Finite Group Databasebeta

← C11×#24146 #14601339

Subgroups — C11×#24146 #14601339

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3508C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic, complemented
4C11×#2548C211yesmaximal, characteristic, complemented
5C11×#2037C212yesmaximal, complemented
6C11×#2004C212yesmaximal, complemented
7C11×#1986C211yesmaximal, characteristic, complemented
8C11×#1965C211yesmaximal, characteristic, complemented
9C11×#1885C212yesmaximal, complemented
10C11×#1856C212yesmaximal, complemented
11C11×#1806C211yesmaximal, characteristic, complemented
12C2×C11×#137C2211yescharacteristic
13C11×#559—21no—
14C11×#559—21no—
15C11×#550—21no—
16C11×#550—21no—
17C11×#546—22no—
18C11×#546—22no—
19C11×#540—22no—
20C11×#535C2212yes—
21C11×#533C2211yescharacteristic
22C11×#532—21no—
23C11×#532—21no—
24C2×C11×#127C2211yescharacteristic
25C2×C11×#124C2212yes—
26C11×#518C2212yes—
27C4×C11×#41C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C11×#479—22no—
30C11×#477—21no—
31C11×#475—21no—
32C11×#441—21no—
33C11×#440—21no—
34C4×C11×Q16—21no—
35C4×C11×SD16—21no—
36C11×#428C2211yescharacteristic
37C11×#428C2212yes—
38C11×#423C2211yescharacteristic
39C2×C11×#104C2212yes—
40C11×#419C2211yescharacteristic
41C11×#419C2212yes—
42C11×#417C2211yescharacteristic
43C2×C11×#100C2212yes—
44C2×C11×#100C2212yes—
45C4×C11×M16C2211yescharacteristic
46C11×#394—22no—
47C11×#390—22no—
48C11×#390C2212yes—
49C4×C11×C4⋊C4C2211yescharacteristic
50C11×#339C2212yes—
51C11×#339C2212yes—
52C11×#339C2212yes—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11D412yes—
58C22×D4×C11D412yes—
59C22×D4×C11C2312yes—
60C11×#137—22no—
61C11×#137—22no—
62C2×C11×Q16—21no—
63C2×C11×SD16—21no—
64C2×C11×M16C2311yescharacteristic
65C2×C11×M16C2312yes—
66C2×C11×M16C2311yescharacteristic
67C11×C4⋊Q8D411yescharacteristic
68C11×C4⋊Q8D411yescharacteristic
69C11×#127—22no—
70C11×#127—21no—
71C11×#127—21no—
72C11×#127—21no—
73C11×#127—21no—
74C11×#125D412yes—
75C11×#124—22no—
76C11×#124—22no—
77C11×#124—22no—
78C11×#124—24no—
79C11×#124—42no—
80C11×#123—24no—
81C11×#123—24no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×#121—22no—
85C11×#121—22no—
86C11×#121—24no—
87C11×#121—24no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#120—24no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11D411yescharacteristic
98C4×Q8×C11D411yescharacteristic
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11D411yescharacteristic
108C4×D4×C11D411yescharacteristic
109C11×#117—21no—
110C11×#117C2311yescharacteristic
111C11×#117C2312yes—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C2×C42×C11C2312yes—
121C2×C42×C11C2311yescharacteristic
122C11×#107—21no—
123C11×#107—22no—
124C11×#106—21no—
125C11×#106—22no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×#104—42no—
129C11×#103—21no—
130C11×#103—21no—
131C11×#103—21no—
132C11×#103—22no—
133C11×#103—22no—
134C11×#102—21no—
135C11×#100—24no—
136C11×#100—42no—
137C11×#97—21no—
138C4×C8×C11—21no—
139C11×#95—21no—
140#24146C1111yesmaximal, characteristic, direct product factor, Sylow
141C24×C11C2×D414yes—
142C11×#41—21no—
143C11×#41—21no—
144C11×#41—21no—
145C11×#41—21no—
146C11×#41—84no—
147C11×#41—84no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×Q8×C11#4112yescomplemented
157C2×D4×C11—21no—
158C2×D4×C11—24no—
159C2×D4×C11—24no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—44no—
171C2×D4×C11—82no—
172C2×D4×C11C2×D411yescharacteristic
173C22×C4×C11—21no—
174C22×C4×C11—24no—
175C22×C4×C11—24no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—21no—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C11×Q16—24no—
185C11×SD16—24no—
186C11×M16—21no—
187C11×M16—22no—
188C11×M16—21no—
189C11×M16—22no—
190C11×M16—21no—
191C11×M16#4112yescomplemented
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4—41no—
205C11×C4⋊C4—41no—
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D412yes—
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C4⋊C4C2×D412yes—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—48no—
219C11×C22⋊C4—84no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—22no—
