Finite Group Databasebeta

← C11×#24056 #14601249

Subgroups — C11×#24056 #14601249

Order 2816.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3484C211yesmaximal, characteristic
2C11×#2849C212yesmaximal, complemented
3C2×C11×#386C211yesmaximal, characteristic, complemented
4C11×#2044C214yesmaximal, complemented
5C11×#1898C212yesmaximal, complemented
6C11×#1867C212yesmaximal, complemented
7C11×#1790C212yesmaximal, complemented
8C11×#1781C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic, complemented
12C11×#546—22no—
13C11×#546—22no—
14D42×C11—22no—
15D42×C11—22no—
16C11×#535—21no—
17C11×#534—21no—
18C11×#534C2212yes—
19C11×#525—21no—
20C2×C11×#123—22no—
21C2×C11×#120—21no—
22C2×C11×#120C2212yes—
23C11×#518C2211yescharacteristic
24C22×C11×C22⋊C4—21no—
25C22×C11×C22⋊C4C2211yescharacteristic, complemented
26C2×C11×#99C2212yes—
27C2×C11×#99C2214yescomplemented
28C2×C11×#99C2212yescomplemented
29C11×#386—21no—
30C11×#386—21no—
31C11×#386—22no—
32C11×#386C2212yes—
33C11×#386C2212yescomplemented
34C11×#386C2214yescomplemented
35C11×#385—22no—
36C11×#385C2214yescomplemented
37C11×#381—22no—
38C11×#379C2212yescomplemented
39C2×C11×#95—21no—
40C11×#342C2214yescomplemented
41C25×C11D411yescharacteristic
42C25×C11C2311yescharacteristic
43C11×H(5,𝔽2)—24no—
44C11×H(5,𝔽2)—42no—
45C2×C11×#41—21no—
46C2×C11×#41—22no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—24no—
54C22×D4×C11—42no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11D411yescharacteristic
57C22×D4×C11D412yes—
58C22×D4×C11D412yes—
59C22×D4×C11C2312yes—
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—22no—
64C23×C4×C11—21no—
65C23×C4×C11—22no—
66C23×C4×C11—21no—
67C23×C4×C11—44no—
68C23×C4×C11D411yescharacteristic
69C23×C4×C11C2312yes—
70C11×#127—22no—
71C11×#124—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—48no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—22no—
86C11×#120—22no—
87C11×#120—22no—
88C11×#120—22no—
89C11×#120—22no—
90C11×#120—22no—
91C11×#120—22no—
92C11×#120—22no—
93C11×#120—22no—
94C11×#120—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C11×#117—21no—
100C2×C11×C4⋊C4—24no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4—44no—
112C2×C11×C22⋊C4D412yes—
113C2×C11×C22⋊C4D412yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2312yes—
117C11×#99—24no—
118C11×#99—42no—
119C11×#99—44no—
120C11×#95—22no—
121C11×#95—22no—
122C11×#95—24no—
123C11×#95—24no—
124#24056C1111yesmaximal, characteristic, direct product factor, Sylow
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—21no—
128C24×C11—22no—
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—42no—
132C24×C11—42no—
133C24×C11—41no—
134C24×C11—42no—
135C24×C11—42no—
136C24×C11C2×D411yescharacteristic
137C24×C11C2×D412yes—
138C24×C11C2×D412yes—
139C24×C11C2×D411yescharacteristic
140C24×C11C2×D412yes—
141C24×C11C2×D411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C24×C11C2411yescharacteristic
144C11×#41—48no—
145C11×#41—42no—
146C11×#41—42no—
147C2×Q8×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—21no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—24no—
162C2×D4×C11—22no—
163C2×D4×C11—24no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—41no—
170C2×D4×C11—41no—
171C2×D4×C11—48no—
172C2×D4×C11—48no—
173C2×D4×C11—48no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11—44no—
177C2×D4×C11—44no—
178C2×D4×C11—82no—
179C2×D4×C11—82no—
180C2×D4×C11#4114yes—
181C22×C4×C11—21no—
182C22×C4×C11—24no—
183C22×C4×C11—22no—
184C22×C4×C11—28no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—22no—
188C22×C4×C11—24no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—22no—
192C22×C4×C11—24no—
193C22×C4×C11—22no—
194C22×C4×C11—44no—
195C22×C4×C11—41no—
196C22×C4×C11—44no—
197C22×C4×C11—48no—
198C22×C4×C11—42no—
199C22×C4×C11—44no—
200C22×C4×C11—42no—
201C22×C4×C11—41no—
202C22×C4×C11—41no—
203C22×C4×C11—42no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—48no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—44no—
231C11×C22⋊C4—44no—
232C11×C22⋊C4—48no—
