Finite Group Databasebeta

← C11×#24415 #14601608

Subgroups — C11×#24415 #14601608

Order 2816.

1402 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3485C211yesmaximal, characteristic
2C11×#3056C212yesmaximal, complemented
3C2×C11×#455C211yesmaximal, characteristic, complemented
4C2×C11×#413C211yesmaximal, characteristic, complemented
5C11×#2432C211yesmaximal, characteristic, complemented
6C11×#2038C212yesmaximal, complemented
7C11×#2005C212yesmaximal, complemented
8C11×#1885C211yesmaximal, characteristic, complemented
9C11×#1871C212yesmaximal, complemented
10C11×#1856C211yesmaximal, characteristic, complemented
11C11×#1792C211yesmaximal, characteristic, complemented
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C2×C11×#137C2212yes—
15C22×C11×M16C2212yescomplemented
16C11×#547—22no—
17C11×#547—22no—
18C11×#546—22no—
19C11×#546—22no—
20C11×#536C2212yes—
21C11×#534—22no—
22C2×C11×C4⋊Q8C2211yescharacteristic, complemented
23C2×C11×#124C2211yescharacteristic
24C11×#525C2212yes—
25C2×C11×#123—22no—
26C2×C11×C22⋊Q8C2211yescharacteristic, complemented
27C11×#518C2211yescharacteristic
28C11×#470—22no—
29C11×#468—22no—
30C11×#467—22no—
31C11×#465—22no—
32C11×#455—24no—
33C11×#428C2212yescomplemented
34C2×C11×#104C2212yes—
35C2×C11×#104C2212yes—
36C11×#419C2212yescomplemented
37C11×#417C2212yes—
38C11×#413—24no—
39C2×C11×#101C2212yescomplemented
40C2×C11×#100C2211yescharacteristic
41C2×C11×#100C2211yescharacteristic
42C11×#394—22no—
43C11×#391C2211yescharacteristic, complemented
44C11×#390C2211yescharacteristic
45C11×#385—22no—
46C4×C11×C22⋊C4C2211yescharacteristic, complemented
47C11×#339C2212yescomplemented
48C11×#339C2212yescomplemented
49C11×H(5,𝔽2)—22no—
50C11×H(5,𝔽2)—22no—
51C11×H(5,𝔽2)—42no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41—22no—
56C2×C11×#41—22no—
57C2×C11×#41—42no—
58C2×C11×#41C2312yes—
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11D412yes—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11D412yes—
66C23×C4×C11C2311yescharacteristic
67C11×#137—24no—
68C11×#137—42no—
69C2×C11×Q16—22no—
70C2×C11×SD16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—24no—
73C2×C11×M16—42no—
74C2×C11×M16C2312yes—
75C2×C11×M16C2312yes—
76C22×C8×C11—22no—
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8—42no—
79C11×#124—22no—
80C11×#124—22no—
81C11×#124—22no—
82C11×#123—24no—
83C11×#123—24no—
84C11×#123—24no—
85C11×#123—22no—
86C11×#123—24no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8D412yes—
92C11×C22⋊Q8D412yes—
93C11×#121—24no—
94C11×#121—24no—
95C11×#121D412yes—
96C11×#121D412yes—
97C11×#120—24no—
98C11×#120—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C11×#117C2312yes—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C11×#107—22no—
119C11×#106—22no—
120C11×#104—24no—
121C11×#104—42no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#103—22no—
125C11×#102—22no—
126C11×#101—24no—
127C11×#100—22no—
128C11×#100D414yescomplemented
129C11×#95—21no—
130C11×#95—22no—
131#24415C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—22no—
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D412yes—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—44no—
140C11×#41—44no—
141C11×#41—44no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—21no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11C2×D412yes—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—24no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—42no—
163C2×D4×C11—44no—
164C2×D4×C11—44no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C2×D4×C11C2×D412yes—
168C2×D4×C11C2×D412yes—
169C2×D4×C11#4112yes—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—24no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—42no—
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2411yescharacteristic
190C11×Q16—44no—
191C11×SD16—44no—
192C11×M16—22no—
193C11×M16—22no—
194C11×M16—22no—
195C11×M16—44no—
196C11×M16C2×D414yes—
197C2×C8×C11—22no—
198C2×C8×C11—22no—
199C2×C8×C11—44no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—44no—
206C11×C4⋊C4—41no—
207C11×C4⋊C4—41no—
208C11×C4⋊C4C2×D412yes—
209C11×C4⋊C4C2×D412yes—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—44no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—44no—