224C42×C11—22no—
225C42×C11—22no—
226C42×C11—41no—
227C42×C11—41no—
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232#3508C2×C1111yescharacteristic
233#3078C2×C1111yescharacteristic, complemented
234C4×#137C2×C1111yescharacteristic, complemented
235#2548C2×C1111yescharacteristic, complemented
236#2037C2×C1112yescomplemented
237#2004C2×C1112yescomplemented
238#1986C2×C1111yescharacteristic, complemented
239#1965C2×C1111yescharacteristic, complemented
240#1885C2×C1112yescomplemented
241#1856C2×C1112yescomplemented
242#1806C2×C1111yescharacteristic, complemented
243C23×C11—24no—
244C23×C11—21no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—44no—
248C23×C11—44no—
249C23×C11C22×D411yescharacteristic
250Q8×C11—22no—
251Q8×C11—21no—
252Q8×C11—21no—
253Q8×C11—22no—
254Q8×C11—42no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—42no—
258D4×C11—21no—
259D4×C11—21no—
260D4×C11—44no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—42no—
264D4×C11—42no—
265D4×C11—42no—
266D4×C11—42no—
267D4×C11—44no—
268D4×C11—82no—
269D4×C11—82no—
270D4×C11—84no—
271D4×C11—84no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—41no—
280C2×C4×C11—42no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11—84no—
292C2×C4×C11—84no—
293C2×C4×C11#12011yescharacteristic
294C2×C4×C11#12011yescharacteristic
295C2×C4×C11#12011yescharacteristic
296C2×C4×C11#12011yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C2×#4111yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C112−1+411yescharacteristic
303C8×C11—22no—
304C8×C11—41no—
305C8×C11—42no—
306C2×#137C22×C1111yescharacteristic
307#559—21no—
308#559—21no—
309#550—21no—
310#550—21no—
311#546—22no—
312#546—22no—
313#540—22no—
314#535C22×C1112yes—
315#533C22×C1111yescharacteristic
316#532—21no—
317#532—21no—
318C2×#127C22×C1111yescharacteristic
319C2×#124C22×C1112yes—
320#518C22×C1112yes—
321C4×#41C22×C1111yescharacteristic
322C2×C4×Q8C22×C1111yescharacteristic
323#479—22no—
324#477—21no—
325#475—21no—
326#441—21no—
327#440—21no—
328C4×Q16—21no—
329C4×SD16—21no—
330#428C22×C1112yes—
331#428C22×C1111yescharacteristic
332#423C22×C1111yescharacteristic
333C2×#104C22×C1112yes—
334#419C22×C1112yes—
335#419C22×C1111yescharacteristic
336#417C22×C1111yescharacteristic
337C2×#100C22×C1112yes—
338C2×#100C22×C1112yes—
339C4×M16C22×C1111yescharacteristic
340#394—22no—
341#390—22no—
342#390C22×C1112yes—
343C4×C4⋊C4C22×C1111yescharacteristic
344#339C22×C1112yes—
345#339C22×C1112yes—
346#339C22×C1112yes—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—41no—
350C22×C11—44no—
351C22×C11—41no—
352C22×C11—44no—
353C22×C11—41no—
354C22×C11—44no—
355C22×C11—84no—
356C22×C11—84no—
357C22×C11C2×#12011yescharacteristic
358C22×C11#54611yescharacteristic
359C22×C11#54711yescharacteristic
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—42no—
369C4×C11—82no—
370C4×C11—81no—
371C4×C11#45512yes—
372C4×C11#52511yescharacteristic
373C4×C11#53711yescharacteristic
374C4×C11#54811yescharacteristic
375C4×C11#55011yescharacteristic
376C2×#41—22no—
377C2×#41—22no—
378C2×#41C23×C1111yescharacteristic
379C22×Q8C23×C1111yescharacteristic
380C22×D4D4×C1112yes—
381C22×D4D4×C1112yes—
382C22×D4C23×C1112yes—
383#137—22no—
384#137—22no—
385C2×Q16—21no—
386C2×SD16—21no—
387C2×M16C23×C1111yescharacteristic
388C2×M16C23×C1112yes—
389C2×M16C23×C1111yescharacteristic
390C4⋊Q8D4×C1111yescharacteristic
391C4⋊Q8D4×C1111yescharacteristic
392#127—22no—
393#127—21no—
394#127—21no—
395#127—21no—
396#127—21no—
397#125D4×C1112yes—
398#124—22no—
399#124—22no—
400#124—22no—
401#124—24no—
402#124—42no—
403#123—24no—
404#123—24no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407#121—22no—
408#121—22no—
409#121—24no—
410#121—24no—
411#121—22no—
412#121—22no—
413#120—24no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8D4×C1111yescharacteristic
421C4×Q8D4×C1111yescharacteristic
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4D4×C1111yescharacteristic
431C4×D4D4×C1111yescharacteristic
432#117—21no—
433#117C23×C1111yescharacteristic
434#117C23×C1112yes—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C1112yes—
444C2×C42C23×C1111yescharacteristic
