Finite Group Databasebeta

← C11×#19092 #14596285

Subgroups — C11×#19092 #14596285

Order 2816.

816 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3563C211yesmaximal, characteristic, complemented
2C11×#3235C211yesmaximal, characteristic, complemented
3C11×#3234C211yesmaximal, characteristic, complemented
4C11×#3219C211yesmaximal, characteristic
5C11×#1663C212yesmaximal, complemented
6C11×#1660C212yesmaximal, complemented
7C11×#1658C212yesmaximal, complemented
8C11×#1657C212yesmaximal, complemented
9C11×#1537C211yesmaximal, characteristic, complemented
10C11×#1535C211yesmaximal, characteristic, complemented
11C11×#1534C211yesmaximal, characteristic, complemented
12C11×#564C2212yes—
13C11×#563C2212yes—
14C11×#557—21no—
15C11×#554—21no—
16C11×#552—21no—
17C11×#552—22no—
18C11×#552—21no—
19C11×#544—21no—
20C11×#544—21no—
21C11×#541—21no—
22C11×#541—22no—
23C11×#539—21no—
24C11×#533C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#529C2211yescharacteristic
27C2×C11×#125C2211yescharacteristic
28C11×#501C2212yes—
29C11×#501C2212yes—
30C11×#497C2211yescharacteristic
31C11×#496C2211yescharacteristic
32C11×#491C2211yescharacteristic
33C11×#490C2212yes—
34C11×#490C2212yes—
35C11×#490C2211yescharacteristic
36C11×#482—22no—
37C11×#481—21no—
38C11×#480—21no—
39C11×#478—22no—
40C11×#476—21no—
41C11×#474—21no—
42C11×#464—21no—
43C11×#463—21no—
44C11×#452—21no—
45C11×#449—21no—
46C11×#432C2211yescharacteristic
47C11×#432C2211yescharacteristic
48C11×#432C2211yescharacteristic
49C11×#330C2212yes—
50C11×#330C2212yes—
51C11×#330C2212yes—
52C11×#330C2212yes—
53C11×#330C2212yes—
54C11×#329C2212yes—
55C2×C11×#41—21no—
56C2×C11×Q16—21no—
57C2×C11×SD16—21no—
58C2×C11×SD16—21no—
59C2×C11×D8—21no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8D411yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×#127C2311yescharacteristic
67C11×#126—22no—
68C11×#126—22no—
69C11×#126—22no—
70C11×#126—22no—
71C11×#126—21no—
72C11×#125—22no—
73C11×#125—22no—
74C11×#125—21no—
75C11×#125—22no—
76C11×#125—22no—
77C11×#125—22no—
78C11×#125—22no—
79C11×#125—22no—
80C11×#125—22no—
81C11×#125—21no—
82C11×#125—21no—
83C11×#125D412yes—
84C11×#125C2311yescharacteristic
85C11×#125C2312yes—
86C11×#125C2312yes—
87C11×#124—21no—
88C11×#124C2311yescharacteristic
89C11×#123—22no—
90C11×#123—22no—
91C11×#123—21no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8D411yescharacteristic
101C11×#121—21no—
102C11×#121—21no—
103C11×#121D411yescharacteristic
104C4×Q8×C11—21no—
105C4×Q8×C11—22no—
106C4×Q8×C11—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11—21no—
109C4×Q8×C11D411yescharacteristic
110C4×D4×C11—22no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11D411yescharacteristic
115C11×#117—22no—
116C11×#117—21no—
117C11×#117—22no—
118C11×#117—21no—
119C11×#117D412yes—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4D411yescharacteristic
124C2×C11×C4⋊C4D411yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C11×#107—22no—
127C11×#107—22no—
128C11×#106—22no—
129C11×#106—22no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×#103—21no—
134C11×#103—21no—
135C11×#102—21no—
136C11×#102—21no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—22no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×#97C2312yes—
145C11×#97C2312yes—
146C11×#97C2311yescharacteristic
147C11×#97C2311yescharacteristic
148#19092C1111yesmaximal, characteristic, direct product factor, Sylow
149C11×#41—81no—
150C11×#41—81no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—41no—
