Finite Group Databasebeta

← C11×#19855 #14597048

Subgroups — C11×#19855 #14597048

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3399C211yesmaximal, characteristic, complemented
2C11×#3394C211yesmaximal, characteristic, complemented
3C11×#3340C211yesmaximal, characteristic, complemented
4C11×#3305C211yesmaximal, characteristic, complemented
5C11×#1715C211yesmaximal, characteristic, complemented
6C11×#1692C211yesmaximal, characteristic, complemented
7C11×#1678C211yesmaximal, characteristic, complemented
8C11×#1667C211yesmaximal, characteristic, complemented
9C11×#1665C211yesmaximal, characteristic, complemented
10C11×#1641C211yesmaximal, characteristic, complemented
11C11×#1630C211yesmaximal, characteristic, complemented
12C11×#1628C211yesmaximal, characteristic, complemented
13C11×#1624C211yesmaximal, characteristic, complemented
14C11×#1582C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#559C2211yescharacteristic
17C11×#556C2211yescharacteristic
18C11×#555C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#496—21no—
22C11×#495—21no—
23C11×#493C2211yescharacteristic
24C11×#492C2211yescharacteristic
25C11×#492C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#485—21no—
29C11×#482—21no—
30C11×#482—21no—
31C11×#477C2211yescharacteristic
32C11×#477C2211yescharacteristic
33C11×#474C2211yescharacteristic
34C11×#466—21no—
35C11×#465—21no—
36C11×#464—21no—
37C11×#463—21no—
38C11×#463—21no—
39C11×#462C2211yescharacteristic
40C11×#460C2211yescharacteristic
41C11×#459—21no—
42C11×#459C2211yescharacteristic
43C11×#459C2211yescharacteristic
44C11×#459C2211yescharacteristic
45C11×#449—21no—
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C11×#442—21no—
49C4×C11×SD16—21no—
50C4×C11×SD16C2211yescharacteristic
51C4×C11×SD16C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C11×#427—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×Q16—21no—
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—41no—
73C2×C11×SD16D411yescharacteristic
74C2×C11×SD16D411yescharacteristic
75C2×C11×D8—21no—
76C2×C11×D8—21no—
77C2×C11×D8—21no—
78C2×C11×D8—21no—
79C2×C11×D8—21no—
80C22×C8×C11—21no—
81C22×C8×C11—21no—
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×#127—21no—
85C11×#127C2311yescharacteristic
86C11×#127C2311yescharacteristic
87C11×#126—41no—
88C11×#124—21no—
89C11×#124—21no—
90C11×#124—21no—
91C11×#124—41no—
92C11×#123—41no—
93C11×C22⋊Q8—21no—
94C11×#121—21no—
95C11×#121—21no—
96C11×#121—21no—
97C11×#121—41no—
98C4×Q8×C11—21no—
99C4×Q8×C11C2311yescharacteristic
100C4×Q8×C11C2311yescharacteristic
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11C2311yescharacteristic
105C4×D4×C11C2311yescharacteristic
106C11×#117—21no—
107C11×#117—21no—
108C11×#117—21no—
109C11×#107—21no—
110C11×#107—21no—
111C11×#107—21no—
112C11×#106—21no—
113C11×#106—21no—
114C11×#106D411yescharacteristic
115C11×#106D411yescharacteristic
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×#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—41no—
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#19855C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—42no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
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—41no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11C2×D411yescharacteristic
161C2×D4×C11C2×D411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C11×Q16—81no—
167C11×SD16—22no—
168C11×SD16—41no—
169C11×SD16—42no—
170C11×SD16—81no—
171C11×SD16—81no—
172C11×SD16—82no—
173C11×D8—42no—
174C11×D8—81no—
175C11×D8—81no—
176C11×D8—81no—
177C11×D8—81no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—42no—
184C2×C8×C11—81no—
185C2×C8×C11C2×D411yescharacteristic
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C2×C8×C11C2×D411yescharacteristic
