Finite Group Databasebeta

← C11×#24140 #14601333

Subgroups — C11×#24140 #14601333

Order 2816.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3505C211yesmaximal, characteristic, complemented
2C11×#2848C211yesmaximal, characteristic, complemented
3C11×#2847C211yesmaximal, characteristic, complemented
4C4×C11×#120C211yesmaximal, characteristic, complemented
5C11×#2044C212yesmaximal, complemented
6C11×#2021C212yesmaximal, complemented
7C11×#1996C211yesmaximal, characteristic, complemented
8C11×#1964C211yesmaximal, characteristic, complemented
9C11×#1889C212yesmaximal, complemented
10C11×#1867C212yesmaximal, complemented
11C11×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C11×#553—21no—
14C11×#553—22no—
15C11×#552—21no—
16C11×#551—22no—
17C11×#548—21no—
18C11×#546—21no—
19C11×#539—21no—
20C11×#538—21no—
21C11×#534C2212yes—
22C11×#529—21no—
23C11×#525—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121—21no—
27C2×C11×#121C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C2×C11×#120C2212yes—
30C11×#518C2212yes—
31C2×C4×D4×C11—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×C11×#99C2212yes—
34C2×C11×#99C2212yes—
35C2×C11×#99C2212yes—
36C11×#386—21no—
37C11×#386—22no—
38C11×#386C2212yes—
39C11×#386C2211yescharacteristic
40C11×#385—21no—
41C11×#385—22no—
42C11×#385C2211yescharacteristic
43C11×#385C2212yes—
44C11×#380—21no—
45C11×#380—21no—
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C11×#379C2211yescharacteristic
49C11×#379C2212yes—
50C4×C11×C22⋊C4—21no—
51C4×C11×C22⋊C4C2211yescharacteristic
52C11×#342C2212yes—
53C11×#342C2212yes—
54C11×#342C2212yes—
55C25×C11C2311yescharacteristic
56C2×C11×#41—21no—
57C22×Q8×C11D411yescharacteristic, complemented
58C22×D4×C11—21no—
59C22×D4×C11—22no—
60C22×D4×C11D411yescharacteristic, complemented
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2312yes—
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11—44no—
70C23×C4×C11D411yescharacteristic, complemented
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C11×#126—22no—
74C11×#126—22no—
75C11×#126—22no—
76C11×#125—21no—
77C11×#125—22no—
78C11×#124—21no—
79C11×#124—22no—
80C11×#123—22no—
81C11×#123—22no—
82C11×#123—22no—
83C11×#123—22no—
84C11×#123—22no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—44no—
92C11×#121—21no—
93C11×#121—22no—
94C11×#121—21no—
95C11×#121—21no—
96C11×#121—21no—
97C11×#121—21no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—44no—
101C11×#120—22no—
102C11×#120—22no—
103C11×#120—22no—
104C11×#120—22no—
105C11×#120—24no—
106C11×#120—42no—
107C4×Q8×C11—21no—
108C4×D4×C11—22no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11—22no—
115C4×D4×C11—22no—
116C4×D4×C11—22no—
117C4×D4×C11—22no—
118C4×D4×C11—44no—
119C11×#117—21no—
120C11×#117—22no—
121C11×#117—22no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—22no—
126C2×C11×C4⋊C4D411yescharacteristic, complemented
127C2×C11×C4⋊C4D411yescharacteristic, complemented
128C2×C11×C4⋊C4D411yescharacteristic, complemented
129C2×C11×C4⋊C4D412yescomplemented
130C2×C11×C22⋊C4—22no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—22no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—22no—
137C2×C11×C22⋊C4—22no—
138C2×C11×C22⋊C4—22no—
139C2×C11×C22⋊C4D411yescharacteristic, complemented
140C2×C11×C22⋊C4D412yescomplemented
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2311yescharacteristic
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2311yescharacteristic
147C2×C42×C11—21no—
148C2×C42×C11D411yescharacteristic, complemented
149C11×#99—24no—
150C11×#99—42no—
151C11×#99—42no—
152C11×#95—21no—
153C11×#95—21no—
154C11×#95—21no—
155C11×#95—22no—
156C11×#95—22no—
157C11×#95—21no—
158C11×#95—21no—
159#24140C1111yesmaximal, characteristic, direct product factor, Sylow
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—42no—
167C24×C11—42no—
