2×D4—442no—
484C2×D4—442no—
485C2×D4Q8×D1112yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—111no—
490C22×C4—112no—
491C22×C4—112no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—224no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—444no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—444no—
508C22×C4—444no—
509C22×C4D4×D1112yes—
510C22×C4C23×D1111yescharacteristic
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—112no—
516C2×C8—112no—
517C2×C8—228no—
518C2×C8—228no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8D4×D1112yes—
524C2×C8D4×D1112yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C22⋊C4—44no—
541C22⋊C4—444no—
542C22⋊C4—444no—
543C22⋊C4—444no—
544C42—21no—
545C42—21no—
546C42—224no—
547C42—221no—
548C42—221no—
549C11C2×#209211yescharacteristic, complemented, Sylow
550C23—22no—
551C23—41no—
552C23—42no—
553C23—42no—
554C23—41no—
555C23—112no—
556C23—114no—
557C23—114no—
558C23—112no—
559C23—112no—
560C23—222no—
561C23—448no—
562C23—4416no—
563C23—441no—
564C23—442no—
565C23—442no—
566C23—441no—
567C23—884no—
568C23—888no—
569C23—884no—
570C23C2×D4×D1111yescharacteristic
571D4—22no—
572D4—22no—
573D4—41no—
574D4—41no—
575D4—222no—
576D4—222no—
577D4—448no—
578D4—441no—
579D4—441no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—114no—
593C2×C4—114no—
594C2×C4—114no—
595C2×C4—114no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—448no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—884no—
607C2×C4—884no—
608C2×C4—884no—
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4C2×Q8×D1111yescharacteristic
612C2×C4#41×D1111yescharacteristic
613C2×C4#41×D1111yescharacteristic
614C2×C4#41×D1111yescharacteristic
615C8—22no—
616C8—22no—
617C8—222no—
618C8—222no—
619C22—44no—
620C22—42no—
621C22—81no—
622C22—82no—
623C22—81no—
624C22—114no—
625C22—118no—
626C22—118no—
627C22—114no—
628C22—114no—
629C22—444no—
630C22—442no—
631C22—8816no—
632C22—881no—
633C22—882no—
634C22—881no—
635C22D11×C22⋊Q811yescharacteristic
636C22D11×#12311yescharacteristic
637C22D11×#12711yescharacteristic
638C22D11×#13512yes—
639C22D11×AGL(1,ℤ/8)12yes—
640C4—42no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—114no—
645C4—442no—
646C4—881no—
647C4—881no—
648C4—881no—
649C4D11×C22⋊Q811yescharacteristic
650C4D11×C22⋊Q811yescharacteristic
651C4D11×#12311yescharacteristic
652C4D11×#12311yescharacteristic
653C2—82no—
654C2—118no—
655C2—882no—
656C2D11×#39911yescharacteristic
657C2D11×#47812yes—
658C2D11×#48212yes—
659C2D11×#49511yescharacteristic
660C2D11×#49611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2092C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenter#2092D11
hypocenterC11C2×#2092
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2092

Complements

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

NH ≅ G/Ntype
1. C2×D11×#107C2semidirect
2. C2×D11×#106C2semidirect
6. D11×#382C2semidirect
7. #13070140C2semidirect
8. #13070139C2semidirect
9. #13070138C2semidirect
10. #13070137C2semidirect
11. #13070136C2semidirect
12. #13070135C2semidirect
13. #13070134C2semidirect
14. D11×#336C2semidirect
15. C11×#2092C2semidirect
24. C2×C11×#107C22semidirect
25. C2×C11×#106C22semidirect
29. C11×#382C22semidirect
35. C2×#66882C22semidirect
36. C2×#66881C22semidirect
38. #10622590C22semidirect
39. #10622590C22semidirect
42. C2×#66872C22semidirect
43. C2×#66872C22semidirect
44. C2×#66871C22semidirect
45. C2×#66871C22semidirect
48. #10622549C22semidirect
55. C11×#336C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622162C22semidirect
233. #2092D11direct (N × H)
316. C2×#107C2×D11semidirect
321. C2×#106C2×D11semidirect
341. #382C2×D11semidirect
346. #336C2×D11semidirect
458. D11#2092direct (N × H)
549. C11C2×#2092semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1072
C2×D11×#1062
C2×D11×#1022
D11×#3902
D11×#3822
#130701402
#130701392
#130701382
#130701372
#130701362
#130701352
#130701342
D11×#3362
C11×#20922
C2×#209211