Finite Group Databasebeta

← C11×#24171 #14601364

Subgroups — C11×#24171 #14601364

Order 2816.

1106 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3511C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C11×#2563C211yesmaximal, characteristic, complemented
5C11×#2040C212yesmaximal, complemented
6C11×#2006C212yesmaximal, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C11×#1980C211yesmaximal, characteristic, complemented
9C11×#1883C212yesmaximal, complemented
10C11×#1860C212yesmaximal, complemented
11C11×#1806C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
14C11×#556—21no—
15C11×#555—21no—
16C11×#554—21no—
17C11×#553—22no—
18C11×#548—22no—
19C11×#547—21no—
20C11×#542—22no—
21C11×#537C2212yes—
22C11×#533—21no—
23C11×#532—21no—
24C11×#532C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic
26C11×#520C2212yes—
27C4×C11×#41C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C11×#463—22no—
30C11×#461—21no—
31C11×#459—21no—
32C11×#442—21no—
33C11×#440—21no—
34C4×C11×SD16—21no—
35C4×C11×D8—21no—
36C11×#428C2211yescharacteristic
37C11×#423C2211yescharacteristic
38C2×C11×#104C2212yes—
39C2×C11×#104C2212yes—
40C2×C11×#104C2212yes—
41C11×#418C2211yescharacteristic
42C11×#417C2211yescharacteristic
43C11×#417C2212yes—
44C4×C11×M16C2211yescharacteristic
45C11×#393—22no—
46C11×#390C2212yes—
47C11×#382C2212yes—
48C11×#380—22no—
49C4×C11×C4⋊C4C2211yescharacteristic
50C11×#343C2212yes—
51C11×#343C2212yes—
52C11×#339C2212yes—
53C2×C11×#41—22no—
54C2×C11×#41C2311yescharacteristic
55C2×C11×#41C2312yes—
56C22×Q8×C11D412yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C11×AGL(1,ℤ/8)—22no—
60C11×AGL(1,ℤ/8)—24no—
61C11×AGL(1,ℤ/8)—22no—
62C11×AGL(1,ℤ/8)—42no—
63C2×C11×SD16—21no—
64C2×C11×SD16—22no—
65C2×C11×D8—21no—
66C2×C11×D8—22no—
67C2×C11×M16C2312yes—
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8D411yescharacteristic
75C11×#127D411yescharacteristic
76C11×#126—24no—
77C11×#125—22no—
78C11×#124—22no—
79C11×#124—24no—
80C11×#124D412yes—
81C11×#123—24no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—24no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11D411yescharacteristic
95C4×Q8×C11D411yescharacteristic
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—24no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11—21no—
107C4×D4×C11D411yescharacteristic
108C4×D4×C11D411yescharacteristic
109C11×#117—22no—
110C11×#117—22no—
111C11×#117—21no—
112C11×#117C2311yescharacteristic
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4D412yes—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—24no—
120C2×C42×C11—21no—
121C2×C42×C11C2312yes—
122C2×C42×C11C2311yescharacteristic
123C11×#107—21no—
124C11×#106—21no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×#104—24no—
128C11×#104—42no—
129C11×#104—42no—
130C11×#103—21no—
131C11×#103—22no—
132C11×#102—21no—
133C11×#102—22no—
134C11×#102—21no—
135C11×#102—21no—
136C11×#97—21no—
137C4×C8×C11—21no—
138C11×#95—21no—
139C11×#95—24no—
140#24171C1111yesmaximal, characteristic, direct product factor, Sylow
141C24×C11—21no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—21no—
145C11×#41—21no—
146C11×#41—21no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—21no—
150C11×#41—84no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11—82no—
154C2×Q8×C11C2×D412yes—
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—22no—
158C2×D4×C11—24no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11C2×D412yes—
167C2×D4×C11C2×D411yescharacteristic
168C2×D4×C11#4112yescomplemented
169C22×C4×C11—24no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11—44no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C11×SD16—24no—
184C11×SD16—44no—
185C11×D8—24no—
186C11×D8—44no—
187C11×M16—21no—
188C11×M16—22no—
189C11×M16—21no—
190C11×M16—22no—
191C11×M16—21no—
192C11×M16#4112yescomplemented
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—22no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4C2×D411yescharacteristic
210C11×C4⋊C4C2×D411yescharacteristic
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—41no—
220C11×C22⋊C4—41no—
221C11×C22⋊C4—84no—
222C42×C11—24no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—22no—
227C42×C11—22no—
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232#3511C2×C1111yescharacteristic, complemented
233#3036C2×C1111yescharacteristic, complemented
