Finite Group Databasebeta

← C11×#24175 #14601368

Subgroups — C11×#24175 #14601368

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3512C211yesmaximal, characteristic
2C11×#3037C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic, complemented
4C11×#2565C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic, complemented
6C11×#2039C211yesmaximal, characteristic, complemented
7C11×#2007C211yesmaximal, characteristic, complemented
8C11×#2007C211yesmaximal, characteristic, complemented
9C11×#1998C211yesmaximal, characteristic, complemented
10C11×#1980C211yesmaximal, characteristic, complemented
11C11×#1882C211yesmaximal, characteristic, complemented
12C11×#1882C211yesmaximal, characteristic, complemented
13C11×#1860C211yesmaximal, characteristic, complemented
14C11×#1859C211yesmaximal, characteristic, complemented
15C11×#1806C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C2×C11×#137C2211yescharacteristic
18C2×C11×#137C2211yescharacteristic
19C11×#553—21no—
20C11×#553—21no—
21C11×#553—22no—
22C11×#553—22no—
23C11×#552—21no—
24C11×#552—21no—
25C11×#541—21no—
26C11×#540—21no—
27C11×#537C2211yescharacteristic
28C11×#537C2211yescharacteristic
29C11×#532C2211yescharacteristic
30C11×#529—21no—
31C11×#529—21no—
32C2×C11×#125C2211yescharacteristic
33C11×#520C2211yescharacteristic
34C11×#520C2211yescharacteristic
35C4×C11×#41C2211yescharacteristic
36C2×C4×Q8×C11C2211yescharacteristic
37C11×#464—21no—
38C11×#464—21no—
39C11×#462—21no—
40C11×#460—21no—
41C11×#441—21no—
42C11×#440—21no—
43C4×C11×Q16—21no—
44C4×C11×SD16—21no—
45C11×#428C2211yescharacteristic
46C11×#423C2211yescharacteristic
47C2×C11×#104C2211yescharacteristic
48C2×C11×#104C2211yescharacteristic
49C2×C11×#104C2211yescharacteristic
50C2×C11×#104C2211yescharacteristic
51C2×C11×#104C2211yescharacteristic
52C2×C11×#104C2211yescharacteristic
53C11×#419C2211yescharacteristic
54C11×#417C2211yescharacteristic
55C11×#417C2211yescharacteristic
56C11×#417C2211yescharacteristic
57C4×C11×M16C2211yescharacteristic
58C11×#398—22no—
59C11×#391C2211yescharacteristic
60C11×#391C2211yescharacteristic
61C11×#387—22no—
62C11×#384C2211yescharacteristic
63C11×#382C2211yescharacteristic
64C4×C11×C4⋊C4C2211yescharacteristic
65C11×#343C2211yescharacteristic
66C11×#343C2211yescharacteristic
67C11×#343C2211yescharacteristic
68C11×#343C2211yescharacteristic
69C11×#339C2211yescharacteristic
70C11×#339C2211yescharacteristic
71C2×C11×#41C2311yescharacteristic
72C2×C11×#41C2311yescharacteristic
73C2×C11×#41C2311yescharacteristic
74C22×Q8×C11C2311yescharacteristic
75C11×#137—22no—
76C11×#137—22no—
77C11×#137—22no—
78C11×#137—22no—
79C11×#137—41no—
80C11×#137—41no—
81C2×C11×Q16—21no—
82C2×C11×Q16—21no—
83C2×C11×Q16—21no—
84C2×C11×SD16—21no—
85C2×C11×SD16—21no—
86C2×C11×SD16—21no—
87C2×C11×M16C2311yescharacteristic
88C2×C11×M16C2311yescharacteristic
89C2×C11×M16C2311yescharacteristic
90C2×C11×M16C2311yescharacteristic
91C11×C4⋊Q8D411yescharacteristic
92C11×#127D411yescharacteristic
93C11×#126—22no—
94C11×#126—22no—
95C11×#126—22no—
96C11×#126—22no—
97C11×#125—22no—
98C11×#125—22no—
99C11×#125—21no—
100C11×#125—21no—
101C11×#125—21no—
102C11×#125—21no—
103C11×#124D411yescharacteristic
104C11×#124D411yescharacteristic
105C11×#123—22no—
106C11×#123—22no—
107C11×#123—22no—
108C11×#123—22no—
109C11×C22⋊Q8—21no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×#121—22no—
