Finite Group Databasebeta

← C11×#24083 #14601276

Subgroups — C11×#24083 #14601276

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3494C211yesmaximal, characteristic
2C11×#3092C211yesmaximal, characteristic, complemented
3C2×C11×#428C211yesmaximal, characteristic, complemented
4C11×#2504C211yesmaximal, characteristic, complemented
5C11×#2061C212yesmaximal, complemented
6C11×#2037C212yesmaximal, complemented
7C11×#1900C211yesmaximal, characteristic, complemented
8C11×#1871C211yesmaximal, characteristic, complemented
9C11×#1860C212yesmaximal, complemented
10C11×#1856C212yesmaximal, complemented
11C11×#1826C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C11×#555—21no—
14C11×#553—21no—
15C11×#553—21no—
16C11×#551—22no—
17C11×#547—21no—
18C11×#546—22no—
19C11×#544C2211yescharacteristic
20C11×#542—21no—
21C11×#540—21no—
22C11×#535C2211yescharacteristic
23C11×#532—21no—
24C11×#529—21no—
25C11×#525C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C11×#520C2211yescharacteristic
28C11×#518C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C11×#484—21no—
32C11×#483—21no—
33C11×#481—21no—
34C11×#480—21no—
35C11×#428—21no—
36C11×#428—21no—
37C11×#428C2212yes—
38C11×#428C2212yes—
39C11×#428C2212yes—
40C2×C11×#107—21no—
41C2×C11×#106—21no—
42C2×C11×#104C2212yes—
43C11×#417C2212yes—
44C2×C11×#100C2212yes—
45C11×#407C2211yescharacteristic
46C11×#397—22no—
47C11×#390C2212yes—
48C11×#386—22no—
49C11×#382C2212yes—
50C4×C11×C22⋊C4C2211yescharacteristic
51C11×#343C2212yes—
52C11×#339C2212yes—
53C11×#339C2212yes—
54C11×#339C2212yes—
55C2×C11×#41—22no—
56C2×C11×#41C2311yescharacteristic
57C22×D4×C11D412yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C2×C11×M16—21no—
62C2×C11×M16—24no—
63C2×C11×M16C2312yes—
64C2×C11×M16C2312yes—
65C22×C8×C11—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×#127—21no—
69C11×#126—22no—
70C11×#126—22no—
71C11×#125—21no—
72C11×#125—21no—
73C11×#124—22no—
74C11×#124—22no—
75C11×#124—21no—
76C11×#123—22no—
77C11×#123—22no—
78C11×#123—22no—
79C11×#123—22no—
80C11×#123—21no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8D411yescharacteristic
84C11×C22⋊Q8D411yescharacteristic
85C11×#121—22no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121D411yescharacteristic
95C11×#121D411yescharacteristic
96C11×#120—21no—
97C11×#120—22no—
98C4×Q8×C11—21no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—22no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C11×#117—22no—
110C11×#117—21no—
111C11×#117—21no—
112C11×#117—21no—
113C11×#117D411yescharacteristic
114C11×#117D411yescharacteristic
115C11×#117C2311yescharacteristic
116C11×#117C2311yescharacteristic
117C11×#117C2311yescharacteristic
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4D411yescharacteristic
125C2×C11×C4⋊C4D411yescharacteristic
126C2×C11×C4⋊C4C2312yes—
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—22no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—24no—
132C2×C11×C22⋊C4D412yes—
133C2×C42×C11—21no—
134C2×C42×C11C2312yes—
135C11×#107—22no—
136C11×#107—22no—
137C11×#107—22no—
138C11×#106—22no—
139C11×#106—22no—
140C11×#106—22no—
141C11×#104—24no—
142C11×#103—22no—
143C11×#102—22no—
144C11×#100—24no—
145C11×C22⋊C8—21no—
146C11×C22⋊C8—21no—
147C11×#95—21no—
148C11×#95—24no—
149#24083C1111yesmaximal, characteristic, direct product factor, Sylow
150C24×C11C2×D411yescharacteristic
151C24×C11C2×D412yes—
152C11×#41—22no—
153C11×#41—22no—
154C11×#41—84no—
155C2×Q8×C11—22no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—21no—
158C2×D4×C11—22no—
159C2×D4×C11—21no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—21no—
163C2×D4×C11—22no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—44no—
169C2×D4×C11C2×D411yescharacteristic
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—41no—
181C22×C4×C11—41no—
182C22×C4×C11—82no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2411yescharacteristic
190C11×M16—24no—
191C11×M16—22no—
192C11×M16—22no—
193C11×M16—22no—
194C11×M16#4114yescomplemented
195C2×C8×C11—24no—
196C2×C8×C11—22no—
197C2×C8×C11—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—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—41no—
211C11×C4⋊C4—41no—
212C11×C4⋊C4C2×D411yescharacteristic
213C11×C4⋊C4C2×D411yescharacteristic
