Finite Group Databasebeta

← C11×#18282 #14595475

Subgroups — C11×#18282 #14595475

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3564C211yesmaximal, characteristic, complemented
2C11×#3114C211yesmaximal, characteristic, complemented
3C11×#3101C211yesmaximal, characteristic, complemented
4C11×#2603C211yesmaximal, characteristic, complemented
5C11×#1612C211yesmaximal, characteristic, complemented
6C11×#1611C211yesmaximal, characteristic, complemented
7C11×#1609C211yesmaximal, characteristic, complemented
8C11×#1608C211yesmaximal, characteristic, complemented
9C11×#1600C211yesmaximal, characteristic
10C11×#1599C211yesmaximal, characteristic, complemented
11C11×#1597C211yesmaximal, characteristic, complemented
12C11×#1596C211yesmaximal, characteristic, complemented
13C11×#1506C211yesmaximal, characteristic, complemented
14C11×#1500C211yesmaximal, characteristic, complemented
15C11×#1473C211yesmaximal, characteristic, complemented
16C11×#563—21no—
17C11×#563—21no—
18C11×#556—21no—
19C11×#554—21no—
20C11×#552—21no—
21C11×#552—21no—
22C11×#551—21no—
23C11×#551—21no—
24C11×#544C2211yescharacteristic
25C11×#543C2211yescharacteristic
26C11×#542—21no—
27C11×#541—21no—
28C11×#541—21no—
29C11×#539—21no—
30C11×#539C2211yescharacteristic
31C11×#538C2211yescharacteristic
32C11×#533C2211yescharacteristic
33C11×#529C2211yescharacteristic
34C2×C11×#126C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C11×#483C2211yescharacteristic
37C11×#483C2211yescharacteristic
38C11×#483C2211yescharacteristic
39C11×#480C2211yescharacteristic
40C11×#478—21no—
41C11×#476—21no—
42C11×#463—21no—
43C11×#461—21no—
44C11×#450C2211yescharacteristic
45C11×#450C2211yescharacteristic
46C11×#450C2211yescharacteristic
47C11×#447C2211yescharacteristic
48C11×#442—21no—
49C11×#440—21no—
50C4×C11×SD16—21no—
51C4×C11×SD16—21no—
52C11×#432C2211yescharacteristic
53C11×#431C2211yescharacteristic
54C11×#398C2211yescharacteristic
55C11×#397C2211yescharacteristic
56C11×#394C2211yescharacteristic
57C11×#392C2211yescharacteristic
58C11×#390—21no—
59C11×#388—21no—
60C11×#386—21no—
61C11×#385—21no—
62C11×#376C2211yescharacteristic
63C11×#328C2211yescharacteristic
64C11×#328C2211yescharacteristic
65C11×#328C2211yescharacteristic
66C11×#328C2211yescharacteristic
67C11×#328C2211yescharacteristic
68C11×#328C2211yescharacteristic
69C11×#327C2211yescharacteristic
70C11×#327C2211yescharacteristic
71C11×#324C2211yescharacteristic
72C11×#324C2211yescharacteristic
73C11×#323C2211yescharacteristic
74C11×#323C2211yescharacteristic
75C22×D4×C11—21no—
76C22×D4×C11C2311yescharacteristic
77C23×C4×C11—21no—
78C2×C11×SD16—21no—
79C2×C11×SD16—21no—
80C2×C11×SD16—21no—
81C2×C11×D8—21no—
82C11×C4⋊Q8—21no—
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8D411yescharacteristic, complemented
86C11×C4⋊Q8D411yescharacteristic, complemented
87C11×#126—21no—
88C11×#126—21no—
89C11×#126—21no—
90C11×#126—21no—
91C11×#126—21no—
92C11×#126—21no—
93C11×#126—21no—
94C11×#126—21no—
95C11×#126—21no—
96C11×#126—21no—
97C11×#126—21no—
98C11×#126—21no—
99C11×#126—21no—
100C11×#125—21no—
101C11×#125—21no—
102C11×#125—21no—
103C11×#125—21no—
104C11×#125—21no—
105C11×#125—21no—
106C11×#125—21no—
107C11×#125—21no—
108C11×#125—21no—
109C11×#125D411yescharacteristic, complemented
110C11×#124—21no—
111C11×#124—21no—
112C11×#124—21no—
113C11×#124D411yescharacteristic, complemented
