Finite Group Databasebeta

← C11×#18199 #14595392

Subgroups — C11×#18199 #14595392

Order 2816.

1200 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3505C211yesmaximal, characteristic
2C2×C11×#451C211yesmaximal, characteristic, complemented
3C2×C11×#448C211yesmaximal, characteristic, complemented
4C11×#2409C211yesmaximal, characteristic, complemented
5C11×#1606C214yesmaximal, complemented
6C11×#1603C214yesmaximal, complemented
7C11×#1520C211yesmaximal, characteristic, complemented
8C11×#1519C211yesmaximal, characteristic, complemented
9C11×#1459C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×C11×Q16—21no—
12C22×C11×SD16—21no—
13C11×#553—22no—
14C11×#553—21no—
15C11×#552—21no—
16C11×#551—22no—
17C11×#548—21no—
18C11×#546—21no—
19C11×#539C2212yes—
20C11×#538C2212yes—
21C11×#534—21no—
22C11×#529—21no—
23C11×#525—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C11×#518—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C11×#451—22no—
30C11×#451C2214yescomplemented
31C11×#448—22no—
32C11×#448C2214yes—
33C2×C11×#103—21no—
34C2×C11×#103—21no—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#395C2212yescomplemented
38C11×#393C2212yescomplemented
39C11×#391—21no—
40C11×#386—21no—
41C11×#385—21no—
42C11×#380C2211yescharacteristic
43C11×#328C2214yescomplemented
44C11×#327C2214yes—
45C11×#324C2212yescomplemented
46C11×#323C2212yescomplemented
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11—21no—
50C22×Q8×C11—21no—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×Q8×C11—44no—
54C22×Q8×C11D411yescharacteristic
55C22×Q8×C11C2312yes—
56C22×D4×C11—21no—
57C22×D4×C11D411yescharacteristic
58C22×D4×C11D411yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C2×C11×Q16—24no—
63C2×C11×Q16—44no—
64C2×C11×SD16—24no—
65C2×C11×SD16—44no—
66C22×C8×C11—21no—
67C22×C8×C11—21no—
68C11×#126—22no—
69C11×#126—22no—
70C11×#126—22no—
71C11×#125—21no—
72C11×#125—22no—
73C11×#124—21no—
74C11×#124—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—22no—
78C11×#123—22no—
79C11×#123—22no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—44no—
85C11×C22⋊Q8D412yes—
86C11×C22⋊Q8C2312yes—
87C11×#121—21no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121D412yes—
94C11×#121C2312yes—
95C11×#120—22no—
96C11×#120—22no—
97C4×Q8×C11—21no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C11×#117—22no—
109C11×#117—21no—
110C11×#117—22no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4D411yescharacteristic
115C2×C11×C4⋊C4D411yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C11×C22⋊C4C2311yescharacteristic
124C2×C42×C11D411yescharacteristic
125C11×#103—24no—
126C11×#103—24no—
127C11×C22⋊C8—21no—
128C11×C22⋊C8—21no—
129C11×C22⋊C8C2312yes—
130C11×C22⋊C8C2312yes—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95C2312yes—
134#18199C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C24×C11C2×D411yescharacteristic
138C11×#41—82no—
139C2×Q8×C11—24no—
140C2×Q8×C11—21no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—44no—
146C2×Q8×C11—42no—
147C2×Q8×C11—42no—
148C2×Q8×C11—42no—
149C2×Q8×C11—42no—
150C2×Q8×C11—44no—
151C2×Q8×C11—44no—
152C2×Q8×C11—41no—
153C2×Q8×C11—41no—
154C2×Q8×C11C2×D412yes—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—22no—
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—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11C2×D412yes—
168C22×C4×C11—21no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—42no—
178C22×C4×C11—44no—
179C22×C4×C11—42no—
180C22×C4×C11—41no—
181C22×C4×C11—41no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2411yescharacteristic
191C11×Q16—48no—
192C11×SD16—48no—
193C2×C8×C11—22no—
194C2×C8×C11—22no—
195C2×C8×C11—42no—
196C2×C8×C11—42no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—44no—
209C11×C4⋊C4C2×D412yes—
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—22no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—21no—
225C11×C22⋊C4—44no—
226C11×C22⋊C4—42no—
227C42×C11—22no—
228C42×C11—22no—
