Finite Group Databasebeta

← C11×#18457 #14595650

Subgroups — C11×#18457 #14595650

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3536C211yesmaximal, characteristic
2C11×#3196C211yesmaximal, characteristic, complemented
3C11×#3187C211yesmaximal, characteristic, complemented
4C11×#2817C211yesmaximal, characteristic, complemented
5C11×#1616C212yesmaximal, complemented
6C11×#1615C212yesmaximal, complemented
7C11×#1604C212yesmaximal, complemented
8C11×#1603C212yesmaximal, complemented
9C11×#1516C211yesmaximal, characteristic, complemented
10C11×#1510C211yesmaximal, characteristic, complemented
11C11×#1472C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#554—21no—
14C11×#548—21no—
15C11×#547—21no—
16C11×#546—21no—
17C11×#546—22no—
18C11×#543—21no—
19C11×#542—21no—
20C11×#539C2212yes—
21C11×#538—21no—
22C11×#537—21no—
23C11×#537C2212yes—
24C11×#525C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C11×#485—21no—
29C11×#484C2211yescharacteristic, complemented
30C11×#483—21no—
31C11×#481C2212yes—
32C11×#481C2211yescharacteristic, complemented
33C11×#470—21no—
34C11×#468—21no—
35C11×#465—22no—
36C11×#452—21no—
37C11×#451C2211yescharacteristic, complemented
38C11×#450—21no—
39C11×#448C2212yes—
40C11×#448C2211yescharacteristic, complemented
41C11×#407C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43C11×#400—21no—
44C11×#400C2212yescomplemented
45C11×#397—22no—
46C11×#395—21no—
47C11×#395C2212yescomplemented
48C11×#381C2211yescharacteristic
49C11×#328C2212yescomplemented
50C11×#327C2212yes—
51C11×#327C2212yes—
52C11×#327C2212yescomplemented
53C11×#324C2212yescomplemented
54C11×#324C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—22no—
57C2×C11×#41D411yescharacteristic
58C22×Q8×C11D411yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×C11×Q16—21no—
64C2×C11×SD16—22no—
65C2×C11×SD16—21no—
66C2×C11×M16—21no—
67C22×C8×C11—21no—
68C11×C4⋊Q8—21no—
69C11×#126—22no—
70C11×#125—22no—
71C11×#124—22no—
72C11×#124—21no—
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—22no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8D411yescharacteristic
95C11×C22⋊Q8C2311yescharacteristic
96C11×#121—21no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—22no—
101C11×#121—21no—
102C11×#121—21no—
103C11×#121—22no—
104C11×#121D412yes—
105C11×#121D411yescharacteristic
106C11×#121C2312yes—
107C11×#121C2311yescharacteristic
108C11×#120—22no—
109C11×#120—21no—
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—22no—
120C2×C11×C4⋊C4D411yescharacteristic
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2312yes—
124C2×C11×C22⋊C4—22no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4D412yes—
129C11×#107—21no—
130C11×#106—22no—
131C11×#106—21no—
132C11×#103—21no—
133C11×#103—22no—
134C11×#103—21no—
135C11×#103—21no—
136C11×#102—22no—
137C11×#102—21no—
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C11×C22⋊C8C2311yescharacteristic
141C11×C22⋊C8C2311yescharacteristic
142C11×C22⋊C8C2312yes—
143C11×#95—21no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95C2312yes—
148#18457C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C11×#41—84no—
152C11×#41—81no—
153C11×#41—82no—
154C2×Q8×C11—22no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—81no—
160C2×Q8×C11—81no—
161C2×Q8×C11C2×D411yescharacteristic
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—21no—
168C2×D4×C11—22no—
169C2×D4×C11—21no—
170C2×D4×C11—81no—
171C2×D4×C11—82no—
172C2×D4×C11C2×D411yescharacteristic
173C2×D4×C11C2×D412yes—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—81no—
183C22×C4×C11C2×D412yes—
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—81no—
192C11×SD16—82no—
193C11×SD16—81no—
194C11×M16—81no—
195C2×C8×C11—22no—
196C2×C8×C11—21no—
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—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—22no—
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×D412yes—
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—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—21no—
227C11×C22⋊C4—21no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—21no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—21no—
232C11×C22⋊C4—41no—
233C11×C22⋊C4—41no—
234C11×C22⋊C4—81no—
