Finite Group Databasebeta

← C11×#19783 #14596976

Subgroups — C11×#19783 #14596976

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3391C211yesmaximal, characteristic, complemented
2C11×#3332C211yesmaximal, characteristic, complemented
3C11×#3305C211yesmaximal, characteristic, complemented
4C11×#3303C211yesmaximal, characteristic, complemented
5C11×#1717C211yesmaximal, characteristic, complemented
6C11×#1697C211yesmaximal, characteristic, complemented
7C11×#1684C211yesmaximal, characteristic, complemented
8C11×#1681C211yesmaximal, characteristic, complemented
9C11×#1667C211yesmaximal, characteristic, complemented
10C11×#1642C211yesmaximal, characteristic, complemented
11C11×#1631C211yesmaximal, characteristic, complemented
12C11×#1625C211yesmaximal, characteristic, complemented
13C11×#1624C211yesmaximal, characteristic, complemented
14C11×#1581C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#555C2211yescharacteristic
17C11×#550C2211yescharacteristic
18C11×#550C2211yescharacteristic
19C11×#547C2211yescharacteristic
20C11×#493—21no—
21C11×#493C2211yescharacteristic
22C11×#492C2211yescharacteristic
23C11×#487C2211yescharacteristic
24C11×#486C2211yescharacteristic
25C11×#486C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#485—21no—
28C11×#482—21no—
29C11×#481—21no—
30C11×#477C2211yescharacteristic
31C11×#476C2211yescharacteristic
32C11×#475C2211yescharacteristic
33C11×#469—21no—
34C11×#466—21no—
35C11×#465—21no—
36C11×#461C2211yescharacteristic
37C11×#459—21no—
38C11×#459—21no—
39C11×#459C2211yescharacteristic
40C11×#459C2211yescharacteristic
41C11×#459C2211yescharacteristic
42C11×#459C2211yescharacteristic
43C11×#449—21no—
44C11×#449—21no—
45C11×#449—21no—
46C8×Q8×C11C2211yescharacteristic
47C4×C11×SD16C2211yescharacteristic
48C4×C11×D8—21no—
49C4×C11×D8C2211yescharacteristic
50C11×#436C2211yescharacteristic
51C8×D4×C11C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C11×#417—21no—
54C11×#416—21no—
55C11×#416—21no—
56C11×#335C2211yescharacteristic
57C11×#335C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#331C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×D4⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—41no—
72C2×C11×SD16D411yescharacteristic
73C2×C11×D8—21no—
74C2×C11×D8—21no—
75C2×C11×D8—21no—
76C2×C11×D8—21no—
77C2×C11×D8—21no—
78C2×C11×D8—21no—
79C2×C11×D8D411yescharacteristic
80C2×C11×M16—21no—
81C22×C8×C11—21no—
82C22×C8×C11—21no—
83C11×C4⋊Q8C2311yescharacteristic
84C11×C4⋊Q8C2311yescharacteristic
85C11×#127—21no—
86C11×#127—21no—
87C11×#127C2311yescharacteristic
88C11×#127C2311yescharacteristic
89C11×#124—41no—
90C11×#123—41no—
91C11×C22⋊Q8—21no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121—21no—
95C11×#121—21no—
96C11×#121—21no—
97C11×#121—41no—
98C11×#121—41no—
99C4×Q8×C11C2311yescharacteristic
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11C2311yescharacteristic
103C4×D4×C11C2311yescharacteristic
104C4×D4×C11C2311yescharacteristic
105C11×#117—21no—
106C11×#117—21no—
107C2×C11×C4⋊C4—21no—
108C11×#107—21no—
109C11×#107D411yescharacteristic
110C11×#106—21no—
111C11×#106—21no—
112C11×#106D411yescharacteristic
113C11×C4⋊C8—21no—
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×#103—21no—
119C11×#103—21no—
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103D411yescharacteristic
124C11×#102—21no—
125C11×#102—21no—
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—41no—
134C11×#102D411yescharacteristic
135C11×#102D411yescharacteristic
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19783C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—42no—
146C11×#41—42no—
147C11×#41—42no—
148C11×#41—81no—
149C11×#41—81no—
150C11×#41—81no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11C2×D411yescharacteristic
167C2×D4×C11C2×D411yescharacteristic
168C2×D4×C11C2×D411yescharacteristic
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—41no—
173C22×C4×C11—41no—
174C22×C4×C11—41no—
175C11×SD16—22no—
176C11×SD16—81no—
177C11×SD16—82no—
178C11×D8—41no—
179C11×D8—42no—
180C11×D8—81no—
181C11×D8—81no—
182C11×D8—81no—
183C11×D8—81no—
184C11×D8—81no—