161C2×D4×C11C2×D411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—41no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C11×Q16—81no—
171C11×SD16—81no—
172C11×SD16—81no—
173C11×D8—81no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D412yes—
205C11×C4⋊C4C2×D412yes—
206C11×C4⋊C4C2×D412yes—
207C11×C4⋊C4C2×D412yes—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—41no—
218C11×C22⋊C4—41no—
219C42×C11—22no—
220C42×C11—22no—
221C42×C11—22no—
222C42×C11—22no—
223C42×C11—21no—
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2411yescharacteristic
228#3563C2×C1111yescharacteristic, complemented
229#3235C2×C1111yescharacteristic, complemented
230#3234C2×C1111yescharacteristic, complemented
231#3219C2×C1111yescharacteristic
232#1663C2×C1112yescomplemented
233#1660C2×C1112yescomplemented
234#1658C2×C1112yescomplemented
235#1657C2×C1112yescomplemented
236#1537C2×C1111yescharacteristic, complemented
237#1535C2×C1111yescharacteristic, complemented
238#1534C2×C1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—41no—
241C23×C11#12011yescharacteristic
242Q8×C11—41no—
243Q8×C11—42no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—81no—
247Q8×C11—82no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—42no—
252D4×C11—42no—
253D4×C11—42no—
254D4×C11—82no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—41no—
268C2×C4×C11—82no—
269C2×C4×C11—81no—
270C2×C4×C11—82no—
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11#12011yescharacteristic
273C2×C4×C11#12011yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C8×C11—42no—
278C8×C11—42no—
279C8×C11—41no—
280C8×C11—41no—
281#564C22×C1112yes—
282#563C22×C1112yes—
283#557—21no—
284#554—21no—
285#552—21no—
286#552—22no—
287#552—21no—
288#544—21no—
289#544—21no—
290#541—21no—
291#541—22no—
292#539—21no—
293#533C22×C1111yescharacteristic
294#532C22×C1111yescharacteristic
295#529C22×C1111yescharacteristic
296C2×#125C22×C1111yescharacteristic
297#501C22×C1112yes—
298#501C22×C1112yes—
299#497C22×C1111yescharacteristic
300#496C22×C1111yescharacteristic
301#491C22×C1111yescharacteristic
302#490C22×C1112yes—
303#490C22×C1112yes—
304#490C22×C1111yescharacteristic
305#482—22no—
306#481—21no—
307#480—21no—
308#478—22no—
309#476—21no—
310#474—21no—
311#464—21no—
312#463—21no—
313#452—21no—
314#449—21no—
315#432C22×C1111yescharacteristic
316#432C22×C1111yescharacteristic
317#432C22×C1111yescharacteristic
318#330C22×C1112yes—
319#330C22×C1112yes—
320#330C22×C1112yes—
321#330C22×C1112yes—
322#330C22×C1112yes—
323#329C22×C1112yes—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11C2×#12011yescharacteristic
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—81no—
348C2×#41—21no—
349C2×Q16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C2×D8—21no—
353C4⋊Q8—22no—
354C4⋊Q8—21no—
355C4⋊Q8—22no—
356C4⋊Q8D4×C1111yescharacteristic
357C4⋊Q8D4×C1111yescharacteristic
358C4⋊Q8C23×C1111yescharacteristic
359#127C23×C1111yescharacteristic
360#126—22no—
361#126—22no—
362#126—22no—
363#126—22no—
364#126—21no—
365#125—22no—
366#125—22no—
367#125—21no—
368#125—22no—
369#125—22no—
370#125—22no—
371#125—22no—
372#125—22no—
373#125—22no—
374#125—21no—
375#125—21no—
376#125D4×C1112yes—
377#125C23×C1112yes—
378#125C23×C1111yescharacteristic
379#125C23×C1112yes—
380#124—21no—
381#124C23×C1111yescharacteristic
382#123—22no—
383#123—22no—
384#123—21no—
385C22⋊Q8—22no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—22no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8D4×C1111yescharacteristic
394#121—21no—
395#121—21no—
396#121D4×C1111yescharacteristic
397C4×Q8—21no—