235C42×C11—22no—
236C42×C11—21no—
237#3536C2×C1111yescharacteristic
238#3196C2×C1111yescharacteristic, complemented
239#3187C2×C1111yescharacteristic, complemented
240#2817C2×C1111yescharacteristic, complemented
241#1616C2×C1112yescomplemented
242#1615C2×C1112yescomplemented
243#1604C2×C1112yescomplemented
244#1603C2×C1112yescomplemented
245#1516C2×C1111yescharacteristic, complemented
246#1510C2×C1111yescharacteristic, complemented
247#1472C2×C1111yescharacteristic, complemented
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—21no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—42no—
254C23×C11—81no—
255C23×C11—81no—
256C23×C11#12011yescharacteristic
257C23×C11#12011yescharacteristic
258C23×C11C22×D411yescharacteristic
259Q8×C11—41no—
260Q8×C11—42no—
261Q8×C11—42no—
262Q8×C11—41no—
263Q8×C11—41no—
264Q8×C11—81no—
265Q8×C11—82no—
266D4×C11—42no—
267D4×C11—41no—
268D4×C11—42no—
269D4×C11—42no—
270D4×C11—44no—
271D4×C11—42no—
272D4×C11—82no—
273D4×C11—81no—
274D4×C11—82no—
275D4×C11—82no—
276C2×C4×C11—21no—
277C2×C4×C11—22no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—24no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—42no—
298C2×C4×C11—81no—
299C2×C4×C11—82no—
300C2×C4×C11—82no—
301C2×C4×C11—82no—
302C2×C4×C11#12011yescharacteristic
303C2×C4×C11#12011yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C8×C11—42no—
307C8×C11—41no—
308C8×C11—41no—
309#562—22no—
310#554—21no—
311#548—21no—
312#547—21no—
313#546—21no—
314#546—22no—
315#543—21no—
316#542—21no—
317#539C22×C1112yes—
318#538—21no—
319#537—21no—
320#537C22×C1112yes—
321#525C22×C1111yescharacteristic
322C2×C22⋊Q8C22×C1111yescharacteristic
323C2×C22⋊Q8C22×C1111yescharacteristic
324C2×#121C22×C1111yescharacteristic
325#485—21no—
326#484C22×C1111yescharacteristic, complemented
327#483—21no—
328#481C22×C1112yes—
329#481C22×C1111yescharacteristic, complemented
330#470—21no—
331#468—21no—
332#465—22no—
333#452—21no—
334#451C22×C1111yescharacteristic, complemented
335#450—21no—
336#448C22×C1112yes—
337#448C22×C1111yescharacteristic, complemented
338#407C22×C1111yescharacteristic
339C2×C22⋊C8C22×C1111yescharacteristic
340#400—21no—
341#400C22×C1112yescomplemented
342#397—22no—
343#395—21no—
344#395C22×C1112yescomplemented
345#381C22×C1111yescharacteristic
346#328C22×C1112yescomplemented
347#327C22×C1112yes—
348#327C22×C1112yes—
349#327C22×C1112yescomplemented
350#324C22×C1112yescomplemented
351#324C22×C1112yescomplemented
352C22×C11—21no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—21no—
357C22×C11—21no—
358C22×C11—21no—
359C22×C11—21no—
360C22×C11—41no—
361C22×C11—42no—
362C22×C11—41no—
363C22×C11—42no—
364C22×C11—41no—
365C22×C11—42no—
366C22×C11—82no—
367C22×C11—162no—
368C22×C11C2×#12011yescharacteristic
369C22×C11#57712yes—
370C4×C11—21no—
371C4×C11—21no—
372C4×C11—21no—
373C4×C11—21no—
374C4×C11—42no—
375C4×C11—42no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—42no—
380C4×C11—82no—
381C4×C11—81no—
382C4×C11—81no—
383C2×#41—21no—
384C2×#41—22no—
385C2×#41D4×C1111yescharacteristic
386C22×Q8D4×C1111yescharacteristic
387C22×Q8C23×C1111yescharacteristic
388C22×D4—21no—
389C22×D4D4×C1111yescharacteristic
390C23×C4C23×C1111yescharacteristic
391C2×Q16—21no—
392C2×SD16—22no—
393C2×SD16—21no—
394C2×M16—21no—
395C22×C8—21no—
396C4⋊Q8—21no—
397#126—22no—
398#125—22no—
399#124—22no—
400#124—21no—
401#124—22no—
402#123—22no—
403#123—22no—
404#123—22no—
405#123—21no—
406#123—22no—
407C22⋊Q8—21no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8D4×C1111yescharacteristic
423C22⋊Q8C23×C1111yescharacteristic
424#121—21no—
425#121—22no—
426#121—22no—
427#121—22no—
428#121—22no—
429#121—21no—
430#121—21no—
431#121—22no—
432#121D4×C1112yes—
433#121D4×C1111yescharacteristic
434#121C23×C1112yes—
435#121C23×C1111yescharacteristic
436#120—22no—
437#120—21no—
438C4×Q8—21no—
439C4×D4—22no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—22no—
444#117D4×C1111yescharacteristic
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4D4×C1111yescharacteristic
449C2×C4⋊C4D4×C1111yescharacteristic
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C4⋊C4C23×C1112yes—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C1112yes—
457#107—21no—
458#106—22no—