168C24×C11C2×D412yes—
169C24×C11C2×D411yescharacteristic
170C24×C11#4112yescomplemented
171C24×C11C2411yescharacteristic
172C11×#41—82no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—42no—
176C2×D4×C11—24no—
177C2×D4×C11—21no—
178C2×D4×C11—22no—
179C2×D4×C11—21no—
180C2×D4×C11—22no—
181C2×D4×C11—22no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—22no—
185C2×D4×C11—21no—
186C2×D4×C11—22no—
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11—42no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C2×D4×C11—44no—
199C22×C4×C11—24no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—42no—
214C22×C4×C11—42no—
215C22×C4×C11—42no—
216C22×C4×C11—42no—
217C22×C4×C11—42no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11—42no—
225C22×C4×C11—41no—
226C22×C4×C11—41no—
227C22×C4×C11—41no—
228C22×C4×C11—41no—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C11×C4⋊C4—22no—
242C11×C4⋊C4—22no—
243C11×C4⋊C4—22no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—22no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—22no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—42no—
254C11×C4⋊C4—42no—
255C11×C4⋊C4—42no—
256C11×C4⋊C4—44no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—22no—
261C11×C22⋊C4—22no—
262C11×C22⋊C4—22no—
263C11×C22⋊C4—22no—
264C11×C22⋊C4—21no—
265C11×C22⋊C4—22no—
266C11×C22⋊C4—21no—
267C11×C22⋊C4—22no—
268C11×C22⋊C4—21no—
269C11×C22⋊C4—22no—
270C11×C22⋊C4—21no—
271C11×C22⋊C4—21no—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—22no—
274C11×C22⋊C4—22no—
275C11×C22⋊C4—21no—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—21no—
279C11×C22⋊C4—44no—
280C11×C22⋊C4—42no—
281C11×C22⋊C4—44no—
282C11×C22⋊C4—44no—
283C11×C22⋊C4—42no—
284C11×C22⋊C4—42no—
285C11×C22⋊C4—44no—
286C11×C22⋊C4#4112yescomplemented
287C42×C11—22no—
288C42×C11—22no—
289C42×C11—21no—
290C42×C11—21no—
291C42×C11—42no—
292#3505C2×C1111yescharacteristic, complemented
293#2848C2×C1111yescharacteristic, complemented
294#2847C2×C1111yescharacteristic, complemented
295C4×#120C2×C1111yescharacteristic, complemented
296#2044C2×C1112yescomplemented
297#2021C2×C1112yescomplemented
298#1996C2×C1111yescharacteristic, complemented
299#1964C2×C1111yescharacteristic, complemented
300#1889C2×C1112yescomplemented
301#1867C2×C1112yescomplemented
302#1799C2×C1111yescharacteristic, complemented
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—21no—
313C23×C11—22no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—41no—
319C23×C11—44no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11C22×D411yescharacteristic
339C23×C11C22×D411yescharacteristic
340C23×C11C22×D411yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C112−1+411yescharacteristic
345Q8×C11—42no—
346Q8×C11—81no—
347D4×C11—48no—
348D4×C11—42no—
349D4×C11—42no—
350D4×C11—41no—
351D4×C11—41no—
352D4×C11—41no—
353D4×C11—42no—
354D4×C11—42no—
355D4×C11—41no—
356D4×C11—42no—
357D4×C11—81no—
358D4×C11—82no—
359D4×C11—82no—
360D4×C11—88no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—21no—
368C2×C4×C11—22no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—21no—
374C2×C4×C11—22no—
375C2×C4×C11—21no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—44no—
382C2×C4×C11—44no—
383C2×C4×C11—44no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—44no—
391C2×C4×C11—42no—
392C2×C4×C11—41no—
393C2×C4×C11—42no—
394C2×C4×C11—41no—
395C2×C4×C11—42no—
396C2×C4×C11—41no—
397C2×C4×C11—42no—
398C2×C4×C11—42no—
399C2×C4×C11—42no—
400C2×C4×C11—41no—
401C2×C4×C11—42no—
402C2×C4×C11—41no—
403C2×C4×C11—42no—
404C2×C4×C11—42no—
405C2×C4×C11—81no—
406C2×C4×C11—82no—
407C2×C4×C11—82no—
408C2×C4×C11#12011yescharacteristic
409C2×C4×C11#12011yescharacteristic
410C2×C4×C11#12011yescharacteristic
411C2×C4×C11#12011yescharacteristic
412C24×C4C22×C1111yescharacteristic
413#553—21no—
414#553—22no—
415#552—21no—
416#551—22no—