214C11×C4⋊C4C2×D411yescharacteristic
215C11×C4⋊C4C2×D411yescharacteristic
216C11×C4⋊C4C2×D411yescharacteristic
217C11×C4⋊C4C2×D411yescharacteristic
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—21no—
225C11×C22⋊C4—21no—
226C11×C22⋊C4—21no—
227C11×C22⋊C4—21no—
228C11×C22⋊C4—21no—
229C11×C22⋊C4—21no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—21no—
233C11×C22⋊C4—21no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—84no—
236C42×C11—22no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—22no—
243C42×C11—22no—
244#3494C2×C1111yescharacteristic
245#3092C2×C1111yescharacteristic, complemented
246C2×#428C2×C1111yescharacteristic, complemented
247#2504C2×C1111yescharacteristic, complemented
248#2061C2×C1112yescomplemented
249#2037C2×C1112yescomplemented
250#1900C2×C1111yescharacteristic, complemented
251#1871C2×C1111yescharacteristic, complemented
252#1860C2×C1112yescomplemented
253#1856C2×C1112yescomplemented
254#1826C2×C1111yescharacteristic, complemented
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—21no—
259C23×C11—24no—
260C23×C11—41no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11#12011yescharacteristic
264C23×C11#12011yescharacteristic
265C23×C11C22×D411yescharacteristic
266Q8×C11—22no—
267Q8×C11—82no—
268D4×C11—22no—
269D4×C11—42no—
270D4×C11—44no—
271D4×C11—42no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—42no—
275D4×C11—81no—
276D4×C11—82no—
277D4×C11—82no—
278D4×C11—82no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—42no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—44no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—81no—
304C2×C4×C11—82no—
305C2×C4×C11—82no—
306C2×C4×C11—82no—
307C2×C4×C11—82no—
308C2×C4×C11—82no—
309C2×C4×C11#12011yescharacteristic
310C2×C4×C11#12011yescharacteristic
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C2×#4112yes—
314C2×C4×C112−1+412yes—
315C8×C11—24no—
316C8×C11—42no—
317C22×M16C22×C1111yescharacteristic
318#555—21no—
319#553—21no—
320#553—21no—
321#551—22no—
322#547—21no—
323#546—22no—
324#544C22×C1111yescharacteristic
325#542—21no—
326#540—21no—
327#535C22×C1111yescharacteristic
328#532—21no—
329#529—21no—
330#525C22×C1111yescharacteristic
331C2×#121C22×C1111yescharacteristic
332#520C22×C1111yescharacteristic
333#518C22×C1111yescharacteristic
334C2×#117C22×C1111yescharacteristic
335C22×C4⋊C4C22×C1111yescharacteristic
336#484—21no—
337#483—21no—
338#481—21no—
339#480—21no—
340#428—21no—
341#428—21no—
342#428C22×C1112yes—
343#428C22×C1112yes—
344#428C22×C1112yes—
345C2×#107—21no—
346C2×#106—21no—
347C2×#104C22×C1112yes—
348#417C22×C1112yes—
349C2×#100C22×C1112yes—
350#407C22×C1111yescharacteristic
351#397—22no—
352#390C22×C1112yes—
353#386—22no—
354#382C22×C1112yes—
355C4×C22⋊C4C22×C1111yescharacteristic
356#343C22×C1112yes—
357#339C22×C1112yes—
358#339C22×C1112yes—
359#339C22×C1112yes—
360C22×C11—21no—
361C22×C11—21no—
362C22×C11—21no—
363C22×C11—21no—
364C22×C11—21no—
365C22×C11—21no—
366C22×C11—21no—
367C22×C11—44no—
368C22×C11—41no—
369C22×C11—42no—
370C22×C11—41no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—41no—
374C22×C11—84no—
375C22×C11#45512yes—
376C22×C11C2×#12011yescharacteristic
377C22×C11#54712yes—
378C4×C11—21no—
379C4×C11—21no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—82no—
389C4×C11—82no—
390C4×C11#52511yescharacteristic
391C4×C11#53611yescharacteristic
392C4×C11#54712yes—
393C2×#41—22no—
394C2×#41C23×C1111yescharacteristic
395C22×D4D4×C1112yes—
396C22×D4C23×C1111yescharacteristic
397C23×C4—21no—
398C23×C4C23×C1111yescharacteristic
399C2×M16—21no—
400C2×M16—24no—
401C2×M16C23×C1112yes—
402C2×M16C23×C1112yes—
403C22×C8—21no—
404C4⋊Q8—21no—
405C4⋊Q8—21no—
406#127—21no—
407#126—22no—
408#126—22no—
409#125—21no—
410#125—21no—
411#124—22no—
412#124—22no—
413#124—21no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418#123—21no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8D4×C1111yescharacteristic
422C22⋊Q8D4×C1111yescharacteristic
423#121—22no—
424#121—22no—
425#121—22no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—21no—
432#121D4×C1111yescharacteristic
433#121D4×C1111yescharacteristic
434#120—21no—
435#120—22no—
436C4×Q8—21no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—21no—
440C4×D4—22no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447#117—22no—
