Finite Group Databasebeta

← C11×#18435 #14595628

Subgroups — C11×#18435 #14595628

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3564C211yesmaximal, characteristic, complemented
2C11×#3215C211yesmaximal, characteristic, complemented
3C11×#3211C211yesmaximal, characteristic, complemented
4C11×#2662C211yesmaximal, characteristic, complemented
5C11×#1606C211yesmaximal, characteristic, complemented
6C11×#1605C211yesmaximal, characteristic, complemented
7C11×#1603C211yesmaximal, characteristic, complemented
8C11×#1602C211yesmaximal, characteristic, complemented
9C11×#1600C211yesmaximal, characteristic
10C11×#1599C211yesmaximal, characteristic, complemented
11C11×#1597C211yesmaximal, characteristic, complemented
12C11×#1596C211yesmaximal, characteristic, complemented
13C11×#1509C211yesmaximal, characteristic, complemented
14C11×#1503C211yesmaximal, 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×C11×#124C2211yescharacteristic
36C11×#497—21no—
37C11×#495—21no—
38C11×#489—21no—
39C11×#488—21no—
40C11×#464—21no—
41C11×#464—21no—
42C11×#464—21no—
43C11×#463—21no—
44C11×#451C2211yescharacteristic
45C11×#451C2211yescharacteristic
46C11×#451C2211yescharacteristic
47C11×#450C2211yescharacteristic
48C11×#450C2211yescharacteristic
49C11×#450C2211yescharacteristic
50C11×#448C2211yescharacteristic
51C11×#447C2211yescharacteristic
52C11×#432C2211yescharacteristic
53C11×#431C2211yescharacteristic
54C11×#396—21no—
55C11×#395C2211yescharacteristic
56C11×#394—21no—
57C11×#394C2211yescharacteristic
58C11×#393C2211yescharacteristic
59C11×#392C2211yescharacteristic
60C11×#390—21no—
61C11×#388—21no—
62C4×C11×C4⋊C4C2211yescharacteristic
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×Q8×C11C2311yescharacteristic
76C22×D4×C11—21no—
77C22×D4×C11C2311yescharacteristic
78C2×C11×Q16—21no—
79C2×C11×Q16—21no—
80C2×C11×Q16—21no—
81C2×C11×SD16—21no—
82C2×C11×SD16—21no—
83C2×C11×SD16—21no—
84C2×C11×SD16—21no—
85C2×C11×D8—21no—
86C11×C4⋊Q8—21no—
87C11×C4⋊Q8—21no—
88C11×C4⋊Q8—21no—
89C11×C4⋊Q8D411yescharacteristic, complemented
90C11×C4⋊Q8D411yescharacteristic, complemented
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×#126—21no—
101C11×#126—21no—
102C11×#126—21no—
103C11×#126—21no—
104C11×#125—21no—
105C11×#125—21no—
106C11×#125—21no—
107C11×#125—21no—
108C11×#125—21no—
109C11×#125—21no—
110C11×#125—21no—
111C11×#125—21no—
112C11×#125—21no—
113C11×#125D411yescharacteristic, complemented
114C11×#124—21no—
115C11×#124—21no—
116C11×#124—21no—
117C11×#124—21no—
118C11×#124—21no—
119C11×#124—21no—
120C11×#124—21no—
121C11×#124D411yescharacteristic, complemented
122C11×#123—21no—
123C11×#123—21no—
124C11×#123—21no—
125C11×#123—21no—
126C11×#123—21no—
127C11×#123—21no—
128C11×#123—21no—
129C11×#123—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⋊Q8—21no—
137C11×C22⋊Q8—21no—
138C11×C22⋊Q8—21no—
139C11×C22⋊Q8—21no—
140C11×C22⋊Q8—21no—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8—21no—
143C11×C22⋊Q8—21no—
144C11×C22⋊Q8C2311yescharacteristic
145C11×C22⋊Q8C2311yescharacteristic
146C11×C22⋊Q8C2311yescharacteristic
147C11×#121—21no—
148C11×#121C2311yescharacteristic
149C11×#120—21no—
150C4×Q8×C11—21no—
151C4×Q8×C11—21no—
152C4×Q8×C11—21no—
