Finite Group Databasebeta

← D11×#1685 #14736262

Subgroups — D11×#1685 #14736262

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#492C211yesmaximal, characteristic, complemented
2D11×#474C211yesmaximal, characteristic, complemented
3D11×#459C211yesmaximal, characteristic
4D11×#436C211yesmaximal, characteristic, complemented
5#13068084C211yesmaximal, characteristic, complemented
6#13068083C211yesmaximal, characteristic, complemented
7#13068082C211yesmaximal, characteristic, complemented
8#13068081C211yesmaximal, characteristic, complemented
9#13068080C211yesmaximal, characteristic, complemented
10#13068079C211yesmaximal, characteristic, complemented
11#13068078C211yesmaximal, characteristic, complemented
12D11×#335C211yesmaximal, characteristic, complemented
13D11×#332C211yesmaximal, characteristic, complemented
14D11×#331C211yesmaximal, characteristic, complemented
15C11×#1685C211yesmaximal, characteristic, complemented
16C2×SD16×D11—21no—
17C2×SD16×D11—21no—
18C2×D8×D11—21no—
19C2×M16×D11—21no—
20D11×C4⋊Q8C2211yescharacteristic
21D11×#127C2211yescharacteristic
22C4×D4×D11C2211yescharacteristic
23C11×#492C2211yescharacteristic, complemented
24C11×#474C2211yescharacteristic, complemented
25C11×#459C2211yescharacteristic
26C11×#436C2211yescharacteristic, complemented
27#10622788—21no—
28#10622788—21no—
29#10622763—21no—
30#10622741—21no—
31#10622700C2211yescharacteristic, complemented
32#10622698C2211yescharacteristic, complemented
33#10622689C2211yescharacteristic, complemented
34#10622685C2211yescharacteristic
35#10622628C2211yescharacteristic
36#10622625C2211yescharacteristic, complemented
37#10622620C2211yescharacteristic, complemented
38#10622503—21no—
39D11×#107—21no—
40#10622459C2211yescharacteristic, complemented
41#10622456C2211yescharacteristic
42#10622451C2211yescharacteristic, complemented
43D11×C4⋊C8C2211yescharacteristic
44D11×C4⋊C8C2211yescharacteristic
45D11×C4⋊C8C2211yescharacteristic
46#10622399—21no—
47D11×#102—21no—
48D11×#102—21no—
49#10622372—21no—
50#10622342—21no—
51D11×C22⋊C8—21no—
52#10622306C2211yescharacteristic, complemented
53#10622301C2211yescharacteristic, complemented
54C4×C8×D11C2211yescharacteristic
55C11×#335C2211yescharacteristic, complemented
56C11×#332C2211yescharacteristic, complemented
57C11×#331C2211yescharacteristic, complemented
58#10622185C2211yescharacteristic, complemented
59#10622182C2211yescharacteristic, complemented
60#10622124C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic, complemented
63#10622120C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622117C2211yescharacteristic, complemented
66#10622096C2211yescharacteristic, complemented
67C2×Q8×D11—21no—
68C2×D4×D11—21no—
69C2×D4×D11—21no—
70C2×D4×D11—21no—
71C2×D4×D11D411yescharacteristic
72C22×C4×D11—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×D8—21no—
76C2×C11×M16—21no—
77C11×C4⋊Q8C2311yescharacteristic
78C11×#127C2311yescharacteristic
79C4×D4×C11C2311yescharacteristic
80#66997—21no—
81C2×#4325—21no—
82C2×#4325—21no—
83#66993—21no—
84#66993—21no—
85#66993—21no—
86D4×Dic11D411yescharacteristic
87C2×#4324—21no—
88C2×#4324—21no—
89C2×#4323—21no—
90C2×#4323—21no—
91C4×C22⋊D11—21no—
92C2×#4318—21no—
93SD16×D11—44no—
94SD16×D11—44no—
95D8×D11—44no—
96M16×D11—44no—
97C2×D88—21no—
98C2×#4314—21no—
99C2×#4314—21no—
100C2×#4313—21no—
101C2×#4313—21no—
102C2×C8×D11—21no—
103C2×C8×D11—21no—
104C2×C8×D11—21no—
105C2×C8×D11D411yescharacteristic
106C2×C8×D11D411yescharacteristic
107#66946D411yescharacteristic