448#117—21no—
449#117—21no—
450#117—21no—
451#117D4×C1111yescharacteristic
452#117D4×C1111yescharacteristic
453#117C23×C1111yescharacteristic
454#117C23×C1111yescharacteristic
455#117C23×C1111yescharacteristic
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4D4×C1111yescharacteristic
463C2×C4⋊C4D4×C1111yescharacteristic
464C2×C4⋊C4C23×C1112yes—
465C2×C4⋊C4C23×C1111yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4D4×C1112yes—
471C2×C42—21no—
472C2×C42C23×C1112yes—
473#107—22no—
474#107—22no—
475#107—22no—
476#106—22no—
477#106—22no—
478#106—22no—
479#104—24no—
480#103—22no—
481#102—22no—
482#100—24no—
483C22⋊C8—21no—
484C22⋊C8—21no—
485#95—21no—
486#95—24no—
487C2×C11—22no—
488C2×C11—22no—
489C2×C11—41no—
490C2×C11—81no—
491C2×C11—82no—
492C2×C11#240611yescharacteristic
493C2×C11C2×#45511yescharacteristic
494C2×C11#302111yescharacteristic
495C24C2×D4×C1111yescharacteristic
496C24C2×D4×C1112yes—
497#41—22no—
498#41—22no—
499#41—84no—
500C2×Q8—22no—
501C2×Q8C2×D4×C1111yescharacteristic
502C2×D4—21no—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—22no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—44no—
514C2×D4C2×D4×C1111yescharacteristic
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—82no—
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1112yes—
534C22×C4C24×C1111yescharacteristic
535M16—24no—
536M16—22no—
537M16—22no—
538M16—22no—
539M16C11×#4114yescomplemented
540C2×C8—24no—
541C2×C8—22no—
542C2×C8—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4C2×D4×C1111yescharacteristic
558C4⋊C4C2×D4×C1111yescharacteristic
559C4⋊C4C2×D4×C1111yescharacteristic
560C4⋊C4C2×D4×C1111yescharacteristic
561C4⋊C4C2×D4×C1111yescharacteristic
562C4⋊C4C2×D4×C1111yescharacteristic
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—42no—
580C22⋊C4—84no—
581C42—22no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—22no—
588C42—22no—
589C11#2408311yescharacteristic, direct product factor, Sylow
590C23—22no—
591C23—22no—
592C23—22no—
593C23—21no—
594C23—24no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23C11×#12011yescharacteristic
599C23C11×#12011yescharacteristic
600C23C22×D4×C1111yescharacteristic
601Q8—22no—
602Q8—82no—
603D4—22no—
604D4—42no—
605D4—44no—
606D4—42no—
607D4—41no—
608D4—41no—
609D4—42no—
610D4—81no—
611D4—82no—
612D4—82no—
613D4—82no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—44no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—81no—
639C2×C4—82no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4—82no—
644C2×C4C11×#12011yescharacteristic
645C2×C4C11×#12011yescharacteristic
646C2×C4C22×D4×C1111yescharacteristic
647C2×C4C22×D4×C1111yescharacteristic
648C2×C4C2×C11×#4112yes—
649C2×C4C11×2−1+412yes—
650C8—24no—
651C8—42no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—44no—
660C22—41no—
661C22—42no—
662C22—41no—
663C22—42no—
664C22—42no—
665C22—41no—
666C22—84no—
667C22C11×#45512yes—
668C22C2×C11×#12011yescharacteristic
669C22C11×#54712yes—
670C4—21no—
671C4—21no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—42no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—82no—
681C4—82no—
682C4C11×#52511yescharacteristic
683C4C11×#53611yescharacteristic
684C4C11×#54712yes—
685C2—22no—
686C2—22no—
687C2—41no—
688C2—82no—
689C2—81no—
690C2C11×#240611yescharacteristic
691C2C2×C11×#45511yescharacteristic
692C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3494C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3092C2semidirect
3. C2×C11×#428C2semidirect
4. C11×#2504C2semidirect
5. C11×#2061C2semidirect
6. C11×#2037C2semidirect
7. C11×#1900C2semidirect
8. C11×#1871C2semidirect
9. C11×#1860C2semidirect
10. C11×#1856C2semidirect
11. C11×#1826C2semidirect
149. #24083C11direct (N × H)
194. C11×M16#41semidirect
245. #3092C2×C11semidirect
246. C2×#428C2×C11semidirect
247. #2504C2×C11semidirect
248. #2061C2×C11semidirect
249. #2037C2×C11semidirect
250. #1900C2×C11semidirect
251. #1871C2×C11semidirect
252. #1860C2×C11semidirect
253. #1856C2×C11semidirect
254. #1826C2×C11semidirect
539. M16C11×#41semidirect
589. C11#24083direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34942
C11×#30922
C2×C11×#4282
C11×#25042
C11×#20612
C11×#20372
C11×#19002
C11×#18712
C11×#18602
C11×#18562
C11×#18262
#2408311