114C11×#121—22no—
115C11×#121—21no—
116C11×#121—21no—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121—21no—
120C11×#121—21no—
121C11×#121—22no—
122C11×#121—22no—
123C4×Q8×C11—21no—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11—21no—
127C4×Q8×C11—21no—
128C4×Q8×C11—21no—
129C4×Q8×C11D411yescharacteristic
130C4×Q8×C11D411yescharacteristic
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—22no—
138C4×D4×C11—22no—
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11D411yescharacteristic
142C4×D4×C11D411yescharacteristic
143C11×#117—22no—
144C11×#117—22no—
145C11×#117—21no—
146C11×#117—21no—
147C11×#117—21no—
148C11×#117C2311yescharacteristic
149C2×C11×C4⋊C4—21no—
150C2×C11×C4⋊C4—21no—
151C2×C11×C4⋊C4—21no—
152C2×C11×C4⋊C4—21no—
153C2×C11×C4⋊C4—22no—
154C2×C11×C4⋊C4D412yes—
155C2×C11×C4⋊C4D412yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C42×C11—21no—
160C2×C42×C11—21no—
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C11×#107—21no—
165C11×#106—21no—
166C11×C4⋊C8—21no—
167C11×C4⋊C8—21no—
168C11×#104—22no—
169C11×#104—22no—
170C11×#104—41no—
171C11×#104—41no—
172C11×#104—41no—
173C11×#104—41no—
174C11×#103—21no—
175C11×#103—21no—
176C11×#103—21no—
177C11×#103—21no—
178C11×#103—21no—
179C11×#102—21no—
180C11×#102—21no—
181C11×#102—21no—
182C11×#97—21no—
183C4×C8×C11—21no—
184C11×#95—21no—
185C11×#95—22no—
186C11×#95—22no—
187C11×#95—22no—
188#24175C1111yesmaximal, characteristic, direct product factor, Sylow
189C11×#41—21no—
190C11×#41—21no—
191C11×#41—21no—
192C11×#41—21no—
193C11×#41—21no—
194C11×#41—21no—
195C11×#41—21no—
196C11×#41—21no—
197C11×#41—21no—
198C11×#41—21no—
199C11×#41—21no—
200C11×#41—21no—
201C2×Q8×C11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11—21no—
204C2×Q8×C11—21no—
205C2×Q8×C11—21no—
206C2×Q8×C11C2×D411yescharacteristic
207C2×Q8×C11C2×D411yescharacteristic
208C2×Q8×C11C2×D411yescharacteristic
209C2×Q8×C11#4112yes—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—21no—
216C2×D4×C11—21no—
217C2×D4×C11C2×D411yescharacteristic
218C2×D4×C11C2×D411yescharacteristic
219C2×D4×C11C2×D411yescharacteristic
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—21no—
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×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2411yescharacteristic
236C11×Q16—24no—
237C11×Q16—42no—
238C11×Q16—42no—
239C11×SD16—24no—
240C11×SD16—42no—
241C11×SD16—42no—
242C11×M16—21no—
243C11×M16—21no—
244C11×M16—21no—
245C11×M16—21no—
246C11×M16—21no—
247C11×M16—21no—
248C11×M16—21no—
249C11×M16#4112yes—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4—22no—
256C11×C4⋊C4—22no—
257C11×C4⋊C4—22no—
258C11×C4⋊C4—22no—
259C11×C4⋊C4—22no—
260C11×C4⋊C4—22no—
261C11×C4⋊C4—22no—
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—42no—
273C11×C4⋊C4—44no—
274C11×C4⋊C4—41no—
275C11×C4⋊C4—41no—
276C11×C4⋊C4C2×D411yescharacteristic
277C11×C4⋊C4C2×D411yescharacteristic
278C11×C22⋊C4—22no—
279C11×C22⋊C4—22no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—21no—
285C11×C22⋊C4—21no—
286C11×C22⋊C4—21no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C42×C11—22no—
292C42×C11—22no—
293C42×C11—21no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11—21no—
297C42×C11—21no—
298C42×C11—21no—
299C42×C11—21no—
300C42×C11—41no—
301C42×C11—41no—
302C42×C11C2×D411yescharacteristic