445#107—21no—
446#107—22no—
447#106—21no—
448#106—22no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451#104—42no—
452#103—21no—
453#103—21no—
454#103—21no—
455#103—22no—
456#103—22no—
457#102—21no—
458#100—24no—
459#100—42no—
460#97—21no—
461C4×C8—21no—
462#95—21no—
463C2×C11—21no—
464C2×C11—21no—
465C2×C11—81no—
466C2×C11—84no—
467C2×C11#240711yescharacteristic
468C2×C11C2×#45511yescharacteristic
469C2×C11#301911yescharacteristic
470C24C2×D4×C1114yes—
471#41—21no—
472#41—21no—
473#41—21no—
474#41—21no—
475#41—84no—
476#41—84no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8C2×D4×C1111yescharacteristic
485C2×Q8C11×#4112yescomplemented
486C2×D4—21no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—44no—
500C2×D4—82no—
501C2×D4C2×D4×C1111yescharacteristic
502C22×C4—21no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4C2×D4×C1111yescharacteristic
511C22×C4C2×D4×C1111yescharacteristic
512C22×C4C24×C1111yescharacteristic
513Q16—24no—
514SD16—24no—
515M16—21no—
516M16—22no—
517M16—21no—
518M16—22no—
519M16—21no—
520M16C11×#4112yescomplemented
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4C2×D4×C1111yescharacteristic
536C4⋊C4C2×D4×C1112yes—
537C4⋊C4C2×D4×C1111yescharacteristic
538C4⋊C4C2×D4×C1112yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—24no—
543C22⋊C4—21no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—48no—
548C22⋊C4—84no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—41no—
556C42—41no—
557C42C2×D4×C1111yescharacteristic
558C42C2×D4×C1111yescharacteristic
559C42C2×D4×C1111yescharacteristic
560C42C2×D4×C1111yescharacteristic
561C11#2414611yescharacteristic, direct product factor, Sylow
562C23—24no—
563C23—21no—
564C23—24no—
565C23—24no—
566C23—44no—
567C23—44no—
568C23C22×D4×C1111yescharacteristic
569Q8—22no—
570Q8—21no—
571Q8—21no—
572Q8—22no—
573Q8—42no—
574Q8—41no—
575Q8—41no—
576Q8—42no—
577D4—21no—
578D4—21no—
579D4—44no—
580D4—41no—
581D4—41no—
582D4—42no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—44no—
587D4—82no—
588D4—82no—
589D4—84no—
590D4—84no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4C11×#12011yescharacteristic
613C2×C4C11×#12011yescharacteristic
614C2×C4C11×#12011yescharacteristic
615C2×C4C11×#12011yescharacteristic
616C2×C4C22×D4×C1111yescharacteristic
617C2×C4C22×D4×C1111yescharacteristic
618C2×C4C2×C11×#4111yescharacteristic
619C2×C4C2×C11×#4111yescharacteristic
620C2×C4C11×H(5,𝔽2)11yescharacteristic
621C2×C4C11×2−1+411yescharacteristic
622C8—22no—
623C8—41no—
624C8—42no—
625C22—21no—
626C22—21no—
627C22—41no—
628C22—44no—
629C22—41no—
630C22—44no—
631C22—41no—
632C22—44no—
633C22—84no—
634C22—84no—
635C22C2×C11×#12011yescharacteristic
636C22C11×#54611yescharacteristic
637C22C11×#54711yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—41no—
642C4—42no—
643C4—41no—
644C4—42no—
645C4—41no—
646C4—42no—
647C4—82no—
648C4—81no—
649C4C11×#45512yes—
650C4C11×#52511yescharacteristic
651C4C11×#53711yescharacteristic
652C4C11×#54811yescharacteristic
653C4C11×#55011yescharacteristic
654C2—21no—
655C2—21no—
656C2—84no—
657C2—81no—
658C2C11×#240711yescharacteristic
659C2C2×C11×#45511yescharacteristic
660C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3508C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3078C2semidirect
3. C4×C11×#137C2semidirect
4. C11×#2548C2semidirect
5. C11×#2037C2semidirect
6. C11×#2004C2semidirect
7. C11×#1986C2semidirect
8. C11×#1965C2semidirect
9. C11×#1885C2semidirect
10. C11×#1856C2semidirect
11. C11×#1806C2semidirect
140. #24146C11direct (N × H)
156. C2×Q8×C11#41semidirect
191. C11×M16#41semidirect
233. #3078C2×C11semidirect
234. C4×#137C2×C11semidirect
235. #2548C2×C11semidirect
236. #2037C2×C11semidirect
237. #2004C2×C11semidirect
238. #1986C2×C11semidirect
239. #1965C2×C11semidirect
240. #1885C2×C11semidirect
241. #1856C2×C11semidirect
242. #1806C2×C11semidirect
485. C2×Q8C11×#41semidirect
520. M16C11×#41semidirect
561. C11#24146direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35082
C11×#30782
C4×C11×#1372
C11×#25482
C11×#20372
C11×#20042
C11×#19862
C11×#19652
C11×#18852
C11×#18562
C11×#18062
#2414611