Finite Group Databasebeta

← C11×#19867 #14597060

Subgroups — C11×#19867 #14597060

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3397C211yesmaximal, characteristic, complemented
2C11×#3391C211yesmaximal, characteristic, complemented
3C11×#3304C211yesmaximal, characteristic, complemented
4C11×#3287C211yesmaximal, characteristic, complemented
5C11×#1721C211yesmaximal, characteristic, complemented
6C11×#1688C211yesmaximal, characteristic, complemented
7C11×#1681C211yesmaximal, characteristic, complemented
8C11×#1667C211yesmaximal, characteristic, complemented
9C11×#1666C211yesmaximal, characteristic, complemented
10C11×#1642C211yesmaximal, characteristic, complemented
11C11×#1628C211yesmaximal, characteristic, complemented
12C11×#1621C211yesmaximal, characteristic, complemented
13C11×#1621C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×#1580C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17C11×#556C2211yescharacteristic
18C11×#550C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#550C2211yescharacteristic
21C11×#496—21no—
22C11×#493—21no—
23C11×#493C2211yescharacteristic
24C11×#493C2211yescharacteristic
25C11×#493C2211yescharacteristic
26C11×#492C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#482—21no—
30C11×#475C2211yescharacteristic
31C11×#466—21no—
32C11×#465—21no—
33C11×#463—21no—
34C11×#461C2211yescharacteristic
35C11×#460—21no—
36C11×#460C2211yescharacteristic
37C11×#460C2211yescharacteristic
38C11×#460C2211yescharacteristic
39C11×#459—21no—
40C11×#459—21no—
41C11×#459C2211yescharacteristic
42C11×#459C2211yescharacteristic
43C11×#459C2211yescharacteristic
44C11×#452—21no—
45C11×#449—21no—
46C11×#449—21no—
47C11×#446C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C11×#440—21no—
50C4×C11×Q16C2211yescharacteristic
51C4×C11×D8—21no—
52C4×C11×D8C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C8×D4×C11C2211yescharacteristic
55C11×#416—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#332C2211yescharacteristic
59C11×#331C2211yescharacteristic
60C11×#331C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41—21no—
70C11×#135—44no—
71C2×C11×Q16D411yescharacteristic
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×SD16—21no—
78C2×C11×D8—21no—
79C2×C11×D8—21no—
80C2×C11×D8—21no—
81C2×C11×D8—21no—
82C2×C11×D8—21no—
83C2×C11×D8—21no—
84C2×C11×D8—21no—
85C2×C11×D8—41no—
86C2×C11×D8D411yescharacteristic
87C22×C8×C11—21no—
88C22×C8×C11—21no—
89C11×C4⋊Q8C2311yescharacteristic
90C11×#127—21no—
91C11×#127—21no—
92C11×#127—21no—
93C11×#127C2311yescharacteristic
94C11×#127C2311yescharacteristic
95C11×#127C2311yescharacteristic
96C11×#126—41no—
97C11×#124—21no—
98C11×C22⋊Q8—21no—
99C11×#121—21no—
100C11×#121—21no—
101C11×#121—21no—
102C11×#121—41no—
103C11×#121—41no—
104C11×#121—41no—
105C4×Q8×C11—21no—
106C4×Q8×C11C2311yescharacteristic
107C4×Q8×C11C2311yescharacteristic
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11C2311yescharacteristic
112C4×D4×C11C2311yescharacteristic
113C11×#117—21no—
114C11×#107D411yescharacteristic
115C11×#107D411yescharacteristic
116C11×#106—21no—
117C11×C4⋊C8—21no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×C4⋊C8C2311yescharacteristic
122C11×C4⋊C8C2311yescharacteristic
123C11×#103—21no—
124C11×#103—21no—
125C11×#103D411yescharacteristic
126C11×#103D411yescharacteristic
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—41no—
136C11×#102D411yescharacteristic
137C11×#102D411yescharacteristic
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C11×#97—21no—
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144C4×C8×C11C2311yescharacteristic
145#19867C1111yesmaximal, characteristic, direct product factor, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C11×#41—42no—
149C11×#41—81no—
150C11×#41—81no—
151C11×#41—81no—
152C2×Q8×C11—21no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11—41no—
168C2×D4×C11—41no—
169C2×D4×C11—41no—
170C2×D4×C11C2×D411yescharacteristic
171C2×D4×C11C2×D411yescharacteristic
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C11×Q16—22no—
178C11×SD16—42no—
179C11×SD16—42no—
180C11×SD16—42no—
181C11×SD16—81no—
182C11×SD16—81no—
183C11×SD16—81no—
184C11×D8—22no—
185C11×D8—42no—
186C11×D8—42no—
187C11×D8—81no—
188C11×D8—81no—
189C11×D8—81no—
190C11×D8—81no—
191C11×D8—81no—
192C11×D8—82no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—42no—