417#548—21no—
418#546—21no—
419#539—21no—
420#538—21no—
421#534C22×C1112yes—
422#529—21no—
423#525—21no—
424C2×C22⋊Q8—21no—
425C2×C22⋊Q8C22×C1111yescharacteristic
426C2×#121—21no—
427C2×#121C22×C1111yescharacteristic
428C2×#120C22×C1111yescharacteristic
429C2×#120C22×C1112yes—
430#518C22×C1112yes—
431C2×C4×D4—21no—
432C2×C4×D4C22×C1111yescharacteristic
433C2×#99C22×C1112yes—
434C2×#99C22×C1112yes—
435C2×#99C22×C1112yes—
436#386—22no—
437#386—21no—
438#386C22×C1112yes—
439#386C22×C1111yescharacteristic
440#385—22no—
441#385—21no—
442#385C22×C1112yes—
443#385C22×C1111yescharacteristic
444#380—21no—
445#380—21no—
446#380C22×C1111yescharacteristic
447#380C22×C1111yescharacteristic
448#379C22×C1112yes—
449#379C22×C1111yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4C22×C1111yescharacteristic
452#342C22×C1112yes—
453#342C22×C1112yes—
454#342C22×C1112yes—
455C22×C11—21no—
456C22×C11—21no—
457C22×C11—21no—
458C22×C11—21no—
459C22×C11—21no—
460C22×C11—21no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—41no—
482C22×C11—42no—
483C22×C11—41no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—41no—
487C22×C11—82no—
488C22×C11—81no—
489C22×C11—82no—
490C22×C11C2×#12011yescharacteristic
491C22×C11#52511yescharacteristic
492C22×C11#53711yescharacteristic
493C22×C11#54611yescharacteristic
494C22×C11#54711yescharacteristic
495C22×C11#54811yescharacteristic
496C22×C11#55011yescharacteristic
497C4×C11—21no—
498C4×C11—21no—
499C4×C11—21no—
500C4×C11—42no—
501C4×C11—41no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—41no—
505C4×C11—42no—
506C4×C11—41no—
507C4×C11—42no—
508C4×C11—82no—
509C4×C11—81no—
510C4×C11—82no—
511C4×C11B(4,𝔽2)12yes—
512C25C23×C1111yescharacteristic
513C2×#41—21no—
514C22×Q8D4×C1111yescharacteristic, complemented
515C22×D4—21no—
516C22×D4—22no—
517C22×D4D4×C1111yescharacteristic, complemented
518C22×D4C23×C1111yescharacteristic
519C22×D4C23×C1112yes—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—44no—
527C23×C4D4×C1111yescharacteristic, complemented
528C23×C4C23×C1111yescharacteristic
529C23×C4C23×C1111yescharacteristic
530#126—22no—
531#126—22no—
532#126—22no—
533#125—21no—
534#125—22no—
535#124—21no—
536#124—22no—
537#123—22no—
538#123—22no—
539#123—22no—
540#123—22no—
541#123—22no—
542C22⋊Q8—21no—
543C22⋊Q8—22no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—44no—
549#121—21no—
550#121—22no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121—21no—
555#121—22no—
556#121—22no—
557#121—44no—
558#120—22no—
559#120—22no—
560#120—22no—
561#120—22no—
562#120—24no—
563#120—42no—
564C4×Q8—21no—
565C4×D4—22no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—44no—
576#117—21no—
577#117—22no—
578#117—22no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4D4×C1111yescharacteristic, complemented
584C2×C4⋊C4D4×C1111yescharacteristic, complemented
585C2×C4⋊C4D4×C1111yescharacteristic, complemented
586C2×C4⋊C4D4×C1112yescomplemented
587C2×C22⋊C4—22no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4D4×C1111yescharacteristic, complemented
597C2×C22⋊C4D4×C1112yescomplemented
598C2×C22⋊C4C23×C1112yes—
599C2×C22⋊C4C23×C1111yescharacteristic
600C2×C22⋊C4C23×C1112yes—
601C2×C22⋊C4C23×C1111yescharacteristic
602C2×C22⋊C4C23×C1112yes—
603C2×C22⋊C4C23×C1111yescharacteristic
604C2×C42—21no—
605C2×C42D4×C1111yescharacteristic, complemented
606#99—24no—
607#99—42no—
608#99—42no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95—22no—
613#95—22no—
614#95—21no—
615#95—21no—
616C2×C11—21no—
617C2×C11—21no—
618C2×C11—21no—
619C2×C11—21no—
620C2×C11—21no—
621C2×C11—21no—
622C2×C11—44no—
623C2×C11—81no—
624C2×C11—82no—
625C2×C11#240711yescharacteristic
626C2×C11C2×B(4,𝔽2)11yescharacteristic
627C2×C11#302511yescharacteristic
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—42no—
635C24—42no—
636C24C2×D4×C1112yes—
637C24C2×D4×C1111yescharacteristic