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D411yescharacteristic
306#3512C2×C1111yescharacteristic
307#3037C2×C1111yescharacteristic, complemented
308C4×#137C2×C1111yescharacteristic, complemented
309#2565C2×C1111yescharacteristic, complemented
310#2040C2×C1111yescharacteristic, complemented
311#2039C2×C1111yescharacteristic, complemented
312#2007C2×C1111yescharacteristic, complemented
313#2007C2×C1111yescharacteristic, complemented
314#1998C2×C1111yescharacteristic, complemented
315#1980C2×C1111yescharacteristic, complemented
316#1882C2×C1111yescharacteristic, complemented
317#1882C2×C1111yescharacteristic, complemented
318#1860C2×C1111yescharacteristic, complemented
319#1859C2×C1111yescharacteristic, complemented
320#1806C2×C1111yescharacteristic, complemented
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11C22×D411yescharacteristic
325Q8×C11—22no—
326Q8×C11—21no—
327Q8×C11—21no—
328Q8×C11—22no—
329Q8×C11—21no—
330Q8×C11—21no—
331Q8×C11—21no—
332Q8×C11—21no—
333Q8×C11—41no—
334Q8×C11—41no—
335D4×C11—21no—
336D4×C11—21no—
337D4×C11—21no—
338D4×C11—21no—
339D4×C11—21no—
340D4×C11—21no—
341D4×C11—41no—
342D4×C11—41no—
343D4×C11—41no—
344D4×C11—41no—
345D4×C11—41no—
346D4×C11—41no—
347D4×C11—81no—
348D4×C11—81no—
349D4×C11—82no—
350D4×C11—82no—
351C2×C4×C11—22no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—41no—
375C2×C4×C11—42no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—81no—
380C2×C4×C11—81no—
381C2×C4×C11—82no—
382C2×C4×C11—82no—
383C2×C4×C11#12011yescharacteristic
384C2×C4×C11#12011yescharacteristic
385C2×C4×C11#12011yescharacteristic
386C2×C4×C11#12011yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C2×#4111yescharacteristic
390C2×C4×C11C2×#4111yescharacteristic
391C2×C4×C11H(5,𝔽2)11yescharacteristic
392C2×C4×C112−1+411yescharacteristic
393C8×C11—22no—
394C8×C11—41no—
395C8×C11—41no—
396C8×C11—41no—
397C2×#137C22×C1111yescharacteristic
398C2×#137C22×C1111yescharacteristic
399C2×#137C22×C1111yescharacteristic
400#553—21no—
401#553—21no—
402#553—22no—
403#553—22no—
404#552—21no—
405#552—21no—
406#541—21no—
407#540—21no—
408#537C22×C1111yescharacteristic
409#537C22×C1111yescharacteristic
410#532C22×C1111yescharacteristic
411#529—21no—
412#529—21no—
413C2×#125C22×C1111yescharacteristic
414#520C22×C1111yescharacteristic
415#520C22×C1111yescharacteristic
416C4×#41C22×C1111yescharacteristic
417C2×C4×Q8C22×C1111yescharacteristic
418#464—21no—
419#464—21no—
420#462—21no—
421#460—21no—
422#441—21no—
423#440—21no—
424C4×Q16—21no—
425C4×SD16—21no—
426#428C22×C1111yescharacteristic
427#423C22×C1111yescharacteristic
428C2×#104C22×C1111yescharacteristic
429C2×#104C22×C1111yescharacteristic
430C2×#104C22×C1111yescharacteristic
431C2×#104C22×C1111yescharacteristic
432C2×#104C22×C1111yescharacteristic
433C2×#104C22×C1111yescharacteristic
434#419C22×C1111yescharacteristic
435#417C22×C1111yescharacteristic
436#417C22×C1111yescharacteristic
437#417C22×C1111yescharacteristic
438C4×M16C22×C1111yescharacteristic
439#398—22no—
440#391C22×C1111yescharacteristic
441#391C22×C1111yescharacteristic
442#387—22no—
443#384C22×C1111yescharacteristic
444#382C22×C1111yescharacteristic
445C4×C4⋊C4C22×C1111yescharacteristic
446#343C22×C1111yescharacteristic
447#343C22×C1111yescharacteristic
448#343C22×C1111yescharacteristic
449#343C22×C1111yescharacteristic