108C4⋊C4×D11—21no—
109C4⋊C4×D11—21no—
110C4⋊C4×D11D411yescharacteristic
111#66941—21no—
112#66941—21no—
113(C22⋊D11)⋊C4—21no—
114C22⋊C4×D11—21no—
115#66927C2311yescharacteristic
116C4×D44C2311yescharacteristic
117C42×D11C2311yescharacteristic
118#66922C2311yescharacteristic
119C11×#107—21no—
120C11×C4⋊C8C2311yescharacteristic
121C11×C4⋊C8C2311yescharacteristic
122C11×C4⋊C8C2311yescharacteristic
123C11×#102—21no—
124C11×#102—21no—
125C11×C22⋊C8—21no—
126C4×C8×C11C2311yescharacteristic
127#66896—21no—
128#66896—21no—
129C22⋊(C11⋊C8)—21no—
130#66885—21no—
131#66885—21no—
132(C2×D11)⋊C8—21no—
133(C2×D11)⋊C8—21no—
134#66882—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137Dic11⋊C8—21no—
138C8×Dic11D411yescharacteristic
139C8×Dic11D411yescharacteristic
140#66873—21no—
141#66873—21no—
142#66871—21no—
143#66871—21no—
144C4⋊(C11⋊C8)C2311yescharacteristic
145C4⋊(C11⋊C8)C2311yescharacteristic
146C4⋊(C11⋊C8)C2311yescharacteristic
147C4×C11⋊C8C2311yescharacteristic
148C2×#1685—111nomaximal, Sylow
149C23×D11—21no—
150C23×D11—41no—
151C2×Q8×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C2×C22⋊D11—21no—
158C2×C22⋊D11—41no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—41no—
161C22×Dic11—21no—
162Q8×D11—42no—
163Q8×D11—42no—
164D4×D11—22no—
165D4×D11—22no—
166D4×D11—42no—
167D4×D11—42no—
168D4×D11—42no—
169D4×D11—42no—
170D4×D11—82no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44C2×D411yescharacteristic
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—42no—
179C2×C4×D11—42no—
180C2×C4×D11—41no—
181C2×C4×D11C2×D411yescharacteristic
182C2×C4×D11C2×D411yescharacteristic
183C2×C4×D11#4111yescharacteristic
184C2×Dic22—21no—
185C2×Dic22—41no—
186C11×SD16—42no—
187C11×SD16—42no—
188C11×D8—42no—
189C11×M16—42no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11C2×D411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C22⋊C4—21no—
199C42×C11C2411yescharacteristic
200C22⋊Dic11—21no—
201#4325—42no—
202#4325—42no—
203#4324—42no—
204#4324—42no—
205#4323—42no—
206#4323—42no—
207(C2×D11)⋊C4—21no—
208(C2×D11)⋊C4—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11C2×D411yescharacteristic
212Dic11⋊C4—21no—
213Dic11⋊C4—41no—
214Dic11⋊C4—41no—
215C4×Dic11C2×D411yescharacteristic
216C4×Dic11C2×D411yescharacteristic
217C4×Dic11#4111yescharacteristic
218#4318—42no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C2×D411yescharacteristic
223C2×C11⋊C8C2×D411yescharacteristic
224D88—42no—
225#4314—42no—
226#4314—42no—
227#4313—42no—
228#4313—42no—
229C8×D11—22no—
230C8×D11—42no—
231C8×D11—42no—
232C8×D11—42no—
233C8×D11D814yescomplemented
234C2×#492—111no—
235C2×#474—111no—
236C2×#459—111no—
237C2×#436—111no—
238#1685—111no—
239#1685—111no—
240#1685—111no—
241#1685—111no—
242#1685—111no—
243#1685—111no—
244#1685—111no—
245#1685D1111yescharacteristic, direct product factor
246C2×#335—111no—
247C2×#332—111no—
248C2×#331—111no—
249C23×C11—21no—
250C23×C11—41no—
251C22×D11—21no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—41no—
256C22×D11—82no—
257C22×D11—82no—
258C22×D11—82no—
259C22×D11#12111yescharacteristic
260Q8×C11—41no—
261Q8×C11—41no—
262D4×C11—21no—
263D4×C11—21no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—81no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C22⋊D11—42no—
277C22⋊D11—82no—
278C22⋊D11—82no—
279C22⋊D11—82no—
280C2×Dic11—21no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283C2×Dic11#12111yescharacteristic
284C2×Dic11#12111yescharacteristic
285C2×Dic11#12111yescharacteristic
