Finite Group Databasebeta

← C11×#18291 #14595484

Subgroups — C11×#18291 #14595484

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3459C211yesmaximal, characteristic
2C11×#3190C212yesmaximal, complemented
3C11×#2638C211yesmaximal, characteristic, complemented
4C11×#1609C212yesmaximal, complemented
5C11×#1608C211yesmaximal, characteristic, complemented
6C11×#1607C211yesmaximal, characteristic, complemented
7C11×#1603C212yesmaximal, complemented
8C11×#1602C211yesmaximal, characteristic, complemented
9C11×#1601C211yesmaximal, characteristic, complemented
10C11×#1516C212yesmaximal, complemented
11C11×#1459C211yesmaximal, characteristic, complemented
12C11×#543C2211yescharacteristic
13C11×#539—22no—
14C11×#539C2212yes—
15C11×#538—22no—
16C11×#538—21no—
17C11×#534—21no—
18C11×#534C2211yescharacteristic
19C11×#529—22no—
20C11×#529—21no—
21C11×#525—22no—
22C11×#525C2212yes—
23C2×C11×C22⋊Q8C2211yescharacteristic, complemented
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C11×#485—22no—
27C11×#483C2212yescomplemented
28C11×#480C2212yes—
29C11×#467—22no—
30C11×#465—22no—
31C11×#452—22no—
32C11×#451C2212yescomplemented
33C11×#448C2212yes—
34C2×C11×C22⋊C8C2212yescomplemented
35C11×#398C2211yescharacteristic, complemented
36C11×#397—21no—
37C11×#397C2211yescharacteristic
38C11×#395C2211yescharacteristic, complemented
39C11×#394—21no—
40C11×#393C2211yescharacteristic
41C11×#387—21no—
42C11×#385—21no—
43C11×#381C2211yescharacteristic, complemented
44C11×#328C2212yescomplemented
45C11×#328C2212yescomplemented
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2212yescomplemented
49C11×#323C2211yescharacteristic
50C11×#323C2211yescharacteristic
51C2×C11×#41D412yes—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×Q16—22no—
59C2×C11×SD16—22no—
60C22×C8×C11—22no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#126—22no—
64C11×#125—21no—
65C11×#125—22no—
66C11×#124—22no—
67C11×#124—21no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8D412yes—
81C11×C22⋊Q8C2312yes—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—21no—
86C11×#121D412yes—
87C11×#121C2312yes—
88C11×#120—22no—
89C11×#120—22no—
90C11×#120—22no—
91C4×Q8×C11—21no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—21no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C11×#117—22no—
101C11×#117D412yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C11×C22⋊C4C2311yescharacteristic
116C2×C42×C11—21no—
117C2×C42×C11D411yescharacteristic
118C11×#107—22no—
119C11×#106—22no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—22no—
123C11×#102—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8C2312yes—
126C11×C22⋊C8C2312yes—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18291C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C24×C11C2×D411yescharacteristic
138C11×#41—82no—
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—81no—
142C2×Q8×C11C2×D412yes—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—41no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11C2×D412yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—81no—
166C22×C4×C11—81no—
167C22×C4×C11—82no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2411yescharacteristic
175C11×Q16—82no—
176C11×SD16—82no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—82no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—81no—
194C11×C4⋊C4C2×D412yes—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C42×C11—22no—
213C42×C11—22no—
214C42×C11—21no—
215C42×C11—21no—
216#3459C2×C1111yescharacteristic
217#3190C2×C1112yescomplemented
218#2638C2×C1111yescharacteristic, complemented
219#1609C2×C1112yescomplemented
220#1608C2×C1111yescharacteristic, complemented
221#1607C2×C1111yescharacteristic, complemented
222#1603C2×C1112yescomplemented
223#1602C2×C1111yescharacteristic, complemented
224#1601C2×C1111yescharacteristic, complemented
225#1516C2×C1112yescomplemented
226#1459C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—42no—
237C23×C11—81no—
238C23×C11—81no—
239C23×C11#12012yes—
240C23×C11#13512yes—
241C23×C11C22×D411yescharacteristic
242Q8×C11—42no—
243Q8×C11—42no—
244Q8×C11—42no—
245Q8×C11—81no—
246D4×C11—42no—
247D4×C11—44no—
248D4×C11—44no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—82no—
252D4×C11—82no—
253D4×C11—81no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—44no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—81no—
284C2×C4×C11—81no—
285C2×C4×C11—82no—
286C2×C4×C11—81no—
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11#12011yescharacteristic
289C2×C4×C11C22×D412yes—
290C8×C11—42no—
291C8×C11—42no—
292#543C22×C1111yescharacteristic
293#539—22no—
294#539C22×C1112yes—
295#538—22no—
296#538—21no—
297#534—21no—
298#534C22×C1111yescharacteristic
299#529—22no—
300#529—21no—
301#525—22no—
302#525C22×C1112yes—
303C2×C22⋊Q8C22×C1111yescharacteristic, complemented
304C2×C4×D4—21no—
305C2×C4×D4C22×C1111yescharacteristic
306#485—22no—
307#483C22×C1112yescomplemented
308#480C22×C1112yes—
309#467—22no—
310#465—22no—
311#452—22no—
312#451C22×C1112yescomplemented
313#448C22×C1112yes—
314C2×C22⋊C8C22×C1112yescomplemented
315#398C22×C1111yescharacteristic, complemented
316#397—21no—
317#397C22×C1111yescharacteristic
318#395C22×C1111yescharacteristic, complemented
319#394—21no—
320#393C22×C1111yescharacteristic
321#387—21no—
322#385—21no—
