Finite Group Databasebeta

← C11×#8489 #14585682

Subgroups — C11×#8489 #14585682

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3560C211yesmaximal, characteristic
2C11×#1553C211yesmaximal, characteristic, complemented
3C11×#1535C211yesmaximal, characteristic, complemented
4C11×#1496C211yesmaximal, characteristic, complemented
5C11×#1482C211yesmaximal, characteristic, complemented
6C11×#1473C211yesmaximal, characteristic, complemented
7C11×#1473C211yesmaximal, characteristic, complemented
8C11×#563—21no—
9C11×#560—21no—
10C11×#553—21no—
11C11×#553—21no—
12C11×#551—21no—
13C11×#547—21no—
14C11×#546—21no—
15C11×#546—21no—
16C11×#542—21no—
17C11×#539—21no—
18C11×#539C411yescharacteristic
19C11×#538—21no—
20C11×#538—21no—
21C11×#538C411yescharacteristic
22C11×#537C411yescharacteristic
23C11×#534C411yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#529C2211yescharacteristic
26C2×C11×#126C2211yescharacteristic
27C11×#432C2211yescharacteristic, complemented
28C11×#432C2211yescharacteristic, complemented
29C11×#431C2211yescharacteristic, complemented
30C11×#431C2211yescharacteristic, complemented
31C11×#332—21no—
32C11×#331—21no—
33C11×#330—21no—
34C11×#329—21no—
35C11×Q8⋊C8—21no—
36C11×D4⋊C8—21no—
37C11×D4⋊C8—21no—
38C11×D4⋊C8—21no—
39C11×#324—21no—
40C11×#324—21no—
41C11×#323—21no—
42C11×#323—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C22×D4×C11—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8D411yescharacteristic
48C11×#127D411yescharacteristic
49C11×#126—21no—
50C11×#126—21no—
51C11×#126—21no—
52C11×#126—21no—
53C11×#126—21no—
54C11×#126—21no—
55C11×#126—21no—
56C11×#126—21no—
57C11×#126—21no—
58C11×#125—21no—
59C11×#125—21no—
60C11×#125D411yescharacteristic
61C11×#124—21no—
62C11×#124—21no—
63C11×#124—21no—
64C11×#124—21no—
65C11×#124D411yescharacteristic
66C11×#123—21no—
67C11×#123—21no—
68C11×#123—21no—
69C11×#123—21no—
70C11×#123—21no—
71C11×#123—21no—
72C11×#123—21no—
73C11×#123—21no—
74C11×#123—21no—
75C11×#123—21no—
76C11×#123—21no—
77C11×#123—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8C2×C411yescharacteristic
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121—21no—
95C11×#121—21no—
96C11×#121—21no—
97C11×#121—21no—
98C11×#121C2×C411yescharacteristic
99C11×#121C2×C411yescharacteristic
100C11×#121C2×C411yescharacteristic
101C11×#120—21no—
102C11×#120—21no—
103C11×#120—21no—
104C11×#120—21no—
105C11×#120—21no—
106C4×Q8×C11D411yescharacteristic
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11—21no—
115C4×D4×C11D411yescharacteristic
116C4×D4×C11D411yescharacteristic
117C4×D4×C11D411yescharacteristic
118C11×#117—21no—
119C11×#117—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4C2×C411yescharacteristic
122C2×C11×C4⋊C4D411yescharacteristic
123C2×C11×C4⋊C4D411yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4C2×C411yescharacteristic
127C2×C11×C22⋊C4D411yescharacteristic
128C2×C11×C22⋊C4D411yescharacteristic
129C2×C42×C11C2311yescharacteristic
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×C22⋊C8—21no—
137C11×C22⋊C8—21no—
138C11×#97—21no—
139C11×#97—21no—
140C4×C8×C11—21no—
141C4×C8×C11—21no—
142#8489C1111yesmaximal, characteristic, direct product factor, Sylow
143C24×C11—21no—
144C24×C11C22⋊C411yescharacteristic
145C11×#41—82no—
146C11×#41—82no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C22⋊C411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—82no—
163C2×D4×C11C22⋊C411yescharacteristic
164C2×D4×C11C22⋊C411yescharacteristic
165C2×D4×C11C22⋊C411yescharacteristic
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C22⋊C411yescharacteristic
175C22×C4×C11C22⋊C411yescharacteristic
176C22×C4×C11C22⋊C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