234C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
235#2563C2×C1111yescharacteristic, complemented
236#2040C2×C1112yescomplemented
237#2006C2×C1112yescomplemented
238#1997C2×C1111yescharacteristic, complemented
239#1980C2×C1111yescharacteristic, complemented
240#1883C2×C1112yescomplemented
241#1860C2×C1112yescomplemented
242#1806C2×C1111yescharacteristic, complemented
243C23×C11—21no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11C22×D411yescharacteristic
251Q8×C11—21no—
252Q8×C11—21no—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—44no—
256Q8×C11—82no—
257D4×C11—21no—
258D4×C11—22no—
259D4×C11—21no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—42no—
264D4×C11—42no—
265D4×C11—41no—
266D4×C11—42no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—42no—
271D4×C11—84no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—24no—
278C2×C4×C11—41no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—42no—
285C2×C4×C11—44no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11—82no—
292C2×C4×C11—84no—
293C2×C4×C11—82no—
294C2×C4×C11#12011yescharacteristic
295C2×C4×C11#12011yescharacteristic
296C2×C4×C11#12011yescharacteristic
297C2×C4×C11#12011yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C112−1+411yescharacteristic
304C8×C11—22no—
305C8×C11—41no—
306C8×C11—42no—
307C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
308C2×AGL(1,ℤ/8)C22×C1112yes—
309#556—21no—
310#555—21no—
311#554—21no—
312#553—22no—
313#548—22no—
314#547—21no—
315#542—22no—
316#537C22×C1112yes—
317#533—21no—
318#532—21no—
319#532C22×C1111yescharacteristic
320C2×C4⋊Q8C22×C1111yescharacteristic
321#520C22×C1112yes—
322C4×#41C22×C1111yescharacteristic
323C2×C4×D4C22×C1111yescharacteristic
324#463—22no—
325#461—21no—
326#459—21no—
327#442—21no—
328#440—21no—
329C4×SD16—21no—
330C4×D8—21no—
331#428C22×C1111yescharacteristic
332#423C22×C1111yescharacteristic
333C2×#104C22×C1112yes—
334C2×#104C22×C1112yes—
335C2×#104C22×C1112yes—
336#418C22×C1111yescharacteristic
337#417C22×C1112yes—
338#417C22×C1111yescharacteristic
339C4×M16C22×C1111yescharacteristic
340#393—22no—
341#390C22×C1112yes—
342#382C22×C1112yes—
343#380—22no—
344C4×C4⋊C4C22×C1111yescharacteristic
345#343C22×C1112yes—
346#343C22×C1112yes—
347#339C22×C1112yes—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—44no—
351C22×C11—42no—
352C22×C11—41no—
353C22×C11—42no—
354C22×C11—41no—
355C22×C11—42no—
356C22×C11—41no—
357C22×C11—42no—
358C22×C11—82no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11C2×#12011yescharacteristic
362C22×C11#54811yescharacteristic
363C22×C11#55011yescharacteristic
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—44no—
372C4×C11—82no—
373C4×C11—81no—
374C4×C11#45412yes—
375C4×C11#52511yescharacteristic
376C4×C11#53711yescharacteristic
377C4×C11#54611yescharacteristic
378C4×C11#54711yescharacteristic
379C2×#41—22no—
380C2×#41C23×C1111yescharacteristic
381C2×#41C23×C1112yes—
382C22×Q8D4×C1112yes—
383C22×D4C23×C1111yescharacteristic
384C23×C4—21no—
385AGL(1,ℤ/8)—22no—
386AGL(1,ℤ/8)—24no—
387AGL(1,ℤ/8)—22no—
388AGL(1,ℤ/8)—42no—
389C2×SD16—21no—
390C2×SD16—22no—
391C2×D8—21no—
392C2×D8—22no—
393C2×M16C23×C1112yes—
394C2×M16C23×C1111yescharacteristic
395C2×M16C23×C1111yescharacteristic
396C4⋊Q8—21no—
397C4⋊Q8—21no—
398C4⋊Q8—21no—
399C4⋊Q8—21no—
400C4⋊Q8D4×C1111yescharacteristic
401#127D4×C1111yescharacteristic
402#126—24no—
403#125—22no—
404#124—22no—
405#124—24no—
406#124D4×C1112yes—
407#123—24no—
408C22⋊Q8—22no—
409C22⋊Q8—24no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412#121—22no—
413#121—22no—
414#121—22no—
415#121—21no—
416#121—21no—
417#121—24no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8D4×C1111yescharacteristic
421C4×Q8D4×C1111yescharacteristic
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—24no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4D4×C1111yescharacteristic
434C4×D4D4×C1111yescharacteristic
435#117—22no—
436#117—22no—
437#117—21no—
438#117C23×C1111yescharacteristic
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4D4×C1112yes—
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C4⋊C4C23×C1112yes—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—24no—
446C2×C42—21no—
447C2×C42C23×C1112yes—
448C2×C42C23×C1111yescharacteristic
449#107—21no—
450#106—21no—
451C4⋊C8—21no—
452C4⋊C8—21no—
453#104—24no—