286D44—21no—
287D44—21no—
288D44—41no—
289D44—41no—
290D44—41no—
291D44—41no—
292D44—81no—
293C4×D11—22no—
294C4×D11—42no—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—42no—
298C4×D11—82no—
299C4×D11C2×D812yes—
300C4×D11AGL(1,ℤ/8)12yes—
301C4×D11AGL(1,ℤ/8)12yes—
302C4×D11#13712yes—
303Dic22—41no—
304Dic22—41no—
305Dic22—82no—
306C8×C11—21no—
307C8×C11—41no—
308C8×C11—41no—
309C8×C11—41no—
310C8×C11C2×D812yescomplemented
311C11⋊C8—21no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314C11⋊C8—41no—
315C11⋊C8C2×D812yescomplemented
316C22×SD16—221no—
317C22×SD16—221no—
318C22×D8—221no—
319C22×M16—221no—
320C2×C4⋊Q8—111no—
321C2×#127—111no—
322C2×C4×D4—111no—
323#492—111no—
324#492—111no—
325#492—111no—
326#492—221no—
327#492—221no—
328#492C2×D1111yescharacteristic, complemented
329#474—111no—
330#474—111no—
331#474—111no—
332#474—221no—
333#474—221no—
334#474C2×D1111yescharacteristic, complemented
335#459—111no—
336#459—111no—
337#459—111no—
338#459—221no—
339#459—221no—
340#459C2×D1111yescharacteristic
341#436—111no—
342#436—111no—
343#436—111no—
344#436—221no—
345#436—221no—
346#436C2×D1111yescharacteristic, complemented
347C2×#107—221no—
348C2×C4⋊C8—111no—
349C2×C4⋊C8—111no—
350C2×C4⋊C8—111no—
351C2×#102—221no—
352C2×#102—221no—
353C2×C22⋊C8—221no—
354C2×C4×C8—111no—
355#335—111no—
356#335—111no—
357#335—111no—
358#335C2×D1111yescharacteristic, complemented
359#332—111no—
360#332—111no—
361#332—111no—
362#332C2×D1111yescharacteristic, complemented
363#331—111no—
364#331—111no—
365#331—111no—
366#331C2×D1111yescharacteristic, complemented
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11C2×#12111yescharacteristic
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—84no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—164no—
382C2×D11#45912yes—
383C2×D11#46812yes—
384C2×D11#47112yes—
385C4×C11—21no—
386C4×C11—41no—
387C4×C11—81no—
388C4×C11C22×D811yescharacteristic
389C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
390C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
391C4×C11C2×#13711yescharacteristic
392Dic11—21no—
393Dic11—41no—
394Dic11—81no—
395Dic11#45912yes—
396Dic11#46812yes—
397C22×Q8—221no—
398C22×D4—111no—
399C22×D4—221no—
400C22×D4—221no—
401C22×D4—221no—
402C23×C4—221no—
403C2×SD16—21no—
404C2×SD16—21no—
405C2×SD16—221no—
406C2×SD16—221no—
407C2×SD16—221no—
408C2×SD16—221no—
409C2×SD16—221no—
410C2×SD16—221no—
411C2×SD16—444no—
412C2×SD16—444no—
413C2×D8—21no—
414C2×D8—221no—
415C2×D8—221no—
416C2×D8—221no—
417C2×D8—444no—
418C2×M16—21no—
419C2×M16—221no—
420C2×M16—221no—
421C2×M16—221no—
422C2×M16—444no—
423C22×C8—111no—
424C22×C8—111no—
425C22×C8—221no—
426C22×C8—221no—
427C22×C8—221no—
428C4⋊Q8—111no—
429C4⋊Q8—221no—
430C4⋊Q8—221no—
431C4⋊Q8—221no—
432C4⋊Q8C22×D1111yescharacteristic
433#127—111no—
434#127—221no—
435#127—221no—
436#127—221no—
437#127C22×D1111yescharacteristic
438C4×D4—111no—
439C4×D4—111no—
440C4×D4—111no—
441C4×D4—221no—
442C4×D4—221no—
443C4×D4C22×D1111yescharacteristic
444C2×C4⋊C4—111no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C42—111no—
449#107—21no—
450#107—221no—
451#107—221no—
452#107—221no—
453C4⋊C8—111no—
454C4⋊C8—111no—
455C4⋊C8—111no—
456C4⋊C8—221no—
457C4⋊C8—221no—
458C4⋊C8—221no—
459C4⋊C8C22×D1111yescharacteristic
460C4⋊C8C22×D1111yescharacteristic
461C4⋊C8C22×D1111yescharacteristic
462#102—21no—
463#102—21no—
464#102—221no—
465#102—221no—
466#102—221no—
467#102—221no—
468#102—221no—
469#102—221no—
470C22⋊C8—21no—