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×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4C22⋊C411yescharacteristic
202C11×C4⋊C4C22⋊C411yescharacteristic
203C11×C4⋊C4C22⋊C411yescharacteristic
204C11×C4⋊C4C22⋊C411yescharacteristic
205C11×C22⋊C4—21no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—21no—
225C11×C22⋊C4—21no—
226C11×C22⋊C4—21no—
227C11×C22⋊C4—21no—
228C11×C22⋊C4—21no—
229C11×C22⋊C4—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11C2×D411yescharacteristic
234C42×C11C2×D411yescharacteristic
235C42×C11C2×D411yescharacteristic
236C42×C11C2×D411yescharacteristic
237#3560C2×C1111yescharacteristic
238#1553C2×C1111yescharacteristic, complemented
239#1535C2×C1111yescharacteristic, complemented
240#1496C2×C1111yescharacteristic, complemented
241#1482C2×C1111yescharacteristic, complemented
242#1473C2×C1111yescharacteristic, complemented
243#1473C2×C1111yescharacteristic, complemented
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—81no—
252C23×C11—81no—
253C23×C11—81no—
254C23×C11C2×C22⋊C411yescharacteristic
255Q8×C11—41no—
256Q8×C11—81no—
257Q8×C11—81no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—42no—
262D4×C11—42no—
263D4×C11—42no—
264D4×C11—81no—
265D4×C11—81no—
266D4×C11—81no—
267D4×C11—81no—
268D4×C11—81no—
269D4×C11—81no—
270D4×C11—81no—
271D4×C11—81no—
272D4×C11—81no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—81no—
288C2×C4×C11—81no—
289C2×C4×C11—81no—
290C2×C4×C11—81no—
291C2×C4×C11—81no—
292C2×C4×C11—81no—
293C2×C4×C11—81no—
294C2×C4×C11—81no—
295C2×C4×C11C2×C22⋊C411yescharacteristic
296C2×C4×C11C2×C22⋊C411yescharacteristic
297C2×C4×C11#12011yescharacteristic
298C2×C4×C11#12011yescharacteristic
299C2×C4×C11#12011yescharacteristic
300C2×C4×C11#12011yescharacteristic
301C8×C11—81no—
302C8×C11—81no—
303C8×C11—81no—
304C8×C11—81no—
305#563—21no—
306#560—21no—
307#553—21no—
308#553—21no—
309#551—21no—
310#547—21no—
311#546—21no—
312#546—21no—
313#542—21no—
314#539—21no—
315#539C4×C1111yescharacteristic
316#538—21no—
317#538—21no—
318#538C4×C1111yescharacteristic
319#537C4×C1111yescharacteristic
320#534C4×C1111yescharacteristic
321#532C22×C1111yescharacteristic
322#529C22×C1111yescharacteristic
323C2×#126C22×C1111yescharacteristic
324#432C22×C1111yescharacteristic, complemented
325#432C22×C1111yescharacteristic, complemented
326#431C22×C1111yescharacteristic, complemented
327#431C22×C1111yescharacteristic, complemented
328#332—21no—
329#331—21no—
330#330—21no—
331#329—21no—
332Q8⋊C8—21no—
333D4⋊C8—21no—
334D4⋊C8—21no—
335D4⋊C8—21no—
336#324—21no—
337#324—21no—
338#323—21no—
339#323—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—161no—
356C22×C11—162no—
357C22×C11#37911yescharacteristic
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C2×#41—21no—
373C2×#41—21no—
374C22×D4—21no—
375C4⋊Q8—21no—
376C4⋊Q8D4×C1111yescharacteristic
377#127D4×C1111yescharacteristic
378#126—21no—
379#126—21no—
380#126—21no—
381#126—21no—
382#126—21no—
383#126—21no—
384#126—21no—
385#126—21no—
386#126—21no—
387#125—21no—
388#125—21no—
389#125D4×C1111yescharacteristic
390#124—21no—
391#124—21no—
392#124—21no—
393#124—21no—
394#124D4×C1111yescharacteristic
395#123—21no—
396#123—21no—
397#123—21no—
398#123—21no—
399#123—21no—
400#123—21no—
401#123—21no—
402#123—21no—
403#123—21no—
404#123—21no—
405#123—21no—
406#123—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8C2×C4×C1111yescharacteristic
415#121—21no—
416#121—21no—
417#121—21no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121C2×C4×C1111yescharacteristic
428#121C2×C4×C1111yescharacteristic
429#121C2×C4×C1111yescharacteristic
430#120—21no—
431#120—21no—
432#120—21no—
433#120—21no—
434#120—21no—
435C4×Q8D4×C1111yescharacteristic