323#381C22×C1111yescharacteristic, complemented
324#328C22×C1112yescomplemented
325#328C22×C1112yescomplemented
326#327C22×C1112yes—
327#327C22×C1112yes—
328#324C22×C1112yescomplemented
329#323C22×C1111yescharacteristic
330#323C22×C1111yescharacteristic
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—42no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—84no—
347C22×C11C2×#12011yescharacteristic
348C22×C11C2×#13511yescharacteristic
349C22×C11#57511yescharacteristic
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11—81no—
363C2×#41D4×C1112yes—
364C22×Q8C23×C1111yescharacteristic
365C22×D4—21no—
366C22×D4D4×C1111yescharacteristic
367C23×C4—21no—
368C23×C4D4×C1111yescharacteristic
369C23×C4C23×C1111yescharacteristic
370C2×Q16—22no—
371C2×SD16—22no—
372C22×C8—22no—
373#126—22no—
374#126—22no—
375#126—22no—
376#125—21no—
377#125—22no—
378#124—22no—
379#124—21no—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—21no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8D4×C1112yes—
393C22⋊Q8C23×C1112yes—
394#121—22no—
395#121—22no—
396#121—22no—
397#121—21no—
398#121D4×C1112yes—
399#121C23×C1112yes—
400#120—22no—
401#120—22no—
402#120—22no—
403C4×Q8—21no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—21no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412#117—22no—
413#117D4×C1112yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4D4×C1111yescharacteristic
427C2×C22⋊C4C23×C1111yescharacteristic
428C2×C42—21no—
429C2×C42D4×C1111yescharacteristic
430#107—22no—
431#106—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#102—22no—
436C22⋊C8—22no—
437C22⋊C8C23×C1112yes—
438C22⋊C8C23×C1112yes—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95C23×C1111yescharacteristic
445#95C23×C1111yescharacteristic
446C2×C11—21no—
447C2×C11—21no—
448C2×C11—42no—
449C2×C11—42no—
450C2×C11—82no—
451C2×C11#300211yescharacteristic
452C2×C11#302211yescharacteristic
453C2×C11#302611yescharacteristic
454C24—21no—
455C24C2×D4×C1111yescharacteristic
456C24C2×D4×C1111yescharacteristic
457#41—82no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—81no—
461C2×Q8C2×D4×C1112yes—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—41no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4C2×D4×C1112yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—82no—
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C2×D4×C1111yescharacteristic
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1112yes—
492C22×C4C2×D4×C1112yes—
493C22×C4C24×C1111yescharacteristic
494Q16—82no—
495SD16—82no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—82no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—42no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—81no—
513C4⋊C4C2×D4×C1112yes—
514C4⋊C4C2×D4×C1112yes—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—81no—
530C22⋊C4—81no—
531C42—22no—
532C42—22no—
533C42—21no—
534C42—21no—
535C11#1829111yescharacteristic, direct product factor, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—42no—
546C23—81no—
547C23—81no—
548C23C11×#12012yes—
549C23C11×#13512yes—
550C23C22×D4×C1111yescharacteristic
551Q8—42no—
552Q8—42no—
553Q8—42no—
554Q8—81no—
555D4—42no—
556D4—44no—
557D4—44no—
558D4—42no—
559D4—42no—
560D4—82no—
561D4—82no—
562D4—81no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—82no—
595C2×C4—81no—
596C2×C4C11×#12011yescharacteristic
597C2×C4C11×#12011yescharacteristic
598C2×C4C22×D4×C1112yes—
599C8—42no—
600C8—42no—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—84no—
617C22C2×C11×#12011yescharacteristic
618C22C2×C11×#13511yescharacteristic
619C22C11×#57511yescharacteristic
620C4—22no—
621C4—21no—
622C4—21no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—42no—
627C4—41no—
628C4—42no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—81no—
633C2—21no—
634C2—21no—
635C2—42no—
636C2—42no—
637C2—82no—
638C2C11×#300211yescharacteristic
639C2C11×#302211yescharacteristic
640C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3459C2
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×#3190C2semidirect
3. C11×#2638C2semidirect
4. C11×#1609C2semidirect
5. C11×#1608C2semidirect
6. C11×#1607C2semidirect
7. C11×#1603C2semidirect
8. C11×#1602C2semidirect
9. C11×#1601C2semidirect
10. C11×#1516C2semidirect
11. C11×#1459C2semidirect
23. C2×C11×C22⋊Q8C22semidirect
27. C11×#483C22semidirect
32. C11×#451C22semidirect
34. C2×C11×C22⋊C8C22semidirect
35. C11×#398C22semidirect
38. C11×#395C22semidirect
43. C11×#381C22semidirect
44. C11×#328C22semidirect
45. C11×#328C22semidirect
48. C11×#324C22semidirect
134. #18291C11direct (N × H)
217. #3190C2×C11semidirect
218. #2638C2×C11semidirect
219. #1609C2×C11semidirect
220. #1608C2×C11semidirect
221. #1607C2×C11semidirect
222. #1603C2×C11semidirect
223. #1602C2×C11semidirect
224. #1601C2×C11semidirect
225. #1516C2×C11semidirect
226. #1459C2×C11semidirect
303. C2×C22⋊Q8C22×C11semidirect
307. #483C22×C11semidirect
312. #451C22×C11semidirect
314. C2×C22⋊C8C22×C11semidirect
315. #398C22×C11semidirect
318. #395C22×C11semidirect
323. #381C22×C11semidirect
324. #328C22×C11semidirect
325. #328C22×C11semidirect
328. #324C22×C11semidirect
535. C11#18291direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34592
C11×#31902
C11×#26382
C11×#16092
C11×#16082
C11×#16072
C11×#16032
C11×#16022
C11×#16012
C11×#15162
C11×#14592
#1829111