Finite Group Databasebeta

← C11×#19010 #14596203

Subgroups — C11×#19010 #14596203

Order 2816.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3529C211yesmaximal, characteristic, complemented
2C11×#3219C211yesmaximal, characteristic, complemented
3C11×#3214C211yesmaximal, characteristic, complemented
4C11×#3180C211yesmaximal, characteristic, complemented
5C11×#1664C211yesmaximal, characteristic, complemented
6C11×#1662C211yesmaximal, characteristic, complemented
7C11×#1661C211yesmaximal, characteristic, complemented
8C11×#1659C211yesmaximal, characteristic, complemented
9C11×#1657C211yesmaximal, characteristic, complemented
10C11×#1656C211yesmaximal, characteristic, complemented
11C11×#1656C211yesmaximal, characteristic, complemented
12C11×#1655C211yesmaximal, characteristic, complemented
13C11×#1535C211yesmaximal, characteristic, complemented
14C11×#1532C211yesmaximal, characteristic, complemented
15C11×#1530C211yesmaximal, characteristic, complemented
16C11×#563—21no—
17C11×#563C2211yescharacteristic
18C11×#562—21no—
19C11×#562—21no—
20C11×#562C2211yescharacteristic
21C11×#562C2211yescharacteristic
22C11×H(3,𝔽4)C2211yescharacteristic
23C11×#560—21no—
24C11×#560—21no—
25C11×#560—21no—
26C11×#532—21no—
27C11×#532C2211yescharacteristic
28C11×#532C2211yescharacteristic, complemented
29C11×#529—21no—
30C11×#529—21no—
31C11×#529C2211yescharacteristic
32C11×#529C2211yescharacteristic
33C11×#525—21no—
34C11×#525—21no—
35C11×#525—21no—
36C11×#501C2211yescharacteristic, complemented
37C11×#497C2211yescharacteristic
38C11×#496C2211yescharacteristic
39C11×#496C2211yescharacteristic
40C11×#496C2211yescharacteristic
41C11×#496C2211yescharacteristic, complemented
42C11×#491C2211yescharacteristic, complemented
43C11×#490C2211yescharacteristic, complemented
44C11×#490C2211yescharacteristic, complemented
45C11×#489C2211yescharacteristic
46C11×#489C2211yescharacteristic
47C11×#489C2211yescharacteristic, complemented
48C11×#466—21no—
49C11×#465—21no—
50C11×#464—21no—
51C11×#463—21no—
52C11×#461—21no—
53C11×#459—21no—
54C11×#452—21no—
55C11×#449—21no—
56C11×#449—21no—
57C11×#449—21no—
58C11×#442—21no—
59C11×#440—21no—
60C11×#432C2211yescharacteristic, complemented
61C11×#432C2211yescharacteristic, complemented
62C2×C11×#97C2211yescharacteristic, complemented
63C11×#330C2211yescharacteristic, complemented
64C11×#330C2211yescharacteristic, complemented
65C11×#330C2211yescharacteristic, complemented
66C11×#330C2211yescharacteristic, complemented
67C11×#329C2211yescharacteristic
68C11×#329C2211yescharacteristic
69C11×#329C2211yescharacteristic
70C11×#329C2211yescharacteristic
71C11×#329C2211yescharacteristic
72C11×#329C2211yescharacteristic
73C11×#329C2211yescharacteristic, complemented
74C11×#329C2211yescharacteristic, complemented
75C2×C11×#41—21no—
76C2×C11×#41—21no—
77C2×C11×#41D411yescharacteristic
78C2×C11×#41D411yescharacteristic
79C23×C4×C11—21no—
80C2×C11×Q16—21no—
81C2×C11×SD16—21no—
82C2×C11×SD16—21no—
83C2×C11×SD16—21no—
84C2×C11×SD16—21no—
85C2×C11×SD16—21no—
86C2×C11×D8—21no—
87C2×C11×D8—21no—
88C2×C11×D8—21no—
89C2×C11×D8—21no—
90C22×C8×C11—21no—
91C11×C4⋊Q8—21no—
92C11×C4⋊Q8D411yescharacteristic
93C11×C4⋊Q8C2311yescharacteristic
94C11×#127—21no—
95C11×#127D411yescharacteristic
96C11×#127C2311yescharacteristic
97C11×#126—21no—
98C11×#126—21no—
99C11×#126—21no—
100C11×#126—21no—
101C11×#126—21no—
102C11×#126—21no—
103C11×#125—21no—
