Finite Group Databasebeta

← C11×#19799 #14596992

Subgroups — C11×#19799 #14596992

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3392C211yesmaximal, characteristic, complemented
2C11×#3368C211yesmaximal, characteristic, complemented
3C11×#3305C211yesmaximal, characteristic, complemented
4C11×#3305C211yesmaximal, characteristic, complemented
5C11×#1717C211yesmaximal, characteristic, complemented
6C11×#1698C211yesmaximal, characteristic, complemented
7C11×#1681C211yesmaximal, characteristic, complemented
8C11×#1678C211yesmaximal, characteristic, complemented
9C11×#1665C211yesmaximal, characteristic, complemented
10C11×#1646C211yesmaximal, characteristic, complemented
11C11×#1636C211yesmaximal, characteristic, complemented
12C11×#1621C211yesmaximal, characteristic, complemented
13C11×#1621C211yesmaximal, characteristic, complemented
14C11×#1582C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic
17C11×#555C2211yescharacteristic
18C11×#550C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C11×#492—21no—
22C11×#492C2211yescharacteristic
23C11×#490—21no—
24C11×#487C2211yescharacteristic
25C11×#486C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#482—21no—
29C11×#482—21no—
30C11×#478—21no—
31C11×#477C2211yescharacteristic
32C11×#477C2211yescharacteristic
33C11×#474C2211yescharacteristic
34C11×#466—21no—
35C11×#466—21no—
36C11×#461—21no—
37C11×#461C2211yescharacteristic
38C11×#460—21no—
39C11×#460—21no—
40C11×#460C2211yescharacteristic
41C11×#460C2211yescharacteristic
42C11×#459C2211yescharacteristic
43C11×#459C2211yescharacteristic
44C11×#449—21no—
45C11×#449—21no—
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C11×#440—21no—
49C4×C11×SD16—21no—
50C4×C11×SD16C2211yescharacteristic
51C4×C11×SD16C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C11×#416—21no—
55C11×#416—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#332C2211yescharacteristic
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×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16D411yescharacteristic
75C2×C11×SD16D411yescharacteristic
76C2×C11×D8—21no—
77C2×C11×D8—21no—
78C2×C11×D8—41no—
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×#127—21no—
85C11×#127—21no—
86C11×#127C2311yescharacteristic
87C11×#127C2311yescharacteristic
88C11×#125—21no—
89C11×#125—41no—
90C11×#124—41no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121—21no—
95C11×#121—41no—
96C11×#121—41no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11C2311yescharacteristic
100C4×Q8×C11C2311yescharacteristic
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11C2311yescharacteristic
104C4×D4×C11C2311yescharacteristic
105C11×#117—21no—
106C11×#117—21no—
107C11×#107—21no—
108C11×#107—21no—
109C11×#107—21no—
110C11×#106D411yescharacteristic
111C11×#106D411yescharacteristic
112C11×C4⋊C8—21no—
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—41no—
122C11×#103D411yescharacteristic
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—21no—
134C11×#102—21no—
135C11×#102D411yescharacteristic
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C11×#97—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19799C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—42no—
146C11×#41—42no—
147C11×#41—81no—
148C11×#41—81no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
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—41no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11C2×D411yescharacteristic
165C2×D4×C11C2×D411yescharacteristic
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—41no—
169C22×C4×C11—41no—
170C11×SD16—22no—
171C11×SD16—41no—
172C11×SD16—42no—
173C11×SD16—42no—
174C11×SD16—81no—
175C11×SD16—81no—
176C11×SD16—81no—
177C11×D8—81no—
178C11×D8—81no—
179C11×D8—82no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—81no—
186C2×C8×C11—81no—
187C2×C8×C11C2×D411yescharacteristic
188C2×C8×C11C2×D411yescharacteristic
189C2×C8×C11C2×D411yescharacteristic