454#104—42no—
455#104—42no—
456#103—21no—
457#103—22no—
458#102—21no—
459#102—22no—
460#102—21no—
461#102—21no—
462#97—21no—
463C4×C8—21no—
464#95—21no—
465#95—24no—
466C2×C11—21no—
467C2×C11—21no—
468C2×C11—81no—
469C2×C11—82no—
470C2×C11—82no—
471C2×C11#240711yescharacteristic
472C2×C11C2×#45411yescharacteristic
473C2×C11#301911yescharacteristic
474C24—21no—
475#41—22no—
476#41—22no—
477#41—21no—
478#41—21no—
479#41—21no—
480#41—22no—
481#41—22no—
482#41—21no—
483#41—84no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—82no—
487C2×Q8C2×D4×C1112yes—
488C2×Q8C2×D4×C1111yescharacteristic
489C2×D4—21no—
490C2×D4—22no—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4C2×D4×C1112yes—
500C2×D4C2×D4×C1111yescharacteristic
501C2×D4C11×#4112yescomplemented
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—44no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4C2×D4×C1111yescharacteristic
513C22×C4C2×D4×C1114yes—
514C22×C4C2×D4×C1111yescharacteristic
515C22×C4C24×C1111yescharacteristic
516SD16—24no—
517SD16—44no—
518D8—24no—
519D8—44no—
520M16—21no—
521M16—22no—
522M16—21no—
523M16—22no—
524M16—21no—
525M16C11×#4112yescomplemented
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—22no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4C2×D4×C1111yescharacteristic
543C4⋊C4C2×D4×C1111yescharacteristic
544C22⋊C4—24no—
545C22⋊C4—24no—
546C22⋊C4—24no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—84no—
555C42—24no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—22no—
560C42—22no—
561C42C2×D4×C1111yescharacteristic
562C42C2×D4×C1111yescharacteristic
563C42C2×D4×C1111yescharacteristic
564C42C2×D4×C1111yescharacteristic
565C11#2417111yescharacteristic, direct product factor, Sylow
566C23—21no—
567C23—22no—
568C23—22no—
569C23—42no—
570C23—42no—
571C23—41no—
572C23—41no—
573C23C22×D4×C1111yescharacteristic
574Q8—21no—
575Q8—21no—
576Q8—22no—
577Q8—22no—
578Q8—44no—
579Q8—82no—
580D4—21no—
581D4—22no—
582D4—21no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—42no—
587D4—42no—
588D4—41no—
589D4—42no—
590D4—41no—
591D4—41no—
592D4—41no—
593D4—42no—
594D4—84no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—24no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—82no—
615C2×C4—84no—
616C2×C4—82no—
617C2×C4C11×#12011yescharacteristic
618C2×C4C11×#12011yescharacteristic
619C2×C4C11×#12011yescharacteristic
620C2×C4C11×#12011yescharacteristic
621C2×C4C22×D4×C1111yescharacteristic
622C2×C4C22×D4×C1111yescharacteristic
623C2×C4C2×C11×#4111yescharacteristic
624C2×C4C2×C11×#4111yescharacteristic
625C2×C4C11×H(5,𝔽2)11yescharacteristic
626C2×C4C11×2−1+411yescharacteristic
627C8—22no—
628C8—41no—
629C8—42no—
630C22—21no—
631C22—21no—
632C22—44no—
633C22—42no—
634C22—41no—
635C22—42no—
636C22—41no—
637C22—42no—
638C22—41no—
639C22—42no—
640C22—82no—
641C22—81no—
642C22—81no—
643C22C2×C11×#12011yescharacteristic
644C22C11×#54811yescharacteristic
645C22C11×#55011yescharacteristic
646C4—21no—
647C4—21no—
648C4—21no—
649C4—42no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—44no—
654C4—82no—
655C4—81no—
656C4C11×#45412yes—
657C4C11×#52511yescharacteristic
658C4C11×#53711yescharacteristic
659C4C11×#54611yescharacteristic
660C4C11×#54711yescharacteristic
661C2—21no—
662C2—21no—
663C2—82no—
664C2—81no—
665C2—82no—
666C2C11×#240711yescharacteristic
667C2C2×C11×#45411yescharacteristic
668C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C11×#3511C2semidirect
2. C11×#3036C2semidirect
3. C4×C11×AGL(1,ℤ/8)C2semidirect
4. C11×#2563C2semidirect
5. C11×#2040C2semidirect
6. C11×#2006C2semidirect
7. C11×#1997C2semidirect
8. C11×#1980C2semidirect
9. C11×#1883C2semidirect
10. C11×#1860C2semidirect
11. C11×#1806C2semidirect
140. #24171C11direct (N × H)
168. C2×D4×C11#41semidirect
192. C11×M16#41semidirect
232. #3511C2×C11semidirect
233. #3036C2×C11semidirect
234. C4×AGL(1,ℤ/8)C2×C11semidirect
235. #2563C2×C11semidirect
236. #2040C2×C11semidirect
237. #2006C2×C11semidirect
238. #1997C2×C11semidirect
239. #1980C2×C11semidirect
240. #1883C2×C11semidirect
241. #1860C2×C11semidirect
242. #1806C2×C11semidirect
501. C2×D4C11×#41semidirect
525. M16C11×#41semidirect
565. C11#24171direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35112
C11×#30362
C4×C11×AGL(1,ℤ/8)2
C11×#25632
C11×#20402
C11×#20062
C11×#19972
C11×#19802
C11×#18832
C11×#18602
C11×#18062
#2417111