Finite Group Databasebeta

← C11×#18967 #14596160

Subgroups — C11×#18967 #14596160

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3546C211yesmaximal, characteristic
2C11×#3227C211yesmaximal, characteristic, complemented
3C11×#3226C211yesmaximal, characteristic, complemented
4C11×#3218C211yesmaximal, characteristic, complemented
5C11×#1654C212yesmaximal, complemented
6C11×#1652C212yesmaximal, complemented
7C11×#1641C212yesmaximal, complemented
8C11×#1639C212yesmaximal, complemented
9C11×#1553C211yesmaximal, characteristic, complemented
10C11×#1496C211yesmaximal, characteristic, complemented
11C11×#1482C211yesmaximal, characteristic, complemented
12C11×#560—22no—
13C11×#556C2211yescharacteristic
14C11×#553—21no—
15C11×#550—21no—
16C11×#550C2211yescharacteristic
17C11×#547C2211yescharacteristic
18C11×#546—21no—
19C11×#546—21no—
20D42×C11C2211yescharacteristic
21C11×#542—21no—
22C11×#538—22no—
23C11×#537—21no—
24C11×#535—21no—
25C11×#535—21no—
26C11×#532C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic, complemented
29C11×#529C2211yescharacteristic
30C11×#500—21no—
31C11×#498C2212yescomplemented
32C11×#497—21no—
33C11×#491—21no—
34C11×#486—21no—
35C11×#486C2212yes—
36C11×#481—22no—
37C11×#480—21no—
38C11×#480—21no—
39C11×#476—22no—
40C11×#474C2212yes—
41C11×#474C2212yescomplemented
42C11×#462C2212yescomplemented
43C11×#461C2212yes—
44C11×#451—21no—
45C11×#448—21no—
46C11×#432C2211yescharacteristic, complemented
47C11×#431C2211yescharacteristic, complemented
48C11×#431C2211yescharacteristic, complemented
49C11×#332C2212yescomplemented
50C11×#331C2212yes—
51C11×Q8⋊C8C2212yescomplemented
52C11×D4⋊C8C2212yes—
53C11×D4⋊C8C2212yes—
54C11×D4⋊C8C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C22×Q8×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C2×C11×Q16—22no—
63C2×C11×SD16—22no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8D411yescharacteristic
68C11×C4⋊Q8C2312yes—
69C11×C4⋊Q8C2311yescharacteristic
70C11×#127—22no—
71C11×#127—21no—
72C11×#127D411yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#126—22no—
75C11×#126—22no—
76C11×#126—21no—
77C11×#125D411yescharacteristic
78C11×#124—22no—
79C11×#124—21no—
80C11×#124—21no—
81C11×#124—21no—
82C11×#124D411yescharacteristic
83C11×#123—22no—
84C11×#123—22no—
85C11×#123—21no—
86C11×#123—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8D411yescharacteristic
91C11×#121—22no—
92C11×#121—22no—
93C11×#121—22no—
94C11×#121—22no—
95C11×#121—22no—
96C11×#121—21no—
97C11×#121—22no—
98C11×#121—21no—
99C11×#121—21no—
100C11×#121—21no—
101C11×#121—21no—
102C11×#121—21no—
103C11×#121D411yescharacteristic
104C11×#121D411yescharacteristic
105C11×#121D411yescharacteristic
106C11×#121D412yes—
107C11×#120—22no—
108C11×#120—22no—
109C11×#120—22no—
110C11×#120—22no—
111C4×Q8×C11—21no—
112C4×Q8×C11C2311yescharacteristic
113C4×D4×C11—22no—
114C4×D4×C11—21no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11D412yes—
119C4×D4×C11C2311yescharacteristic
120C4×D4×C11C2311yescharacteristic
121C4×D4×C11C2311yescharacteristic
122C11×#117—21no—
123C11×#117—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C22⋊C4—22no—
128C2×C42×C11C2311yescharacteristic
129C11×#107—22no—
130C11×#107—22no—
131C11×#106—24no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#103—22no—
136C11×#103—22no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—24no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C4×C8×C11—21no—
145C4×C8×C11C2312yes—
146#18967C1111yesmaximal, characteristic, direct product factor, Sylow
147C24×C11—22no—
148C11×#41—82no—
149C11×#41—82no—
150C11×#41—82no—
151C11×#41—82no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—22no—
155C2×Q8×C11—41no—
156C2×Q8×C11—82no—
157C2×Q8×C11C2×D411yescharacteristic
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—82no—
172C2×D4×C11—82no—
173C2×D4×C11C2×D411yescharacteristic
174C2×D4×C11C2×D411yescharacteristic
175C2×D4×C11C2×D411yescharacteristic
176C2×D4×C11C2×D412yes—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—22no—
183C22×C4×C11—41no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C11×Q16—82no—
188C11×SD16—82no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C2×C8×C11—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
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—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4—41no—
