Finite Group Databasebeta

← C11×#18957 #14596150

Subgroups — C11×#18957 #14596150

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3547C211yesmaximal, characteristic
2C11×#3238C211yesmaximal, characteristic, complemented
3C11×#3227C211yesmaximal, characteristic, complemented
4C11×#3209C211yesmaximal, characteristic, complemented
5C11×#1637C212yesmaximal, complemented
6C11×#1635C212yesmaximal, complemented
7C11×#1634C212yesmaximal, complemented
8C11×#1632C212yesmaximal, complemented
9C11×#1554C211yesmaximal, characteristic, complemented
10C11×#1496C211yesmaximal, characteristic, complemented
11C11×#1482C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#555—21no—
14C11×#555C2211yescharacteristic
15C11×#554C2211yescharacteristic
16C11×#553—21no—
17C11×#552—21no—
18D4×Q8×C11C2211yescharacteristic
19C11×#548—21no—
20C11×#547C2211yescharacteristic
21C11×#544—21no—
22C11×#542—22no—
23C11×#540—21no—
24C11×#537—21no—
25C11×#536—21no—
26C11×#533C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic
29C11×#529C2211yescharacteristic
30C11×#501—21no—
31C11×#498—21no—
32C11×#494C2212yes—
33C11×#489—21no—
34C11×#487C2212yes—
35C11×#486—21no—
36C11×#483—21no—
37C11×#481—21no—
38C11×#481—21no—
39C11×#480—21no—
40C11×#477C2212yes—
41C11×#476C2212yes—
42C11×#476C2212yes—
43C11×#476C2212yes—
44C11×#462—22no—
45C11×#451—22no—
46C11×#432C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#431C2211yescharacteristic
49C11×#333C2212yes—
50C11×#332C2212yes—
51C11×Q8⋊C8C2212yes—
52C11×D4⋊C8C2212yes—
53C11×D4⋊C8C2212yes—
54C11×D4⋊C8C2212yes—
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11—21no—
59C2×C11×Q16—24no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8D411yescharacteristic
66C11×C4⋊Q8C2312yes—
67C11×C4⋊Q8C2311yescharacteristic
68C11×C4⋊Q8C2311yescharacteristic
69C11×#127D411yescharacteristic
70C11×#126—22no—
71C11×#126—21no—
72C11×#125—22no—
73C11×#125—21no—
74C11×#125—21no—
75C11×#125D411yescharacteristic
76C11×#124—22no—
77C11×#124—22no—
78C11×#124—22no—
79C11×#124—21no—
80C11×#124D411yescharacteristic
81C11×#123—22no—
82C11×#123—22no—
83C11×#123—22no—
84C11×#123—21no—
85C11×#123—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8D411yescharacteristic
95C11×C22⋊Q8D412yes—
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—21no—
101C11×#121—21no—
102C11×#121—21no—
103C11×#121—21no—
104C11×#121D411yescharacteristic
105C11×#121D411yescharacteristic
106C11×#121D411yescharacteristic
107C4×Q8×C11—21no—
108C4×Q8×C11D412yes—
109C4×Q8×C11C2311yescharacteristic
110C4×D4×C11—22no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11—21no—
115C4×D4×C11C2311yescharacteristic
116C4×D4×C11C2311yescharacteristic
117C4×D4×C11C2311yescharacteristic
118C11×#117—22no—
119C11×#117—21no—
120C11×#117—21no—
121C11×#117—21no—
122C11×#117—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C42×C11C2311yescharacteristic
128C11×#107—22no—
129C11×#106—22no—
130C11×#106—22no—
131C11×#106—22no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#103—22no—
136C11×#103—24no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—22no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C4×C8×C11—21no—
145C4×C8×C11C2312yes—
146#18957C1111yesmaximal, characteristic, direct product factor, Sylow
147C11×#41—82no—
148C11×#41—82no—
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11—41no—
154C2×Q8×C11—82no—
155C2×Q8×C11—82no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×Q8×C11C2×D412yes—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11C2×D411yescharacteristic
