Finite Group Databasebeta

← C11×#18453 #14595646

Subgroups — C11×#18453 #14595646

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3536C211yesmaximal, characteristic
2C11×#3196C211yesmaximal, characteristic, complemented
3C11×#3189C211yesmaximal, characteristic, complemented
4C11×#2816C211yesmaximal, characteristic, complemented
5C11×#1618C212yesmaximal, complemented
6C11×#1614C212yesmaximal, complemented
7C11×#1606C212yesmaximal, complemented
8C11×#1602C212yesmaximal, complemented
9C11×#1516C211yesmaximal, characteristic, complemented
10C11×#1511C211yesmaximal, characteristic, complemented
11C11×#1471C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#554—21no—
14C11×#548—21no—
15C11×#547—21no—
16C11×#546—22no—
17C11×#546—21no—
18C11×#543C2212yes—
19C11×#542—21no—
20C11×#539—21no—
21C11×#538C2212yes—
22C11×#537—21no—
23C11×#537—21no—
24C11×#525C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C11×#485—21no—
29C11×#484—21no—
30C11×#484C2211yescharacteristic
31C11×#484C2212yes—
32C11×#481C2211yescharacteristic
33C11×#470—21no—
34C11×#468—21no—
35C11×#467—22no—
36C11×#452—21no—
37C11×#451—21no—
38C11×#451C2212yes—
39C11×#451C2211yescharacteristic
40C11×#448C2211yescharacteristic
41C11×#407C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43C11×#399C2212yes—
44C11×#398—21no—
45C11×#394—21no—
46C11×#394—22no—
47C11×#393C2212yes—
48C11×#381C2211yescharacteristic
49C11×#328C2212yes—
50C11×#328C2212yes—
51C11×#328C2212yes—
52C11×#327C2212yes—
53C11×#323C2212yes—
54C11×#323C2212yes—
55C2×C11×#41—22no—
56C2×C11×#41—21no—
57C2×C11×#41D411yescharacteristic
58C22×Q8×C11D411yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11D412yes—
61C22×D4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×C11×Q16—22no—
64C2×C11×Q16—21no—
65C2×C11×SD16—21no—
66C2×C11×M16—21no—
67C22×C8×C11—21no—
68C11×C4⋊Q8—21no—
69C11×#126—22no—
70C11×#125—22no—
71C11×#124—21no—
72C11×#124—22no—
73C11×#124—22no—
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—21no—
78C11×#123—22no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8D412yes—
93C11×C22⋊Q8D411yescharacteristic
94C11×C22⋊Q8C2312yes—
95C11×C22⋊Q8C2311yescharacteristic
96C11×#121—21no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—22no—
101C11×#121—22no—
102C11×#121—21no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121D411yescharacteristic
107C11×#121C2311yescharacteristic
108C11×#120—21no—
109C11×#120—22no—
110C4×Q8×C11—21no—
111C4×D4×C11—22no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11—21no—
115C4×D4×C11—22no—
116C11×#117D411yescharacteristic
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—22no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4D411yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—22no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—22no—
129C2×C11×C22⋊C4—22no—
130C2×C11×C22⋊C4C2312yes—
131C11×#107—22no—
132C11×#107—21no—
133C11×#106—21no—
134C11×#103—22no—
135C11×#103—21no—
136C11×#103—21no—
137C11×#103—22no—
138C11×#103—21no—
139C11×#102—21no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8C2312yes—
143C11×C22⋊C8C2311yescharacteristic
144C11×C22⋊C8C2311yescharacteristic
145C11×#95—21no—
146C11×#95—22no—
147C11×#95C2312yes—
148#18453C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11C2×D412yes—
150C24×C11C2×D411yescharacteristic
151C11×#41—81no—
152C11×#41—84no—
153C11×#41—82no—
154C2×Q8×C11—22no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—81no—
159C2×Q8×C11—81no—
160C2×Q8×C11C2×D411yescharacteristic
161C2×Q8×C11C2×D412yes—
162C2×D4×C11—21no—
163C2×D4×C11—22no—
164C2×D4×C11—21no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—21no—
168C2×D4×C11—22no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—81no—
172C2×D4×C11—82no—
173C2×D4×C11C2×D411yescharacteristic
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—22no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—81no—
184C22×C4×C11C2×D412yes—
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—82no—
192C11×Q16—81no—
193C11×SD16—81no—
194C11×M16—81no—
195C2×C8×C11—21no—
196C2×C8×C11—22no—