471C22⋊C8—221no—
472C22⋊C8—221no—
473C22⋊C8—221no—
474C4×C8—111no—
475C4×C8—111no—
476C4×C8—111no—
477C4×C8C22×D1111yescharacteristic
478C2×C11—81no—
479C2×C11—161no—
480C2×C11C2×#45911yescharacteristic
481C2×C11C2×#46811yescharacteristic
482C2×C11C2×#47111yescharacteristic
483D11—81no—
484D11—161no—
485D11#168514yesdirect product factor
486C24—221no—
487C24—441no—
488C2×Q8—21no—
489C2×Q8—221no—
490C2×Q8—441no—
491C2×Q8—442no—
492C2×Q8—442no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—111no—
497C2×D4—222no—
498C2×D4—222no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—442no—
504C2×D4—442no—
505C2×D4—442no—
506C2×D4—442no—
507C2×D4—441no—
508C2×D4—441no—
509C2×D4—441no—
510C2×D4—882no—
511C2×D4D4×D1111yescharacteristic
512C22×C4—21no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—441no—
523SD16—42no—
524SD16—42no—
525SD16—442no—
526SD16—442no—
527SD16—442no—
528SD16—442no—
529SD16—442no—
530SD16—442no—
531D8—42no—
532D8—442no—
533D8—442no—
534D8—442no—
535M16—42no—
536M16—442no—
537M16—442no—
538M16—442no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—111no—
543C2×C8—114no—
544C2×C8—111no—
545C2×C8—222no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—442no—
550C2×C8—442no—
551C2×C8—442no—
552C2×C8D4×D1111yescharacteristic
553C2×C8D4×D1111yescharacteristic
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—111no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—441no—
561C4⋊C4—441no—
562C4⋊C4D4×D1111yescharacteristic
563C22⋊C4—21no—
564C22⋊C4—221no—
565C22⋊C4—221no—
566C22⋊C4—221no—
567C42—111no—
568C42—111no—
569C42—111no—
570C42C23×D1111yescharacteristic
571C11C2×#168511yescharacteristic, complemented, Sylow
572C23—21no—
573C23—41no—
574C23—111no—
575C23—221no—
576C23—442no—
577C23—442no—
578C23—442no—
579C23—441no—
580C23—882no—
581C23—882no—
582C23—882no—
583Q8—41no—
584Q8—41no—
585Q8—441no—
586Q8—441no—
587Q8—882no—
588D4—21no—
589D4—21no—
590D4—41no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—81no—
595D4—221no—
596D4—221no—
597D4—442no—
598D4—441no—
599D4—441no—
600D4—441no—
601D4—441no—
602D4—881no—
603D4—882no—
604D4—882no—
605D4—882no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—111no—
611C2×C4—111no—
612C2×C4—112no—
613C2×C4—112no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—111no—
617C2×C4—222no—
618C2×C4—221no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—882no—
626C2×C4C2×D4×D1111yescharacteristic
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C8—21no—
630C8—41no—
631C8—41no—
632C8—41no—
633C8—112no—
634C8—221no—
635C8—441no—
636C8—441no—
637C8—441no—
638C8D8×D1112yescomplemented
639C22—41no—
640C22—41no—
641C22—41no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—112no—
646C22—112no—
647C22—112no—
648C22—441no—
649C22—441no—
650C22—441no—
651C22—884no—
652C22—881no—
653C22—881no—
654C22—881no—
655C22—1764no—
656C22D11×#12111yescharacteristic
657C4—21no—
658C4—41no—
659C4—81no—
660C4—112no—
661C4—112no—
662C4—221no—
663C4—441no—
664C4—881no—
665C4C2×D8×D1111yescharacteristic
666C4D11×AGL(1,ℤ/8)11yescharacteristic
667C4D11×AGL(1,ℤ/8)11yescharacteristic
668C4D11×#13711yescharacteristic
669C2—81no—
670C2—114no—
671C2—161no—
672C2—881no—
673C2—1761no—
674C2D11×#45911yescharacteristic
675C2D11×#46811yescharacteristic
676C2D11×#47111yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1685C2
socleC22×C11C2×#121
prime radicalD11×#459C2
hypercenter#1685D11
hypocenterC11C2×#1685
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1685