185C11×M16—81no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—81no—
192C2×C8×C11—81no—
193C2×C8×C11C2×D411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C2×C8×C11C2×D411yescharacteristic
196C2×C8×C11C2×D411yescharacteristic
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—41no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C11×C22⋊C4—41no—
214C11×C22⋊C4—41no—
215C42×C11—21no—
216C42×C11—41no—
217C42×C11C2411yescharacteristic
218#3391C2×C1111yescharacteristic, complemented
219#3332C2×C1111yescharacteristic, complemented
220#3305C2×C1111yescharacteristic, complemented
221#3303C2×C1111yescharacteristic, complemented
222#1717C2×C1111yescharacteristic, complemented
223#1697C2×C1111yescharacteristic, complemented
224#1684C2×C1111yescharacteristic, complemented
225#1681C2×C1111yescharacteristic, complemented
226#1667C2×C1111yescharacteristic, complemented
227#1642C2×C1111yescharacteristic, complemented
228#1631C2×C1111yescharacteristic, complemented
229#1625C2×C1111yescharacteristic, complemented
230#1624C2×C1111yescharacteristic, complemented
231#1581C2×C1111yescharacteristic, complemented
232SD16⋊C8C2×C1111yescharacteristic, complemented
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—41no—
237C23×C11—41no—
238Q8×C11—21no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—81no—
242Q8×C11#13512yes—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—21no—
248D4×C11—21no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—82no—
258D4×C11—82no—
259D4×C11—81no—
260D4×C11—81no—
261D4×C11—82no—
262D4×C11—161no—
263D4×C11—161no—
264D4×C11—161no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
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—82no—
279C2×C4×C11—82no—
280C2×C4×C11—82no—
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C8×C11—21no—
285C8×C11—21no—
286C8×C11—21no—
287C8×C11—21no—
288C8×C11—41no—
289C8×C11—41no—
290C8×C11—41no—
291C8×C11—41no—
292C8×C11—41no—
293#555C22×C1111yescharacteristic
294#550C22×C1111yescharacteristic
295#550C22×C1111yescharacteristic
296#547C22×C1111yescharacteristic
297#493—21no—
298#493C22×C1111yescharacteristic
299#492C22×C1111yescharacteristic
300#487C22×C1111yescharacteristic
301#486C22×C1111yescharacteristic
302#486C22×C1111yescharacteristic
303#486C22×C1111yescharacteristic
304#485—21no—
305#482—21no—
306#481—21no—
307#477C22×C1111yescharacteristic
308#476C22×C1111yescharacteristic
309#475C22×C1111yescharacteristic
310#469—21no—
311#466—21no—
312#465—21no—
313#461C22×C1111yescharacteristic
314#459—21no—
315#459—21no—
316#459C22×C1111yescharacteristic
317#459C22×C1111yescharacteristic
318#459C22×C1111yescharacteristic
319#459C22×C1111yescharacteristic
320#449—21no—
321#449—21no—
322#449—21no—
323C8×Q8C22×C1111yescharacteristic
324C4×SD16C22×C1111yescharacteristic
325C4×D8—21no—
326C4×D8C22×C1111yescharacteristic
327#436C22×C1111yescharacteristic
328C8×D4C22×C1111yescharacteristic
329C8×D4C22×C1111yescharacteristic
330#417—21no—
331#416—21no—
332#416—21no—
333#335C22×C1111yescharacteristic
334#335C22×C1111yescharacteristic
335#333C22×C1111yescharacteristic
336#332C22×C1111yescharacteristic
337#331C22×C1111yescharacteristic
338#331C22×C1111yescharacteristic
339Q8⋊C8C22×C1111yescharacteristic
340D4⋊C8C22×C1111yescharacteristic
341D4⋊C8C22×C1111yescharacteristic
342D4⋊C8C22×C1111yescharacteristic
343#322C22×C1111yescharacteristic
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11D4211yescharacteristic
360C4×C11—22no—
361C4×C11—21no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11C2×#13511yescharacteristic
369C4×C11#57511yescharacteristic
370C4×C11#57611yescharacteristic
371C4×C11#57611yescharacteristic
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×SD16—21no—
376C2×SD16—41no—
377C2×SD16D4×C1111yescharacteristic
378C2×D8—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—21no—
384C2×D8D4×C1111yescharacteristic
385C2×M16—21no—
386C22×C8—21no—
387C22×C8—21no—
388C4⋊Q8C23×C1111yescharacteristic
389C4⋊Q8C23×C1111yescharacteristic
390#127—21no—
391#127—21no—
392#127C23×C1111yescharacteristic
393#127C23×C1111yescharacteristic
394#124—41no—
395#123—41no—
