Finite Group Databasebeta

← C11×#18968 #14596161

Subgroups — C11×#18968 #14596161

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3547C211yesmaximal, characteristic
2C11×#3239C211yesmaximal, characteristic, complemented
3C11×#3229C211yesmaximal, characteristic, complemented
4C11×#3206C211yesmaximal, characteristic, complemented
5C11×#1654C212yesmaximal, complemented
6C11×#1651C212yesmaximal, complemented
7C11×#1646C212yesmaximal, complemented
8C11×#1643C212yesmaximal, 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×#498C2212yes—
32C11×#492—21no—
33C11×#489—21no—
34C11×#487—21no—
35C11×#487C2212yes—
36C11×#484—21no—
37C11×#483—22no—
38C11×#481—21no—
39C11×#475—22no—
40C11×#475C2212yes—
41C11×#474C2212yes—
42C11×#461C2212yes—
43C11×#461C2212yes—
44C11×#448—21no—
45C11×#448—21no—
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×SD16—22no—
60C2×C11×SD16—22no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8C2312yes—
68C11×C4⋊Q8C2311yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×#127D411yescharacteristic
71C11×#126—22no—
72C11×#126—21no—
73C11×#125—22no—
74C11×#125—21no—
75C11×#125—21no—
76C11×#125D411yescharacteristic
77C11×#124—22no—
78C11×#124—22no—
79C11×#124—22no—
80C11×#124—21no—
81C11×#124D411yescharacteristic
82C11×#123—22no—
83C11×#123—22no—
84C11×#123—22no—
85C11×#123—21no—
86C11×#123—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8D411yescharacteristic
96C11×C22⋊Q8D412yes—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—22no—
101C11×#121—21no—
102C11×#121—21no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121D411yescharacteristic
106C11×#121D411yescharacteristic
107C11×#121D411yescharacteristic
108C4×Q8×C11—21no—
109C4×Q8×C11D412yes—
110C4×Q8×C11C2311yescharacteristic
111C4×D4×C11—22no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11—21no—
115C4×D4×C11—21no—
116C4×D4×C11C2311yescharacteristic
117C4×D4×C11C2311yescharacteristic
118C4×D4×C11C2311yescharacteristic
119C11×#117—22no—
120C11×#117—21no—
121C11×#117—21no—
122C11×#117—21no—
123C11×#117—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C42×C11C2311yescharacteristic
129C11×#107—22no—
130C11×#106—24no—
131C11×#106—22no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#103—22no—
136C11×#103—24no—
137C11×#103—22no—
138C11×#103—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#18968C1111yesmaximal, 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×SD16—82no—
179C11×SD16—82no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4—41no—
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D412yes—
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
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—
220C11×C22⋊C4—21no—
221C42×C11—22no—
222C42×C11—22no—
223C42×C11—21no—
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2411yescharacteristic
228#3547C2×C1111yescharacteristic
229#3239C2×C1111yescharacteristic, complemented
230#3229C2×C1111yescharacteristic, complemented
231#3206C2×C1111yescharacteristic, complemented
232#1654C2×C1112yescomplemented
233#1651C2×C1112yescomplemented
234#1646C2×C1112yescomplemented
235#1643C2×C1112yescomplemented
236#1554C2×C1111yescharacteristic, complemented
237#1496C2×C1111yescharacteristic, complemented
238#1482C2×C1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11#12011yescharacteristic
243Q8×C11—22no—
244Q8×C11—42no—
245Q8×C11—42no—
246Q8×C11—42no—
247Q8×C11—42no—
248Q8×C11—81no—
249Q8×C11—82no—
250Q8×C11—82no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—81no—
255D4×C11—81no—
256D4×C11—81no—
257D4×C11—81no—
258D4×C11—81no—
259D4×C11—82no—
260D4×C11—82no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—82no—
276C2×C4×C11—82no—
277C2×C4×C11—82no—
278C2×C4×C11—82no—
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11#12011yescharacteristic
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C8×C11—42no—
286C8×C11—42no—
287C8×C11—42no—
288#562—22no—
289#555—21no—
290#555C22×C1111yescharacteristic
291#554C22×C1111yescharacteristic
292#553—21no—
293#552—21no—
294D4×Q8C22×C1111yescharacteristic
295#548—21no—
296#547C22×C1111yescharacteristic
297#544—21no—
298#542—22no—
299#540—21no—
300#537—21no—
301#536—21no—
302#533C22×C1111yescharacteristic
303#532C22×C1111yescharacteristic
304C2×C4⋊Q8C22×C1111yescharacteristic
305#529C22×C1111yescharacteristic
306#501—21no—
307#498C22×C1112yes—
308#492—21no—
309#489—21no—
310#487—21no—
311#487C22×C1112yes—
312#484—21no—
313#483—22no—
314#481—21no—
315#475—22no—
316#475C22×C1112yes—
317#474C22×C1112yes—
318#461C22×C1112yes—
319#461C22×C1112yes—
320#448—21no—
321#448—21no—
322#432C22×C1111yescharacteristic
323#431C22×C1111yescharacteristic
324#431C22×C1111yescharacteristic
325#333C22×C1112yes—
326#332C22×C1112yes—
327Q8⋊C8C22×C1112yes—
328D4⋊C8C22×C1112yes—