114C11×#123—21no—
115C11×#123—21no—
116C11×#123—21no—
117C11×#123—21no—
118C11×#123—21no—
119C11×#123—21no—
120C11×#123—21no—
121C11×#123—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8—21no—
128C11×C22⋊Q8—21no—
129C11×C22⋊Q8—21no—
130C11×C22⋊Q8—21no—
131C11×C22⋊Q8—21no—
132C11×C22⋊Q8—21no—
133C11×C22⋊Q8—21no—
134C11×C22⋊Q8—21no—
135C11×C22⋊Q8—21no—
136C11×C22⋊Q8C2311yescharacteristic
137C11×C22⋊Q8C2311yescharacteristic
138C11×C22⋊Q8C2311yescharacteristic
139C11×#121—21no—
140C11×#121C2311yescharacteristic
141C11×#120—21no—
142C4×Q8×C11—21no—
143C4×Q8×C11—21no—
144C4×Q8×C11—21no—
145C4×Q8×C11D411yescharacteristic, complemented
146C4×Q8×C11D411yescharacteristic, complemented
147C4×Q8×C11D411yescharacteristic, complemented
148C4×D4×C11—21no—
149C4×D4×C11—21no—
150C4×D4×C11—21no—
151C4×D4×C11—21no—
152C4×D4×C11—21no—
153C4×D4×C11—21no—
154C4×D4×C11—21no—
155C4×D4×C11—21no—
156C4×D4×C11—21no—
157C4×D4×C11D411yescharacteristic, complemented
158C11×#117—21no—
159C11×#117—21no—
160C11×#117—21no—
161C11×#117—21no—
162C11×#117—21no—
163C11×#117—21no—
164C2×C11×C4⋊C4—21no—
165C2×C11×C4⋊C4—21no—
166C2×C11×C4⋊C4D411yescharacteristic
167C2×C11×C4⋊C4D411yescharacteristic
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4—21no—
171C2×C11×C22⋊C4—21no—
172C2×C11×C22⋊C4—21no—
173C2×C11×C22⋊C4—21no—
174C2×C11×C22⋊C4—21no—
175C2×C11×C22⋊C4—21no—
176C2×C11×C22⋊C4D411yescharacteristic
177C2×C11×C22⋊C4D411yescharacteristic
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C42×C11—21no—
180C2×C42×C11C2311yescharacteristic
181C11×#107—21no—
182C11×#106—21no—
183C11×#106—21no—
184C11×#106—21no—
185C11×C4⋊C8—21no—
186C11×C4⋊C8—21no—
187C11×#103—21no—
188C11×#103—21no—
189C11×#103—21no—
190C11×#102—21no—
191C11×#102—21no—
192C11×#102—21no—
193C11×#102—21no—
194C11×#102—21no—
195C11×C22⋊C8C2311yescharacteristic
196C11×C22⋊C8C2311yescharacteristic
197C11×C22⋊C8C2311yescharacteristic
198C11×C22⋊C8C2311yescharacteristic
199C11×#97—21no—
200C4×C8×C11—21no—
201C11×#95—21no—
202C11×#95—21no—
203C11×#95—21no—
204C11×#95C2311yescharacteristic
205C11×#95C2311yescharacteristic
206#18282C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—21no—
208C24×C11C2×D411yescharacteristic
209C2×Q8×C11—21no—
210C2×Q8×C11—21no—
211C2×Q8×C11—21no—
212C2×Q8×C11C2×D411yescharacteristic
213C2×Q8×C11C2×D411yescharacteristic
214C2×Q8×C11C2×D411yescharacteristic
215C2×D4×C11—21no—
216C2×D4×C11—21no—
217C2×D4×C11—21no—
218C2×D4×C11—21no—
219C2×D4×C11—21no—
220C2×D4×C11—42no—
221C2×D4×C11—42no—
222C2×D4×C11—42no—
223C2×D4×C11—81no—
224C2×D4×C11C2×D411yescharacteristic
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—41no—
234C22×C4×C11—41no—
235C22×C4×C11—81no—
236C22×C4×C11—81no—
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C11×SD16—42no—
244C11×SD16—42no—
245C11×SD16—42no—
246C11×D8—42no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—81no—
283C11×C4⋊C4C2×D411yescharacteristic
284C11×C4⋊C4C2×D411yescharacteristic
285C11×C4⋊C4C2×D411yescharacteristic
286C11×C4⋊C4C2×D411yescharacteristic
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—21no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—21no—
295C11×C22⋊C4—21no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—21no—
301C11×C22⋊C4—21no—
302C11×C22⋊C4—21no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—21no—
