Finite Group Databasebeta

← C11×#19843 #14597036

Subgroups — C11×#19843 #14597036

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3368C211yesmaximal, characteristic, complemented
2C11×#3363C211yesmaximal, characteristic, complemented
3C11×#3362C211yesmaximal, characteristic, complemented
4C11×#3287C211yesmaximal, characteristic
5C11×#1717C211yesmaximal, characteristic, complemented
6C11×#1698C211yesmaximal, characteristic, complemented
7C11×#1683C211yesmaximal, characteristic, complemented
8C11×#1682C211yesmaximal, characteristic, complemented
9C11×#1668C211yesmaximal, characteristic, complemented
10C11×#1641C211yesmaximal, characteristic, complemented
11C11×#1631C211yesmaximal, characteristic, complemented
12C11×#1626C211yesmaximal, characteristic, complemented
13C11×#1623C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17Q82×C11C2211yescharacteristic
18C11×#557C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#550C2211yescharacteristic
21C11×#493C2211yescharacteristic
22C11×#492C2211yescharacteristic
23C11×#490—21no—
24C11×#487—21no—
25C11×#487C2211yescharacteristic
26C11×#486—21no—
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#486C2211yescharacteristic
30C11×#478—21no—
31C11×#477—21no—
32C11×#477C2211yescharacteristic
33C11×#476—21no—
34C11×#476C2211yescharacteristic
35C11×#474C2211yescharacteristic
36C11×#466—21no—
37C11×#462—21no—
38C11×#462C2211yescharacteristic
39C11×#460—21no—
40C11×#460—21no—
41C11×#460C2211yescharacteristic
42C11×#460C2211yescharacteristic
43C11×#460C2211yescharacteristic
44C11×#460C2211yescharacteristic
45C11×#449—21no—
46C11×#449—21no—
47C11×#446C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C8×Q8×C11C2211yescharacteristic
50C11×#440—21no—
51C4×C11×Q16—21no—
52C4×C11×Q16C2211yescharacteristic
53C4×C11×SD16—21no—
54C4×C11×SD16C2211yescharacteristic
55C8×D4×C11C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#335C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#332C2211yescharacteristic
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×Q16—21no—
71C2×C11×Q16D411yescharacteristic
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—41no—
77C2×C11×SD16D411yescharacteristic
78C2×C11×D8—21no—
79C2×C11×D8—21no—
80C22×C8×C11—21no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—21no—
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8—41no—
85C11×C4⋊Q8C2311yescharacteristic
86C11×C4⋊Q8C2311yescharacteristic
87C11×#127—21no—
88C11×#127—21no—
89C11×#127C2311yescharacteristic
90C11×#127C2311yescharacteristic
91C11×#125—21no—
92C11×#125—41no—
93C11×#121—21no—
94C11×#121—21no—
95C11×#121—41no—
96C11×#121—41no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11—21no—
100C4×Q8×C11—21no—
101C4×Q8×C11C2311yescharacteristic
102C4×Q8×C11C2311yescharacteristic
103C4×Q8×C11C2311yescharacteristic
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11C2311yescharacteristic
107C11×#107—21no—
108C11×#107—21no—
109C11×#107D411yescharacteristic
110C11×#106—21no—
111C11×#106D411yescharacteristic
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×C4⋊C8—21no—
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×C4⋊C8C2311yescharacteristic
119C11×#103—21no—
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103D411yescharacteristic
124C11×#103D411yescharacteristic
125C11×#103D411yescharacteristic
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×#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#19843C1111yesmaximal, characteristic, direct product factor, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C11×#41—81no—
149C11×#41—81no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—41no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×Q8×C11C2×D411yescharacteristic
155C2×Q8×C11C2×D411yescharacteristic
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—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11C2×D411yescharacteristic
167C22×C4×C11—21no—
168C22×C4×C11—41no—
169C22×C4×C11—41no—
170C11×Q16—22no—
171C11×Q16—42no—
172C11×SD16—22no—
173C11×SD16—42no—
174C11×SD16—42no—
175C11×SD16—42no—
176C11×SD16—42no—