153C4×Q8×C11D411yescharacteristic, complemented
154C4×Q8×C11D411yescharacteristic, complemented
155C4×Q8×C11D411yescharacteristic, complemented
156C4×D4×C11—21no—
157C4×D4×C11—21no—
158C4×D4×C11—21no—
159C4×D4×C11—21no—
160C4×D4×C11—21no—
161C4×D4×C11D411yescharacteristic, complemented
162C11×#117—21no—
163C11×#117—21no—
164C11×#117—21no—
165C11×#117—21no—
166C11×#117—21no—
167C11×#117—21no—
168C2×C11×C4⋊C4—21no—
169C2×C11×C4⋊C4—21no—
170C2×C11×C4⋊C4—21no—
171C2×C11×C4⋊C4D411yescharacteristic
172C2×C11×C4⋊C4D411yescharacteristic
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4—21no—
175C2×C11×C22⋊C4—21no—
176C2×C11×C22⋊C4—21no—
177C2×C11×C22⋊C4—21no—
178C2×C11×C22⋊C4—21no—
179C2×C11×C22⋊C4—21no—
180C2×C11×C22⋊C4—21no—
181C2×C11×C22⋊C4D411yescharacteristic
182C2×C11×C22⋊C4D411yescharacteristic
183C2×C11×C22⋊C4C2311yescharacteristic
184C2×C42×C11—21no—
185C2×C42×C11C2311yescharacteristic
186C11×C4⋊C8—21no—
187C11×C4⋊C8—21no—
188C11×#103—21no—
189C11×#103—21no—
190C11×#103—21no—
191C11×#103—21no—
192C11×#102—21no—
193C11×#102—21no—
194C11×#102—21no—
195C11×#102—21no—
196C11×C22⋊C8C2311yescharacteristic
197C11×C22⋊C8C2311yescharacteristic
198C11×C22⋊C8C2311yescharacteristic
199C11×C22⋊C8C2311yescharacteristic
200C11×#97—21no—
201C4×C8×C11—21no—
202C11×#95—21no—
203C11×#95—21no—
204C11×#95C2311yescharacteristic
205C11×#95C2311yescharacteristic
206#18435C1111yesmaximal, 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×C11—21no—
213C2×Q8×C11—21no—
214C2×Q8×C11—81no—
215C2×Q8×C11C2×D411yescharacteristic
216C2×Q8×C11C2×D411yescharacteristic
217C2×Q8×C11C2×D411yescharacteristic
218C2×D4×C11—21no—
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—42no—
224C2×D4×C11—81no—
225C2×D4×C11—81no—
226C2×D4×C11—81no—
227C2×D4×C11C2×D411yescharacteristic
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C11×Q16—81no—
243C11×Q16—81no—
244C11×Q16—81no—
245C11×SD16—81no—
246C11×SD16—81no—
247C11×SD16—81no—
248C11×SD16—81no—
249C11×D8—81no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—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—21no—
283C11×C4⋊C4—42no—
284C11×C4⋊C4—81no—
285C11×C4⋊C4C2×D411yescharacteristic
286C11×C4⋊C4C2×D411yescharacteristic
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D411yescharacteristic
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—21no—
309C11×C22⋊C4—21no—
310C11×C22⋊C4—42no—
311C11×C22⋊C4—41no—
312C11×C22⋊C4—41no—
313C11×C22⋊C4—41no—
314C11×C22⋊C4—41no—
315C11×C22⋊C4—81no—
316C11×C22⋊C4—81no—
317C11×C22⋊C4—81no—
318C42×C11—21no—
319C42×C11—21no—
320C42×C11—21no—
321C42×C11—21no—
322C42×C11—21no—
323C42×C11—21no—
324C42×C11—21no—
325C42×C11—81no—
326C42×C11C2×D411yescharacteristic
327C42×C11C2×D411yescharacteristic
328C42×C11C2×D411yescharacteristic
329C42×C11C2×D411yescharacteristic
330#3564C2×C1111yescharacteristic, complemented
331#3215C2×C1111yescharacteristic, complemented
332#3211C2×C1111yescharacteristic, complemented
333#2662C2×C1111yescharacteristic, complemented
334#1606C2×C1111yescharacteristic, complemented
335#1605C2×C1111yescharacteristic, complemented
336#1603C2×C1111yescharacteristic, complemented
337#1602C2×C1111yescharacteristic, complemented
338#1600C2×C1111yescharacteristic