307C11×C22⋊C4—21no—
308C11×C22⋊C4—42no—
309C11×C22⋊C4—42no—
310C11×C22⋊C4—41no—
311C11×C22⋊C4—41no—
312C11×C22⋊C4—81no—
313C11×C22⋊C4—81no—
314C42×C11—21no—
315C42×C11—21no—
316C42×C11—21no—
317C42×C11—21no—
318C42×C11—21no—
319C42×C11—21no—
320C42×C11—21no—
321C42×C11—42no—
322C42×C11C2×D411yescharacteristic
323C42×C11C2×D411yescharacteristic
324C42×C11C2×D411yescharacteristic
325C42×C11C2×D411yescharacteristic
326#3564C2×C1111yescharacteristic, complemented
327#3114C2×C1111yescharacteristic, complemented
328#3101C2×C1111yescharacteristic, complemented
329#2603C2×C1111yescharacteristic, complemented
330#1612C2×C1111yescharacteristic, complemented
331#1611C2×C1111yescharacteristic, complemented
332#1609C2×C1111yescharacteristic, complemented
333#1608C2×C1111yescharacteristic, complemented
334#1600C2×C1111yescharacteristic
335#1599C2×C1111yescharacteristic, complemented
336#1597C2×C1111yescharacteristic, complemented
337#1596C2×C1111yescharacteristic, complemented
338#1506C2×C1111yescharacteristic, complemented
339#1500C2×C1111yescharacteristic, complemented
340#1473C2×C1111yescharacteristic, complemented
341C23×C11—22no—
342C23×C11—21no—
343C23×C11—21no—
344C23×C11—21no—
345C23×C11—21no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11C22×D411yescharacteristic
355Q8×C11—41no—
356Q8×C11—41no—
357Q8×C11—41no—
358Q8×C11—81no—
359Q8×C11—81no—
360Q8×C11—81no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—41no—
364D4×C11—41no—
365D4×C11—41no—
366D4×C11—41no—
367D4×C11—41no—
368D4×C11—81no—
369D4×C11—81no—
370D4×C11—84no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—22no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—81no—
399C2×C4×C11—82no—
400C2×C4×C11—82no—
401C2×C4×C11—81no—
402C2×C4×C11—81no—
403C2×C4×C11—81no—
404C2×C4×C11—81no—
405C2×C4×C11#12011yescharacteristic
406C2×C4×C11#12011yescharacteristic
407C2×C4×C11#12011yescharacteristic
408C2×C4×C11#12011yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C8×C11—41no—
412C8×C11—41no—
413C8×C11—41no—
414C8×C11—41no—
415#563—21no—
416#563—21no—
417#556—21no—
418#554—21no—
419#552—21no—
420#552—21no—
421#551—21no—
422#551—21no—
423#544C22×C1111yescharacteristic
424#543C22×C1111yescharacteristic
425#542—21no—
426#541—21no—
427#541—21no—
428#539—21no—
429#539C22×C1111yescharacteristic
430#538C22×C1111yescharacteristic
431#533C22×C1111yescharacteristic
432#529C22×C1111yescharacteristic
433C2×#126C22×C1111yescharacteristic
434C2×C4×D4C22×C1111yescharacteristic
435#483C22×C1111yescharacteristic
436#483C22×C1111yescharacteristic
437#483C22×C1111yescharacteristic
438#480C22×C1111yescharacteristic
439#478—21no—
440#476—21no—
441#463—21no—
442#461—21no—
443#450C22×C1111yescharacteristic
444#450C22×C1111yescharacteristic
445#450C22×C1111yescharacteristic
446#447C22×C1111yescharacteristic
447#442—21no—
448#440—21no—
449C4×SD16—21no—
450C4×SD16—21no—
451#432C22×C1111yescharacteristic
452#431C22×C1111yescharacteristic
453#398C22×C1111yescharacteristic
454#397C22×C1111yescharacteristic
455#394C22×C1111yescharacteristic
456#392C22×C1111yescharacteristic
457#390—21no—
458#388—21no—
459#386—21no—
460#385—21no—
461#376C22×C1111yescharacteristic
462#328C22×C1111yescharacteristic
463#328C22×C1111yescharacteristic
464#328C22×C1111yescharacteristic
465#328C22×C1111yescharacteristic
466#328C22×C1111yescharacteristic
467#328C22×C1111yescharacteristic