197C2×C8×C11—21no—
198C2×C8×C11—81no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—41no—
213C11×C4⋊C4—41no—
214C11×C4⋊C4—82no—
215C11×C4⋊C4C2×D411yescharacteristic
216C11×C4⋊C4C2×D412yes—
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—22no—
224C11×C22⋊C4—21no—
225C11×C22⋊C4—21no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—21no—
228C11×C22⋊C4—21no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—21no—
232C11×C22⋊C4—41no—
233C11×C22⋊C4—41no—
234C11×C22⋊C4—81no—
235C11×C22⋊C4—82no—
236C11×C22⋊C4—82no—
237C42×C11—22no—
238C42×C11—21no—
239#3536C2×C1111yescharacteristic
240#3196C2×C1111yescharacteristic, complemented
241#3189C2×C1111yescharacteristic, complemented
242#2816C2×C1111yescharacteristic, complemented
243#1618C2×C1112yescomplemented
244#1614C2×C1112yescomplemented
245#1606C2×C1112yescomplemented
246#1602C2×C1112yescomplemented
247#1516C2×C1111yescharacteristic, complemented
248#1511C2×C1111yescharacteristic, complemented
249#1471C2×C1111yescharacteristic, complemented
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—21no—
253C23×C11—24no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11#12011yescharacteristic
259C23×C11#12011yescharacteristic
260C23×C11C22×D411yescharacteristic
261Q8×C11—42no—
262Q8×C11—41no—
263Q8×C11—42no—
264Q8×C11—41no—
265Q8×C11—41no—
266Q8×C11—42no—
267Q8×C11—82no—
268D4×C11—41no—
269D4×C11—42no—
270D4×C11—44no—
271D4×C11—42no—
272D4×C11—42no—
273D4×C11—81no—
274D4×C11—82no—
275D4×C11—81no—
276D4×C11—82no—
277D4×C11—82no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—41no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—42no—
301C2×C4×C11—81no—
302C2×C4×C11—82no—
303C2×C4×C11—82no—
304C2×C4×C11—82no—
305C2×C4×C11#12011yescharacteristic
306C2×C4×C11#12011yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C8×C11—42no—
310C8×C11—41no—
311C8×C11—41no—
312#562—22no—
313#554—21no—
314#548—21no—
315#547—21no—
316#546—22no—
317#546—21no—
318#543C22×C1112yes—
319#542—21no—
320#539—21no—
321#538C22×C1112yes—
322#537—21no—
323#537—21no—
324#525C22×C1111yescharacteristic
325C2×C22⋊Q8C22×C1111yescharacteristic
326C2×C22⋊Q8C22×C1111yescharacteristic
327C2×#121C22×C1111yescharacteristic
328#485—21no—
329#484—21no—
330#484C22×C1111yescharacteristic
331#484C22×C1112yes—
332#481C22×C1111yescharacteristic
333#470—21no—
334#468—21no—
335#467—22no—
336#452—21no—
337#451—21no—
338#451C22×C1111yescharacteristic
339#451C22×C1112yes—
340#448C22×C1111yescharacteristic
341#407C22×C1111yescharacteristic
342C2×C22⋊C8C22×C1111yescharacteristic
343#399C22×C1112yes—
344#398—21no—
345#394—21no—
346#394—22no—
347#393C22×C1112yes—
348#381C22×C1111yescharacteristic
349#328C22×C1112yes—
350#328C22×C1112yes—
351#328C22×C1112yes—
352#327C22×C1112yes—
353#323C22×C1112yes—
354#323C22×C1112yes—
355C22×C11—21no—
356C22×C11—21no—
357C22×C11—21no—
358C22×C11—21no—
359C22×C11—21no—
360C22×C11—21no—
361C22×C11—21no—
362C22×C11—21no—
363C22×C11—41no—
364C22×C11—42no—
365C22×C11—41no—
366C22×C11—42no—
367C22×C11—41no—
368C22×C11—42no—
369C22×C11—82no—
370C22×C11—84no—
371C22×C11C2×#12011yescharacteristic
372C22×C11#57812yes—
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—21no—
376C4×C11—21no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—82no—
384C4×C11—81no—
385C4×C11—81no—
386C2×#41—22no—
387C2×#41—21no—
388C2×#41D4×C1111yescharacteristic
389C22×Q8D4×C1111yescharacteristic
390C22×Q8C23×C1111yescharacteristic
391C22×D4D4×C1112yes—
392C22×D4D4×C1111yescharacteristic
393C23×C4C23×C1111yescharacteristic
394C2×Q16—22no—
395C2×Q16—21no—
396C2×SD16—21no—
397C2×M16—21no—
398C22×C8—21no—
399C4⋊Q8—21no—
400#126—22no—
401#125—22no—
402#124—21no—
403#124—22no—
404#124—22no—
405#123—22no—
406#123—22no—
407#123—22no—
408#123—21no—
409#123—22no—
410C22⋊Q8—21no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8D4×C1112yes—
424C22⋊Q8D4×C1111yescharacteristic
425C22⋊Q8C23×C1112yes—
426C22⋊Q8C23×C1111yescharacteristic
427#121—21no—
428#121—22no—
429#121—22no—
430#121—22no—
431#121—22no—
432#121—22no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121—21no—