638C24C11×#4112yescomplemented
639C24C24×C1111yescharacteristic
640#41—82no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—42no—
644C2×D4—24no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4C2×D4×C1111yescharacteristic
698C22×C4C2×D4×C1112yes—
699C22×C4C2×D4×C1111yescharacteristic
700C22×C4C2×D4×C1111yescharacteristic
701C22×C4C2×D4×C1111yescharacteristic
702C22×C4C2×D4×C1111yescharacteristic
703C22×C4C2×D4×C1112yes—
704C22×C4C2×D4×C1111yescharacteristic
705C22×C4C2×D4×C1112yes—
706C22×C4C2×D4×C1111yescharacteristic
707C22×C4C2×D4×C1111yescharacteristic
708C22×C4C2×D4×C1111yescharacteristic
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—21no—
714C4⋊C4—22no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—22no—
720C4⋊C4—21no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—44no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—24no—
728C22⋊C4—22no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—21no—
733C22⋊C4—22no—
734C22⋊C4—21no—
735C22⋊C4—22no—
736C22⋊C4—21no—
737C22⋊C4—22no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—21no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—44no—
750C22⋊C4—42no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—42no—
754C22⋊C4C11×#4112yescomplemented
755C42—22no—
756C42—22no—
757C42—21no—
758C42—21no—
759C42—42no—
760C11#2414011yescharacteristic, direct product factor, Sylow
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C1111yescharacteristic
797C23C22×D4×C1111yescharacteristic
798C23C22×D4×C1111yescharacteristic
799C23C2×C11×#4111yescharacteristic
800C23C2×C11×#4111yescharacteristic
801C23C11×H(5,𝔽2)11yescharacteristic
802C23C11×2−1+411yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4C11×#12011yescharacteristic
867C2×C4C11×#12011yescharacteristic
868C2×C4C11×#12011yescharacteristic
869C2×C4C11×#12011yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×C11×#12011yescharacteristic
906C22C11×#52511yescharacteristic
907C22C11×#53711yescharacteristic
908C22C11×#54611yescharacteristic
909C22C11×#54711yescharacteristic
910C22C11×#54811yescharacteristic
911C22C11×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4C11×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C11×#240711yescharacteristic
937C2C2×C11×B(4,𝔽2)11yescharacteristic
938C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3505C2semidirect
2. C11×#2848C2semidirect
3. C11×#2847C2semidirect
4. C4×C11×#120C2semidirect
5. C11×#2044C2semidirect
6. C11×#2021C2semidirect
7. C11×#1996C2semidirect
8. C11×#1964C2semidirect
9. C11×#1889C2semidirect
10. C11×#1867C2semidirect
11. C11×#1799C2semidirect
57. C22×Q8×C11D4semidirect
60. C22×D4×C11D4semidirect
70. C23×C4×C11D4semidirect
126. C2×C11×C4⋊C4D4semidirect
127. C2×C11×C4⋊C4D4semidirect
128. C2×C11×C4⋊C4D4semidirect
129. C2×C11×C4⋊C4D4semidirect
139. C2×C11×C22⋊C4D4semidirect
140. C2×C11×C22⋊C4D4semidirect
148. C2×C42×C11D4semidirect
159. #24140C11direct (N × H)
170. C24×C11#41semidirect
286. C11×C22⋊C4#41semidirect
292. #3505C2×C11semidirect
293. #2848C2×C11semidirect
294. #2847C2×C11semidirect
295. C4×#120C2×C11semidirect
296. #2044C2×C11semidirect
297. #2021C2×C11semidirect
298. #1996C2×C11semidirect
299. #1964C2×C11semidirect
300. #1889C2×C11semidirect
301. #1867C2×C11semidirect
302. #1799C2×C11semidirect
514. C22×Q8D4×C11semidirect
517. C22×D4D4×C11semidirect
527. C23×C4D4×C11semidirect
583. C2×C4⋊C4D4×C11semidirect
584. C2×C4⋊C4D4×C11semidirect
585. C2×C4⋊C4D4×C11semidirect
586. C2×C4⋊C4D4×C11semidirect
596. C2×C22⋊C4D4×C11semidirect
597. C2×C22⋊C4D4×C11semidirect
605. C2×C42D4×C11semidirect
638. C24C11×#41semidirect
754. C22⋊C4C11×#41semidirect
760. C11#24140direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35052
C11×#28482
C11×#28472
C4×C11×#1202
C11×#20442
C11×#20212
C11×#19962
C11×#19642
C11×#18892
C11×#18672
C11×#17992
#2414011