233C11×C22⋊C4—44no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—44no—
236C42×C11—22no—
237#3484C2×C1111yescharacteristic
238#2849C2×C1112yescomplemented
239C2×#386C2×C1111yescharacteristic, complemented
240#2044C2×C1114yescomplemented
241#1898C2×C1112yescomplemented
242#1867C2×C1112yescomplemented
243#1790C2×C1112yescomplemented
244#1781C2×C1111yescharacteristic, complemented
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—22no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—24no—
262C23×C11—42no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—42no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—48no—
271C23×C11—48no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—48no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—81no—
283C23×C11—81no—
284C23×C11—84no—
285C23×C11—81no—
286C23×C11—81no—
287C23×C11#12012yes—
288C23×C11#12011yescharacteristic
289C23×C11#12011yescharacteristic
290C23×C11#12312yescomplemented
291C23×C11C22×D411yescharacteristic
292C23×C11C22×D412yes—
293C23×C11C2×#4112yes—
294C23×C11H(5,𝔽2)12yes—
295Q8×C11—42no—
296D4×C11—28no—
297D4×C11—44no—
298D4×C11—42no—
299D4×C11—44no—
300D4×C11—44no—
301D4×C11—42no—
302D4×C11—42no—
303D4×C11—44no—
304D4×C11—44no—
305D4×C11—44no—
306D4×C11—44no—
307D4×C11—82no—
308D4×C11—82no—
309D4×C11—82no—
310D4×C11—82no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—24no—
314C2×C4×C11—28no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—24no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11—42no—
327C2×C4×C11—44no—
328C2×C4×C11—48no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—44no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—44no—
335C2×C4×C11—42no—
336C2×C4×C11—44no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—44no—
340C2×C4×C11—81no—
341C2×C4×C11—81no—
342C2×C4×C11—84no—
343C2×C4×C11#12312yescomplemented
344C2×H(5,𝔽2)C22×C1111yescharacteristic
345C23×D4C22×C1111yescharacteristic
346C24×C4C22×C1111yescharacteristic, complemented
347#546—22no—
348#546—22no—
349D42—22no—
350D42—22no—
351#535—21no—
352#534—21no—
353#534C22×C1112yes—
354#525—21no—
355C2×#123—22no—
356C2×#120—21no—
357C2×#120C22×C1112yes—
358#518C22×C1111yescharacteristic
359C22×C22⋊C4—21no—
360C22×C22⋊C4C22×C1111yescharacteristic, complemented
361C2×#99C22×C1112yes—
362C2×#99C22×C1114yescomplemented
363C2×#99C22×C1112yescomplemented
364#386—22no—
365#386—21no—
366#386—21no—
367#386C22×C1112yes—
368#386C22×C1114yescomplemented
369#386C22×C1112yescomplemented
370#385—22no—
371#385C22×C1114yescomplemented
372#381—22no—
373#379C22×C1112yescomplemented
374C2×#95—21no—
375#342C22×C1114yescomplemented
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—22no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—22no—
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—48no—
393C22×C11—48no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—42no—
401C22×C11—41no—
402C22×C11—42no—
403C22×C11—41no—
404C22×C11—42no—
405C22×C11—41no—
406C22×C11—81no—
407C22×C11—84no—
408C22×C11—84no—
409C22×C11—84no—
410C22×C11—81no—
411C22×C11—162no—
412C22×C11B(4,𝔽2)12yes—
413C22×C11#45812yes—
414C22×C11C2×#12011yescharacteristic
415C22×C11C2×#12311yescharacteristic
416C22×C11#53411yescharacteristic
417C22×C11#54614yes—
418C4×C11—22no—
419C4×C11—41no—
420C4×C11—42no—
421C4×C11—44no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—84no—
425C4×C11—82no—
426C25D4×C1111yescharacteristic
427C25C23×C1111yescharacteristic
428H(5,𝔽2)—24no—
429H(5,𝔽2)—42no—
430C2×#41—21no—
431C2×#41—22no—
432C22×D4—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—24no—
439C22×D4—42no—
440C22×D4D4×C1111yescharacteristic
441C22×D4D4×C1111yescharacteristic
442C22×D4D4×C1112yes—
443C22×D4D4×C1112yes—
444C22×D4C23×C1112yes—
445C22×D4C23×C1111yescharacteristic
446C22×D4C23×C1111yescharacteristic
447C23×C4—21no—
448C23×C4—22no—
449C23×C4—21no—
450C23×C4—22no—
451C23×C4—21no—
452C23×C4—44no—
453C23×C4D4×C1111yescharacteristic
454C23×C4C23×C1112yes—
455#127—22no—
456#124—22no—
457#123—22no—
458#123—22no—
459#123—22no—
460#123—48no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463#121—21no—