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4D4×C1111yescharacteristic
445C4×D4D4×C1111yescharacteristic
446C4×D4D4×C1111yescharacteristic
447#117—21no—
448#117—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4C2×C4×C1111yescharacteristic
451C2×C4⋊C4D4×C1111yescharacteristic
452C2×C4⋊C4D4×C1111yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4C2×C4×C1111yescharacteristic
456C2×C22⋊C4D4×C1111yescharacteristic
457C2×C22⋊C4D4×C1111yescharacteristic
458C2×C42C23×C1111yescharacteristic
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—21no—
462C4⋊C8—21no—
463C22⋊C8—21no—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8—21no—
467#97—21no—
468#97—21no—
469C4×C8—21no—
470C4×C8—21no—
471C2×C11—41no—
472C2×C11—81no—
473C2×C11—81no—
474C2×C11—81no—
475C2×C11—81no—
476C2×C11#179111yescharacteristic
477C2×C11#179411yescharacteristic
478C2×C11#179511yescharacteristic
479C24—21no—
480C24C11×C22⋊C411yescharacteristic
481#41—82no—
482#41—82no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8C11×C22⋊C411yescharacteristic
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—82no—
499C2×D4C11×C22⋊C411yescharacteristic
500C2×D4C11×C22⋊C411yescharacteristic
501C2×D4C11×C22⋊C411yescharacteristic
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4C11×C22⋊C411yescharacteristic
511C22×C4C11×C22⋊C411yescharacteristic
512C22×C4C11×C22⋊C411yescharacteristic
513C22×C4C22×C4×C1111yescharacteristic
514C22×C4C2×D4×C1111yescharacteristic
515C22×C4C2×D4×C1111yescharacteristic
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4C11×C22⋊C411yescharacteristic
538C4⋊C4C11×C22⋊C411yescharacteristic
539C4⋊C4C11×C22⋊C411yescharacteristic
540C4⋊C4C11×C22⋊C411yescharacteristic
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42C2×D4×C1111yescharacteristic
570C42C2×D4×C1111yescharacteristic
571C42C2×D4×C1111yescharacteristic
572C42C2×D4×C1111yescharacteristic
573C11#848911yescharacteristic, direct product factor, Sylow
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23C2×C11×C22⋊C411yescharacteristic
585Q8—41no—
586Q8—81no—
587Q8—81no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—42no—
592D4—42no—
593D4—42no—
594D4—81no—
595D4—81no—
596D4—81no—
597D4—81no—
598D4—81no—
599D4—81no—
600D4—81no—
601D4—81no—
602D4—81no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4C2×C11×C22⋊C411yescharacteristic
626C2×C4C2×C11×C22⋊C411yescharacteristic
627C2×C4C11×#12011yescharacteristic
628C2×C4C11×#12011yescharacteristic
629C2×C4C11×#12011yescharacteristic
630C2×C4C11×#12011yescharacteristic
631C8—81no—
632C8—81no—
633C8—81no—
634C8—81no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—161no—
651C22—162no—
652C22C11×#37911yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C2—41no—
668C2—81no—
669C2—81no—
670C2—81no—
671C2—81no—
672C2C11×#179111yescharacteristic
673C2C11×#179411yescharacteristic
674C2C11×#179511yescharacteristic
subgroupG/H
center, socleC22×C11#379
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3560C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1553C2semidirect
3. C11×#1535C2semidirect
4. C11×#1496C2semidirect
5. C11×#1482C2semidirect
6. C11×#1473C2semidirect
7. C11×#1473C2semidirect
27. C11×#432C22semidirect
28. C11×#432C22semidirect
29. C11×#431C22semidirect
30. C11×#431C22semidirect
142. #8489C11direct (N × H)
238. #1553C2×C11semidirect
239. #1535C2×C11semidirect
240. #1496C2×C11semidirect
241. #1482C2×C11semidirect
242. #1473C2×C11semidirect
243. #1473C2×C11semidirect
324. #432C22×C11semidirect
325. #432C22×C11semidirect
326. #431C22×C11semidirect
327. #431C22×C11semidirect
573. C11#8489direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35602
C11×#15532
C11×#15352
C11×#14962
C11×#14822
C11×#14732
#848911