Finite Group Databasebeta

← C11×#18244 #14595437

Subgroups — C11×#18244 #14595437

Order 2816.

956 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×#3559C211yesmaximal, characteristic, complemented
2C11×#3114C211yesmaximal, characteristic, complemented
3C11×#3100C211yesmaximal, characteristic, complemented
4C11×#2633C211yesmaximal, characteristic, complemented
5C11×#1610C212yesmaximal, complemented
6C11×#1609C212yesmaximal, complemented
7C11×#1598C212yesmaximal, complemented
8C11×#1597C212yesmaximal, complemented
9C11×#1521C211yesmaximal, characteristic, complemented
10C11×#1514C211yesmaximal, characteristic, complemented
11C11×#1470C211yesmaximal, characteristic, complemented
12C11×#563—21no—
13C11×#562—21no—
14C11×#554—21no—
15C11×#553—21no—
16C11×#553—21no—
17C11×#547—22no—
18C11×#547—21no—
19C11×#544—21no—
20C11×#540—21no—
21C11×#539—22no—
22C11×#539C2212yes—
23C11×#537C2212yes—
24C11×#532C2211yescharacteristic
25C11×#529C2211yescharacteristic
26C2×C11×#125C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C11×#483C2211yescharacteristic
29C11×#480C2211yescharacteristic
30C11×#480C2212yes—
31C11×#478—21no—
32C11×#474—21no—
33C11×#463—21no—
34C11×#459—21no—
35C11×#450C2211yescharacteristic
36C11×#447C2212yes—
37C11×#447C2211yescharacteristic
38C11×#442—21no—
39C11×#440—21no—
40C4×C11×D8—22no—
41C11×#432C2211yescharacteristic
42C11×#431C2211yescharacteristic
43C11×#399—21no—
44C11×#398C2212yes—
45C11×#397—21no—
46C11×#394C2212yes—
47C11×#385—22no—
48C11×#383C2211yescharacteristic
49C11×#328C2212yes—
50C11×#327C2212yes—
51C11×#327C2212yes—
52C11×#327C2212yes—
53C11×#324C2212yes—
54C11×#324C2212yes—
55C2×C11×#41—21no—
56C2×C11×#41—22no—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C2×C11×SD16—21no—
60C2×C11×D8—22no—
61C2×C11×D8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8D411yescharacteristic
65C11×#127D411yescharacteristic
66C11×#126—22no—
67C11×#126—22no—
68C11×#126—21no—
69C11×#125—21no—
70C11×#125—22no—
71C11×#125—21no—
72C11×#125—21no—
73C11×#125—21no—
74C11×#125—21no—
75C11×#125D411yescharacteristic
76C11×#124—21no—
77C11×#124D411yescharacteristic
78C11×#123—22no—
79C11×#123—22no—
80C11×#123—22no—
81C11×#123—22no—
82C11×#123—22no—
83C11×#123—21no—
84C11×#123—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8C2311yescharacteristic
92C11×#121—21no—
93C11×#121—22no—
94C11×#121—21no—
95C11×#121—22no—
96C11×#121—22no—
97C11×#121—21no—
98C11×#121—22no—
99C11×#121C2311yescharacteristic
100C11×#121C2312yes—
101C4×Q8×C11D411yescharacteristic
102C4×D4×C11—22no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11—22no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11D411yescharacteristic
113C4×D4×C11D412yes—
114C11×#117—21no—
115C11×#117—21no—
116C2×C11×C4⋊C4—22no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—22no—
119C2×C11×C4⋊C4D412yes—
120C2×C11×C4⋊C4D411yescharacteristic
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2312yes—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—22no—
126C2×C11×C22⋊C4—22no—
127C2×C42×C11C2311yescharacteristic
128C11×#107—22no—
129C11×#107—21no—
130C11×#106—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×#103—21no—
134C11×#102—22no—
135C11×#102—21no—
136C11×#102—22no—
137C11×#102—21no—
138C11×#102—21no—
139C11×C22⋊C8C2311yescharacteristic
140C11×C22⋊C8C2311yescharacteristic
141C11×C22⋊C8C2312yes—
142C11×#97—21no—
143C4×C8×C11—21no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—22no—
147C11×#95C2312yes—
148#18244C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C11×#41—82no—
151C11×#41—82no—
152C11×#41—82no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—42no—
165C2×D4×C11C2×D411yescharacteristic
166C2×D4×C11C2×D412yes—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11—82no—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C11×SD16—42no—
183C11×D8—44no—
184C11×D8—42no—