339#1599C2×C1111yescharacteristic, complemented
340#1597C2×C1111yescharacteristic, complemented
341#1596C2×C1111yescharacteristic, complemented
342#1509C2×C1111yescharacteristic, complemented
343#1503C2×C1111yescharacteristic, complemented
344#1473C2×C1111yescharacteristic, complemented
345C23×C11—21no—
346C23×C11—21no—
347C23×C11—21no—
348C23×C11—21no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11C22×D411yescharacteristic
359Q8×C11—41no—
360Q8×C11—41no—
361Q8×C11—41no—
362Q8×C11—41no—
363Q8×C11—41no—
364Q8×C11—41no—
365Q8×C11—41no—
366Q8×C11—81no—
367Q8×C11—81no—
368Q8×C11—81no—
369D4×C11—41no—
370D4×C11—41no—
371D4×C11—41no—
372D4×C11—41no—
373D4×C11—41no—
374D4×C11—41no—
375D4×C11—41no—
376D4×C11—81no—
377D4×C11—81no—
378D4×C11—84no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—22no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—81no—
407C2×C4×C11—81no—
408C2×C4×C11—81no—
409C2×C4×C11—81no—
410C2×C4×C11—81no—
411C2×C4×C11#12011yescharacteristic
412C2×C4×C11#12011yescharacteristic
413C2×C4×C11#12011yescharacteristic
414C2×C4×C11#12011yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C8×C11—41no—
418C8×C11—41no—
419C8×C11—41no—
420C8×C11—41no—
421#563—21no—
422#563—21no—
423#556—21no—
424#554—21no—
425#552—21no—
426#552—21no—
427#551—21no—
428#551—21no—
429#544C22×C1111yescharacteristic
430#543C22×C1111yescharacteristic
431#542—21no—
432#541—21no—
433#541—21no—
434#539—21no—
435#539C22×C1111yescharacteristic
436#538C22×C1111yescharacteristic
437#533C22×C1111yescharacteristic
438#529C22×C1111yescharacteristic
439C2×#126C22×C1111yescharacteristic
440C2×#124C22×C1111yescharacteristic
441#497—21no—
442#495—21no—
443#489—21no—
444#488—21no—
445#464—21no—
446#464—21no—
447#464—21no—
448#463—21no—
449#451C22×C1111yescharacteristic
450#451C22×C1111yescharacteristic
451#451C22×C1111yescharacteristic
452#450C22×C1111yescharacteristic
453#450C22×C1111yescharacteristic
454#450C22×C1111yescharacteristic
455#448C22×C1111yescharacteristic
456#447C22×C1111yescharacteristic
457#432C22×C1111yescharacteristic
458#431C22×C1111yescharacteristic
459#396—21no—
460#395C22×C1111yescharacteristic
461#394—21no—
462#394C22×C1111yescharacteristic
463#393C22×C1111yescharacteristic
464#392C22×C1111yescharacteristic
465#390—21no—
466#388—21no—
467C4×C4⋊C4C22×C1111yescharacteristic
468#328C22×C1111yescharacteristic
469#328C22×C1111yescharacteristic
470#328C22×C1111yescharacteristic
471#328C22×C1111yescharacteristic
472#328C22×C1111yescharacteristic
473#328C22×C1111yescharacteristic
474#327C22×C1111yescharacteristic
475#327C22×C1111yescharacteristic
476#324C22×C1111yescharacteristic
477#324C22×C1111yescharacteristic
478#323C22×C1111yescharacteristic
479#323C22×C1111yescharacteristic
480C22×C11—21no—
481C22×C11—21no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—81no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11—81no—
494C22×C11—81no—
495C22×C11—81no—
496C22×C11—81no—
497C22×C11C2×#12011yescharacteristic
498C22×C11#57711yescharacteristic
499C22×C11#57811yescharacteristic
500C4×C11—21no—
501C4×C11—21no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—42no—
507C4×C11—41no—
508C4×C11—41no—
509C4×C11—41no—
510C4×C11—41no—
511C4×C11—41no—