199C2×C8×C11—81no—
200C2×C8×C11C2×D411yescharacteristic
201C2×C8×C11C2×D411yescharacteristic
202C2×C8×C11C2×D411yescharacteristic
203C2×C8×C11C2×D411yescharacteristic
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—41no—
209C11×C4⋊C4C2×D411yescharacteristic
210C11×C4⋊C4C2×D411yescharacteristic
211C11×C4⋊C4C2×D411yescharacteristic
212C11×C4⋊C4C2×D411yescharacteristic
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—41no—
216C11×C22⋊C4—41no—
217C11×C22⋊C4—41no—
218C11×C22⋊C4—41no—
219C11×C22⋊C4—41no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—41no—
223C42×C11C2411yescharacteristic
224#3397C2×C1111yescharacteristic, complemented
225#3391C2×C1111yescharacteristic, complemented
226#3304C2×C1111yescharacteristic, complemented
227#3287C2×C1111yescharacteristic, complemented
228#1721C2×C1111yescharacteristic, complemented
229#1688C2×C1111yescharacteristic, complemented
230#1681C2×C1111yescharacteristic, complemented
231#1667C2×C1111yescharacteristic, complemented
232#1666C2×C1111yescharacteristic, complemented
233#1642C2×C1111yescharacteristic, complemented
234#1628C2×C1111yescharacteristic, complemented
235#1621C2×C1111yescharacteristic, complemented
236#1621C2×C1111yescharacteristic, complemented
237#1584C2×C1111yescharacteristic, complemented
238#1580C2×C1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244Q8×C11—21no—
245Q8×C11—21no—
246Q8×C11—21no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11AGL(1,ℤ/8)12yes—
250D4×C11—21no—
251D4×C11—21no—
252D4×C11—21no—
253D4×C11—21no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—82no—
267D4×C11—82no—
268D4×C11—81no—
269D4×C11—81no—
270D4×C11—81no—
271D4×C11—82no—
272D4×C11—161no—
273D4×C11—161no—
274D4×C11—161no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—82no—
287C2×C4×C11—82no—
288C2×C4×C11—82no—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—21no—
295C8×C11—41no—
296C8×C11—41no—
297C8×C11—41no—
298C8×C11—41no—
299C8×C11—41no—
300C8×C11#13512yescomplemented
301C2×#135—21no—
302#556C22×C1111yescharacteristic
303#550C22×C1111yescharacteristic
304#550C22×C1111yescharacteristic
305#550C22×C1111yescharacteristic
306#496—21no—
307#493—21no—
308#493C22×C1111yescharacteristic
309#493C22×C1111yescharacteristic
310#493C22×C1111yescharacteristic
311#492C22×C1111yescharacteristic
312#486C22×C1111yescharacteristic
313#486C22×C1111yescharacteristic
314#482—21no—
315#475C22×C1111yescharacteristic
316#466—21no—
317#465—21no—
318#463—21no—
319#461C22×C1111yescharacteristic
320#460—21no—
321#460C22×C1111yescharacteristic
322#460C22×C1111yescharacteristic
323#460C22×C1111yescharacteristic
324#459—21no—
325#459—21no—
326#459C22×C1111yescharacteristic
327#459C22×C1111yescharacteristic
328#459C22×C1111yescharacteristic
329#452—21no—
330#449—21no—
331#449—21no—
332#446C22×C1111yescharacteristic
333C8×Q8C22×C1111yescharacteristic
334#440—21no—
335C4×Q16C22×C1111yescharacteristic
336C4×D8—21no—
337C4×D8C22×C1111yescharacteristic
338C8×D4C22×C1111yescharacteristic
339C8×D4C22×C1111yescharacteristic
340#416—21no—
341#335C22×C1111yescharacteristic
342#334C22×C1111yescharacteristic
343#332C22×C1111yescharacteristic
344#331C22×C1111yescharacteristic
345#331C22×C1111yescharacteristic
346#331C22×C1111yescharacteristic
347Q8⋊C8C22×C1111yescharacteristic
348Q8⋊C8C22×C1111yescharacteristic
349D4⋊C8C22×C1111yescharacteristic
350D4⋊C8C22×C1111yescharacteristic
351#322C22×C1111yescharacteristic
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11D4211yescharacteristic
368C4×C11—22no—
369C4×C11—21no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—81no—
376C4×C11C2×#13511yescharacteristic
377C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
378C4×C11#57611yescharacteristic
379C4×C11#57611yescharacteristic
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—21no—
383#135—44no—
384C2×Q16D4×C1111yescharacteristic
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×D8—21no—
396C2×D8—21no—
397C2×D8—21no—
398C2×D8—41no—
399C2×D8D4×C1111yescharacteristic
400C22×C8—21no—
401C22×C8—21no—
402C4⋊Q8C23×C1111yescharacteristic
403#127—21no—
404#127—21no—
405#127—21no—
406#127C23×C1111yescharacteristic
407#127C23×C1111yescharacteristic
408#127C23×C1111yescharacteristic
409#126—41no—
410#124—21no—
411C22⋊Q8—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—41no—
416#121—41no—
417#121—41no—
418C4×Q8—21no—
419C4×Q8C23×C1111yescharacteristic