104C11×#125—21no—
105C11×#125C2311yescharacteristic
106C11×#125C2311yescharacteristic
107C11×#124—21no—
108C11×#124—21no—
109C11×#124—21no—
110C11×#124—21no—
111C11×#124—21no—
112C11×#124C2311yescharacteristic
113C11×#124C2311yescharacteristic
114C11×#124C2311yescharacteristic
115C11×#124C2311yescharacteristic
116C11×#123—21no—
117C11×#123—21no—
118C11×#123—21no—
119C11×#123—21no—
120C11×#123—21no—
121C11×#123—21no—
122C11×#123—21no—
123C11×#123—21no—
124C11×#123—21no—
125C11×#123—21no—
126C11×#123—21no—
127C11×#123—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⋊Q8D411yescharacteristic
137C11×C22⋊Q8D411yescharacteristic
138C11×#121—21no—
139C11×#121—21no—
140C11×#121—21no—
141C11×#121—21no—
142C11×#121—21no—
143C11×#121—21no—
144C11×#121—21no—
145C11×#121—21no—
146C11×#121—21no—
147C11×#121—21no—
148C11×#121—21no—
149C11×#121—21no—
150C11×#121—21no—
151C11×#121—21no—
152C11×#121—21no—
153C11×#121—21no—
154C11×#121D411yescharacteristic
155C11×#121D411yescharacteristic
156C11×#120—21no—
157C11×#120—21no—
158C11×#120—21no—
159C11×#120—21no—
160C11×#120—21no—
161C11×#120—21no—
162C4×Q8×C11D411yescharacteristic
163C4×Q8×C11D411yescharacteristic
164C4×D4×C11—21no—
165C4×D4×C11—21no—
166C4×D4×C11—21no—
167C4×D4×C11—21no—
168C4×D4×C11—21no—
169C4×D4×C11—21no—
170C4×D4×C11—21no—
171C4×D4×C11—21no—
172C4×D4×C11—21no—
173C4×D4×C11—21no—
174C4×D4×C11D411yescharacteristic
175C4×D4×C11D411yescharacteristic
176C11×#117—21no—
177C11×#117—21no—
178C11×#117—21no—
179C2×C42×C11—21no—
180C2×C42×C11C2311yescharacteristic
181C11×#107—21no—
182C11×#106—21no—
183C11×C4⋊C8—21no—
184C11×C4⋊C8—21no—
185C11×#103—21no—
186C11×#103—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×#102—21no—
196C11×#102—21no—
197C11×C22⋊C8—21no—
198C11×C22⋊C8—21no—
199C11×#97—21no—
200C11×#97C2311yescharacteristic
201C11×#97C2311yescharacteristic
202C11×#97C2311yescharacteristic
203C11×#97C2311yescharacteristic
204C11×#97C2311yescharacteristic
205C11×#97C2311yescharacteristic
206#19010C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—21no—
208C11×#41—81no—
209C11×#41—81no—
210C11×#41—82no—
211C11×#41—81no—
212C11×#41—81no—
213C2×Q8×C11—21no—
214C2×Q8×C11—21no—
215C2×Q8×C11C2×D411yescharacteristic
216C2×Q8×C11C2×D411yescharacteristic
217C2×Q8×C11C2×D411yescharacteristic
218C2×Q8×C11C2×D411yescharacteristic
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—21no—
235C2×D4×C11—41no—
236C2×D4×C11C2×D411yescharacteristic
237C2×D4×C11C2×D411yescharacteristic
238C2×D4×C11C2×D411yescharacteristic
239C2×D4×C11C2×D411yescharacteristic
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—41no—
250C22×C4×C11—82no—
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C11×Q16—81no—
255C11×SD16—42no—
256C11×SD16—81no—
257C11×SD16—81no—
258C11×SD16—81no—
259C11×SD16—81no—
260C11×D8—42no—
261C11×D8—81no—
262C11×D8—81no—
263C11×D8—81no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—42no—
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—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4C2×D411yescharacteristic
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D411yescharacteristic
292C11×C4⋊C4C2×D411yescharacteristic
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—21no—
311C11×C22⋊C4—21no—
312C11×C22⋊C4—21no—
313C11×C22⋊C4—21no—
314C11×C22⋊C4—21no—
315C11×C22⋊C4—21no—
316C11×C22⋊C4—21no—
317C11×C22⋊C4—41no—
318C11×C22⋊C4—41no—
319C42×C11—21no—