468#327C22×C1111yescharacteristic
469#327C22×C1111yescharacteristic
470#324C22×C1111yescharacteristic
471#324C22×C1111yescharacteristic
472#323C22×C1111yescharacteristic
473#323C22×C1111yescharacteristic
474C22×C11—21no—
475C22×C11—21no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—42no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11—81no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11C2×#12011yescharacteristic
492C22×C11#57711yescharacteristic
493C22×C11#57711yescharacteristic
494C4×C11—21no—
495C4×C11—21no—
496C4×C11—21no—
497C4×C11—21no—
498C4×C11—21no—
499C4×C11—21no—
500C4×C11—42no—
501C4×C11—41no—
502C4×C11—41no—
503C4×C11—41no—
504C4×C11—41no—
505C4×C11—41no—
506C4×C11—41no—
507C4×C11—41no—
508C4×C11—41no—
509C4×C11—41no—
510C4×C11—41no—
511C4×C11—81no—
512C4×C11—81no—
513C22×D4—21no—
514C22×D4C23×C1111yescharacteristic
515C23×C4—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×D8—21no—
520C4⋊Q8—21no—
521C4⋊Q8—21no—
522C4⋊Q8—21no—
523C4⋊Q8D4×C1111yescharacteristic, complemented
524C4⋊Q8D4×C1111yescharacteristic, complemented
525#126—21no—
526#126—21no—
527#126—21no—
528#126—21no—
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#125—21no—
539#125—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125D4×C1111yescharacteristic, complemented
548#124—21no—
549#124—21no—
550#124—21no—
551#124D4×C1111yescharacteristic, complemented
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8C23×C1111yescharacteristic
575C22⋊Q8C23×C1111yescharacteristic
576C22⋊Q8C23×C1111yescharacteristic
577#121—21no—
578#121C23×C1111yescharacteristic
579#120—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8D4×C1111yescharacteristic, complemented
584C4×Q8D4×C1111yescharacteristic, complemented
585C4×Q8D4×C1111yescharacteristic, complemented
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4D4×C1111yescharacteristic, complemented
596#117—21no—
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4D4×C1111yescharacteristic
605C2×C4⋊C4D4×C1111yescharacteristic
606C2×C4⋊C4C23×C1111yescharacteristic
607C2×C4⋊C4C23×C1111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4D4×C1111yescharacteristic
615C2×C22⋊C4D4×C1111yescharacteristic
616C2×C22⋊C4C23×C1111yescharacteristic
617C2×C42—21no—
618C2×C42C23×C1111yescharacteristic
619#107—21no—
620#106—21no—
621#106—21no—
622#106—21no—
623C4⋊C8—21no—
624C4⋊C8—21no—
625#103—21no—
626#103—21no—
627#103—21no—
628#102—21no—
629#102—21no—
630#102—21no—
631#102—21no—
632#102—21no—
633C22⋊C8C23×C1111yescharacteristic
634C22⋊C8C23×C1111yescharacteristic
635C22⋊C8C23×C1111yescharacteristic
636C22⋊C8C23×C1111yescharacteristic
637#97—21no—
638C4×C8—21no—
639#95—21no—
640#95—21no—
641#95—21no—
642#95C23×C1111yescharacteristic
643#95C23×C1111yescharacteristic
644C2×C11—21no—
645C2×C11—21no—
646C2×C11—81no—
647C2×C11—81no—
648C2×C11—82no—
649C2×C11#301011yescharacteristic
650C2×C11#301811yescharacteristic
651C2×C11#302511yescharacteristic
652C24—21no—
653C24C2×D4×C1111yescharacteristic
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C1111yescharacteristic
658C2×Q8C2×D4×C1111yescharacteristic
659C2×Q8C2×D4×C1111yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—81no—
669C2×D4C2×D4×C1111yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—81no—
681C22×C4—81no—
682C22×C4C2×D4×C1111yescharacteristic