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D412yes—
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
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—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—21no—
225C42×C11—22no—
226C42×C11—21no—
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2411yescharacteristic
231#3546C2×C1111yescharacteristic
232#3227C2×C1111yescharacteristic, complemented
233#3226C2×C1111yescharacteristic, complemented
234#3218C2×C1111yescharacteristic, complemented
235#1654C2×C1112yescomplemented
236#1652C2×C1112yescomplemented
237#1641C2×C1112yescomplemented
238#1639C2×C1112yescomplemented
239#1553C2×C1111yescharacteristic, complemented
240#1496C2×C1111yescharacteristic, complemented
241#1482C2×C1111yescharacteristic, complemented
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—22no—
245C23×C11—21no—
246C23×C11—82no—
247C23×C11—82no—
248C23×C11—82no—
249C23×C11#12011yescharacteristic
250Q8×C11—22no—
251Q8×C11—42no—
252Q8×C11—42no—
253Q8×C11—42no—
254Q8×C11—81no—
255Q8×C11—82no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—42no—
260D4×C11—42no—
261D4×C11—42no—
262D4×C11—81no—
263D4×C11—81no—
264D4×C11—81no—
265D4×C11—81no—
266D4×C11—81no—
267D4×C11—82no—
268D4×C11—82no—
269D4×C11—82no—
270D4×C11—82no—
271D4×C11—82no—
272D4×C11—82no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—41no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—82no—
287C2×C4×C11—82no—
288C2×C4×C11—82no—
289C2×C4×C11—82no—
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12011yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C8×C11—42no—
297C8×C11—42no—
298C8×C11—42no—
299#560—22no—
300#556C22×C1111yescharacteristic
301#553—21no—
302#550—21no—
303#550C22×C1111yescharacteristic
304#547C22×C1111yescharacteristic
305#546—21no—
306#546—21no—
307D42C22×C1111yescharacteristic
308#542—21no—
309#538—22no—
310#537—21no—
311#535—21no—
312#535—21no—
313#532C22×C1111yescharacteristic
314#532C22×C1111yescharacteristic
315C2×C4⋊Q8C22×C1111yescharacteristic, complemented
316#529C22×C1111yescharacteristic
317#500—21no—
318#498C22×C1112yescomplemented
319#497—21no—
320#491—21no—
321#486—21no—
322#486C22×C1112yes—
323#481—22no—
324#480—21no—
325#480—21no—
326#476—22no—
327#474C22×C1112yes—
328#474C22×C1112yescomplemented
329#462C22×C1112yescomplemented
330#461C22×C1112yes—
331#451—21no—
332#448—21no—
333#432C22×C1111yescharacteristic, complemented
334#431C22×C1111yescharacteristic, complemented
335#431C22×C1111yescharacteristic, complemented
336#332C22×C1112yescomplemented
337#331C22×C1112yes—
338Q8⋊C8C22×C1112yescomplemented
339D4⋊C8C22×C1112yes—
340D4⋊C8C22×C1112yes—
341D4⋊C8C22×C1112yescomplemented
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—42no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—42no—
352C22×C11—41no—
353C22×C11—42no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—164no—
358C22×C11C2×#12011yescharacteristic
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—82no—
370C4×C11#57612yes—
371C4×C11#57712yes—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C22×Q8—21no—
377C22×D4—21no—
378C22×D4—21no—
379C2×Q16—22no—
380C2×SD16—22no—
381C4⋊Q8—21no—
382C4⋊Q8—21no—
383C4⋊Q8—21no—
384C4⋊Q8D4×C1111yescharacteristic
385C4⋊Q8C23×C1112yes—
386C4⋊Q8C23×C1111yescharacteristic
387#127—22no—
388#127—21no—
389#127D4×C1111yescharacteristic
390#127C23×C1111yescharacteristic
391#126—22no—
392#126—22no—
393#126—21no—
394#125D4×C1111yescharacteristic
395#124—22no—
396#124—21no—
397#124—21no—
398#124—21no—
399#124D4×C1111yescharacteristic
400#123—22no—
401#123—22no—
402#123—21no—
403#123—22no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8D4×C1111yescharacteristic
408#121—22no—
409#121—22no—
410#121—22no—
411#121—22no—
412#121—22no—
413#121—21no—
414#121—22no—
415#121—21no—
416#121—21no—
417#121—21no—
418#121—21no—
419#121—21no—
420#121D4×C1111yescharacteristic
421#121D4×C1111yescharacteristic
422#121D4×C1111yescharacteristic
423#121D4×C1112yes—
424#120—22no—
425#120—22no—
426#120—22no—
427#120—22no—
428C4×Q8—21no—
429C4×Q8C23×C1111yescharacteristic
430C4×D4—22no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4D4×C1112yes—
436C4×D4C23×C1111yescharacteristic
437C4×D4C23×C1111yescharacteristic