320C42×C11—21no—
321C42×C11—21no—
322C42×C11—21no—
323C42×C11C2×D411yescharacteristic
324C42×C11C2×D411yescharacteristic
325C42×C11C2×D411yescharacteristic
326C42×C11C2411yescharacteristic
327#3529C2×C1111yescharacteristic, complemented
328#3219C2×C1111yescharacteristic, complemented
329#3214C2×C1111yescharacteristic, complemented
330#3180C2×C1111yescharacteristic, complemented
331#1664C2×C1111yescharacteristic, complemented
332#1662C2×C1111yescharacteristic, complemented
333#1661C2×C1111yescharacteristic, complemented
334#1659C2×C1111yescharacteristic, complemented
335#1657C2×C1111yescharacteristic, complemented
336#1656C2×C1111yescharacteristic, complemented
337#1656C2×C1111yescharacteristic, complemented
338#1655C2×C1111yescharacteristic, complemented
339#1535C2×C1111yescharacteristic, complemented
340#1532C2×C1111yescharacteristic, complemented
341#1530C2×C1111yescharacteristic, complemented
342C23×C11—21no—
343C23×C11—21no—
344C23×C11—21no—
345C23×C11—21no—
346C23×C11—41no—
347C23×C11—81no—
348C23×C11—81no—
349C23×C11—81no—
350C23×C11#12011yescharacteristic
351Q8×C11—41no—
352Q8×C11—41no—
353Q8×C11—41no—
354Q8×C11—41no—
355Q8×C11—41no—
356Q8×C11—41no—
357Q8×C11—81no—
358D4×C11—41no—
359D4×C11—41no—
360D4×C11—41no—
361D4×C11—41no—
362D4×C11—41no—
363D4×C11—41no—
364D4×C11—41no—
365D4×C11—41no—
366D4×C11—41no—
367D4×C11—41no—
368D4×C11—81no—
369D4×C11—81no—
370D4×C11—81no—
371D4×C11—81no—
372D4×C11—81no—
373D4×C11—81no—
374D4×C11—81no—
375D4×C11—81no—
376D4×C11—81no—
377D4×C11—81no—
378D4×C11—81no—
379D4×C11—81no—
380D4×C11—81no—
381D4×C11—82no—
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—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—42no—
394C2×C4×C11—42no—
395C2×C4×C11—42no—
396C2×C4×C11—42no—
397C2×C4×C11—41no—
398C2×C4×C11—82no—
399C2×C4×C11—81no—
400C2×C4×C11—81no—
401C2×C4×C11—81no—
402C2×C4×C11—81no—
403C2×C4×C11—81no—
404C2×C4×C11#12011yescharacteristic
405C2×C4×C11#12011yescharacteristic
406C2×C4×C11#12011yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C8×C11—22no—
411C8×C11—41no—
412C8×C11—41no—
413C8×C11—41no—
414C8×C11—41no—
415C8×C11—41no—
416#563—21no—
417#563C22×C1111yescharacteristic
418#562—21no—
419#562—21no—
420#562C22×C1111yescharacteristic
421#562C22×C1111yescharacteristic
422H(3,𝔽4)C22×C1111yescharacteristic
423#560—21no—
424#560—21no—
425#560—21no—
426#532—21no—
427#532C22×C1111yescharacteristic
428#532C22×C1111yescharacteristic, complemented
429#529—21no—
430#529—21no—
431#529C22×C1111yescharacteristic
432#529C22×C1111yescharacteristic
433#525—21no—
434#525—21no—
435#525—21no—
436#501C22×C1111yescharacteristic, complemented
437#497C22×C1111yescharacteristic
438#496C22×C1111yescharacteristic
439#496C22×C1111yescharacteristic
440#496C22×C1111yescharacteristic
441#496C22×C1111yescharacteristic, complemented
442#491C22×C1111yescharacteristic, complemented
443#490C22×C1111yescharacteristic, complemented
444#490C22×C1111yescharacteristic, complemented
445#489C22×C1111yescharacteristic
446#489C22×C1111yescharacteristic
447#489C22×C1111yescharacteristic, complemented
448#466—21no—
449#465—21no—
450#464—21no—
451#463—21no—
452#461—21no—
453#459—21no—
454#452—21no—
455#449—21no—
456#449—21no—
457#449—21no—
458#442—21no—
459#440—21no—
460#432C22×C1111yescharacteristic, complemented
461#432C22×C1111yescharacteristic, complemented
462C2×#97C22×C1111yescharacteristic, complemented