185C2×C8×C11—22no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—82no—
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C4⋊C4C2×D412yes—
210C11×C4⋊C4C2×D411yescharacteristic
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—44no—
224C11×C22⋊C4—41no—
225C11×C22⋊C4—41no—
226C11×C22⋊C4—82no—
227C42×C11—22no—
228C42×C11—21no—
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2×D411yescharacteristic
233#3559C2×C1111yescharacteristic, complemented
234#3114C2×C1111yescharacteristic, complemented
235#3100C2×C1111yescharacteristic, complemented
236#2633C2×C1111yescharacteristic, complemented
237#1610C2×C1112yescomplemented
238#1609C2×C1112yescomplemented
239#1598C2×C1112yescomplemented
240#1597C2×C1112yescomplemented
241#1521C2×C1111yescharacteristic, complemented
242#1514C2×C1111yescharacteristic, complemented
243#1470C2×C1111yescharacteristic, complemented
244C23×C11—22no—
245C23×C11—21no—
246C23×C11—22no—
247C23×C11—41no—
248C23×C11—42no—
249C23×C11—41no—
250C23×C11—42no—
251C23×C11C22×D411yescharacteristic
252Q8×C11—41no—
253Q8×C11—81no—
254Q8×C11—82no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—42no—
258D4×C11—41no—
259D4×C11—42no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—42no—
263D4×C11—42no—
264D4×C11—42no—
265D4×C11—81no—
266D4×C11—82no—
267D4×C11—82no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—41no—
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—82no—
291C2×C4×C11—82no—
292C2×C4×C11#12011yescharacteristic
293C2×C4×C11#12011yescharacteristic
294C2×C4×C11#12011yescharacteristic
295C2×C4×C11#12011yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C8×C11—42no—
299C8×C11—41no—
300C8×C11—41no—
301#563—21no—
302#562—21no—
303#554—21no—
304#553—21no—
305#553—21no—
306#547—22no—
307#547—21no—
308#544—21no—
309#540—21no—
310#539—22no—
311#539C22×C1112yes—
312#537C22×C1112yes—
313#532C22×C1111yescharacteristic
314#529C22×C1111yescharacteristic
315C2×#125C22×C1111yescharacteristic
316C2×C4×D4C22×C1111yescharacteristic
317#483C22×C1111yescharacteristic
318#480C22×C1112yes—
319#480C22×C1111yescharacteristic
320#478—21no—
321#474—21no—
322#463—21no—
323#459—21no—
324#450C22×C1111yescharacteristic
325#447C22×C1112yes—
326#447C22×C1111yescharacteristic
327#442—21no—
328#440—21no—
329C4×D8—22no—
330#432C22×C1111yescharacteristic
331#431C22×C1111yescharacteristic
332#399—21no—
333#398C22×C1112yes—
334#397—21no—
335#394C22×C1112yes—
336#385—22no—
337#383C22×C1111yescharacteristic
338#328C22×C1112yes—
339#327C22×C1112yes—
340#327C22×C1112yes—
341#327C22×C1112yes—
342#324C22×C1112yes—
343#324C22×C1112yes—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—44no—
347C22×C11—42no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—41no—
354C22×C11—82no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11C2×#12011yescharacteristic
358C22×C11#57612yes—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—42no—
370C4×C11—41no—
371C4×C11—82no—
372C4×C11—81no—
373C2×#41—21no—
374C2×#41—22no—
375C22×D4C23×C1111yescharacteristic
376C23×C4—21no—
377C2×SD16—21no—
378C2×D8—22no—
379C2×D8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—22no—
382C4⋊Q8D4×C1111yescharacteristic
383#127D4×C1111yescharacteristic
384#126—22no—
385#126—22no—
386#126—21no—
387#125—21no—
388#125—22no—
389#125—21no—
390#125—21no—
391#125—21no—
392#125—21no—
393#125D4×C1111yescharacteristic
394#124—21no—
395#124D4×C1111yescharacteristic
396#123—22no—
397#123—22no—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—21no—
402#123—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8C23×C1111yescharacteristic
410#121—21no—
411#121—22no—
412#121—21no—
413#121—22no—
414#121—22no—
415#121—21no—
416#121—22no—
417#121C23×C1111yescharacteristic
418#121C23×C1112yes—
419C4×Q8D4×C1111yescharacteristic
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—22no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4D4×C1111yescharacteristic