177C11×SD16—82no—
178C11×D8—42no—
179C11×D8—81no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—42no—
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C2×C8×C11C2×D411yescharacteristic
189C2×C8×C11C2×D411yescharacteristic
190C11×C4⋊C4—21no—
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⋊C4—41no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C22⋊C4—21no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—41no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—41no—
213C42×C11—41no—
214C42×C11C2411yescharacteristic
215#3368C2×C1111yescharacteristic, complemented
216#3363C2×C1111yescharacteristic, complemented
217#3362C2×C1111yescharacteristic, complemented
218#3287C2×C1111yescharacteristic
219#1717C2×C1111yescharacteristic, complemented
220#1698C2×C1111yescharacteristic, complemented
221#1683C2×C1111yescharacteristic, complemented
222#1682C2×C1111yescharacteristic, complemented
223#1668C2×C1111yescharacteristic, complemented
224#1641C2×C1111yescharacteristic, complemented
225#1631C2×C1111yescharacteristic, complemented
226#1626C2×C1111yescharacteristic, complemented
227#1623C2×C1111yescharacteristic, complemented
228#1584C2×C1111yescharacteristic, complemented
229SD16⋊C8C2×C1111yescharacteristic, complemented
230C23×C11—21no—
231C23×C11—41no—
232C23×C11—41no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—21no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—81no—
240Q8×C11—161no—
241Q8×C11#13512yescomplemented
242Q8×C11AGL(1,ℤ/8)12yes—
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—
259C2×C4×C11—21no—
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—82no—
271C2×C4×C11—82no—
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—21no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C2×#135—21no—
285Q82C22×C1111yescharacteristic
286#557C22×C1111yescharacteristic
287#550C22×C1111yescharacteristic
288#550C22×C1111yescharacteristic
289#493C22×C1111yescharacteristic
290#492C22×C1111yescharacteristic
291#490—21no—
292#487—21no—
293#487C22×C1111yescharacteristic
294#486—21no—
295#486C22×C1111yescharacteristic
296#486C22×C1111yescharacteristic
297#486C22×C1111yescharacteristic
298#478—21no—
299#477—21no—
300#477C22×C1111yescharacteristic
301#476—21no—
302#476C22×C1111yescharacteristic
303#474C22×C1111yescharacteristic
304#466—21no—
305#462—21no—
306#462C22×C1111yescharacteristic
307#460—21no—
308#460—21no—
309#460C22×C1111yescharacteristic
310#460C22×C1111yescharacteristic
311#460C22×C1111yescharacteristic
312#460C22×C1111yescharacteristic
313#449—21no—
314#449—21no—
315#446C22×C1111yescharacteristic
316C8×Q8C22×C1111yescharacteristic
317C8×Q8C22×C1111yescharacteristic
318#440—21no—
319C4×Q16—21no—
320C4×Q16C22×C1111yescharacteristic
321C4×SD16—21no—
322C4×SD16C22×C1111yescharacteristic
323C8×D4C22×C1111yescharacteristic
324#335C22×C1111yescharacteristic
325#335C22×C1111yescharacteristic
326#333C22×C1111yescharacteristic
327#332C22×C1111yescharacteristic
328#331C22×C1111yescharacteristic
329#331C22×C1111yescharacteristic
330Q8⋊C8C22×C1111yescharacteristic
331Q8⋊C8C22×C1111yescharacteristic
332Q8⋊C8C22×C1111yescharacteristic
333D4⋊C8C22×C1111yescharacteristic
334#322C22×C1111yescharacteristic
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11D4211yescharacteristic
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—21no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11C2×#13511yescharacteristic
356C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
357C4×C11#57711yescharacteristic
358C4×C11#57811yescharacteristic
359C2×#41—21no—
360C2×#41—21no—
361#135—44no—
362C2×Q16—21no—
363C2×Q16D4×C1111yescharacteristic
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—41no—
369C2×SD16D4×C1111yescharacteristic
370C2×D8—21no—
371C2×D8—21no—
372C22×C8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—41no—
377C4⋊Q8C23×C1111yescharacteristic
378C4⋊Q8C23×C1111yescharacteristic
379#127—21no—
380#127—21no—
381#127C23×C1111yescharacteristic
382#127C23×C1111yescharacteristic
383#125—21no—
384#125—41no—
385#121—21no—
386#121—21no—
387#121—41no—
