Finite Group Databasebeta

← C11×#19868 #14597061

Subgroups — C11×#19868 #14597061

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3399C211yesmaximal, characteristic, complemented
2C11×#3392C211yesmaximal, characteristic, complemented
3C11×#3365C211yesmaximal, characteristic, complemented
4C11×#3287C211yesmaximal, characteristic, complemented
5C11×#1721C211yesmaximal, characteristic, complemented
6C11×#1686C211yesmaximal, characteristic, complemented
7C11×#1681C211yesmaximal, characteristic, complemented
8C11×#1668C211yesmaximal, characteristic, complemented
9C11×#1668C211yesmaximal, characteristic, complemented
10C11×#1642C211yesmaximal, characteristic, complemented
11C11×#1626C211yesmaximal, characteristic, complemented
12C11×#1621C211yesmaximal, characteristic, complemented
13C11×#1620C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17C11×#559C2211yescharacteristic
18C11×#557C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#550C2211yescharacteristic
21C11×#496—21no—
22C11×#493C2211yescharacteristic
23C11×#493C2211yescharacteristic
24C11×#493C2211yescharacteristic
25C11×#492—21no—
26C11×#492C2211yescharacteristic
27C11×#488—21no—
28C11×#486C2211yescharacteristic
29C11×#486C2211yescharacteristic
30C11×#478—21no—
31C11×#475C2211yescharacteristic
32C11×#466—21no—
33C11×#464—21no—
34C11×#463—21no—
35C11×#461—21no—
36C11×#461C2211yescharacteristic
37C11×#460—21no—
38C11×#460C2211yescharacteristic
39C11×#460C2211yescharacteristic
40C11×#460C2211yescharacteristic
41C11×#460C2211yescharacteristic
42C11×#460C2211yescharacteristic
43C11×#459—21no—
44C11×#459C2211yescharacteristic
45C11×#449—21no—
46C11×#449—21no—
47C11×#446C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C8×Q8×C11C2211yescharacteristic
50C11×#442—21no—
51C4×C11×Q16C2211yescharacteristic
52C4×C11×SD16—21no—
53C4×C11×SD16—21no—
54C4×C11×SD16C2211yescharacteristic
55C8×D4×C11C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#335C2211yescharacteristic
58C11×#332C2211yescharacteristic
59C11×#331C2211yescharacteristic
60C11×#331C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C11×#135—44no—
70C2×C11×Q16D411yescharacteristic
71C2×C11×SD16—21no—
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×SD16—21no—
79C2×C11×SD16D411yescharacteristic
80C2×C11×D8—21no—
81C2×C11×D8—21no—
82C2×C11×D8—21no—
83C2×C11×D8—21no—
84C2×C11×D8—21no—
85C2×C11×D8—41no—
86C22×C8×C11—21no—
87C11×C4⋊Q8—21no—
88C11×C4⋊Q8C2311yescharacteristic
89C11×#127—21no—
90C11×#127—21no—
91C11×#127C2311yescharacteristic
92C11×#127C2311yescharacteristic
93C11×#127C2311yescharacteristic
94C11×#125—21no—
95C11×#125—41no—
96C11×#124—21no—
97C11×#124—21no—
98C11×#123—41no—
99C11×#121—21no—
100C11×#121—21no—
101C11×#121—41no—
102C11×#121—41no—
103C4×Q8×C11—21no—
104C4×Q8×C11—21no—
105C4×Q8×C11C2311yescharacteristic
106C4×Q8×C11C2311yescharacteristic
107C4×Q8×C11C2311yescharacteristic
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11C2311yescharacteristic
113C11×#107D411yescharacteristic
114C11×#106—21no—
115C11×#106D411yescharacteristic
116C11×C4⋊C8—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×#103D411yescharacteristic
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—21no—
136C11×#102—41no—
137C11×#102D411yescharacteristic
138C11×C22⋊C8—21no—
139C11×#97—21no—
140C4×C8×C11—21no—
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144C4×C8×C11C2311yescharacteristic
145#19868C1111yesmaximal, characteristic, direct product factor, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C11×#41—81no—
149C11×#41—81no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
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—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11C2×D411yescharacteristic
168C22×C4×C11—21no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C22×C4×C11—41no—
172C11×Q16—22no—
173C11×SD16—22no—
174C11×SD16—42no—
175C11×SD16—42no—
176C11×SD16—42no—
177C11×SD16—42no—
178C11×SD16—81no—
179C11×SD16—81no—
180C11×SD16—81no—
181C11×SD16—81no—
182C11×D8—42no—
183C11×D8—42no—
184C11×D8—81no—
185C11×D8—81no—
186C11×D8—81no—
187C11×D8—82no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—42no—
194C2×C8×C11C2×D411yescharacteristic
195C2×C8×C11C2×D411yescharacteristic