229C42×C11—21no—
230C42×C11—21no—
231#3505C2×C1111yescharacteristic
232C2×#451C2×C1111yescharacteristic, complemented
233C2×#448C2×C1111yescharacteristic, complemented
234#2409C2×C1111yescharacteristic, complemented
235#1606C2×C1114yescomplemented
236#1603C2×C1114yescomplemented
237#1520C2×C1111yescharacteristic, complemented
238#1519C2×C1111yescharacteristic, complemented
239#1459C2×C1111yescharacteristic, complemented
240C23×C11—21no—
241C23×C11—22no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—42no—
249C23×C11—81no—
250C23×C11—81no—
251C23×C11#12011yescharacteristic
252C23×C11#12011yescharacteristic
253C23×C11#13512yes—
254C23×C11#13712yes—
255C23×C11C22×D411yescharacteristic
256Q8×C11—24no—
257Q8×C11—24no—
258Q8×C11—42no—
259Q8×C11—44no—
260Q8×C11—42no—
261Q8×C11—42no—
262Q8×C11—44no—
263Q8×C11—42no—
264D4×C11—42no—
265D4×C11—42no—
266D4×C11—42no—
267D4×C11—42no—
268D4×C11—42no—
269D4×C11—44no—
270D4×C11—42no—
271D4×C11—82no—
272D4×C11—82no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—24no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—42no—
289C2×C4×C11—44no—
290C2×C4×C11—44no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—81no—
300C2×C4×C11—81no—
301C2×C4×C11—81no—
302C2×C4×C11—82no—
303C2×C4×C11—82no—
304C2×C4×C11#12011yescharacteristic
305C2×C4×C11#12011yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C8×C11—42no—
309C8×C11—42no—
310C23×Q8C22×C1111yescharacteristic
311C22×Q16—21no—
312C22×SD16—21no—
313#553—22no—
314#553—21no—
315#552—21no—
316#551—22no—
317#548—21no—
318#546—21no—
319#539C22×C1112yes—
320#538C22×C1112yes—
321#534—21no—
322#529—21no—
323#525—21no—
324C2×C22⋊Q8—21no—
325C2×C22⋊Q8C22×C1111yescharacteristic
326C2×#121C22×C1111yescharacteristic
327#518—21no—
328C2×C4×D4C22×C1111yescharacteristic
329#451—22no—
330#451C22×C1114yescomplemented
331#448—22no—
332#448C22×C1114yes—
333C2×#103—21no—
334C2×#103—21no—
335C2×C22⋊C8C22×C1111yescharacteristic
336C2×C22⋊C8C22×C1111yescharacteristic
337#395C22×C1112yescomplemented
338#393C22×C1112yescomplemented
339#391—21no—
340#386—21no—
341#385—21no—
342#380C22×C1111yescharacteristic
343#328C22×C1114yescomplemented
344#327C22×C1114yes—
345#324C22×C1112yescomplemented
346#323C22×C1112yescomplemented
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—21no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—41no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—42no—
362C22×C11—81no—
363C22×C11—162no—
364C22×C11#45212yes—
365C22×C11#45212yes—
366C22×C11C2×#12011yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11C2×#13711yescharacteristic
369C4×C11—21no—
370C4×C11—21no—
371C4×C11—21no—
372C4×C11—41no—
373C4×C11—42no—
374C4×C11—41no—
375C4×C11—42no—
376C4×C11—44no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—82no—
380C4×C11B(4,𝔽2)12yes—
381C2×#41—21no—
382C22×Q8—21no—
383C22×Q8—21no—
384C22×Q8—21no—
385C22×Q8—21no—
386C22×Q8—21no—
387C22×Q8—44no—
388C22×Q8D4×C1111yescharacteristic
389C22×Q8C23×C1112yes—
390C22×D4—21no—
391C22×D4D4×C1111yescharacteristic
392C22×D4D4×C1111yescharacteristic
393C23×C4—21no—
394C23×C4D4×C1111yescharacteristic
395C23×C4C23×C1111yescharacteristic
396C2×Q16—24no—
397C2×Q16—44no—
398C2×SD16—24no—
399C2×SD16—44no—
400C22×C8—21no—
401C22×C8—21no—
402#126—22no—
403#126—22no—
404#126—22no—
405#125—21no—
406#125—22no—
407#124—21no—
408#124—22no—
409#123—22no—
410#123—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414C22⋊Q8—21no—
415C22⋊Q8—22no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—44no—
419C22⋊Q8D4×C1112yes—
420C22⋊Q8C23×C1112yes—
421#121—21no—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—21no—
426#121—21no—
427#121D4×C1112yes—
428#121C23×C1112yes—
429#120—22no—
430#120—22no—
431C4×Q8—21no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—22no—
441C4×D4—22no—
442#117—22no—
443#117—21no—
444#117—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4D4×C1111yescharacteristic
449C2×C4⋊C4D4×C1111yescharacteristic