512C4×C11—41no—
513C4×C11—41no—
514C4×C11—41no—
515C4×C11—41no—
516C4×C11—41no—
517C4×C11—81no—
518C4×C11—81no—
519C22×Q8C23×C1111yescharacteristic
520C22×D4—21no—
521C22×D4C23×C1111yescharacteristic
522C2×Q16—21no—
523C2×Q16—21no—
524C2×Q16—21no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×D8—21no—
530C4⋊Q8—21no—
531C4⋊Q8—21no—
532C4⋊Q8—21no—
533C4⋊Q8D4×C1111yescharacteristic, complemented
534C4⋊Q8D4×C1111yescharacteristic, complemented
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125—21no—
551#125—21no—
552#125—21no—
553#125—21no—
554#125—21no—
555#125—21no—
556#125—21no—
557#125D4×C1111yescharacteristic, complemented
558#124—21no—
559#124—21no—
560#124—21no—
561#124—21no—
562#124—21no—
563#124—21no—
564#124—21no—
565#124D4×C1111yescharacteristic, complemented
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8—21no—
585C22⋊Q8—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8C23×C1111yescharacteristic
589C22⋊Q8C23×C1111yescharacteristic
590C22⋊Q8C23×C1111yescharacteristic
591#121—21no—
592#121C23×C1111yescharacteristic
593#120—21no—
594C4×Q8—21no—
595C4×Q8—21no—
596C4×Q8—21no—
597C4×Q8D4×C1111yescharacteristic, complemented
598C4×Q8D4×C1111yescharacteristic, complemented
599C4×Q8D4×C1111yescharacteristic, complemented
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4D4×C1111yescharacteristic, complemented
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610#117—21no—
611#117—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4D4×C1111yescharacteristic
616C2×C4⋊C4D4×C1111yescharacteristic
617C2×C4⋊C4C23×C1111yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4D4×C1111yescharacteristic
626C2×C22⋊C4D4×C1111yescharacteristic
627C2×C22⋊C4C23×C1111yescharacteristic
628C2×C42—21no—
629C2×C42C23×C1111yescharacteristic
630C4⋊C8—21no—
631C4⋊C8—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640C22⋊C8C23×C1111yescharacteristic
641C22⋊C8C23×C1111yescharacteristic
642C22⋊C8C23×C1111yescharacteristic
643C22⋊C8C23×C1111yescharacteristic
644#97—21no—
645C4×C8—21no—
646#95—21no—
647#95—21no—
648#95C23×C1111yescharacteristic
649#95C23×C1111yescharacteristic
650C2×C11—21no—
651C2×C11—21no—
652C2×C11—81no—
653C2×C11—81no—
654C2×C11—161no—
655C2×C11#301311yescharacteristic
656C2×C11#301811yescharacteristic
657C2×C11#302711yescharacteristic
658C24—21no—
659C24C2×D4×C1111yescharacteristic
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—81no—
666C2×Q8C2×D4×C1111yescharacteristic
667C2×Q8C2×D4×C1111yescharacteristic
668C2×Q8C2×D4×C1111yescharacteristic
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—42no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C2×D4×C1111yescharacteristic
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4C2×D4×C1111yescharacteristic
688C22×C4C2×D4×C1111yescharacteristic
689C22×C4C2×D4×C1111yescharacteristic
690C22×C4C2×D4×C1111yescharacteristic
691C22×C4C2×D4×C1111yescharacteristic
692C22×C4C24×C1111yescharacteristic
693Q16—81no—
694Q16—81no—
695Q16—81no—
696SD16—81no—
697SD16—81no—
698SD16—81no—
699SD16—81no—
700D8—81no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—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—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—81no—