196C2×C8×C11C2×D411yescharacteristic
197C2×C8×C11C2×D411yescharacteristic
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—41no—
204C11×C4⋊C4—41no—
205C11×C4⋊C4—41no—
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C4⋊C4C2×D411yescharacteristic
210C11×C22⋊C4—21no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C11×C22⋊C4—41no—
214C11×C22⋊C4—41no—
215C11×C22⋊C4—41no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—41no—
220C42×C11C2411yescharacteristic
221#3399C2×C1111yescharacteristic, complemented
222#3392C2×C1111yescharacteristic, complemented
223#3365C2×C1111yescharacteristic, complemented
224#3287C2×C1111yescharacteristic, complemented
225#1721C2×C1111yescharacteristic, complemented
226#1686C2×C1111yescharacteristic, complemented
227#1681C2×C1111yescharacteristic, complemented
228#1668C2×C1111yescharacteristic, complemented
229#1668C2×C1111yescharacteristic, complemented
230#1642C2×C1111yescharacteristic, complemented
231#1626C2×C1111yescharacteristic, complemented
232#1621C2×C1111yescharacteristic, complemented
233#1620C2×C1111yescharacteristic, complemented
234#1584C2×C1111yescharacteristic, complemented
235SD16⋊C8C2×C1111yescharacteristic, complemented
236C23×C11—21no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240Q8×C11—21no—
241Q8×C11—21no—
242Q8×C11—21no—
243Q8×C11—21no—
244Q8×C11—21no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11AGL(1,ℤ/8)12yes—
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—41no—
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—82no—
263D4×C11—81no—
264D4×C11—81no—
265D4×C11—81no—
266D4×C11—82no—
267D4×C11—161no—
268D4×C11—161no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—82no—
280C2×C4×C11—82no—
281C2×C4×C11—161no—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C8×C11—21no—
286C8×C11—21no—
287C8×C11—21no—
288C8×C11—41no—
289C8×C11—41no—
290C8×C11—41no—
291C8×C11—41no—
292C8×C11—41no—
293C8×C11#13512yescomplemented
294C2×#135—21no—
295#559C22×C1111yescharacteristic
296#557C22×C1111yescharacteristic
297#550C22×C1111yescharacteristic
298#550C22×C1111yescharacteristic
299#496—21no—
300#493C22×C1111yescharacteristic
301#493C22×C1111yescharacteristic
302#493C22×C1111yescharacteristic
303#492—21no—
304#492C22×C1111yescharacteristic
305#488—21no—
306#486C22×C1111yescharacteristic
307#486C22×C1111yescharacteristic
308#478—21no—
309#475C22×C1111yescharacteristic
310#466—21no—
311#464—21no—
312#463—21no—
313#461—21no—
314#461C22×C1111yescharacteristic
315#460—21no—
316#460C22×C1111yescharacteristic
317#460C22×C1111yescharacteristic
318#460C22×C1111yescharacteristic
319#460C22×C1111yescharacteristic
320#460C22×C1111yescharacteristic
321#459—21no—
322#459C22×C1111yescharacteristic
323#449—21no—
324#449—21no—
325#446C22×C1111yescharacteristic
326C8×Q8C22×C1111yescharacteristic
327C8×Q8C22×C1111yescharacteristic
328#442—21no—
329C4×Q16C22×C1111yescharacteristic
330C4×SD16—21no—
331C4×SD16—21no—
332C4×SD16C22×C1111yescharacteristic
333C8×D4C22×C1111yescharacteristic
334#335C22×C1111yescharacteristic
335#335C22×C1111yescharacteristic
336#332C22×C1111yescharacteristic
337#331C22×C1111yescharacteristic
338#331C22×C1111yescharacteristic
339#331C22×C1111yescharacteristic
340Q8⋊C8C22×C1111yescharacteristic
341Q8⋊C8C22×C1111yescharacteristic
342Q8⋊C8C22×C1111yescharacteristic
343D4⋊C8C22×C1111yescharacteristic
344#322C22×C1111yescharacteristic
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11D4211yescharacteristic
358C4×C11—22no—
359C4×C11—21no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11C2×#13511yescharacteristic
368C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C4×C11#57611yescharacteristic
370C4×C11#57711yescharacteristic
371C2×#41—21no—
372C2×#41—21no—
373#135—44no—
374C2×Q16D4×C1111yescharacteristic
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C1111yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—41no—
390C22×C8—21no—
391C4⋊Q8—21no—
392C4⋊Q8C23×C1111yescharacteristic
393#127—21no—
394#127—21no—
395#127C23×C1111yescharacteristic
396#127C23×C1111yescharacteristic
397#127C23×C1111yescharacteristic
398#125—21no—
399#125—41no—
400#124—21no—
401#124—21no—
402#123—41no—
403#121—21no—
404#121—21no—
405#121—41no—