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C22⋊C4—22no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C1111yescharacteristic
457C2×C22⋊C4C23×C1111yescharacteristic
458C2×C42D4×C1111yescharacteristic
459#103—24no—
460#103—24no—
461C22⋊C8—21no—
462C22⋊C8—21no—
463C22⋊C8C23×C1112yes—
464C22⋊C8C23×C1112yes—
465#95—22no—
466#95—22no—
467#95C23×C1112yes—
468C2×C11—21no—
469C2×C11—21no—
470C2×C11—22no—
471C2×C11—22no—
472C2×C11—81no—
473C2×C11—82no—
474C2×C11C2×#45211yescharacteristic
475C2×C11#302211yescharacteristic
476C2×C11C2×B(4,𝔽2)11yescharacteristic
477C24—21no—
478C24C2×D4×C1111yescharacteristic
479C24C2×D4×C1111yescharacteristic
480#41—82no—
481C2×Q8—24no—
482C2×Q8—21no—
483C2×Q8—24no—
484C2×Q8—24no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—44no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8C2×D4×C1112yes—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4C2×D4×C1112yes—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4—44no—
521C22×C4—42no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4C2×D4×C1111yescharacteristic
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C24×C1111yescharacteristic
533Q16—48no—
534SD16—48no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—42no—
538C2×C8—42no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—44no—
551C4⋊C4C2×D4×C1112yes—
552C4⋊C4C2×D4×C1112yes—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—21no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—44no—
568C22⋊C4—42no—
569C42—22no—
570C42—22no—
571C42—21no—
572C42—21no—
573C11#1819911yescharacteristic, direct product factor, Sylow
574C23—21no—
575C23—22no—
576C23—21no—
577C23—21no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—42no—
583C23—81no—
584C23—81no—
585C23C11×#12011yescharacteristic
586C23C11×#12011yescharacteristic
587C23C11×#13512yes—
588C23C11×#13712yes—
589C23C22×D4×C1111yescharacteristic
590Q8—24no—
591Q8—24no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—44no—
596Q8—44no—
597Q8—42no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603D4—44no—
604D4—42no—
605D4—82no—
606D4—82no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—81no—
636C2×C4—82no—
637C2×C4—82no—
638C2×C4C11×#12011yescharacteristic
639C2×C4C11×#12011yescharacteristic
640C2×C4C22×D4×C1111yescharacteristic
641C2×C4C22×D4×C1111yescharacteristic
642C8—42no—
643C8—42no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—41no—
657C22—41no—
658C22—42no—
659C22—81no—
660C22—162no—
661C22C11×#45212yes—
662C22C11×#45212yes—
663C22C2×C11×#12011yescharacteristic
664C22C2×C11×#13511yescharacteristic
665C22C2×C11×#13711yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—41no—
670C4—42no—
671C4—41no—
672C4—42no—
673C4—44no—
674C4—41no—
675C4—42no—
676C4—82no—
677C4C11×B(4,𝔽2)12yes—
678C2—21no—
679C2—21no—
680C2—22no—
681C2—22no—
682C2—81no—
683C2—82no—
684C2C2×C11×#45211yescharacteristic
685C2C11×#302211yescharacteristic
686C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3505C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#451C2semidirect
3. C2×C11×#448C2semidirect
4. C11×#2409C2semidirect
5. C11×#1606C2semidirect
6. C11×#1603C2semidirect
7. C11×#1520C2semidirect
8. C11×#1519C2semidirect
9. C11×#1459C2semidirect
30. C11×#451C22semidirect
37. C11×#395C22semidirect
38. C11×#393C22semidirect
43. C11×#328C22semidirect
45. C11×#324C22semidirect
46. C11×#323C22semidirect
134. #18199C11direct (N × H)
232. C2×#451C2×C11semidirect
233. C2×#448C2×C11semidirect
234. #2409C2×C11semidirect
235. #1606C2×C11semidirect
236. #1603C2×C11semidirect
237. #1520C2×C11semidirect
238. #1519C2×C11semidirect
239. #1459C2×C11semidirect
330. #451C22×C11semidirect
337. #395C22×C11semidirect
338. #393C22×C11semidirect
343. #328C22×C11semidirect
345. #324C22×C11semidirect
346. #323C22×C11semidirect
573. C11#18199direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35052
C2×C11×#4512
C2×C11×#4482
C11×#24092
C11×#16062
C11×#16032
C11×#15202
C11×#15192
C11×#14592
#1819911