388#121—41no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8C23×C1111yescharacteristic
394C4×Q8C23×C1111yescharacteristic
395C4×Q8C23×C1111yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C1111yescharacteristic
399#107—21no—
400#107—21no—
401#107D4×C1111yescharacteristic
402#106—21no—
403#106D4×C1111yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C1111yescharacteristic
408C4⋊C8C23×C1111yescharacteristic
409C4⋊C8C23×C1111yescharacteristic
410C4⋊C8C23×C1111yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103D4×C1111yescharacteristic
416#103D4×C1111yescharacteristic
417#103D4×C1111yescharacteristic
418#102—21no—
419#102—21no—
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—41no—
429#102D4×C1111yescharacteristic
430C22⋊C8—21no—
431#97—21no—
432C4×C8—21no—
433C4×C8—21no—
434C4×C8C23×C1111yescharacteristic
435C4×C8C23×C1111yescharacteristic
436C4×C8C23×C1111yescharacteristic
437C2×C11—81no—
438C2×C11—161no—
439C2×C11—161no—
440C2×C11#326511yescharacteristic
441C2×C11#328511yescharacteristic
442C2×C11#328811yescharacteristic
443#41—42no—
444#41—42no—
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—41no—
450C2×Q8C2×D4×C1111yescharacteristic
451C2×Q8C2×D4×C1111yescharacteristic
452C2×Q8C2×D4×C1111yescharacteristic
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C2×D4×C1111yescharacteristic
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467Q16—22no—
468Q16—42no—
469SD16—22no—
470SD16—42no—
471SD16—42no—
472SD16—42no—
473SD16—42no—
474SD16—82no—
475D8—42no—
476D8—81no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
483C2×C8C2×D4×C1111yescharacteristic
484C2×C8C2×D4×C1111yescharacteristic
485C2×C8C2×D4×C1111yescharacteristic
486C2×C8C2×D4×C1111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4C2×D4×C1111yescharacteristic
500C4⋊C4C2×D4×C1111yescharacteristic
501C4⋊C4C2×D4×C1111yescharacteristic
502C4⋊C4C2×D4×C1111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—41no—
510C42—41no—
511C42C24×C1111yescharacteristic
512C11#1984311yescharacteristic, direct product factor, Sylow
513C23—21no—
514C23—41no—
515C23—41no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523Q8—161no—
524Q8C11×#13512yescomplemented
525Q8C11×AGL(1,ℤ/8)12yes—
526D4—21no—
527D4—21no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—82no—
537D4—81no—
538D4—81no—
539D4—82no—
540D4—161no—
541D4—161no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4C22×D4×C1111yescharacteristic
556C2×C4C22×D4×C1111yescharacteristic
557C2×C4C11×H(5,𝔽2)11yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C1111yescharacteristic
577C4—22no—
578C4—22no—
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4C2×C11×#13511yescharacteristic
588C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
589C4C11×#57711yescharacteristic
590C4C11×#57811yescharacteristic
591C2—81no—
592C2—161no—
593C2—161no—
594C2C11×#326511yescharacteristic
595C2C11×#328511yescharacteristic
596C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3287C2
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×#3368C2semidirect
2. C11×#3363C2semidirect
3. C11×#3362C2semidirect
5. C11×#1717C2semidirect
6. C11×#1698C2semidirect
7. C11×#1683C2semidirect
8. C11×#1682C2semidirect
9. C11×#1668C2semidirect
10. C11×#1641C2semidirect
11. C11×#1631C2semidirect
12. C11×#1626C2semidirect
13. C11×#1623C2semidirect
14. C11×#1584C2semidirect
15. C11×SD16⋊C8C2semidirect
145. #19843C11direct (N × H)
215. #3368C2×C11semidirect
216. #3363C2×C11semidirect
217. #3362C2×C11semidirect
219. #1717C2×C11semidirect
220. #1698C2×C11semidirect
221. #1683C2×C11semidirect
222. #1682C2×C11semidirect
223. #1668C2×C11semidirect
224. #1641C2×C11semidirect
225. #1631C2×C11semidirect
226. #1626C2×C11semidirect
227. #1623C2×C11semidirect
228. #1584C2×C11semidirect
229. SD16⋊C8C2×C11semidirect
241. Q8×C11#135semidirect
512. C11#19843direct (N × H)
524. Q8C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#33682
C11×#33632
C11×#33622
C11×#32872
C11×#17172
C11×#16982
C11×#16832
C11×#16822
C11×#16682
C11×#16412
C11×#16312
C11×#16262
C11×#16232
C11×#15842
C11×SD16⋊C82
#1984311