406#121—41no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8C23×C1111yescharacteristic
410C4×Q8C23×C1111yescharacteristic
411C4×Q8C23×C1111yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4C23×C1111yescharacteristic
417#107D4×C1111yescharacteristic
418#106—21no—
419#106D4×C1111yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8C23×C1111yescharacteristic
424C4⋊C8C23×C1111yescharacteristic
425C4⋊C8C23×C1111yescharacteristic
426C4⋊C8C23×C1111yescharacteristic
427#103—21no—
428#103—21no—
429#103D4×C1111yescharacteristic
430#103D4×C1111yescharacteristic
431#103D4×C1111yescharacteristic
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—41no—
441#102D4×C1111yescharacteristic
442C22⋊C8—21no—
443#97—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C1111yescharacteristic
447C4×C8C23×C1111yescharacteristic
448C4×C8C23×C1111yescharacteristic
449C2×C11—81no—
450C2×C11—161no—
451C2×C11—161no—
452C2×C11—161no—
453C2×C11#326511yescharacteristic
454C2×C11#328711yescharacteristic
455C2×C11#328811yescharacteristic
456#41—42no—
457#41—42no—
458#41—81no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8C2×D4×C1111yescharacteristic
462C2×Q8C2×D4×C1111yescharacteristic
463C2×Q8C2×D4×C1111yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4C2×D4×C1111yescharacteristic
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482Q16—22no—
483SD16—22no—
484SD16—42no—
485SD16—42no—
486SD16—42no—
487SD16—42no—
488SD16—81no—
489SD16—81no—
490SD16—81no—
491SD16—81no—
492D8—42no—
493D8—42no—
494D8—81no—
495D8—81no—
496D8—81no—
497D8—82no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—42no—
504C2×C8C2×D4×C1111yescharacteristic
505C2×C8C2×D4×C1111yescharacteristic
506C2×C8C2×D4×C1111yescharacteristic
507C2×C8C2×D4×C1111yescharacteristic
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4C2×D4×C1111yescharacteristic
517C4⋊C4C2×D4×C1111yescharacteristic
518C4⋊C4C2×D4×C1111yescharacteristic
519C4⋊C4C2×D4×C1111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—41no—
530C42C24×C1111yescharacteristic
531C11#1986811yescharacteristic, direct product factor, Sylow
532C23—21no—
533C23—41no—
534C23—41no—
535C23—41no—
536Q8—21no—
537Q8—21no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—41no—
542Q8—41no—
543Q8C11×AGL(1,ℤ/8)12yes—
544D4—21no—
545D4—21no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—82no—
559D4—81no—
560D4—81no—
561D4—81no—
562D4—82no—
563D4—161no—
564D4—161no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—161no—
578C2×C4C22×D4×C1111yescharacteristic
579C2×C4C22×D4×C1111yescharacteristic
580C2×C4C11×H(5,𝔽2)11yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8C11×#13512yescomplemented
590C22—41no—
591C22—41no—
592C22—41no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22D42×C1111yescharacteristic
603C4—22no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4C2×C11×#13511yescharacteristic
613C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
614C4C11×#57611yescharacteristic
615C4C11×#57711yescharacteristic
616C2—81no—
617C2—161no—
618C2—161no—
619C2—161no—
620C2C11×#326511yescharacteristic
621C2C11×#328711yescharacteristic
622C2C11×#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×#3399C2semidirect
2. C11×#3392C2semidirect
3. C11×#3365C2semidirect
4. C11×#3287C2semidirect
5. C11×#1721C2semidirect
6. C11×#1686C2semidirect
7. C11×#1681C2semidirect
8. C11×#1668C2semidirect
9. C11×#1668C2semidirect
10. C11×#1642C2semidirect
11. C11×#1626C2semidirect
12. C11×#1621C2semidirect
13. C11×#1620C2semidirect
14. C11×#1584C2semidirect
15. C11×SD16⋊C8C2semidirect
145. #19868C11direct (N × H)
221. #3399C2×C11semidirect
222. #3392C2×C11semidirect
223. #3365C2×C11semidirect
224. #3287C2×C11semidirect
225. #1721C2×C11semidirect
226. #1686C2×C11semidirect
227. #1681C2×C11semidirect
228. #1668C2×C11semidirect
229. #1668C2×C11semidirect
230. #1642C2×C11semidirect
231. #1626C2×C11semidirect
232. #1621C2×C11semidirect
233. #1620C2×C11semidirect
234. #1584C2×C11semidirect
235. SD16⋊C8C2×C11semidirect
293. C8×C11#135semidirect
531. C11#19868direct (N × H)
589. C8C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#33992
C11×#33922
C11×#33652
C11×#32872
C11×#17212
C11×#16862
C11×#16812
C11×#16682
C11×#16422
C11×#16262
C11×#16212
C11×#16202
C11×#15842
C11×SD16⋊C82
#1986811