683C22×C4C2×D4×C1111yescharacteristic
684C22×C4C2×D4×C1111yescharacteristic
685C22×C4C2×D4×C1111yescharacteristic
686C22×C4C2×D4×C1111yescharacteristic
687C22×C4C24×C1111yescharacteristic
688SD16—42no—
689SD16—42no—
690SD16—42no—
691D8—42no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—81no—
728C4⋊C4C2×D4×C1111yescharacteristic
729C4⋊C4C2×D4×C1111yescharacteristic
730C4⋊C4C2×D4×C1111yescharacteristic
731C4⋊C4C2×D4×C1111yescharacteristic
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—42no—
754C22⋊C4—42no—
755C22⋊C4—41no—
756C22⋊C4—41no—
757C22⋊C4—81no—
758C22⋊C4—81no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—42no—
767C42C2×D4×C1111yescharacteristic
768C42C2×D4×C1111yescharacteristic
769C42C2×D4×C1111yescharacteristic
770C42C2×D4×C1111yescharacteristic
771C11#1828211yescharacteristic, direct product factor, Sylow
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23C22×D4×C1111yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—81no—
790Q8—81no—
791Q8—81no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—81no—
800D4—81no—
801D4—84no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—81no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4C11×#12011yescharacteristic
837C2×C4C11×#12011yescharacteristic
838C2×C4C11×#12011yescharacteristic
839C2×C4C11×#12011yescharacteristic
840C2×C4C22×D4×C1111yescharacteristic
841C2×C4C22×D4×C1111yescharacteristic
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—42no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22C2×C11×#12011yescharacteristic
864C22C11×#57711yescharacteristic
865C22C11×#57711yescharacteristic
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C2—21no—
886C2—21no—
887C2—82no—
888C2—81no—
889C2—81no—
890C2C11×#301011yescharacteristic
891C2C11×#301811yescharacteristic
892C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#1600C2
LCSG ▷ C22×C4 ▷ 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×#3564C2semidirect
2. C11×#3114C2semidirect
3. C11×#3101C2semidirect
4. C11×#2603C2semidirect
5. C11×#1612C2semidirect
6. C11×#1611C2semidirect
7. C11×#1609C2semidirect
8. C11×#1608C2semidirect
10. C11×#1599C2semidirect
11. C11×#1597C2semidirect
12. C11×#1596C2semidirect
13. C11×#1506C2semidirect
14. C11×#1500C2semidirect
15. C11×#1473C2semidirect
85. C11×C4⋊Q8D4semidirect
86. C11×C4⋊Q8D4semidirect
109. C11×#125D4semidirect
113. C11×#124D4semidirect
145. C4×Q8×C11D4semidirect
146. C4×Q8×C11D4semidirect
147. C4×Q8×C11D4semidirect
157. C4×D4×C11D4semidirect
206. #18282C11direct (N × H)
326. #3564C2×C11semidirect
327. #3114C2×C11semidirect
328. #3101C2×C11semidirect
329. #2603C2×C11semidirect
330. #1612C2×C11semidirect
331. #1611C2×C11semidirect
332. #1609C2×C11semidirect
333. #1608C2×C11semidirect
335. #1599C2×C11semidirect
336. #1597C2×C11semidirect
337. #1596C2×C11semidirect
338. #1506C2×C11semidirect
339. #1500C2×C11semidirect
340. #1473C2×C11semidirect
523. C4⋊Q8D4×C11semidirect
524. C4⋊Q8D4×C11semidirect
547. #125D4×C11semidirect
551. #124D4×C11semidirect
583. C4×Q8D4×C11semidirect
584. C4×Q8D4×C11semidirect
585. C4×Q8D4×C11semidirect
595. C4×D4D4×C11semidirect
771. C11#18282direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35642
C11×#31142
C11×#31012
C11×#26032
C11×#16122
C11×#16112
C11×#16092
C11×#16082
C11×#16002
C11×#15992
C11×#15972
C11×#15962
C11×#15062
C11×#15002
C11×#14732
#1828211