Finite Group Databasebeta

← C11×#19871 #14597064

Subgroups — C11×#19871 #14597064

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3399C211yesmaximal, characteristic, complemented
2C11×#3396C211yesmaximal, characteristic, complemented
3C11×#3394C211yesmaximal, characteristic, complemented
4C11×#3304C211yesmaximal, characteristic, complemented
5C11×#1721C211yesmaximal, characteristic, complemented
6C11×#1686C211yesmaximal, characteristic, complemented
7C11×#1682C211yesmaximal, characteristic, complemented
8C11×#1668C211yesmaximal, characteristic, complemented
9C11×#1667C211yesmaximal, characteristic, complemented
10C11×#1640C211yesmaximal, characteristic, complemented
11C11×#1628C211yesmaximal, characteristic, complemented
12C11×#1621C211yesmaximal, characteristic, complemented
13C11×#1620C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#559C2211yescharacteristic
17C11×#559C2211yescharacteristic
18C11×#556C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#496—21no—
21C11×#495—21no—
22C11×#495—21no—
23C11×#493C2211yescharacteristic
24C11×#493C2211yescharacteristic
25C11×#493C2211yescharacteristic
26C11×#492C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#482—21no—
30C11×#475C2211yescharacteristic
31C11×#465—21no—
32C11×#464—21no—
33C11×#463—21no—
34C11×#463—21no—
35C11×#463—21no—
36C11×#463—21no—
37C11×#462C2211yescharacteristic
38C11×#460C2211yescharacteristic
39C11×#460C2211yescharacteristic
40C11×#460C2211yescharacteristic
41C11×#460C2211yescharacteristic
42C11×#459—21no—
43C11×#459C2211yescharacteristic
44C11×#459C2211yescharacteristic
45C11×#452—21no—
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C11×#442—21no—
50C4×C11×Q16C2211yescharacteristic
51C4×C11×SD16—21no—
52C4×C11×SD16C2211yescharacteristic
53C4×C11×D8—21no—
54C8×D4×C11C2211yescharacteristic
55C11×#416—21no—
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×Q16—21no—
69C2×C11×Q16D411yescharacteristic
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16D411yescharacteristic
77C2×C11×D8—21no—
78C2×C11×D8—21no—
79C2×C11×D8—21no—
80C2×C11×D8—21no—
81C2×C11×D8—21no—
82C2×C11×D8—21no—
83C2×C11×D8—41no—
84C22×C8×C11—21no—
85C11×C4⋊Q8C2311yescharacteristic
86C11×#127—21no—
87C11×#127C2311yescharacteristic
88C11×#127C2311yescharacteristic
89C11×#127C2311yescharacteristic
90C11×#126—41no—
91C11×#124—21no—
92C11×#124—21no—
93C11×#124—21no—
94C11×#124—21no—
95C11×#124—21no—
96C11×#123—41no—
97C11×#123—41no—
98C11×C22⋊Q8—21no—
99C11×#121—21no—
100C11×#121—41no—
101C4×Q8×C11—21no—
102C4×Q8×C11C2311yescharacteristic
103C4×Q8×C11C2311yescharacteristic
104C4×Q8×C11C2311yescharacteristic
105C4×D4×C11—21no—
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11C2311yescharacteristic
111C11×#117—21no—
112C11×#107D411yescharacteristic
113C11×#106—21no—
114C11×#106D411yescharacteristic
115C11×C4⋊C8—21no—
116C11×C4⋊C8—21no—
117C11×C4⋊C8—21no—
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×C4⋊C8C2311yescharacteristic
122C11×#103—21no—
123C11×#103—21no—
124C11×#103D411yescharacteristic
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×C22⋊C8—21no—
138C11×#97—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19871C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—42no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
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×C11C2×D411yescharacteristic
163C22×C4×C11—21no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C11×Q16—41no—
168C11×Q16—81no—
169C11×SD16—22no—
170C11×SD16—42no—
171C11×SD16—81no—
172C11×SD16—81no—
173C11×SD16—81no—
174C11×SD16—81no—
175C11×SD16—81no—
176C11×D8—42no—
177C11×D8—42no—
178C11×D8—81no—
179C11×D8—81no—
180C11×D8—81no—
181C11×D8—81no—
182C11×D8—82no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—81no—
189C2×C8×C11C2×D411yescharacteristic
190C2×C8×C11C2×D411yescharacteristic
191C2×C8×C11C2×D411yescharacteristic
