Finite Group Databasebeta

← C11×#18956 #14596149

Subgroups — C11×#18956 #14596149

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3547C211yesmaximal, characteristic, complemented
2C11×#3217C211yesmaximal, characteristic, complemented
3C11×#3208C211yesmaximal, characteristic, complemented
4C11×#3205C211yesmaximal, characteristic, complemented
5C11×#1627C212yesmaximal, complemented
6C11×#1625C212yesmaximal, complemented
7C11×#1624C212yesmaximal, complemented
8C11×#1622C212yesmaximal, complemented
9C11×#1554C211yesmaximal, characteristic, complemented
10C11×#1496C211yesmaximal, characteristic, complemented
11C11×#1482C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#555—21no—
14C11×#555C2211yescharacteristic, complemented
15C11×#554C2211yescharacteristic, complemented
16C11×#553—21no—
17C11×#552—21no—
18D4×Q8×C11C2211yescharacteristic, complemented
19C11×#548—21no—
20C11×#547C2211yescharacteristic, complemented
21C11×#544—21no—
22C11×#542—22no—
23C11×#540—21no—
24C11×#537—21no—
25C11×#536—21no—
26C11×#533C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C2×C11×#127C2211yescharacteristic
29C11×#529C2211yescharacteristic
30C11×#496—21no—
31C11×#493—21no—
32C11×#492C2212yes—
33C11×#490—21no—
34C11×#486—21no—
35C11×#486C2212yes—
36C11×#460—22no—
37C11×#460C2212yes—
38C11×#459C2212yes—
39C11×#459C2212yes—
40C11×#459C2212yes—
41C11×#450—22no—
42C11×#450—21no—
43C11×#447—21no—
44C11×#447—21no—
45C11×#447—21no—
46C11×#432C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#431C2211yescharacteristic
49C11×#333C2212yescomplemented
50C11×#332C2212yescomplemented
51C11×Q8⋊C8C2212yescomplemented
52C11×D4⋊C8C2212yescomplemented
53C11×D4⋊C8C2212yescomplemented
54C11×D4⋊C8C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×Q8×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C2×C11×SD16—24no—
62C2×C11×SD16—22no—
63C2×C11×D8—22no—
64C2×C11×D8—22no—
65C2×C11×D8—22no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8D411yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#127—21no—
72C11×#127—21no—
73C11×#127—21no—
74C11×#127D411yescharacteristic
75C11×#127C2312yes—
76C11×#126—22no—
77C11×#126—21no—
78C11×#125—22no—
79C11×#125—21no—
80C11×#125—21no—
81C11×#125D411yescharacteristic
82C11×#124—22no—
83C11×#124—22no—
84C11×#124—22no—
85C11×#124—21no—
86C11×#124D411yescharacteristic
87C11×#123—22no—
88C11×#123—22no—
89C11×#123—22no—
90C11×#123—21no—
91C11×#123—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8—21no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8D411yescharacteristic
101C11×C22⋊Q8D412yes—
102C11×#121—22no—
103C11×#121—22no—
104C11×#121—22no—
105C11×#121—22no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121—21no—
109C11×#121—21no—
110C11×#121D411yescharacteristic
111C11×#121D411yescharacteristic
112C11×#121D411yescharacteristic
113C4×Q8×C11—21no—
114C4×Q8×C11D412yes—
115C4×Q8×C11C2311yescharacteristic
116C4×D4×C11—22no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11C2311yescharacteristic
122C4×D4×C11C2311yescharacteristic
123C4×D4×C11C2311yescharacteristic
124C11×#117—22no—
125C11×#117—21no—
126C11×#117—21no—
127C11×#117—21no—
128C11×#117—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C42×C11C2311yescharacteristic
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#102—22no—
136C11×#102—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#18956C1111yesmaximal, characteristic, direct product factor, Sylow
147C24×C11—41no—
148C11×#41—82no—
149C11×#41—82no—
150C2×Q8×C11—22no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—82no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×Q8×C11C2×D412yes—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—41no—
167C2×D4×C11—41no—
168C2×D4×C11—41no—
169C2×D4×C11—82no—
170C2×D4×C11—82no—
171C2×D4×C11—82no—
172C2×D4×C11C2×D411yescharacteristic
173C2×D4×C11C2×D411yescharacteristic
174C2×D4×C11C2×D411yescharacteristic
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C11×SD16—82no—
185C11×SD16—84no—
186C11×D8—82no—
187C11×D8—82no—
188C11×D8—82no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C2×C8×C11—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