463#330C22×C1111yescharacteristic, complemented
464#330C22×C1111yescharacteristic, complemented
465#330C22×C1111yescharacteristic, complemented
466#330C22×C1111yescharacteristic, complemented
467#329C22×C1111yescharacteristic
468#329C22×C1111yescharacteristic
469#329C22×C1111yescharacteristic
470#329C22×C1111yescharacteristic
471#329C22×C1111yescharacteristic
472#329C22×C1111yescharacteristic
473#329C22×C1111yescharacteristic, complemented
474#329C22×C1111yescharacteristic, complemented
475C22×C11—21no—
476C22×C11—21no—
477C22×C11—21no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11—41no—
489C22×C11—41no—
490C22×C11—84no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11—81no—
494C22×C11C2×#12011yescharacteristic
495C4×C11—21no—
496C4×C11—21no—
497C4×C11—21no—
498C4×C11—21no—
499C4×C11—21no—
500C4×C11—21no—
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—81no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41D4×C1111yescharacteristic
513C2×#41D4×C1111yescharacteristic
514C23×C4—21no—
515C2×Q16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—21no—
521C2×D8—21no—
522C2×D8—21no—
523C2×D8—21no—
524C2×D8—21no—
525C22×C8—21no—
526C4⋊Q8—21no—
527C4⋊Q8D4×C1111yescharacteristic
528C4⋊Q8C23×C1111yescharacteristic
529#127—21no—
530#127D4×C1111yescharacteristic
531#127C23×C1111yescharacteristic
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#125C23×C1111yescharacteristic
541#125C23×C1111yescharacteristic
542#124—21no—
543#124—21no—
544#124—21no—
545#124—21no—
546#124—21no—
547#124C23×C1111yescharacteristic
548#124C23×C1111yescharacteristic
549#124C23×C1111yescharacteristic
550#124C23×C1111yescharacteristic
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—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⋊Q8D4×C1111yescharacteristic
572C22⋊Q8D4×C1111yescharacteristic
573#121—21no—
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121D4×C1111yescharacteristic
590#121D4×C1111yescharacteristic
591#120—21no—
592#120—21no—
593#120—21no—
594#120—21no—
595#120—21no—
596#120—21no—
597C4×Q8D4×C1111yescharacteristic
598C4×Q8D4×C1111yescharacteristic
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4D4×C1111yescharacteristic
610C4×D4D4×C1111yescharacteristic
611#117—21no—
612#117—21no—
613#117—21no—
614C2×C42—21no—
615C2×C42C23×C1111yescharacteristic
616#107—21no—
617#106—21no—
618C4⋊C8—21no—
619C4⋊C8—21no—
620#103—21no—
621#103—21no—
622#103—21no—
623#103—21no—
624#103—21no—
625#102—21no—
626#102—21no—
627#102—21no—
628#102—21no—
629#102—21no—
630#102—21no—
631#102—21no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634#97—21no—
635#97C23×C1111yescharacteristic
636#97C23×C1111yescharacteristic
637#97C23×C1111yescharacteristic
638#97C23×C1111yescharacteristic
639#97C23×C1111yescharacteristic
640#97C23×C1111yescharacteristic
641C2×C11—41no—
642C2×C11—81no—
643C2×C11—81no—
644C2×C11—81no—
645C2×C11—81no—
646C2×C11—161no—
647C2×C11#301811yescharacteristic
648C2×C11#301911yescharacteristic
649C2×C11#302111yescharacteristic
650C24—21no—
651#41—81no—
652#41—81no—
653#41—82no—
654#41—81no—
655#41—81no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8C2×D4×C1111yescharacteristic
659C2×Q8C2×D4×C1111yescharacteristic
660C2×Q8C2×D4×C1111yescharacteristic
661C2×Q8C2×D4×C1111yescharacteristic
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4C2×D4×C1111yescharacteristic
680C2×D4C2×D4×C1111yescharacteristic