450#339C22×C1111yescharacteristic
451#339C22×C1111yescharacteristic
452C22×C11—21no—
453C22×C11—21no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11—41no—
463C22×C11C2×#12011yescharacteristic
464C22×C11#54811yescharacteristic
465C22×C11#55011yescharacteristic
466C4×C11—21no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—21no—
470C4×C11—42no—
471C4×C11—41no—
472C4×C11—41no—
473C4×C11—41no—
474C4×C11—42no—
475C4×C11—42no—
476C4×C11—41no—
477C4×C11—42no—
478C4×C11—41no—
479C4×C11—81no—
480C4×C11—81no—
481C4×C11#52511yescharacteristic
482C4×C11#53711yescharacteristic
483C4×C11#54611yescharacteristic
484C4×C11#54711yescharacteristic
485C2×#41C23×C1111yescharacteristic
486C2×#41C23×C1111yescharacteristic
487C2×#41C23×C1111yescharacteristic
488C22×Q8C23×C1111yescharacteristic
489#137—22no—
490#137—22no—
491#137—22no—
492#137—22no—
493#137—41no—
494#137—41no—
495C2×Q16—21no—
496C2×Q16—21no—
497C2×Q16—21no—
498C2×SD16—21no—
499C2×SD16—21no—
500C2×SD16—21no—
501C2×M16C23×C1111yescharacteristic
502C2×M16C23×C1111yescharacteristic
503C2×M16C23×C1111yescharacteristic
504C2×M16C23×C1111yescharacteristic
505C4⋊Q8D4×C1111yescharacteristic
506#127D4×C1111yescharacteristic
507#126—22no—
508#126—22no—
509#126—22no—
510#126—22no—
511#125—22no—
512#125—22no—
513#125—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#124D4×C1111yescharacteristic
518#124D4×C1111yescharacteristic
519#123—22no—
520#123—22no—
521#123—22no—
522#123—22no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527#121—22no—
528#121—22no—
529#121—21no—
530#121—21no—
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—22no—
536#121—22no—
537C4×Q8—21no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—21no—
543C4×Q8D4×C1111yescharacteristic
544C4×Q8D4×C1111yescharacteristic
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—21no—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4D4×C1111yescharacteristic
556C4×D4D4×C1111yescharacteristic
557#117—22no—
558#117—22no—
559#117—21no—
560#117—21no—
561#117—21no—
562#117C23×C1111yescharacteristic
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4D4×C1112yes—
569C2×C4⋊C4D4×C1112yes—
570C2×C4⋊C4C23×C1111yescharacteristic
571C2×C4⋊C4C23×C1111yescharacteristic
572C2×C4⋊C4C23×C1111yescharacteristic
573C2×C42—21no—
574C2×C42—21no—
575C2×C42C23×C1111yescharacteristic
576C2×C42C23×C1111yescharacteristic
577C2×C42C23×C1111yescharacteristic
578#107—21no—
579#106—21no—
580C4⋊C8—21no—
581C4⋊C8—21no—
582#104—22no—
583#104—22no—
584#104—41no—
585#104—41no—
586#104—41no—
587#104—41no—
588#103—21no—
589#103—21no—
590#103—21no—
591#103—21no—
592#103—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#97—21no—
597C4×C8—21no—
598#95—21no—
599#95—22no—
600#95—22no—
601#95—22no—
602C2×C11—21no—
603C2×C11—21no—
604C2×C11—81no—
605C2×C11—81no—
606C2×C11—81no—
607C2×C11#240711yescharacteristic
608C2×C11#301811yescharacteristic
609C2×C11#302211yescharacteristic
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8C2×D4×C1111yescharacteristic
628C2×Q8C2×D4×C1111yescharacteristic
629C2×Q8C2×D4×C1111yescharacteristic
630C2×Q8C11×#4112yes—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4C2×D4×C1111yescharacteristic
639C2×D4C2×D4×C1111yescharacteristic
640C2×D4C2×D4×C1111yescharacteristic
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4C2×D4×C1112yes—
653C22×C4C2×D4×C1112yes—