431C4×D4D4×C1112yes—
432#117—21no—
433#117—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4D4×C1112yes—
438C2×C4⋊C4D4×C1111yescharacteristic
439C2×C4⋊C4D4×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1112yes—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C42C23×C1111yescharacteristic
446#107—22no—
447#107—21no—
448#106—21no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451#103—21no—
452#102—22no—
453#102—21no—
454#102—22no—
455#102—21no—
456#102—21no—
457C22⋊C8C23×C1111yescharacteristic
458C22⋊C8C23×C1111yescharacteristic
459C22⋊C8C23×C1112yes—
460#97—21no—
461C4×C8—21no—
462#95—21no—
463#95—21no—
464#95—22no—
465#95C23×C1112yes—
466C2×C11—22no—
467C2×C11—81no—
468C2×C11—82no—
469C2×C11—82no—
470C2×C11#300811yescharacteristic
471C2×C11#302011yescharacteristic
472C2×C11#302511yescharacteristic
473C24—21no—
474#41—82no—
475#41—82no—
476#41—82no—
477C2×Q8—22no—
478C2×Q8—21no—
479C2×Q8C2×D4×C1111yescharacteristic
480C2×D4—21no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—42no—
489C2×D4C2×D4×C1111yescharacteristic
490C2×D4C2×D4×C1112yes—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—82no—
501C22×C4C2×D4×C1112yes—
502C22×C4C2×D4×C1111yescharacteristic
503C22×C4C2×D4×C1112yes—
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C24×C1111yescharacteristic
506SD16—42no—
507D8—44no—
508D8—42no—
509C2×C8—22no—
510C2×C8—21no—
511C2×C8—21no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—82no—
532C4⋊C4C2×D4×C1111yescharacteristic
533C4⋊C4C2×D4×C1112yes—
534C4⋊C4C2×D4×C1111yescharacteristic
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C22⋊C4—22no—
547C22⋊C4—44no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—82no—
551C42—22no—
552C42—21no—
553C42C2×D4×C1111yescharacteristic
554C42C2×D4×C1111yescharacteristic
555C42C2×D4×C1111yescharacteristic
556C42C2×D4×C1111yescharacteristic
557C11#1824411yescharacteristic, direct product factor, Sylow
558C23—22no—
559C23—21no—
560C23—22no—
561C23—41no—
562C23—42no—
563C23—41no—
564C23—42no—
565C23C22×D4×C1111yescharacteristic
566Q8—41no—
567Q8—81no—
568Q8—82no—
569D4—22no—
570D4—22no—
571D4—42no—
572D4—41no—
573D4—42no—
574D4—41no—
575D4—41no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—81no—
580D4—82no—
581D4—82no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4C11×#12011yescharacteristic
607C2×C4C11×#12011yescharacteristic
608C2×C4C11×#12011yescharacteristic
609C2×C4C11×#12011yescharacteristic
610C2×C4C22×D4×C1111yescharacteristic
611C2×C4C22×D4×C1111yescharacteristic
612C8—42no—
613C8—41no—
614C8—41no—
615C22—21no—
616C22—21no—
617C22—44no—
618C22—42no—
619C22—41no—
620C22—41no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—41no—
625C22—82no—
626C22—81no—
627C22—81no—
628C22C2×C11×#12011yescharacteristic
629C22C11×#57612yes—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—42no—
638C4—41no—
639C4—41no—
640C4—42no—
641C4—41no—
642C4—82no—
643C4—81no—
644C2—22no—
645C2—82no—
646C2—81no—
647C2—82no—
648C2C11×#300811yescharacteristic
649C2C11×#302011yescharacteristic
650C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C11×#3559C2semidirect
2. C11×#3114C2semidirect
3. C11×#3100C2semidirect
4. C11×#2633C2semidirect
5. C11×#1610C2semidirect
6. C11×#1609C2semidirect
7. C11×#1598C2semidirect
8. C11×#1597C2semidirect
9. C11×#1521C2semidirect
10. C11×#1514C2semidirect
11. C11×#1470C2semidirect
148. #18244C11direct (N × H)
233. #3559C2×C11semidirect
234. #3114C2×C11semidirect
235. #3100C2×C11semidirect
236. #2633C2×C11semidirect
237. #1610C2×C11semidirect
238. #1609C2×C11semidirect
239. #1598C2×C11semidirect
240. #1597C2×C11semidirect
241. #1521C2×C11semidirect
242. #1514C2×C11semidirect
243. #1470C2×C11semidirect
557. C11#18244direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35592
C11×#31142
C11×#31002
C11×#26332
C11×#16102
C11×#16092
C11×#15982
C11×#15972
C11×#15212
C11×#15142
C11×#14702
#1824411