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—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C4⋊C4C2×D411yescharacteristic
210C11×C4⋊C4C2×D412yes—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
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—
226C42×C11—22no—
227C42×C11—22no—
228C42×C11—21no—
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2411yescharacteristic
233#3547C2×C1111yescharacteristic, complemented
234#3217C2×C1111yescharacteristic, complemented
235#3208C2×C1111yescharacteristic, complemented
236#3205C2×C1111yescharacteristic, complemented
237#1627C2×C1112yescomplemented
238#1625C2×C1112yescomplemented
239#1624C2×C1112yescomplemented
240#1622C2×C1112yescomplemented
241#1554C2×C1111yescharacteristic, complemented
242#1496C2×C1111yescharacteristic, complemented
243#1482C2×C1111yescharacteristic, complemented
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—42no—
248C23×C11—82no—
249C23×C11—82no—
250C23×C11—82no—
251C23×C11#12011yescharacteristic
252Q8×C11—22no—
253Q8×C11—42no—
254Q8×C11—42no—
255Q8×C11—81no—
256Q8×C11—82no—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—44no—
261D4×C11—42no—
262D4×C11—42no—
263D4×C11—42no—
264D4×C11—42no—
265D4×C11—81no—
266D4×C11—81no—
267D4×C11—82no—
268D4×C11—82no—
269D4×C11—82no—
270D4×C11—81no—
271D4×C11—81no—
272D4×C11—81no—
273D4×C11—82no—
274D4×C11—82no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—21no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—82no—
289C2×C4×C11—82no—
290C2×C4×C11—82no—
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12011yescharacteristic
293C2×C4×C11#12011yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C8×C11—42no—
298C8×C11—42no—
299C8×C11—42no—
300#562—22no—
301#555—21no—
302#555C22×C1111yescharacteristic, complemented
303#554C22×C1111yescharacteristic, complemented
304#553—21no—
305#552—21no—
306D4×Q8C22×C1111yescharacteristic, complemented
307#548—21no—
308#547C22×C1111yescharacteristic, complemented
309#544—21no—
310#542—22no—
311#540—21no—
312#537—21no—
313#536—21no—
314#533C22×C1111yescharacteristic
315#532C22×C1111yescharacteristic
316C2×#127C22×C1111yescharacteristic
317#529C22×C1111yescharacteristic
318#496—21no—
319#493—21no—
320#492C22×C1112yes—
321#490—21no—
322#486—21no—
323#486C22×C1112yes—
324#460—22no—
325#460C22×C1112yes—
326#459C22×C1112yes—
327#459C22×C1112yes—
328#459C22×C1112yes—
329#450—22no—
330#450—21no—
331#447—21no—
332#447—21no—
333#447—21no—
334#432C22×C1111yescharacteristic
335#431C22×C1111yescharacteristic
336#431C22×C1111yescharacteristic
337#333C22×C1112yescomplemented
338#332C22×C1112yescomplemented
339Q8⋊C8C22×C1112yescomplemented
340D4⋊C8C22×C1112yescomplemented
341D4⋊C8C22×C1112yescomplemented
342D4⋊C8C22×C1112yescomplemented
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—21no—
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—82no—
356C22×C11—82no—
357C22×C11—82no—
358C22×C11—164no—
359C22×C11C2×#12011yescharacteristic
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—42no—
371C4×C11#57612yes—
372C4×C11#57712yes—
373C2×#41—21no—
374C2×#41—21no—
375C22×Q8—21no—
376C22×D4—21no—
377C22×D4—21no—
378C22×D4—21no—
379C2×SD16—24no—
380C2×SD16—22no—
381C2×D8—22no—
382C2×D8—22no—
383C2×D8—22no—
384C4⋊Q8—22no—
385C4⋊Q8—21no—
386C4⋊Q8D4×C1111yescharacteristic
387C4⋊Q8C23×C1111yescharacteristic
388C4⋊Q8C23×C1111yescharacteristic
389#127—21no—
390#127—21no—
391#127—21no—
392#127D4×C1111yescharacteristic
393#127C23×C1112yes—
394#126—22no—
395#126—21no—
396#125—22no—
397#125—21no—
398#125—21no—
399#125D4×C1111yescharacteristic
400#124—22no—
401#124—22no—
402#124—22no—
403#124—21no—
404#124D4×C1111yescharacteristic
405#123—22no—
406#123—22no—
407#123—22no—
408#123—21no—
409#123—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—22no—
418C22⋊Q8D4×C1111yescharacteristic
419C22⋊Q8D4×C1112yes—
420#121—22no—
421#121—22no—
422#121—22no—
423#121—22no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121D4×C1111yescharacteristic
429#121D4×C1111yescharacteristic
430#121D4×C1111yescharacteristic
431C4×Q8—21no—
432C4×Q8D4×C1112yes—
433C4×Q8C23×C1111yescharacteristic
434C4×D4—22no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4C23×C1111yescharacteristic
440C4×D4C23×C1111yescharacteristic