329D4⋊C8C22×C1112yes—
330D4⋊C8C22×C1112yes—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11C2×#12011yescharacteristic
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—82no—
356C4×C11#57712yes—
357C4×C11#57712yes—
358C2×#41—21no—
359C2×#41—21no—
360C22×Q8—21no—
361C22×Q8—21no—
362C2×SD16—22no—
363C2×SD16—22no—
364C4⋊Q8—22no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8D4×C1111yescharacteristic
370C4⋊Q8C23×C1112yes—
371C4⋊Q8C23×C1111yescharacteristic
372C4⋊Q8C23×C1111yescharacteristic
373#127D4×C1111yescharacteristic
374#126—22no—
375#126—21no—
376#125—22no—
377#125—21no—
378#125—21no—
379#125D4×C1111yescharacteristic
380#124—22no—
381#124—22no—
382#124—22no—
383#124—21no—
384#124D4×C1111yescharacteristic
385#123—22no—
386#123—22no—
387#123—22no—
388#123—21no—
389#123—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—21no—
393C22⋊Q8—22no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—22no—
398C22⋊Q8D4×C1111yescharacteristic
399C22⋊Q8D4×C1112yes—
400#121—22no—
401#121—22no—
402#121—22no—
403#121—22no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121D4×C1111yescharacteristic
409#121D4×C1111yescharacteristic
410#121D4×C1111yescharacteristic
411C4×Q8—21no—
412C4×Q8D4×C1112yes—
413C4×Q8C23×C1111yescharacteristic
414C4×D4—22no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4C23×C1111yescharacteristic
420C4×D4C23×C1111yescharacteristic
421C4×D4C23×C1111yescharacteristic
422#117—22no—
423#117—21no—
424#117—21no—
425#117—21no—
426#117—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C42C23×C1111yescharacteristic
432#107—22no—
433#106—24no—
434#106—22no—
435C4⋊C8—21no—
436C4⋊C8C23×C1112yes—
437C4⋊C8C23×C1112yes—
438#103—24no—
439#103—22no—
440#103—22no—
441#103—22no—
442#102—22no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446#97—21no—
447C4×C8—21no—
448C4×C8C23×C1112yes—
449C2×C11—41no—
450C2×C11—81no—
451C2×C11—81no—
452C2×C11—81no—
453C2×C11#300911yescharacteristic
454C2×C11#301011yescharacteristic
455C2×C11#302211yescharacteristic
456#41—82no—
457#41—82no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—22no—
462C2×Q8—41no—
463C2×Q8—82no—
464C2×Q8—82no—
465C2×Q8C2×D4×C1111yescharacteristic
466C2×Q8C2×D4×C1112yes—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4C2×D4×C1111yescharacteristic
475C2×D4C2×D4×C1111yescharacteristic
476C2×D4C2×D4×C1111yescharacteristic
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1111yescharacteristic
487SD16—82no—
488SD16—82no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4C2×D4×C1111yescharacteristic
511C4⋊C4C2×D4×C1111yescharacteristic
512C4⋊C4C2×D4×C1111yescharacteristic
513C4⋊C4C2×D4×C1112yes—
514C4⋊C4C2×D4×C1111yescharacteristic
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C42—22no—
531C42—22no—
532C42—21no—
533C42C2×D4×C1111yescharacteristic
534C42C2×D4×C1111yescharacteristic
535C42C2×D4×C1111yescharacteristic
536C42C24×C1111yescharacteristic
537C11#1896811yescharacteristic, direct product factor, Sylow
538C23—21no—
539C23—21no—
540C23—21no—
541C23C11×#12011yescharacteristic
542Q8—22no—
543Q8—42no—
544Q8—42no—
545Q8—42no—
546Q8—42no—
547Q8—81no—
548Q8—82no—
549Q8—82no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4—81no—
554D4—81no—
555D4—81no—
556D4—81no—
557D4—81no—
558D4—82no—
559D4—82no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C11×#12011yescharacteristic
579C2×C4C11×#12011yescharacteristic
580C2×C4C11×#12011yescharacteristic
581C2×C4C22×D4×C1111yescharacteristic
582C2×C4C22×D4×C1111yescharacteristic
583C2×C4C22×D4×C1111yescharacteristic
584C8—42no—
585C8—42no—
586C8—42no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22C2×C11×#12011yescharacteristic
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—41no—
605C4—41no—
606C4—42no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—82no—
612C4C11×#57712yes—
613C4C11×#57712yes—
614C2—41no—
615C2—81no—
616C2—81no—
617C2—81no—
618C2C11×#300911yescharacteristic
619C2C11×#301011yescharacteristic
620C2C11×#302211yescharacteristic
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×#3239C2semidirect
3. C11×#3229C2semidirect
4. C11×#3206C2semidirect
5. C11×#1654C2semidirect
6. C11×#1651C2semidirect
7. C11×#1646C2semidirect
8. C11×#1643C2semidirect
9. C11×#1554C2semidirect
10. C11×#1496C2semidirect
11. C11×#1482C2semidirect
146. #18968C11direct (N × H)
229. #3239C2×C11semidirect
230. #3229C2×C11semidirect
231. #3206C2×C11semidirect
232. #1654C2×C11semidirect
233. #1651C2×C11semidirect
234. #1646C2×C11semidirect
235. #1643C2×C11semidirect
236. #1554C2×C11semidirect
237. #1496C2×C11semidirect
238. #1482C2×C11semidirect
537. C11#18968direct (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×#32392
C11×#32292
C11×#32062
C11×#16542
C11×#16512
C11×#16462
C11×#16432
C11×#15542
C11×#14962
C11×#14822
#1896811