396C22⋊Q8—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—41no—
403#121—41no—
404C4×Q8C23×C1111yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C23×C1111yescharacteristic
408C4×D4C23×C1111yescharacteristic
409C4×D4C23×C1111yescharacteristic
410#117—21no—
411#117—21no—
412C2×C4⋊C4—21no—
413#107—21no—
414#107D4×C1111yescharacteristic
415#106—21no—
416#106—21no—
417#106D4×C1111yescharacteristic
418C4⋊C8—21no—
419C4⋊C8C23×C1111yescharacteristic
420C4⋊C8C23×C1111yescharacteristic
421C4⋊C8C23×C1111yescharacteristic
422C4⋊C8C23×C1111yescharacteristic
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103D4×C1111yescharacteristic
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—41no—
439#102D4×C1111yescharacteristic
440#102D4×C1111yescharacteristic
441#102D4×C1111yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C4×C8—21no—
446C4×C8C23×C1111yescharacteristic
447C4×C8C23×C1111yescharacteristic
448C4×C8C23×C1111yescharacteristic
449C2×C11—81no—
450C2×C11—81no—
451C2×C11—81no—
452C2×C11—161no—
453C2×C11—161no—
454C2×C11#326811yescharacteristic
455C2×C11#328011yescharacteristic
456C2×C11#328811yescharacteristic
457#41—42no—
458#41—42no—
459#41—42no—
460#41—81no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8C2×D4×C1111yescharacteristic
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4C2×D4×C1111yescharacteristic
479C2×D4C2×D4×C1111yescharacteristic
480C2×D4C2×D4×C1111yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487SD16—22no—
488SD16—81no—
489SD16—82no—
490D8—41no—
491D8—42no—
492D8—81no—
493D8—81no—
494D8—81no—
495D8—81no—
496D8—81no—
497M16—81no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—81no—
504C2×C8—81no—
505C2×C8C2×D4×C1111yescharacteristic
506C2×C8C2×D4×C1111yescharacteristic
507C2×C8C2×D4×C1111yescharacteristic
508C2×C8C2×D4×C1111yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C1111yescharacteristic
516C4⋊C4C2×D4×C1111yescharacteristic
517C4⋊C4C2×D4×C1111yescharacteristic
518C4⋊C4C2×D4×C1111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—41no—
529C42C24×C1111yescharacteristic
530C11#1978311yescharacteristic, direct product factor, Sylow
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—41no—
536Q8—21no—
537Q8—41no—
538Q8—41no—
539Q8—81no—
540Q8C11×#13512yes—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—82no—
556D4—82no—
557D4—81no—
558D4—81no—
559D4—82no—
560D4—161no—
561D4—161no—
562D4—161no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4C22×D4×C1111yescharacteristic
580C2×C4C22×D4×C1111yescharacteristic
581C2×C4C11×H(5,𝔽2)11yescharacteristic
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C8—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22D42×C1111yescharacteristic
607C4—22no—
608C4—21no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4C2×C11×#13511yescharacteristic
616C4C11×#57511yescharacteristic
617C4C11×#57611yescharacteristic
618C4C11×#57611yescharacteristic
619C2—81no—
620C2—81no—
621C2—81no—
622C2—161no—
623C2—161no—
624C2C11×#326811yescharacteristic
625C2C11×#328011yescharacteristic
626C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3391C2semidirect
2. C11×#3332C2semidirect
3. C11×#3305C2semidirect
4. C11×#3303C2semidirect
5. C11×#1717C2semidirect
6. C11×#1697C2semidirect
7. C11×#1684C2semidirect
8. C11×#1681C2semidirect
9. C11×#1667C2semidirect
10. C11×#1642C2semidirect
11. C11×#1631C2semidirect
12. C11×#1625C2semidirect
13. C11×#1624C2semidirect
14. C11×#1581C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19783C11direct (N × H)
218. #3391C2×C11semidirect
219. #3332C2×C11semidirect
220. #3305C2×C11semidirect
221. #3303C2×C11semidirect
222. #1717C2×C11semidirect
223. #1697C2×C11semidirect
224. #1684C2×C11semidirect
225. #1681C2×C11semidirect
226. #1667C2×C11semidirect
227. #1642C2×C11semidirect
228. #1631C2×C11semidirect
229. #1625C2×C11semidirect
230. #1624C2×C11semidirect
231. #1581C2×C11semidirect
232. SD16⋊C8C2×C11semidirect
530. C11#19783direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33912
C11×#33322
C11×#33052
C11×#33032
C11×#17172
C11×#16972
C11×#16842
C11×#16812
C11×#16672
C11×#16422
C11×#16312
C11×#16252
C11×#16242
C11×#15812
C11×SD16⋊C82
#1978311