Complements

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

NH ≅ G/Ntype
1. D11×#492C2semidirect
2. D11×#474C2semidirect
4. D11×#436C2semidirect
5. #13068084C2semidirect
6. #13068083C2semidirect
7. #13068082C2semidirect
8. #13068081C2semidirect
9. #13068080C2semidirect
10. #13068079C2semidirect
11. #13068078C2semidirect
12. D11×#335C2semidirect
13. D11×#332C2semidirect
14. D11×#331C2semidirect
15. C11×#1685C2semidirect
23. C11×#492C22semidirect
24. C11×#474C22semidirect
26. C11×#436C22semidirect
31. #10622700C22semidirect
32. #10622698C22semidirect
33. #10622689C22semidirect
36. #10622625C22semidirect
37. #10622620C22semidirect
40. #10622459C22semidirect
42. #10622451C22semidirect
52. #10622306C22semidirect
53. #10622301C22semidirect
55. C11×#335C22semidirect
56. C11×#332C22semidirect
57. C11×#331C22semidirect
58. #10622185C22semidirect
59. #10622182C22semidirect
60. #10622124C22semidirect
61. #10622123C22semidirect
62. #10622123C22semidirect
63. #10622120C22semidirect
64. #10622117C22semidirect
65. #10622117C22semidirect
66. #10622096C22semidirect
233. C8×D11D8semidirect
245. #1685D11direct (N × H)
310. C8×C11C2×D8semidirect
315. C11⋊C8C2×D8semidirect
328. #492C2×D11semidirect
334. #474C2×D11semidirect
346. #436C2×D11semidirect
358. #335C2×D11semidirect
362. #332C2×D11semidirect
366. #331C2×D11semidirect
485. D11#1685direct (N × H)
571. C11C2×#1685semidirect
638. C8D8×D11semidirect

Maximal subgroups

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

subgroupindex
D11×#4922
D11×#4742
D11×#4592
D11×#4362
#130680842
#130680832
#130680822
#130680812
#130680802
#130680792
#130680782
D11×#3352
D11×#3322
D11×#3312
C11×#16852
C2×#168511