190C2×C8×C11C2×D411yescharacteristic
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4—41no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C22⋊C4—21no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—41no—
209C11×C22⋊C4—41no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—41no—
213C42×C11—41no—
214C42×C11C2411yescharacteristic
215#3392C2×C1111yescharacteristic, complemented
216#3368C2×C1111yescharacteristic, complemented
217#3305C2×C1111yescharacteristic, complemented
218#3305C2×C1111yescharacteristic, complemented
219#1717C2×C1111yescharacteristic, complemented
220#1698C2×C1111yescharacteristic, complemented
221#1681C2×C1111yescharacteristic, complemented
222#1678C2×C1111yescharacteristic, complemented
223#1665C2×C1111yescharacteristic, complemented
224#1646C2×C1111yescharacteristic, complemented
225#1636C2×C1111yescharacteristic, complemented
226#1621C2×C1111yescharacteristic, complemented
227#1621C2×C1111yescharacteristic, complemented
228#1582C2×C1111yescharacteristic, complemented
229SD16⋊C8C2×C1111yescharacteristic, complemented
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—41no—
233C23×C11—41no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—21no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—81no—
240Q8×C11#13512yes—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—82no—
254D4×C11—81no—
255D4×C11—81no—
256D4×C11—82no—
257D4×C11—161no—
258D4×C11—161no—
259D4×C11—161no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—82no—
273C2×C4×C11—82no—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11—41no—
285C8×C11—41no—
286#557C22×C1111yescharacteristic
287#555C22×C1111yescharacteristic
288#550C22×C1111yescharacteristic
289#550C22×C1111yescharacteristic
290#493C22×C1111yescharacteristic
291#492—21no—
292#492C22×C1111yescharacteristic
293#490—21no—
294#487C22×C1111yescharacteristic
295#486C22×C1111yescharacteristic
296#486C22×C1111yescharacteristic
297#486C22×C1111yescharacteristic
298#482—21no—
299#482—21no—
300#478—21no—
301#477C22×C1111yescharacteristic
302#477C22×C1111yescharacteristic
303#474C22×C1111yescharacteristic
304#466—21no—
305#466—21no—
306#461—21no—
307#461C22×C1111yescharacteristic
308#460—21no—
309#460—21no—
310#460C22×C1111yescharacteristic
311#460C22×C1111yescharacteristic
312#459C22×C1111yescharacteristic
313#459C22×C1111yescharacteristic
314#449—21no—
315#449—21no—
316#446C22×C1111yescharacteristic
317C8×Q8C22×C1111yescharacteristic
318#440—21no—
319C4×SD16—21no—
320C4×SD16C22×C1111yescharacteristic
321C4×SD16C22×C1111yescharacteristic
322C8×D4C22×C1111yescharacteristic
323C8×D4C22×C1111yescharacteristic
324#416—21no—
325#416—21no—
326#335C22×C1111yescharacteristic
327#334C22×C1111yescharacteristic
328#333C22×C1111yescharacteristic
329#332C22×C1111yescharacteristic
330#331C22×C1111yescharacteristic
331#331C22×C1111yescharacteristic
332Q8⋊C8C22×C1111yescharacteristic
333Q8⋊C8C22×C1111yescharacteristic
334D4⋊C8C22×C1111yescharacteristic
335D4⋊C8C22×C1111yescharacteristic
336#322C22×C1111yescharacteristic
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
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×C11D4211yescharacteristic
350C4×C11—22no—
351C4×C11—21no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11C2×#13511yescharacteristic
360C4×C11#57511yescharacteristic
361C4×C11#57611yescharacteristic
362C4×C11#57711yescharacteristic
363C2×#41—21no—
364C2×#41—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16D4×C1111yescharacteristic
371C2×SD16D4×C1111yescharacteristic
372C2×D8—21no—
373C2×D8—21no—
374C2×D8—41no—
375C22×C8—21no—
376C22×C8—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C1111yescharacteristic
379C4⋊Q8C23×C1111yescharacteristic
380#127—21no—
381#127—21no—
382#127C23×C1111yescharacteristic
383#127C23×C1111yescharacteristic
384#125—21no—
385#125—41no—
386#124—41no—
387#121—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—41no—