222C42×C11—22no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—22no—
226#3485C2×C1111yescharacteristic
227#3056C2×C1112yescomplemented
228C2×#455C2×C1111yescharacteristic, complemented
229C2×#413C2×C1111yescharacteristic, complemented
230#2432C2×C1111yescharacteristic, complemented
231#2038C2×C1112yescomplemented
232#2005C2×C1112yescomplemented
233#1885C2×C1111yescharacteristic, complemented
234#1871C2×C1112yescomplemented
235#1856C2×C1111yescharacteristic, complemented
236#1792C2×C1111yescharacteristic, complemented
237C23×C11—22no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—44no—
247C23×C11—82no—
248C23×C11—82no—
249C23×C11#12012yes—
250C23×C11#12114yes—
251C23×C11C22×D411yescharacteristic
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—42no—
255Q8×C11—42no—
256Q8×C11—42no—
257Q8×C11—42no—
258D4×C11—24no—
259D4×C11—22no—
260D4×C11—24no—
261D4×C11—22no—
262D4×C11—48no—
263D4×C11—48no—
264D4×C11—42no—
265D4×C11—42no—
266D4×C11—82no—
267D4×C11—82no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—44no—
282C2×C4×C11—44no—
283C2×C4×C11—41no—
284C2×C4×C11—44no—
285C2×C4×C11—41no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—41no—
289C2×C4×C11—42no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—82no—
297C2×C4×C11—82no—
298C2×C4×C11#12011yescharacteristic
299C2×C4×C11#12011yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D412yes—
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11H(5,𝔽2)12yes—
304C8×C11—24no—
305C8×C11—42no—
306C2×H(5,𝔽2)C22×C1111yescharacteristic
307C22×#41C22×C1111yescharacteristic
308C2×#137C22×C1112yes—
309C22×M16C22×C1112yescomplemented
310#547—22no—
311#547—22no—
312#546—22no—
313#546—22no—
314#536C22×C1112yes—
315#534—22no—
316C2×C4⋊Q8C22×C1111yescharacteristic, complemented
317C2×#124C22×C1111yescharacteristic
318#525C22×C1112yes—
319C2×#123—22no—
320C2×C22⋊Q8C22×C1111yescharacteristic, complemented
321#518C22×C1111yescharacteristic
322#470—22no—
323#468—22no—
324#467—22no—
325#465—22no—
326#455—24no—
327#428C22×C1112yescomplemented
328C2×#104C22×C1112yes—
329C2×#104C22×C1112yes—
330#419C22×C1112yescomplemented
331#417C22×C1112yes—
332#413—24no—
333C2×#101C22×C1112yescomplemented
334C2×#100C22×C1111yescharacteristic
335C2×#100C22×C1111yescharacteristic
336#394—22no—
337#391C22×C1111yescharacteristic, complemented
338#390C22×C1111yescharacteristic
339#385—22no—
340C4×C22⋊C4C22×C1111yescharacteristic, complemented
341#339C22×C1112yescomplemented
342#339C22×C1112yescomplemented
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—22no—
346C22×C11—24no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—44no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—81no—
356C22×C11—82no—
357C22×C11—81no—
358C22×C11—164no—
359C22×C11C2×#12011yescharacteristic
360C22×C11C2×#12111yescharacteristic
361C22×C11#53411yescharacteristic
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11D4212yes—
373C4×C11#54612yes—
374H(5,𝔽2)—22no—
375H(5,𝔽2)—22no—
376H(5,𝔽2)—42no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—22no—
382C2×#41—42no—
383C2×#41C23×C1112yes—
384C22×Q8C23×C1111yescharacteristic
385C22×Q8C23×C1111yescharacteristic
386C22×D4—22no—
387C22×D4—22no—
388C22×D4D4×C1112yes—
389C22×D4C23×C1111yescharacteristic
390C23×C4D4×C1112yes—
391C23×C4C23×C1111yescharacteristic
392#137—24no—
393#137—42no—
394C2×Q16—22no—
395C2×SD16—22no—
396C2×M16—22no—
397C2×M16—24no—
398C2×M16—42no—
399C2×M16C23×C1112yes—
400C2×M16C23×C1112yes—
401C22×C8—22no—
402C4⋊Q8—22no—
403C4⋊Q8—42no—
404#124—22no—
405#124—22no—
406#124—22no—
407#123—24no—
408#123—24no—
409#123—24no—
410#123—22no—
411#123—24no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8D4×C1112yes—
417C22⋊Q8D4×C1112yes—
418#121—24no—
419#121—24no—
420#121D4×C1112yes—
421#121D4×C1112yes—
422#120—24no—
423#120—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428#117C23×C1112yes—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C42C23×C1111yescharacteristic
442C2×C42C23×C1111yescharacteristic
443#107—22no—
444#106—22no—
445#104—24no—
446#104—42no—
447#103—22no—
448#103—22no—
449#103—22no—
450#102—22no—
451#101—24no—
452#100—22no—
453#100D4×C1114yescomplemented
454#95—21no—
455#95—22no—
456C2×C11—21no—
457C2×C11—21no—
458C2×C11—42no—