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
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#3399C2×C1111yescharacteristic, complemented
216#3394C2×C1111yescharacteristic, complemented
217#3340C2×C1111yescharacteristic, complemented
218#3305C2×C1111yescharacteristic, complemented
219#1715C2×C1111yescharacteristic, complemented
220#1692C2×C1111yescharacteristic, complemented
221#1678C2×C1111yescharacteristic, complemented
222#1667C2×C1111yescharacteristic, complemented
223#1665C2×C1111yescharacteristic, complemented
224#1641C2×C1111yescharacteristic, complemented
225#1630C2×C1111yescharacteristic, complemented
226#1628C2×C1111yescharacteristic, complemented
227#1624C2×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—21no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—81no—
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—81no—
254D4×C11—81no—
255D4×C11—82no—
256D4×C11—161no—
257D4×C11—161no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—82no—
271C2×C4×C11—161no—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11#13512yes—
284#559C22×C1111yescharacteristic
285#556C22×C1111yescharacteristic
286#555C22×C1111yescharacteristic
287#550C22×C1111yescharacteristic
288#498C22×C1111yescharacteristic
289#496—21no—
290#495—21no—
291#493C22×C1111yescharacteristic
292#492C22×C1111yescharacteristic
293#492C22×C1111yescharacteristic
294#486C22×C1111yescharacteristic
295#486C22×C1111yescharacteristic
296#485—21no—
297#482—21no—
298#482—21no—
299#477C22×C1111yescharacteristic
300#477C22×C1111yescharacteristic
301#474C22×C1111yescharacteristic
302#466—21no—
303#465—21no—
304#464—21no—
305#463—21no—
306#463—21no—
307#462C22×C1111yescharacteristic
308#460C22×C1111yescharacteristic
309#459—21no—
310#459C22×C1111yescharacteristic
311#459C22×C1111yescharacteristic
312#459C22×C1111yescharacteristic
313#449—21no—
314#446C22×C1111yescharacteristic
315C8×Q8C22×C1111yescharacteristic
316#442—21no—
317C4×SD16—21no—
318C4×SD16C22×C1111yescharacteristic
319C4×SD16C22×C1111yescharacteristic
320C8×D4C22×C1111yescharacteristic
321C8×D4C22×C1111yescharacteristic
322#427—21no—
323#416—21no—
324#335C22×C1111yescharacteristic
325#334C22×C1111yescharacteristic
326#333C22×C1111yescharacteristic
327#332C22×C1111yescharacteristic
328#331C22×C1111yescharacteristic
329#331C22×C1111yescharacteristic
330Q8⋊C8C22×C1111yescharacteristic
331Q8⋊C8C22×C1111yescharacteristic
332D4⋊C8C22×C1111yescharacteristic
333D4⋊C8C22×C1111yescharacteristic
334#322C22×C1111yescharacteristic
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11D4211yescharacteristic
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11C2×#13511yescharacteristic
358C4×C11#57511yescharacteristic
359C4×C11#57611yescharacteristic
360C4×C11#57711yescharacteristic
361C2×#41—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—41no—
367C2×SD16D4×C1111yescharacteristic
368C2×SD16D4×C1111yescharacteristic
369C2×D8—21no—
370C2×D8—21no—
371C2×D8—21no—
372C2×D8—21no—
373C2×D8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C4⋊Q8C23×C1111yescharacteristic
377C4⋊Q8C23×C1111yescharacteristic
378#127—21no—
379#127C23×C1111yescharacteristic
380#127C23×C1111yescharacteristic
381#126—41no—
382#124—21no—
383#124—21no—
384#124—21no—
385#124—41no—
386#123—41no—
387C22⋊Q8—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—41no—
392C4×Q8—21no—
393C4×Q8C23×C1111yescharacteristic
394C4×Q8C23×C1111yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C1111yescharacteristic
399C4×D4C23×C1111yescharacteristic
400#117—21no—
401#117—21no—
402#117—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#106—21no—
407#106—21no—
408#106D4×C1111yescharacteristic
409#106D4×C1111yescharacteristic