166C2×D4×C11C2×D411yescharacteristic
167C2×D4×C11C2×D411yescharacteristic
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—41no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C11×Q16—84no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—41no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4C2×D412yes—
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C42×C11—22no—
221C42×C11—22no—
222C42×C11—21no—
223C42×C11C2×D411yescharacteristic
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2411yescharacteristic
227#3547C2×C1111yescharacteristic
228#3238C2×C1111yescharacteristic, complemented
229#3227C2×C1111yescharacteristic, complemented
230#3209C2×C1111yescharacteristic, complemented
231#1637C2×C1112yescomplemented
232#1635C2×C1112yescomplemented
233#1634C2×C1112yescomplemented
234#1632C2×C1112yescomplemented
235#1554C2×C1111yescharacteristic, complemented
236#1496C2×C1111yescharacteristic, complemented
237#1482C2×C1111yescharacteristic, complemented
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11#12011yescharacteristic
242Q8×C11—22no—
243Q8×C11—42no—
244Q8×C11—44no—
245Q8×C11—42no—
246Q8×C11—81no—
247Q8×C11—82no—
248Q8×C11—82no—
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—81no—
253D4×C11—81no—
254D4×C11—81no—
255D4×C11—81no—
256D4×C11—81no—
257D4×C11—82no—
258D4×C11—82no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—82no—
274C2×C4×C11—82no—
275C2×C4×C11—82no—
276C2×C4×C11—82no—
277C2×C4×C11#12011yescharacteristic
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C8×C11—42no—
284C8×C11—42no—
285C8×C11—42no—
286#562—22no—
287#555—21no—
288#555C22×C1111yescharacteristic
289#554C22×C1111yescharacteristic
290#553—21no—
291#552—21no—
292D4×Q8C22×C1111yescharacteristic
293#548—21no—
294#547C22×C1111yescharacteristic
295#544—21no—
296#542—22no—
297#540—21no—
298#537—21no—
299#536—21no—
300#533C22×C1111yescharacteristic
301#532C22×C1111yescharacteristic
302C2×C4⋊Q8C22×C1111yescharacteristic
303#529C22×C1111yescharacteristic
304#501—21no—
305#498—21no—
306#494C22×C1112yes—
307#489—21no—
308#487C22×C1112yes—
309#486—21no—
310#483—21no—
311#481—21no—
312#481—21no—
313#480—21no—
314#477C22×C1112yes—
315#476C22×C1112yes—
316#476C22×C1112yes—
317#476C22×C1112yes—
318#462—22no—
319#451—22no—
320#432C22×C1111yescharacteristic
321#431C22×C1111yescharacteristic
322#431C22×C1111yescharacteristic
323#333C22×C1112yes—
324#332C22×C1112yes—
325Q8⋊C8C22×C1112yes—
326D4⋊C8C22×C1112yes—
327D4⋊C8C22×C1112yes—
328D4⋊C8C22×C1112yes—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×#12011yescharacteristic
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—82no—
354C4×C11#57712yes—
355C4×C11#57812yes—
356C2×#41—21no—
357C2×#41—21no—
358C22×Q8—21no—
359C22×Q8—21no—
360C2×Q16—24no—
361C4⋊Q8—22no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8D4×C1111yescharacteristic
367C4⋊Q8C23×C1112yes—
368C4⋊Q8C23×C1111yescharacteristic
369C4⋊Q8C23×C1111yescharacteristic
370#127D4×C1111yescharacteristic
371#126—22no—
372#126—21no—
373#125—22no—
374#125—21no—
375#125—21no—
376#125D4×C1111yescharacteristic
377#124—22no—
378#124—22no—
379#124—22no—
380#124—21no—
381#124D4×C1111yescharacteristic
382#123—22no—
383#123—22no—
384#123—22no—
385#123—21no—
386#123—22no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—21no—
390C22⋊Q8—22no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—22no—
395C22⋊Q8D4×C1111yescharacteristic
396C22⋊Q8D4×C1112yes—
397#121—22no—
398#121—22no—
399#121—22no—
400#121—22no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121D4×C1111yescharacteristic