654C22×C4C2×D4×C1111yescharacteristic
655C22×C4C2×D4×C1111yescharacteristic
656C22×C4C24×C1111yescharacteristic
657Q16—24no—
658Q16—42no—
659Q16—42no—
660SD16—24no—
661SD16—42no—
662SD16—42no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16C11×#4112yes—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—44no—
695C4⋊C4—41no—
696C4⋊C4—41no—
697C4⋊C4C2×D4×C1111yescharacteristic
698C4⋊C4C2×D4×C1111yescharacteristic
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C42—22no—
713C42—22no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—41no—
722C42—41no—
723C42C2×D4×C1111yescharacteristic
724C42C2×D4×C1111yescharacteristic
725C42C2×D4×C1111yescharacteristic
726C42C2×D4×C1111yescharacteristic
727C11#2417511yescharacteristic, direct product factor, Sylow
728C23—21no—
729C23—21no—
730C23—21no—
731C23C22×D4×C1111yescharacteristic
732Q8—22no—
733Q8—21no—
734Q8—21no—
735Q8—22no—
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—21no—
740Q8—41no—
741Q8—41no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—21no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—81no—
755D4—81no—
756D4—82no—
757D4—82no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—82no—
789C2×C4—82no—
790C2×C4C11×#12011yescharacteristic
791C2×C4C11×#12011yescharacteristic
792C2×C4C11×#12011yescharacteristic
793C2×C4C11×#12011yescharacteristic
794C2×C4C22×D4×C1111yescharacteristic
795C2×C4C22×D4×C1111yescharacteristic
796C2×C4C2×C11×#4111yescharacteristic
797C2×C4C2×C11×#4111yescharacteristic
798C2×C4C11×H(5,𝔽2)11yescharacteristic
799C2×C4C11×2−1+411yescharacteristic
800C8—22no—
801C8—41no—
802C8—41no—
803C8—41no—
804C22—21no—
805C22—21no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22C2×C11×#12011yescharacteristic
816C22C11×#54811yescharacteristic
817C22C11×#55011yescharacteristic
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—42no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—42no—
828C4—41no—
829C4—42no—
830C4—41no—
831C4—81no—
832C4—81no—
833C4C11×#52511yescharacteristic
834C4C11×#53711yescharacteristic
835C4C11×#54611yescharacteristic
836C4C11×#54711yescharacteristic
837C2—21no—
838C2—21no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2C11×#240711yescharacteristic
843C2C11×#301811yescharacteristic
844C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3512C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3037C2semidirect
3. C4×C11×#137C2semidirect
4. C11×#2565C2semidirect
5. C11×#2040C2semidirect
6. C11×#2039C2semidirect
7. C11×#2007C2semidirect
8. C11×#2007C2semidirect
9. C11×#1998C2semidirect
10. C11×#1980C2semidirect
11. C11×#1882C2semidirect
12. C11×#1882C2semidirect
13. C11×#1860C2semidirect
14. C11×#1859C2semidirect
15. C11×#1806C2semidirect
188. #24175C11direct (N × H)
307. #3037C2×C11semidirect
308. C4×#137C2×C11semidirect
309. #2565C2×C11semidirect
310. #2040C2×C11semidirect
311. #2039C2×C11semidirect
312. #2007C2×C11semidirect
313. #2007C2×C11semidirect
314. #1998C2×C11semidirect
315. #1980C2×C11semidirect
316. #1882C2×C11semidirect
317. #1882C2×C11semidirect
318. #1860C2×C11semidirect
319. #1859C2×C11semidirect
320. #1806C2×C11semidirect
727. C11#24175direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35122
C11×#30372
C4×C11×#1372
C11×#25652
C11×#20402
C11×#20392
C11×#20072
C11×#19982
C11×#19802
C11×#18822
C11×#18602
C11×#18592
C11×#18062
#2417511