464#121—21no—
465#121—22no—
466#121—22no—
467#121—22no—
468#121—22no—
469#121—22no—
470#121—22no—
471#120—22no—
472#120—22no—
473#120—22no—
474#120—22no—
475#120—22no—
476#120—22no—
477#120—22no—
478#120—22no—
479#120—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—22no—
484#117—21no—
485C2×C4⋊C4—24no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—44no—
497C2×C22⋊C4D4×C1112yes—
498C2×C22⋊C4D4×C1112yes—
499C2×C22⋊C4C23×C1112yes—
500C2×C22⋊C4C23×C1114yes—
501C2×C22⋊C4C23×C1112yes—
502#99—24no—
503#99—42no—
504#99—44no—
505#95—22no—
506#95—22no—
507#95—24no—
508#95—24no—
509C2×C11—21no—
510C2×C11—24no—
511C2×C11—21no—
512C2×C11—22no—
513C2×C11—22no—
514C2×C11—42no—
515C2×C11—42no—
516C2×C11—81no—
517C2×C11—82no—
518C2×C11#240511yescharacteristic
519C2×C11C2×B(4,𝔽2)11yescharacteristic
520C2×C11C2×#45811yescharacteristic
521C24—22no—
522C24—22no—
523C24—21no—
524C24—22no—
525C24—21no—
526C24—21no—
527C24—42no—
528C24—42no—
529C24—41no—
530C24—42no—
531C24—42no—
532C24C2×D4×C1111yescharacteristic
533C24C2×D4×C1112yes—
534C24C2×D4×C1112yes—
535C24C2×D4×C1111yescharacteristic
536C24C2×D4×C1112yes—
537C24C2×D4×C1111yescharacteristic
538C24C2×D4×C1111yescharacteristic
539C24C24×C1111yescharacteristic
540#41—48no—
541#41—42no—
542#41—42no—
543C2×Q8—21no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—24no—
558C2×D4—22no—
559C2×D4—24no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4C11×#4114yes—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—44no—
591C22×C4—41no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—42no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×D4×C1112yes—
603C22×C4C2×D4×C1111yescharacteristic
604C22×C4C2×D4×C1111yescharacteristic
605C22×C4C2×D4×C1112yes—
606C22×C4C2×D4×C1112yes—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—48no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—48no—
629C22⋊C4—42no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C42—22no—
633C11#2405611yescharacteristic, direct product factor, Sylow
634C23—21no—
635C23—21no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23C11×#12012yes—
677C23C11×#12011yescharacteristic
678C23C11×#12011yescharacteristic
679C23C11×#12312yescomplemented
680C23C22×D4×C1111yescharacteristic
681C23C22×D4×C1112yes—
682C23C2×C11×#4112yes—
683C23C11×H(5,𝔽2)12yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4C11×#12312yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C11×B(4,𝔽2)12yes—
770C22C11×#45812yes—
771C22C2×C11×#12011yescharacteristic
772C22C2×C11×#12311yescharacteristic
773C22C11×#53411yescharacteristic
774C22C11×#54614yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C11×#240511yescharacteristic
793C2C2×C11×B(4,𝔽2)11yescharacteristic
794C2C2×C11×#45811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC11×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2849C2semidirect
3. C2×C11×#386C2semidirect
4. C11×#2044C2semidirect
5. C11×#1898C2semidirect
6. C11×#1867C2semidirect
7. C11×#1790C2semidirect
8. C11×#1781C2semidirect
11. C24×C4×C11C22semidirect
25. C22×C11×C22⋊C4C22semidirect
27. C2×C11×#99C22semidirect
28. C2×C11×#99C22semidirect
33. C11×#386C22semidirect
34. C11×#386C22semidirect
36. C11×#385C22semidirect
38. C11×#379C22semidirect
40. C11×#342C22semidirect
124. #24056C11direct (N × H)
238. #2849C2×C11semidirect
239. C2×#386C2×C11semidirect
240. #2044C2×C11semidirect
241. #1898C2×C11semidirect
242. #1867C2×C11semidirect
243. #1790C2×C11semidirect
244. #1781C2×C11semidirect
290. C23×C11#123semidirect
343. C2×C4×C11#123semidirect
346. C24×C4C22×C11semidirect
360. C22×C22⋊C4C22×C11semidirect
362. C2×#99C22×C11semidirect
363. C2×#99C22×C11semidirect
368. #386C22×C11semidirect
369. #386C22×C11semidirect
371. #385C22×C11semidirect
373. #379C22×C11semidirect
375. #342C22×C11semidirect
633. C11#24056direct (N × H)
679. C23C11×#123semidirect
732. C2×C4C11×#123semidirect

Maximal subgroups

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

subgroupindex
C11×#34842
C11×#28492
C2×C11×#3862
C11×#20442
C11×#18982
C11×#18672
C11×#17902
C11×#17812
#2405611