406#121D4×C1111yescharacteristic
407#121D4×C1111yescharacteristic
408C4×Q8—21no—
409C4×Q8D4×C1112yes—
410C4×Q8C23×C1111yescharacteristic
411C4×D4—22no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4C23×C1111yescharacteristic
417C4×D4C23×C1111yescharacteristic
418C4×D4C23×C1111yescharacteristic
419#117—22no—
420#117—21no—
421#117—21no—
422#117—21no—
423#117—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C42C23×C1111yescharacteristic
429#107—22no—
430#106—22no—
431#106—22no—
432#106—22no—
433C4⋊C8—21no—
434C4⋊C8C23×C1112yes—
435C4⋊C8C23×C1112yes—
436#103—22no—
437#103—24no—
438#102—22no—
439#102—22no—
440#102—22no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444#97—21no—
445C4×C8—21no—
446C4×C8C23×C1112yes—
447C2×C11—41no—
448C2×C11—81no—
449C2×C11—81no—
450C2×C11—81no—
451C2×C11#300911yescharacteristic
452C2×C11#301111yescharacteristic
453C2×C11#302111yescharacteristic
454#41—82no—
455#41—82no—
456C2×Q8—22no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—41no—
461C2×Q8—82no—
462C2×Q8—82no—
463C2×Q8C2×D4×C1111yescharacteristic
464C2×Q8C2×D4×C1112yes—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4C2×D4×C1111yescharacteristic
473C2×D4C2×D4×C1111yescharacteristic
474C2×D4C2×D4×C1111yescharacteristic
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C2×D4×C1111yescharacteristic
485Q16—84no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4C2×D4×C1112yes—
508C4⋊C4C2×D4×C1111yescharacteristic
509C4⋊C4C2×D4×C1111yescharacteristic
510C4⋊C4C2×D4×C1111yescharacteristic
511C4⋊C4C2×D4×C1111yescharacteristic
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C42—22no—
528C42—22no—
529C42—21no—
530C42C2×D4×C1111yescharacteristic
531C42C2×D4×C1111yescharacteristic
532C42C2×D4×C1111yescharacteristic
533C42C24×C1111yescharacteristic
534C11#1895711yescharacteristic, direct product factor, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23C11×#12011yescharacteristic
539Q8—22no—
540Q8—42no—
541Q8—44no—
542Q8—42no—
543Q8—81no—
544Q8—82no—
545Q8—82no—
546D4—22no—
547D4—22no—
548D4—22no—
549D4—81no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4C11×#12011yescharacteristic
575C2×C4C11×#12011yescharacteristic
576C2×C4C11×#12011yescharacteristic
577C2×C4C22×D4×C1111yescharacteristic
578C2×C4C22×D4×C1111yescharacteristic
579C2×C4C22×D4×C1111yescharacteristic
580C8—42no—
581C8—42no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C2×C11×#12011yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—42no—
607C4—82no—
608C4C11×#57712yes—
609C4C11×#57812yes—
610C2—41no—
611C2—81no—
612C2—81no—
613C2—81no—
614C2C11×#300911yescharacteristic
615C2C11×#301111yescharacteristic
616C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3547C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3238C2semidirect
3. C11×#3227C2semidirect
4. C11×#3209C2semidirect
5. C11×#1637C2semidirect
6. C11×#1635C2semidirect
7. C11×#1634C2semidirect
8. C11×#1632C2semidirect
9. C11×#1554C2semidirect
10. C11×#1496C2semidirect
11. C11×#1482C2semidirect
146. #18957C11direct (N × H)
228. #3238C2×C11semidirect
229. #3227C2×C11semidirect
230. #3209C2×C11semidirect
231. #1637C2×C11semidirect
232. #1635C2×C11semidirect
233. #1634C2×C11semidirect
234. #1632C2×C11semidirect
235. #1554C2×C11semidirect
236. #1496C2×C11semidirect
237. #1482C2×C11semidirect
534. C11#18957direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35472
C11×#32382
C11×#32272
C11×#32092
C11×#16372
C11×#16352
C11×#16342
C11×#16322
C11×#15542
C11×#14962
C11×#14822
#1895711