459C2×C11—44no—
460C2×C11—82no—
461C2×C11#241011yescharacteristic
462C2×C11#301811yescharacteristic
463C2×C11#302211yescharacteristic
464C24—22no—
465C24C2×D4×C1111yescharacteristic
466C24C2×D4×C1112yes—
467#41—22no—
468#41—22no—
469#41—22no—
470#41—22no—
471#41—44no—
472#41—44no—
473#41—44no—
474#41—44no—
475#41—44no—
476#41—44no—
477C2×Q8—21no—
478C2×Q8—22no—
479C2×Q8—21no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—22no—
485C2×Q8C2×D4×C1112yes—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—42no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4C2×D4×C1112yes—
500C2×D4C2×D4×C1112yes—
501C2×D4C11×#4112yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4C2×D4×C1112yes—
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C2×D4×C1112yes—
520C22×C4C2×D4×C1112yes—
521C22×C4C24×C1111yescharacteristic
522Q16—44no—
523SD16—44no—
524M16—22no—
525M16—22no—
526M16—22no—
527M16—44no—
528M16C2×D4×C1114yes—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—44no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—44no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4C2×D4×C1112yes—
541C4⋊C4C2×D4×C1112yes—
542C22⋊C4—24no—
543C22⋊C4—24no—
544C22⋊C4—24no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—44no—
552C22⋊C4—42no—
553C22⋊C4—44no—
554C42—22no—
555C42—21no—
556C42—21no—
557C42—22no—
558C11#2441511yescharacteristic, direct product factor, Sylow
559C23—22no—
560C23—21no—
561C23—21no—
562C23—22no—
563C23—22no—
564C23—41no—
565C23—41no—
566C23—42no—
567C23—42no—
568C23—44no—
569C23—82no—
570C23—82no—
571C23C11×#12012yes—
572C23C11×#12114yes—
573C23C22×D4×C1111yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—42no—
577Q8—42no—
578Q8—42no—
579Q8—42no—
580D4—24no—
581D4—22no—
582D4—24no—
583D4—22no—
584D4—48no—
585D4—48no—
586D4—42no—
587D4—42no—
588D4—82no—
589D4—82no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—41no—
606C2×C4—44no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—82no—
619C2×C4—82no—
620C2×C4C11×#12011yescharacteristic
621C2×C4C11×#12011yescharacteristic
622C2×C4C22×D4×C1111yescharacteristic
623C2×C4C22×D4×C1112yes—
624C2×C4C2×C11×#4111yescharacteristic
625C2×C4C11×H(5,𝔽2)12yes—
626C8—24no—
627C8—42no—
628C22—21no—
629C22—21no—
630C22—22no—
631C22—24no—
632C22—22no—
633C22—22no—
634C22—44no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—81no—
641C22—82no—
642C22—81no—
643C22—164no—
644C22C2×C11×#12011yescharacteristic
645C22C2×C11×#12111yescharacteristic
646C22C11×#53411yescharacteristic
647C4—21no—
648C4—21no—
649C4—42no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4D42×C1112yes—
658C4C11×#54612yes—
659C2—21no—
660C2—21no—
661C2—42no—
662C2—44no—
663C2—82no—
664C2C11×#241011yescharacteristic
665C2C11×#301811yescharacteristic
666C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3485C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3056C2semidirect
3. C2×C11×#455C2semidirect
4. C2×C11×#413C2semidirect
5. C11×#2432C2semidirect
6. C11×#2038C2semidirect
7. C11×#2005C2semidirect
8. C11×#1885C2semidirect
9. C11×#1871C2semidirect
10. C11×#1856C2semidirect
11. C11×#1792C2semidirect
15. C22×C11×M16C22semidirect
22. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
33. C11×#428C22semidirect
36. C11×#419C22semidirect
39. C2×C11×#101C22semidirect
43. C11×#391C22semidirect
46. C4×C11×C22⋊C4C22semidirect
47. C11×#339C22semidirect
48. C11×#339C22semidirect
128. C11×#100D4semidirect
131. #24415C11direct (N × H)
227. #3056C2×C11semidirect
228. C2×#455C2×C11semidirect
229. C2×#413C2×C11semidirect
230. #2432C2×C11semidirect
231. #2038C2×C11semidirect
232. #2005C2×C11semidirect
233. #1885C2×C11semidirect
234. #1871C2×C11semidirect
235. #1856C2×C11semidirect
236. #1792C2×C11semidirect
309. C22×M16C22×C11semidirect
316. C2×C4⋊Q8C22×C11semidirect
320. C2×C22⋊Q8C22×C11semidirect
327. #428C22×C11semidirect
330. #419C22×C11semidirect
333. C2×#101C22×C11semidirect
337. #391C22×C11semidirect
340. C4×C22⋊C4C22×C11semidirect
341. #339C22×C11semidirect
342. #339C22×C11semidirect
453. #100D4×C11semidirect
558. C11#24415direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34852
C11×#30562
C2×C11×#4552
C2×C11×#4132
C11×#24322
C11×#20382
C11×#20052
C11×#18852
C11×#18712
C11×#18562
C11×#17922
#2441511