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8C23×C1111yescharacteristic
413C4⋊C8C23×C1111yescharacteristic
414C4⋊C8C23×C1111yescharacteristic
415C4⋊C8C23×C1111yescharacteristic
416#103—21no—
417#103—21no—
418#103—21no—
419#103D4×C1111yescharacteristic
420#103D4×C1111yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—41no—
429#102D4×C1111yescharacteristic
430#102D4×C1111yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433#97—21no—
434C4×C8—21no—
435C4×C8C23×C1111yescharacteristic
436C4×C8C23×C1111yescharacteristic
437C4×C8C23×C1111yescharacteristic
438C2×C11—81no—
439C2×C11—81no—
440C2×C11—161no—
441C2×C11—161no—
442C2×C11#326811yescharacteristic
443C2×C11#328411yescharacteristic
444C2×C11#328811yescharacteristic
445#41—42no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C2×D4×C1111yescharacteristic
450C2×Q8C2×D4×C1111yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4C2×D4×C1111yescharacteristic
461C2×D4C2×D4×C1111yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—41no—
466Q16—81no—
467SD16—22no—
468SD16—41no—
469SD16—42no—
470SD16—81no—
471SD16—81no—
472SD16—82no—
473D8—42no—
474D8—81no—
475D8—81no—
476D8—81no—
477D8—81no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—42no—
484C2×C8—81no—
485C2×C8C2×D4×C1111yescharacteristic
486C2×C8C2×D4×C1111yescharacteristic
487C2×C8C2×D4×C1111yescharacteristic
488C2×C8C2×D4×C1111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C1111yescharacteristic
497C4⋊C4C2×D4×C1111yescharacteristic
498C4⋊C4C2×D4×C1111yescharacteristic
499C4⋊C4C2×D4×C1111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C42—21no—
511C42—21no—
512C42—41no—
513C42—41no—
514C42C24×C1111yescharacteristic
515C11#1985511yescharacteristic, direct product factor, Sylow
516C23—21no—
517C23—21no—
518C23—41no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—21no—
523Q8—21no—
524Q8—41no—
525Q8—41no—
526Q8—81no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—81no—
541D4—82no—
542D4—161no—
543D4—161no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—161no—
558C2×C4C22×D4×C1111yescharacteristic
559C2×C4C22×D4×C1111yescharacteristic
560C2×C4C11×H(5,𝔽2)11yescharacteristic
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8C11×#13512yes—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22D42×C1111yescharacteristic
583C4—21no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—81no—
591C4—81no—
592C4C2×C11×#13511yescharacteristic
593C4C11×#57511yescharacteristic
594C4C11×#57611yescharacteristic
595C4C11×#57711yescharacteristic
596C2—81no—
597C2—81no—
598C2—161no—
599C2—161no—
600C2C11×#326811yescharacteristic
601C2C11×#328411yescharacteristic
602C2C11×#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×#3394C2semidirect
3. C11×#3340C2semidirect
4. C11×#3305C2semidirect
5. C11×#1715C2semidirect
6. C11×#1692C2semidirect
7. C11×#1678C2semidirect
8. C11×#1667C2semidirect
9. C11×#1665C2semidirect
10. C11×#1641C2semidirect
11. C11×#1630C2semidirect
12. C11×#1628C2semidirect
13. C11×#1624C2semidirect
14. C11×#1582C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19855C11direct (N × H)
215. #3399C2×C11semidirect
216. #3394C2×C11semidirect
217. #3340C2×C11semidirect
218. #3305C2×C11semidirect
219. #1715C2×C11semidirect
220. #1692C2×C11semidirect
221. #1678C2×C11semidirect
222. #1667C2×C11semidirect
223. #1665C2×C11semidirect
224. #1641C2×C11semidirect
225. #1630C2×C11semidirect
226. #1628C2×C11semidirect
227. #1624C2×C11semidirect
228. #1582C2×C11semidirect
229. SD16⋊C8C2×C11semidirect
515. C11#19855direct (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×#33942
C11×#33402
C11×#33052
C11×#17152
C11×#16922
C11×#16782
C11×#16672
C11×#16652
C11×#16412
C11×#16302
C11×#16282
C11×#16242
C11×#15822
C11×SD16⋊C82
#1985511