192C2×C8×C11C2×D411yescharacteristic
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—41no—
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C22⋊C4—21no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—41no—
209C11×C22⋊C4—41no—
210C11×C22⋊C4—41no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—41no—
217C42×C11C2411yescharacteristic
218#3399C2×C1111yescharacteristic, complemented
219#3396C2×C1111yescharacteristic, complemented
220#3394C2×C1111yescharacteristic, complemented
221#3304C2×C1111yescharacteristic, complemented
222#1721C2×C1111yescharacteristic, complemented
223#1686C2×C1111yescharacteristic, complemented
224#1682C2×C1111yescharacteristic, complemented
225#1668C2×C1111yescharacteristic, complemented
226#1667C2×C1111yescharacteristic, complemented
227#1640C2×C1111yescharacteristic, complemented
228#1628C2×C1111yescharacteristic, complemented
229#1621C2×C1111yescharacteristic, complemented
230#1620C2×C1111yescharacteristic, complemented
231#1584C2×C1111yescharacteristic, complemented
232SD16⋊C8C2×C1111yescharacteristic, complemented
233C23×C11—21no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237Q8×C11—21no—
238Q8×C11—21no—
239Q8×C11—21no—
240Q8×C11—21no—
241Q8×C11—21no—
242Q8×C11—21no—
243Q8×C11—41no—
244Q8×C11—41no—
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—41no—
248D4×C11—41no—
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—41no—
258D4×C11—41no—
259D4×C11—81no—
260D4×C11—81no—
261D4×C11—81no—
262D4×C11—82no—
263D4×C11—161no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—82no—
275C2×C4×C11—161no—
276C2×C4×C11—161no—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—41no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11—41no—
287C8×C11—41no—
288C8×C11#13512yes—
289#559C22×C1111yescharacteristic
290#559C22×C1111yescharacteristic
291#556C22×C1111yescharacteristic
292#550C22×C1111yescharacteristic
293#496—21no—
294#495—21no—
295#495—21no—
296#493C22×C1111yescharacteristic
297#493C22×C1111yescharacteristic
298#493C22×C1111yescharacteristic
299#492C22×C1111yescharacteristic
300#486C22×C1111yescharacteristic
301#486C22×C1111yescharacteristic
302#482—21no—
303#475C22×C1111yescharacteristic
304#465—21no—
305#464—21no—
306#463—21no—
307#463—21no—
308#463—21no—
309#463—21no—
310#462C22×C1111yescharacteristic
311#460C22×C1111yescharacteristic
312#460C22×C1111yescharacteristic
313#460C22×C1111yescharacteristic
314#460C22×C1111yescharacteristic
315#459—21no—
316#459C22×C1111yescharacteristic
317#459C22×C1111yescharacteristic
318#452—21no—
319#446C22×C1111yescharacteristic
320C8×Q8C22×C1111yescharacteristic
321C8×Q8C22×C1111yescharacteristic
322#442—21no—
323C4×Q16C22×C1111yescharacteristic
324C4×SD16—21no—
325C4×SD16C22×C1111yescharacteristic
326C4×D8—21no—
327C8×D4C22×C1111yescharacteristic
328#416—21no—
329#335C22×C1111yescharacteristic
330#335C22×C1111yescharacteristic
331#332C22×C1111yescharacteristic
332#331C22×C1111yescharacteristic
333#331C22×C1111yescharacteristic
334#331C22×C1111yescharacteristic
335Q8⋊C8C22×C1111yescharacteristic
336Q8⋊C8C22×C1111yescharacteristic
337Q8⋊C8C22×C1111yescharacteristic
338D4⋊C8C22×C1111yescharacteristic
339#322C22×C1111yescharacteristic
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11D4211yescharacteristic
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—81no—
362C4×C11C2×#13511yescharacteristic
363C4×C11#57511yescharacteristic
364C4×C11#57611yescharacteristic
365C4×C11#57611yescharacteristic
366C2×#41—21no—
367C2×Q16—21no—
368C2×Q16D4×C1111yescharacteristic
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16D4×C1111yescharacteristic
376C2×D8—21no—
377C2×D8—21no—
378C2×D8—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×D8—41no—
383C22×C8—21no—
384C4⋊Q8C23×C1111yescharacteristic
385#127—21no—
386#127C23×C1111yescharacteristic
387#127C23×C1111yescharacteristic
388#127C23×C1111yescharacteristic