459#106—21no—
460#103—21no—
461#103—22no—
462#103—21no—
463#103—21no—
464#102—22no—
465#102—21no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8C23×C1111yescharacteristic
469C22⋊C8C23×C1111yescharacteristic
470C22⋊C8C23×C1112yes—
471#95—21no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95C23×C1112yes—
476C2×C11—22no—
477C2×C11—41no—
478C2×C11—41no—
479C2×C11—81no—
480C2×C11—82no—
481C2×C11#300911yescharacteristic
482C2×C11#302011yescharacteristic
483C2×C11#302611yescharacteristic
484C24—21no—
485C24C2×D4×C1111yescharacteristic
486#41—84no—
487#41—81no—
488#41—82no—
489C2×Q8—22no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—81no—
495C2×Q8—81no—
496C2×Q8C2×D4×C1111yescharacteristic
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—81no—
506C2×D4—82no—
507C2×D4C2×D4×C1111yescharacteristic
508C2×D4C2×D4×C1112yes—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—81no—
518C22×C4C2×D4×C1112yes—
519C22×C4C2×D4×C1112yes—
520C22×C4C2×D4×C1111yescharacteristic
521C22×C4C2×D4×C1111yescharacteristic
522C22×C4C2×D4×C1111yescharacteristic
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1111yescharacteristic
525C22×C4C24×C1111yescharacteristic
526Q16—81no—
527SD16—82no—
528SD16—81no—
529M16—81no—
530C2×C8—22no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—81no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—82no—
550C4⋊C4C2×D4×C1112yes—
551C4⋊C4C2×D4×C1111yescharacteristic
552C4⋊C4C2×D4×C1111yescharacteristic
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—21no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—22no—
564C22⋊C4—21no—
565C22⋊C4—22no—
566C22⋊C4—21no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—81no—
570C42—22no—
571C42—21no—
572C11#1845711yescharacteristic, direct product factor, Sylow
573C23—22no—
574C23—22no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—81no—
580C23—81no—
581C23C11×#12011yescharacteristic
582C23C11×#12011yescharacteristic
583C23C22×D4×C1111yescharacteristic
584Q8—41no—
585Q8—42no—
586Q8—42no—
587Q8—41no—
588Q8—41no—
589Q8—81no—
590Q8—82no—
591D4—42no—
592D4—41no—
593D4—42no—
594D4—42no—
595D4—44no—
596D4—42no—
597D4—82no—
598D4—81no—
599D4—82no—
600D4—82no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—81no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4—82no—
627C2×C4C11×#12011yescharacteristic
628C2×C4C11×#12011yescharacteristic
629C2×C4C22×D4×C1111yescharacteristic
630C2×C4C22×D4×C1111yescharacteristic
631C8—42no—
632C8—41no—
633C8—41no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—41no—
643C22—42no—
644C22—41no—
645C22—42no—
646C22—41no—
647C22—42no—
648C22—82no—
649C22—162no—
650C22C2×C11×#12011yescharacteristic
651C22C11×#57712yes—
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—82no—
663C4—81no—
664C4—81no—
665C2—22no—
666C2—41no—
667C2—41no—
668C2—82no—
669C2—81no—
670C2C11×#300911yescharacteristic
671C2C11×#302011yescharacteristic
672C2C11×#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×#3187C2semidirect
4. C11×#2817C2semidirect
5. C11×#1616C2semidirect
6. C11×#1615C2semidirect
7. C11×#1604C2semidirect
8. C11×#1603C2semidirect
9. C11×#1516C2semidirect
10. C11×#1510C2semidirect
11. C11×#1472C2semidirect
29. C11×#484C22semidirect
32. C11×#481C22semidirect
37. C11×#451C22semidirect
40. C11×#448C22semidirect
44. C11×#400C22semidirect
47. C11×#395C22semidirect
49. C11×#328C22semidirect
52. C11×#327C22semidirect
53. C11×#324C22semidirect
54. C11×#324C22semidirect
148. #18457C11direct (N × H)
238. #3196C2×C11semidirect
239. #3187C2×C11semidirect
240. #2817C2×C11semidirect
241. #1616C2×C11semidirect
242. #1615C2×C11semidirect
243. #1604C2×C11semidirect
244. #1603C2×C11semidirect
245. #1516C2×C11semidirect
246. #1510C2×C11semidirect
247. #1472C2×C11semidirect
326. #484C22×C11semidirect
329. #481C22×C11semidirect
334. #451C22×C11semidirect
337. #448C22×C11semidirect
341. #400C22×C11semidirect
344. #395C22×C11semidirect
346. #328C22×C11semidirect
349. #327C22×C11semidirect
350. #324C22×C11semidirect
351. #324C22×C11semidirect
572. C11#18457direct (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×#31872
C11×#28172
C11×#16162
C11×#16152
C11×#16042
C11×#16032
C11×#15162
C11×#15102
C11×#14722
#1845711