441C4×D4C23×C1111yescharacteristic
442#117—22no—
443#117—21no—
444#117—21no—
445#117—21no—
446#117—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C42C23×C1111yescharacteristic
450C4⋊C8—21no—
451C4⋊C8C23×C1112yes—
452C4⋊C8C23×C1112yes—
453#102—22no—
454#102—22no—
455#102—22no—
456#102—22no—
457#102—24no—
458C22⋊C8—21no—
459C22⋊C8—21no—
460C22⋊C8—21no—
461#97—21no—
462C4×C8—21no—
463C4×C8C23×C1112yes—
464C2×C11—41no—
465C2×C11—81no—
466C2×C11—81no—
467C2×C11—81no—
468C2×C11—162no—
469C2×C11#300811yescharacteristic
470C2×C11#301011yescharacteristic
471C2×C11#302111yescharacteristic
472C24—41no—
473#41—82no—
474#41—82no—
475C2×Q8—22no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—82no—
479C2×Q8C2×D4×C1111yescharacteristic
480C2×Q8C2×D4×C1112yes—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—82no—
495C2×D4—82no—
496C2×D4—82no—
497C2×D4C2×D4×C1111yescharacteristic
498C2×D4C2×D4×C1111yescharacteristic
499C2×D4C2×D4×C1111yescharacteristic
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C2×D4×C1111yescharacteristic
508C22×C4C2×D4×C1111yescharacteristic
509SD16—82no—
510SD16—84no—
511D8—82no—
512D8—82no—
513D8—82no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4C2×D4×C1111yescharacteristic
532C4⋊C4C2×D4×C1111yescharacteristic
533C4⋊C4C2×D4×C1111yescharacteristic
534C4⋊C4C2×D4×C1111yescharacteristic
535C4⋊C4C2×D4×C1112yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
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—
551C42—22no—
552C42—22no—
553C42—21no—
554C42C2×D4×C1111yescharacteristic
555C42C2×D4×C1111yescharacteristic
556C42C2×D4×C1111yescharacteristic
557C42C24×C1111yescharacteristic
558C11#1895611yescharacteristic, direct product factor, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—42no—
563C23—82no—
564C23—82no—
565C23—82no—
566C23C11×#12011yescharacteristic
567Q8—22no—
568Q8—42no—
569Q8—42no—
570Q8—81no—
571Q8—82no—
572D4—22no—
573D4—22no—
574D4—22no—
575D4—44no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—81no—
581D4—81no—
582D4—82no—
583D4—82no—
584D4—82no—
585D4—81no—
586D4—81no—
587D4—81no—
588D4—82no—
589D4—82no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4C11×#12011yescharacteristic
607C2×C4C11×#12011yescharacteristic
608C2×C4C11×#12011yescharacteristic
609C2×C4C22×D4×C1111yescharacteristic
610C2×C4C22×D4×C1111yescharacteristic
611C2×C4C22×D4×C1111yescharacteristic
612C8—42no—
613C8—42no—
614C8—42no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—164no—
631C22C2×C11×#12011yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—42no—
643C4C11×#57612yes—
644C4C11×#57712yes—
645C2—41no—
646C2—81no—
647C2—81no—
648C2—81no—
649C2—162no—
650C2C11×#300811yescharacteristic
651C2C11×#301011yescharacteristic
652C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
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
1. C11×#3547C2semidirect
2. C11×#3217C2semidirect
3. C11×#3208C2semidirect
4. C11×#3205C2semidirect
5. C11×#1627C2semidirect
6. C11×#1625C2semidirect
7. C11×#1624C2semidirect
8. C11×#1622C2semidirect
9. C11×#1554C2semidirect
10. C11×#1496C2semidirect
11. C11×#1482C2semidirect
14. C11×#555C22semidirect
15. C11×#554C22semidirect
18. D4×Q8×C11C22semidirect
20. C11×#547C22semidirect
49. C11×#333C22semidirect
50. C11×#332C22semidirect
51. C11×Q8⋊C8C22semidirect
52. C11×D4⋊C8C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×D4⋊C8C22semidirect
146. #18956C11direct (N × H)
233. #3547C2×C11semidirect
234. #3217C2×C11semidirect
235. #3208C2×C11semidirect
236. #3205C2×C11semidirect
237. #1627C2×C11semidirect
238. #1625C2×C11semidirect
239. #1624C2×C11semidirect
240. #1622C2×C11semidirect
241. #1554C2×C11semidirect
242. #1496C2×C11semidirect
243. #1482C2×C11semidirect
302. #555C22×C11semidirect
303. #554C22×C11semidirect
306. D4×Q8C22×C11semidirect
308. #547C22×C11semidirect
337. #333C22×C11semidirect
338. #332C22×C11semidirect
339. Q8⋊C8C22×C11semidirect
340. D4⋊C8C22×C11semidirect
341. D4⋊C8C22×C11semidirect
342. D4⋊C8C22×C11semidirect
558. C11#18956direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35472
C11×#32172
C11×#32082
C11×#32052
C11×#16272
C11×#16252
C11×#16242
C11×#16222
C11×#15542
C11×#14962
C11×#14822
#1895611