389#126—41no—
390#124—21no—
391#124—21no—
392#124—21no—
393#124—21no—
394#124—21no—
395#123—41no—
396#123—41no—
397C22⋊Q8—21no—
398#121—21no—
399#121—41no—
400C4×Q8—21no—
401C4×Q8C23×C1111yescharacteristic
402C4×Q8C23×C1111yescharacteristic
403C4×Q8C23×C1111yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4C23×C1111yescharacteristic
410#117—21no—
411#107D4×C1111yescharacteristic
412#106—21no—
413#106D4×C1111yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8C23×C1111yescharacteristic
418C4⋊C8C23×C1111yescharacteristic
419C4⋊C8C23×C1111yescharacteristic
420C4⋊C8C23×C1111yescharacteristic
421#103—21no—
422#103—21no—
423#103D4×C1111yescharacteristic
424#103D4×C1111yescharacteristic
425#103D4×C1111yescharacteristic
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—41no—
435#102D4×C1111yescharacteristic
436C22⋊C8—21no—
437#97—21no—
438C4×C8—21no—
439C4×C8—21no—
440C4×C8C23×C1111yescharacteristic
441C4×C8C23×C1111yescharacteristic
442C4×C8C23×C1111yescharacteristic
443C2×C11—81no—
444C2×C11—161no—
445C2×C11—161no—
446C2×C11—161no—
447C2×C11#326811yescharacteristic
448C2×C11#328711yescharacteristic
449C2×C11#328811yescharacteristic
450#41—42no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8C2×D4×C1111yescharacteristic
454C2×Q8C2×D4×C1111yescharacteristic
455C2×Q8C2×D4×C1111yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4C2×D4×C1111yescharacteristic
468C22×C4—21no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—41no—
473Q16—81no—
474SD16—22no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481D8—42no—
482D8—42no—
483D8—81no—
484D8—81no—
485D8—81no—
486D8—81no—
487D8—82no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—81no—
494C2×C8C2×D4×C1111yescharacteristic
495C2×C8C2×D4×C1111yescharacteristic
496C2×C8C2×D4×C1111yescharacteristic
497C2×C8C2×D4×C1111yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4C2×D4×C1111yescharacteristic
505C4⋊C4C2×D4×C1111yescharacteristic
506C4⋊C4C2×D4×C1111yescharacteristic
507C4⋊C4C2×D4×C1111yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—41no—
522C42C24×C1111yescharacteristic
523C11#1987111yescharacteristic, direct product factor, Sylow
524C23—21no—
525C23—41no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—82no—
554D4—161no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C22×D4×C1111yescharacteristic
570C2×C4C11×H(5,𝔽2)11yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8C11×#13512yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C1111yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4C2×C11×#13511yescharacteristic
603C4C11×#57511yescharacteristic
604C4C11×#57611yescharacteristic
605C4C11×#57611yescharacteristic
606C2—81no—
607C2—161no—
608C2—161no—
609C2—161no—
610C2C11×#326811yescharacteristic
611C2C11×#328711yescharacteristic
612C2C11×#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×#3396C2semidirect
3. C11×#3394C2semidirect
4. C11×#3304C2semidirect
5. C11×#1721C2semidirect
6. C11×#1686C2semidirect
7. C11×#1682C2semidirect
8. C11×#1668C2semidirect
9. C11×#1667C2semidirect
10. C11×#1640C2semidirect
11. C11×#1628C2semidirect
12. C11×#1621C2semidirect
13. C11×#1620C2semidirect
14. C11×#1584C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19871C11direct (N × H)
218. #3399C2×C11semidirect
219. #3396C2×C11semidirect
220. #3394C2×C11semidirect
221. #3304C2×C11semidirect
222. #1721C2×C11semidirect
223. #1686C2×C11semidirect
224. #1682C2×C11semidirect
225. #1668C2×C11semidirect
226. #1667C2×C11semidirect
227. #1640C2×C11semidirect
228. #1628C2×C11semidirect
229. #1621C2×C11semidirect
230. #1620C2×C11semidirect
231. #1584C2×C11semidirect
232. SD16⋊C8C2×C11semidirect
523. C11#19871direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33992
C11×#33962
C11×#33942
C11×#33042
C11×#17212
C11×#16862
C11×#16822
C11×#16682
C11×#16672
C11×#16402
C11×#16282
C11×#16212
C11×#16202
C11×#15842
C11×SD16⋊C82
#1987111