681C2×D4C2×D4×C1111yescharacteristic
682C2×D4C2×D4×C1111yescharacteristic
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—41no—
693C22×C4—82no—
694C22×C4C2×D4×C1111yescharacteristic
695C22×C4C2×D4×C1111yescharacteristic
696C22×C4C2×D4×C1111yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—42no—
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⋊C4C2×D4×C1111yescharacteristic
733C4⋊C4C2×D4×C1111yescharacteristic
734C4⋊C4C2×D4×C1111yescharacteristic
735C4⋊C4C2×D4×C1111yescharacteristic
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—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—41no—
761C22⋊C4—41no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42C2×D4×C1111yescharacteristic
767C42C2×D4×C1111yescharacteristic
768C42C2×D4×C1111yescharacteristic
769C42C24×C1111yescharacteristic
770C11#1901011yescharacteristic, direct product factor, Sylow
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23C11×#12011yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4C11×#12011yescharacteristic
834C2×C4C11×#12011yescharacteristic
835C2×C4C11×#12011yescharacteristic
836C2×C4C22×D4×C1111yescharacteristic
837C2×C4C22×D4×C1111yescharacteristic
838C2×C4C22×D4×C1111yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×C11×#12011yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C11×#301811yescharacteristic
887C2C11×#301911yescharacteristic
888C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
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×#3529C2semidirect
2. C11×#3219C2semidirect
3. C11×#3214C2semidirect
4. C11×#3180C2semidirect
5. C11×#1664C2semidirect
6. C11×#1662C2semidirect
7. C11×#1661C2semidirect
8. C11×#1659C2semidirect
9. C11×#1657C2semidirect
10. C11×#1656C2semidirect
11. C11×#1656C2semidirect
12. C11×#1655C2semidirect
13. C11×#1535C2semidirect
14. C11×#1532C2semidirect
15. C11×#1530C2semidirect
28. C11×#532C22semidirect
36. C11×#501C22semidirect
41. C11×#496C22semidirect
42. C11×#491C22semidirect
43. C11×#490C22semidirect
44. C11×#490C22semidirect
47. C11×#489C22semidirect
60. C11×#432C22semidirect
61. C11×#432C22semidirect
62. C2×C11×#97C22semidirect
63. C11×#330C22semidirect
64. C11×#330C22semidirect
65. C11×#330C22semidirect
66. C11×#330C22semidirect
73. C11×#329C22semidirect
74. C11×#329C22semidirect
206. #19010C11direct (N × H)
327. #3529C2×C11semidirect
328. #3219C2×C11semidirect
329. #3214C2×C11semidirect
330. #3180C2×C11semidirect
331. #1664C2×C11semidirect
332. #1662C2×C11semidirect
333. #1661C2×C11semidirect
334. #1659C2×C11semidirect
335. #1657C2×C11semidirect
336. #1656C2×C11semidirect
337. #1656C2×C11semidirect
338. #1655C2×C11semidirect
339. #1535C2×C11semidirect
340. #1532C2×C11semidirect
341. #1530C2×C11semidirect
428. #532C22×C11semidirect
436. #501C22×C11semidirect
441. #496C22×C11semidirect
442. #491C22×C11semidirect
443. #490C22×C11semidirect
444. #490C22×C11semidirect
447. #489C22×C11semidirect
460. #432C22×C11semidirect
461. #432C22×C11semidirect
462. C2×#97C22×C11semidirect
463. #330C22×C11semidirect
464. #330C22×C11semidirect
465. #330C22×C11semidirect
466. #330C22×C11semidirect
473. #329C22×C11semidirect
474. #329C22×C11semidirect
770. C11#19010direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35292
C11×#32192
C11×#32142
C11×#31802
C11×#16642
C11×#16622
C11×#16612
C11×#16592
C11×#16572
C11×#16562
C11×#16552
C11×#15352
C11×#15322
C11×#15302
#1901011