392#121—41no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8C23×C1111yescharacteristic
396C4×Q8C23×C1111yescharacteristic
397C4×D4—21no—
398C4×D4—21no—
399C4×D4C23×C1111yescharacteristic
400C4×D4C23×C1111yescharacteristic
401#117—21no—
402#117—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#106D4×C1111yescharacteristic
407#106D4×C1111yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C1111yescharacteristic
411C4⋊C8C23×C1111yescharacteristic
412C4⋊C8C23×C1111yescharacteristic
413C4⋊C8C23×C1111yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—41no—
418#103D4×C1111yescharacteristic
419#103D4×C1111yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102D4×C1111yescharacteristic
432#102D4×C1111yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435#97—21no—
436C4×C8—21no—
437C4×C8C23×C1111yescharacteristic
438C4×C8C23×C1111yescharacteristic
439C4×C8C23×C1111yescharacteristic
440C2×C11—81no—
441C2×C11—81no—
442C2×C11—161no—
443C2×C11—161no—
444C2×C11#326811yescharacteristic
445C2×C11#328211yescharacteristic
446C2×C11#328811yescharacteristic
447#41—42no—
448#41—42no—
449#41—81no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8C2×D4×C1111yescharacteristic
454C2×Q8C2×D4×C1111yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C1111yescharacteristic
467C2×D4C2×D4×C1111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472SD16—22no—
473SD16—41no—
474SD16—42no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—81no—
480D8—81no—
481D8—82no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—81no—
488C2×C8—81no—
489C2×C8C2×D4×C1111yescharacteristic
490C2×C8C2×D4×C1111yescharacteristic
491C2×C8C2×D4×C1111yescharacteristic
492C2×C8C2×D4×C1111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C1111yescharacteristic
503C4⋊C4C2×D4×C1111yescharacteristic
504C4⋊C4C2×D4×C1111yescharacteristic
505C4⋊C4C2×D4×C1111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C42—21no—
513C42—21no—
514C42—41no—
515C42—41no—
516C42C24×C1111yescharacteristic
517C11#1979911yescharacteristic, direct product factor, Sylow
518C23—21no—
519C23—21no—
520C23—41no—
521C23—41no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—81no—
528Q8C11×#13512yes—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—82no—
542D4—81no—
543D4—81no—
544D4—82no—
545D4—161no—
546D4—161no—
547D4—161no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4C22×D4×C1111yescharacteristic
563C2×C4C22×D4×C1111yescharacteristic
564C2×C4C11×H(5,𝔽2)11yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22D42×C1111yescharacteristic
587C4—22no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4C2×C11×#13511yescharacteristic
597C4C11×#57511yescharacteristic
598C4C11×#57611yescharacteristic
599C4C11×#57711yescharacteristic
600C2—81no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C11×#326811yescharacteristic
605C2C11×#328211yescharacteristic
606C2C11×#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×#3392C2semidirect
2. C11×#3368C2semidirect
3. C11×#3305C2semidirect
4. C11×#3305C2semidirect
5. C11×#1717C2semidirect
6. C11×#1698C2semidirect
7. C11×#1681C2semidirect
8. C11×#1678C2semidirect
9. C11×#1665C2semidirect
10. C11×#1646C2semidirect
11. C11×#1636C2semidirect
12. C11×#1621C2semidirect
13. C11×#1621C2semidirect
14. C11×#1582C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19799C11direct (N × H)
215. #3392C2×C11semidirect
216. #3368C2×C11semidirect
217. #3305C2×C11semidirect
218. #3305C2×C11semidirect
219. #1717C2×C11semidirect
220. #1698C2×C11semidirect
221. #1681C2×C11semidirect
222. #1678C2×C11semidirect
223. #1665C2×C11semidirect
224. #1646C2×C11semidirect
225. #1636C2×C11semidirect
226. #1621C2×C11semidirect
227. #1621C2×C11semidirect
228. #1582C2×C11semidirect
229. SD16⋊C8C2×C11semidirect
517. C11#19799direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33922
C11×#33682
C11×#33052
C11×#17172
C11×#16982
C11×#16812
C11×#16782
C11×#16652
C11×#16462
C11×#16362
C11×#16212
C11×#15822
C11×SD16⋊C82
#1979911