736C4⋊C4C2×D4×C1111yescharacteristic
737C4⋊C4C2×D4×C1111yescharacteristic
738C4⋊C4C2×D4×C1111yescharacteristic
739C4⋊C4C2×D4×C1111yescharacteristic
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—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—42no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C22⋊C4—41no—
765C22⋊C4—41no—
766C22⋊C4—81no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C42—21no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—21no—
776C42—81no—
777C42C2×D4×C1111yescharacteristic
778C42C2×D4×C1111yescharacteristic
779C42C2×D4×C1111yescharacteristic
780C42C2×D4×C1111yescharacteristic
781C11#1843511yescharacteristic, direct product factor, Sylow
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23C22×D4×C1111yescharacteristic
796Q8—41no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—81no—
804Q8—81no—
805Q8—81no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—81no—
814D4—81no—
815D4—84no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4C11×#12011yescharacteristic
849C2×C4C11×#12011yescharacteristic
850C2×C4C11×#12011yescharacteristic
851C2×C4C11×#12011yescharacteristic
852C2×C4C22×D4×C1111yescharacteristic
853C2×C4C22×D4×C1111yescharacteristic
854C8—41no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—21no—
859C22—21no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22C2×C11×#12011yescharacteristic
876C22C11×#57711yescharacteristic
877C22C11×#57811yescharacteristic
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—42no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—81no—
897C2—21no—
898C2—21no—
899C2—81no—
900C2—81no—
901C2—161no—
902C2C11×#301311yescharacteristic
903C2C11×#301811yescharacteristic
904C2C11×#302711yescharacteristic
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×#3215C2semidirect
3. C11×#3211C2semidirect
4. C11×#2662C2semidirect
5. C11×#1606C2semidirect
6. C11×#1605C2semidirect
7. C11×#1603C2semidirect
8. C11×#1602C2semidirect
10. C11×#1599C2semidirect
11. C11×#1597C2semidirect
12. C11×#1596C2semidirect
13. C11×#1509C2semidirect
14. C11×#1503C2semidirect
15. C11×#1473C2semidirect
89. C11×C4⋊Q8D4semidirect
90. C11×C4⋊Q8D4semidirect
113. C11×#125D4semidirect
121. C11×#124D4semidirect
153. C4×Q8×C11D4semidirect
154. C4×Q8×C11D4semidirect
155. C4×Q8×C11D4semidirect
161. C4×D4×C11D4semidirect
206. #18435C11direct (N × H)
330. #3564C2×C11semidirect
331. #3215C2×C11semidirect
332. #3211C2×C11semidirect
333. #2662C2×C11semidirect
334. #1606C2×C11semidirect
335. #1605C2×C11semidirect
336. #1603C2×C11semidirect
337. #1602C2×C11semidirect
339. #1599C2×C11semidirect
340. #1597C2×C11semidirect
341. #1596C2×C11semidirect
342. #1509C2×C11semidirect
343. #1503C2×C11semidirect
344. #1473C2×C11semidirect
533. C4⋊Q8D4×C11semidirect
534. C4⋊Q8D4×C11semidirect
557. #125D4×C11semidirect
565. #124D4×C11semidirect
597. C4×Q8D4×C11semidirect
598. C4×Q8D4×C11semidirect
599. C4×Q8D4×C11semidirect
605. C4×D4D4×C11semidirect
781. C11#18435direct (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×#32152
C11×#32112
C11×#26622
C11×#16062
C11×#16052
C11×#16032
C11×#16022
C11×#16002
C11×#15992
C11×#15972
C11×#15962
C11×#15092
C11×#15032
C11×#14732
#1843511