398C4×Q8—22no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8D4×C1111yescharacteristic
403C4×D4—22no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4D4×C1111yescharacteristic
408#117—22no—
409#117—21no—
410#117—22no—
411#117—21no—
412#117D4×C1112yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4D4×C1111yescharacteristic
417C2×C4⋊C4D4×C1111yescharacteristic
418C2×C42C23×C1111yescharacteristic
419#107—22no—
420#107—22no—
421#106—22no—
422#106—22no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8—21no—
426#103—21no—
427#103—21no—
428#102—21no—
429#102—21no—
430#102—22no—
431#102—22no—
432#102—22no—
433#102—22no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437#97C23×C1112yes—
438#97C23×C1112yes—
439#97C23×C1111yescharacteristic
440#97C23×C1111yescharacteristic
441C2×C11—41no—
442C2×C11—81no—
443C2×C11—161no—
444C2×C11#302011yescharacteristic
445C2×C11#302011yescharacteristic
446C2×C11#302111yescharacteristic
447#41—81no—
448#41—81no—
449C2×Q8—22no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8C2×D4×C1111yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4C2×D4×C1111yescharacteristic
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468Q16—81no—
469SD16—81no—
470SD16—81no—
471D8—81no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—21no—
475C2×C8—21no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4C2×D4×C1111yescharacteristic
501C4⋊C4C2×D4×C1111yescharacteristic
502C4⋊C4C2×D4×C1112yes—
503C4⋊C4C2×D4×C1112yes—
504C4⋊C4C2×D4×C1112yes—
505C4⋊C4C2×D4×C1112yes—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—21no—
510C22⋊C4—22no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C42—22no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—21no—
522C42C2×D4×C1111yescharacteristic
523C42C2×D4×C1111yescharacteristic
524C42C2×D4×C1111yescharacteristic
525C42C24×C1111yescharacteristic
526C11#1909211yescharacteristic, direct product factor, Sylow
527C23—21no—
528C23—41no—
529C23C11×#12011yescharacteristic
530Q8—41no—
531Q8—42no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—82no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—82no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—81no—
558C2×C4—82no—
559C2×C4C11×#12011yescharacteristic
560C2×C4C11×#12011yescharacteristic
561C2×C4C11×#12011yescharacteristic
562C2×C4C22×D4×C1111yescharacteristic
563C2×C4C22×D4×C1111yescharacteristic
564C2×C4C22×D4×C1111yescharacteristic
565C8—41no—
566C8—41no—
567C8—42no—
568C8—42no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22C2×C11×#12011yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—42no—
589C4—42no—
590C4—42no—
591C4—41no—
592C4—81no—
593C2—41no—
594C2—81no—
595C2—161no—
596C2C11×#302011yescharacteristic
597C2C11×#302011yescharacteristic
598C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3219C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3563C2semidirect
2. C11×#3235C2semidirect
3. C11×#3234C2semidirect
5. C11×#1663C2semidirect
6. C11×#1660C2semidirect
7. C11×#1658C2semidirect
8. C11×#1657C2semidirect
9. C11×#1537C2semidirect
10. C11×#1535C2semidirect
11. C11×#1534C2semidirect
148. #19092C11direct (N × H)
228. #3563C2×C11semidirect
229. #3235C2×C11semidirect
230. #3234C2×C11semidirect
232. #1663C2×C11semidirect
233. #1660C2×C11semidirect
234. #1658C2×C11semidirect
235. #1657C2×C11semidirect
236. #1537C2×C11semidirect
237. #1535C2×C11semidirect
238. #1534C2×C11semidirect
526. C11#19092direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35632
C11×#32352
C11×#32342
C11×#32192
C11×#16632
C11×#16602
C11×#16582
C11×#16572
C11×#15372
C11×#15352
C11×#15342
#1909211