438C4×D4C23×C1111yescharacteristic
439#117—21no—
440#117—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C22⋊C4—22no—
445C2×C42C23×C1111yescharacteristic
446#107—22no—
447#107—22no—
448#106—24no—
449C4⋊C8—21no—
450C4⋊C8C23×C1112yes—
451C4⋊C8C23×C1112yes—
452#103—22no—
453#103—22no—
454#102—22no—
455#102—22no—
456#102—24no—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—21no—
460#97—21no—
461C4×C8—21no—
462C4×C8C23×C1112yes—
463C2×C11—41no—
464C2×C11—81no—
465C2×C11—82no—
466C2×C11—81no—
467C2×C11—81no—
468C2×C11#300811yescharacteristic
469C2×C11#300911yescharacteristic
470C2×C11#302211yescharacteristic
471C24—22no—
472#41—82no—
473#41—82no—
474#41—82no—
475#41—82no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—22no—
479C2×Q8—41no—
480C2×Q8—82no—
481C2×Q8C2×D4×C1111yescharacteristic
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—82no—
496C2×D4—82no—
497C2×D4C2×D4×C1111yescharacteristic
498C2×D4C2×D4×C1111yescharacteristic
499C2×D4C2×D4×C1111yescharacteristic
500C2×D4C2×D4×C1112yes—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—41no—
508C22×C4C2×D4×C1111yescharacteristic
509C22×C4C2×D4×C1111yescharacteristic
510C22×C4C2×D4×C1111yescharacteristic
511Q16—82no—
512SD16—82no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4C2×D4×C1111yescharacteristic
529C4⋊C4C2×D4×C1111yescharacteristic
530C4⋊C4C2×D4×C1112yes—
531C4⋊C4C2×D4×C1111yescharacteristic
532C4⋊C4C2×D4×C1111yescharacteristic
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C42—22no—
550C42—21no—
551C42C2×D4×C1111yescharacteristic
552C42C2×D4×C1111yescharacteristic
553C42C2×D4×C1111yescharacteristic
554C42C24×C1111yescharacteristic
555C11#1896711yescharacteristic, direct product factor, Sylow
556C23—21no—
557C23—21no—
558C23—22no—
559C23—21no—
560C23—82no—
561C23—82no—
562C23—82no—
563C23C11×#12011yescharacteristic
564Q8—22no—
565Q8—42no—
566Q8—42no—
567Q8—42no—
568Q8—81no—
569Q8—82no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—81no—
577D4—81no—
578D4—81no—
579D4—81no—
580D4—81no—
581D4—82no—
582D4—82no—
583D4—82no—
584D4—82no—
585D4—82no—
586D4—82no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4C11×#12011yescharacteristic
605C2×C4C11×#12011yescharacteristic
606C2×C4C11×#12011yescharacteristic
607C2×C4C22×D4×C1111yescharacteristic
608C2×C4C22×D4×C1111yescharacteristic
609C2×C4C22×D4×C1111yescharacteristic
610C8—42no—
611C8—42no—
612C8—42no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—41no—
617C22—41no—
618C22—42no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—42no—
623C22—41no—
624C22—42no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—164no—
629C22C2×C11×#12011yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—82no—
641C4C11×#57612yes—
642C4C11×#57712yes—
643C2—41no—
644C2—81no—
645C2—81no—
646C2—82no—
647C2—81no—
648C2C11×#300811yescharacteristic
649C2C11×#300911yescharacteristic
650C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3546C2
LCSG ▷ C42 ▷ 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×#3227C2semidirect
3. C11×#3226C2semidirect
4. C11×#3218C2semidirect
5. C11×#1654C2semidirect
6. C11×#1652C2semidirect
7. C11×#1641C2semidirect
8. C11×#1639C2semidirect
9. C11×#1553C2semidirect
10. C11×#1496C2semidirect
11. C11×#1482C2semidirect
28. C2×C11×C4⋊Q8C22semidirect
31. C11×#498C22semidirect
41. C11×#474C22semidirect
42. C11×#462C22semidirect
46. C11×#432C22semidirect
47. C11×#431C22semidirect
48. C11×#431C22semidirect
49. C11×#332C22semidirect
51. C11×Q8⋊C8C22semidirect
54. C11×D4⋊C8C22semidirect
146. #18967C11direct (N × H)
232. #3227C2×C11semidirect
233. #3226C2×C11semidirect
234. #3218C2×C11semidirect
235. #1654C2×C11semidirect
236. #1652C2×C11semidirect
237. #1641C2×C11semidirect
238. #1639C2×C11semidirect
239. #1553C2×C11semidirect
240. #1496C2×C11semidirect
241. #1482C2×C11semidirect
315. C2×C4⋊Q8C22×C11semidirect
318. #498C22×C11semidirect
328. #474C22×C11semidirect
329. #462C22×C11semidirect
333. #432C22×C11semidirect
334. #431C22×C11semidirect
335. #431C22×C11semidirect
336. #332C22×C11semidirect
338. Q8⋊C8C22×C11semidirect
341. D4⋊C8C22×C11semidirect
555. C11#18967direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35462
C11×#32272
C11×#32262
C11×#32182
C11×#16542
C11×#16522
C11×#16412
C11×#16392
C11×#15532
C11×#14962
C11×#14822
#1896711