437#121D4×C1111yescharacteristic
438#121C23×C1111yescharacteristic
439#120—21no—
440#120—22no—
441C4×Q8—21no—
442C4×D4—22no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—22no—
447#117D4×C1111yescharacteristic
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4D4×C1111yescharacteristic
453C2×C4⋊C4D4×C1111yescharacteristic
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4C23×C1112yes—
462#107—22no—
463#107—21no—
464#106—21no—
465#103—22no—
466#103—21no—
467#103—21no—
468#103—22no—
469#103—21no—
470#102—21no—
471C22⋊C8—21no—
472C22⋊C8—21no—
473C22⋊C8C23×C1112yes—
474C22⋊C8C23×C1111yescharacteristic
475C22⋊C8C23×C1111yescharacteristic
476#95—21no—
477#95—22no—
478#95C23×C1112yes—
479C2×C11—22no—
480C2×C11—41no—
481C2×C11—41no—
482C2×C11—81no—
483C2×C11—82no—
484C2×C11#301111yescharacteristic
485C2×C11#301911yescharacteristic
486C2×C11#302611yescharacteristic
487C24C2×D4×C1112yes—
488C24C2×D4×C1111yescharacteristic
489#41—81no—
490#41—84no—
491#41—82no—
492C2×Q8—22no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—81no—
497C2×Q8—81no—
498C2×Q8C2×D4×C1111yescharacteristic
499C2×Q8C2×D4×C1112yes—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—81no—
510C2×D4—82no—
511C2×D4C2×D4×C1111yescharacteristic
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—81no—
522C22×C4C2×D4×C1112yes—
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1111yescharacteristic
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C24×C1111yescharacteristic
529Q16—82no—
530Q16—81no—
531SD16—81no—
532M16—81no—
533C2×C8—21no—
534C2×C8—22no—
535C2×C8—21no—
536C2×C8—81no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—82no—
553C4⋊C4C2×D4×C1111yescharacteristic
554C4⋊C4C2×D4×C1112yes—
555C4⋊C4C2×D4×C1111yescharacteristic
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—21no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—81no—
573C22⋊C4—82no—
574C22⋊C4—82no—
575C42—22no—
576C42—21no—
577C11#1845311yescharacteristic, direct product factor, Sylow
578C23—22no—
579C23—22no—
580C23—21no—
581C23—24no—
582C23—41no—
583C23—41no—
584C23—42no—
585C23—42no—
586C23C11×#12011yescharacteristic
587C23C11×#12011yescharacteristic
588C23C22×D4×C1111yescharacteristic
589Q8—42no—
590Q8—41no—
591Q8—42no—
592Q8—41no—
593Q8—41no—
594Q8—42no—
595Q8—82no—
596D4—41no—
597D4—42no—
598D4—44no—
599D4—42no—
600D4—42no—
601D4—81no—
602D4—82no—
603D4—81no—
604D4—82no—
605D4—82no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—81no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4—82no—
633C2×C4C11×#12011yescharacteristic
634C2×C4C11×#12011yescharacteristic
635C2×C4C22×D4×C1111yescharacteristic
636C2×C4C22×D4×C1111yescharacteristic
637C8—42no—
638C8—41no—
639C8—41no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—41no—
649C22—42no—
650C22—41no—
651C22—42no—
652C22—41no—
653C22—42no—
654C22—82no—
655C22—84no—
656C22C2×C11×#12011yescharacteristic
657C22C11×#57812yes—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—21no—
662C4—41no—
663C4—42no—
664C4—42no—
665C4—41no—
666C4—41no—
667C4—42no—
668C4—82no—
669C4—81no—
670C4—81no—
671C2—22no—
672C2—41no—
673C2—41no—
674C2—82no—
675C2—81no—
676C2C11×#301111yescharacteristic
677C2C11×#301911yescharacteristic
678C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3536C2
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. C11×#3196C2semidirect
3. C11×#3189C2semidirect
4. C11×#2816C2semidirect
5. C11×#1618C2semidirect
6. C11×#1614C2semidirect
7. C11×#1606C2semidirect
8. C11×#1602C2semidirect
9. C11×#1516C2semidirect
10. C11×#1511C2semidirect
11. C11×#1471C2semidirect
148. #18453C11direct (N × H)
240. #3196C2×C11semidirect
241. #3189C2×C11semidirect
242. #2816C2×C11semidirect
243. #1618C2×C11semidirect
244. #1614C2×C11semidirect
245. #1606C2×C11semidirect
246. #1602C2×C11semidirect
247. #1516C2×C11semidirect
248. #1511C2×C11semidirect
249. #1471C2×C11semidirect
577. C11#18453direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35362
C11×#31962
C11×#31892
C11×#28162
C11×#16182
C11×#16142
C11×#16062
C11×#16022
C11×#15162
C11×#15112
C11×#14712
#1845311