420C4×Q8C23×C1111yescharacteristic
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4C23×C1111yescharacteristic
425C4×D4C23×C1111yescharacteristic
426#117—21no—
427#107D4×C1111yescharacteristic
428#107D4×C1111yescharacteristic
429#106—21no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8C23×C1111yescharacteristic
433C4⋊C8C23×C1111yescharacteristic
434C4⋊C8C23×C1111yescharacteristic
435C4⋊C8C23×C1111yescharacteristic
436#103—21no—
437#103—21no—
438#103D4×C1111yescharacteristic
439#103D4×C1111yescharacteristic
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—41no—
449#102D4×C1111yescharacteristic
450#102D4×C1111yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453#97—21no—
454C4×C8—21no—
455C4×C8C23×C1111yescharacteristic
456C4×C8C23×C1111yescharacteristic
457C4×C8C23×C1111yescharacteristic
458C2×C11—81no—
459C2×C11—81no—
460C2×C11—161no—
461C2×C11—161no—
462C2×C11—161no—
463C2×C11#326411yescharacteristic
464C2×C11#328711yescharacteristic
465C2×C11#328811yescharacteristic
466#41—42no—
467#41—42no—
468#41—42no—
469#41—81no—
470#41—81no—
471#41—81no—
472C2×Q8—21no—
473C2×Q8C2×D4×C1111yescharacteristic
474C2×Q8C2×D4×C1111yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4C2×D4×C1111yescharacteristic
491C2×D4C2×D4×C1111yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497Q16—22no—
498SD16—42no—
499SD16—42no—
500SD16—42no—
501SD16—81no—
502SD16—81no—
503SD16—81no—
504D8—22no—
505D8—42no—
506D8—42no—
507D8—81no—
508D8—81no—
509D8—81no—
510D8—81no—
511D8—81no—
512D8—82no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—42no—
519C2×C8—81no—
520C2×C8C2×D4×C1111yescharacteristic
521C2×C8C2×D4×C1111yescharacteristic
522C2×C8C2×D4×C1111yescharacteristic
523C2×C8C2×D4×C1111yescharacteristic
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—41no—
529C4⋊C4C2×D4×C1111yescharacteristic
530C4⋊C4C2×D4×C1111yescharacteristic
531C4⋊C4C2×D4×C1111yescharacteristic
532C4⋊C4C2×D4×C1111yescharacteristic
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C42—21no—
541C42—21no—
542C42—41no—
543C42C24×C1111yescharacteristic
544C11#1986711yescharacteristic, direct product factor, Sylow
545C23—21no—
546C23—21no—
547C23—41no—
548C23—41no—
549C23—41no—
550Q8—21no—
551Q8—21no—
552Q8—21no—
553Q8—41no—
554Q8—41no—
555Q8C11×AGL(1,ℤ/8)12yes—
556D4—21no—
557D4—21no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—82no—
573D4—82no—
574D4—81no—
575D4—81no—
576D4—81no—
577D4—82no—
578D4—161no—
579D4—161no—
580D4—161no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4C22×D4×C1111yescharacteristic
596C2×C4C22×D4×C1111yescharacteristic
597C2×C4C11×H(5,𝔽2)11yescharacteristic
598C8—21no—
599C8—21no—
600C8—21no—
601C8—41no—
602C8—41no—
603C8—41no—
604C8—41no—
605C8—41no—
606C8C11×#13512yescomplemented
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22D42×C1111yescharacteristic
623C4—22no—
624C4—21no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4C2×C11×#13511yescharacteristic
632C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
633C4C11×#57611yescharacteristic
634C4C11×#57611yescharacteristic
635C2—81no—
636C2—81no—
637C2—161no—
638C2—161no—
639C2—161no—
640C2C11×#326411yescharacteristic
641C2C11×#328711yescharacteristic
642C2C11×#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×#3397C2semidirect
2. C11×#3391C2semidirect
3. C11×#3304C2semidirect
4. C11×#3287C2semidirect
5. C11×#1721C2semidirect
6. C11×#1688C2semidirect
7. C11×#1681C2semidirect
8. C11×#1667C2semidirect
9. C11×#1666C2semidirect
10. C11×#1642C2semidirect
11. C11×#1628C2semidirect
12. C11×#1621C2semidirect
13. C11×#1621C2semidirect
14. C11×#1584C2semidirect
15. C11×#1580C2semidirect
145. #19867C11direct (N × H)
224. #3397C2×C11semidirect
225. #3391C2×C11semidirect
226. #3304C2×C11semidirect
227. #3287C2×C11semidirect
228. #1721C2×C11semidirect
229. #1688C2×C11semidirect
230. #1681C2×C11semidirect
231. #1667C2×C11semidirect
232. #1666C2×C11semidirect
233. #1642C2×C11semidirect
234. #1628C2×C11semidirect
235. #1621C2×C11semidirect
236. #1621C2×C11semidirect
237. #1584C2×C11semidirect
238. #1580C2×C11semidirect
300. C8×C11#135semidirect
544. C11#19867direct (N × H)
606. C8C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#33972
C11×#33912
C11×#33042
C11×#32872
C11×#17212
C11×#16882
C11×#16812
C11×#16672
C11×#16662
C11×#16422
C11×#16282
C11×#16212
C11×#15842
C11×#15802
#1986711