Finite Group Databasebeta

← C11×#24372 #14601565

Subgroups — C11×#24372 #14601565

Order 2816.

1698 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C11×#459C212yesmaximal, complemented
3C2×C11×#449C211yesmaximal, characteristic, complemented
4C11×#2433C211yesmaximal, characteristic, complemented
5C11×#2339C211yesmaximal, characteristic, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#2014C212yesmaximal, complemented
8C11×#1895C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal, complemented
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C2×C11×AGL(1,ℤ/8)—24no—
15C2×C11×AGL(1,ℤ/8)—28no—
16C22×C11×SD16C2212yes—
17C22×C11×SD16C2211yescharacteristic, complemented
18C22×C11×D8C2212yes—
19C22×C11×D8C2211yescharacteristic, complemented
20C22×C11×M16C2211yescharacteristic
21C2×C11×#127C2212yes—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120—22no—
24C2×C4×D4×C11C2212yescomplemented
25C11×#459—28no—
26C11×#449—24no—
27C2×C11×C4⋊C8C2212yescomplemented
28C2×C11×#103C2211yescharacteristic, complemented
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2211yescharacteristic, complemented
32C2×C11×#102C2212yescomplemented
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#392—21no—
35C11×#392—21no—
36C11×#391C2212yescomplemented
37C11×#390C2212yes—
38C11×#386—22no—
39C11×#381—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C22⋊C4C2211yescharacteristic
42C2×C11×#95—21no—
43C11×#340C2212yescomplemented
44C11×#336C2212yescomplemented
45C25×C11—21no—
46C2×C11×#41—22no—
47C2×C11×#41—24no—
48C2×C11×#41—42no—
49C2×C11×#41D414yescomplemented
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—42no—
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2312yes—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—22no—
65C23×C4×C11C2311yescharacteristic
66C11×AGL(1,ℤ/8)—232no—
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16—22no—
70C2×C11×SD16—24no—
71C2×C11×SD16—42no—
72C2×C11×D8—24no—
73C2×C11×D8—24no—
74C2×C11×D8—22no—
75C2×C11×D8—24no—
76C2×C11×D8D418yescomplemented
77C2×C11×M16—22no—
78C2×C11×M16—24no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2312yes—
82C11×#127—24no—
83C11×#127—42no—
84C11×#121—22no—
85C11×#121—22no—
86C11×#120—48no—
87C4×D4×C11—24no—
88C4×D4×C11—42no—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4D412yes—
97C2×C42×C11C2312yes—
98C11×C4⋊C8—24no—
99C11×#103—22no—
100C11×#102—24no—
101C11×#102—22no—
102C11×#102—24no—
103C11×#102—42no—
104C11×C22⋊C8—22no—
105C11×#95—21no—
106C11×#95—22no—
107C11×#95—22no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110#24372C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—44no—
115C24×C11—44no—
116C24×C11—42no—
117C24×C11—81no—
118C24×C11—81no—
119C24×C11C2×D411yescharacteristic
120C11×#41—28no—
121C11×#41—44no—
122C11×#41—48no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11C2×D412yes—
127C2×D4×C11—28no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—48no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—44no—
151C2×D4×C11—82no—
152C2×D4×C11—82no—
153C2×D4×C11C2×D414yes—
154C2×D4×C11C2×D412yes—
155C2×D4×C11C2×D414yes—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—44no—
163C22×C4×C11—44no—
164C22×C4×C11—44no—
165C22×C4×C11—82no—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11#4112yes—
171C22×C4×C11C2411yescharacteristic
172C11×SD16—216no—
173C11×SD16—44no—
174C11×D8—216no—
175C11×D8—44no—
176C11×M16—28no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11C2×D414yes—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—44no—
190C11×C22⋊C4—44no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—44no—
193C11×C22⋊C4—81no—
194C42×C11—22no—
195C42×C11—22no—
196C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
197C2×#459C2×C1112yescomplemented
198C2×#449C2×C1111yescharacteristic, complemented
199#2433C2×C1111yescharacteristic, complemented
200#2339C2×C1111yescharacteristic, complemented
201#2055C2×C1112yescomplemented
202#2014C2×C1112yescomplemented
203#1895C2×C1111yescharacteristic, complemented
204#1879C2×C1112yescomplemented
205#1851C2×C1111yescharacteristic, complemented
206#1786C2×C1111yescharacteristic, complemented
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—24no—
214C23×C11—48no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—41no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—84no—
230C23×C11—84no—
231C23×C11—88no—
232C23×C11—88no—
233C23×C11#12112yes—
234C23×C11C22×D411yescharacteristic
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—42no—
238D4×C11—24no—
239D4×C11—22no—
240D4×C11—24no—
241D4×C11—24no—
242D4×C11—48no—
243D4×C11—48no—
244D4×C11—41no—
245D4×C11—42no—
246D4×C11—41no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—88no—
250D4×C11—88no—
251D4×C11—84no—
252D4×C11#12014yescomplemented
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—48no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—88no—
271C2×C4×C11#12112yes—
272C2×C4×C11AGL(1,ℤ/8)14yescomplemented
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D412yes—
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)12yes—
277C8×C11—24no—
278C8×C11—41no—
279C8×C11—41no—
280C22×#41C22×C1111yescharacteristic
281C23×D4C22×C1111yescharacteristic
282C2×AGL(1,ℤ/8)—24no—
283C2×AGL(1,ℤ/8)—28no—
284C22×SD16C22×C1112yes—
285C22×SD16C22×C1111yescharacteristic, complemented
286C22×D8C22×C1112yes—
287C22×D8C22×C1111yescharacteristic, complemented
288C22×M16C22×C1111yescharacteristic
289C2×#127C22×C1112yes—
290C2×#121C22×C1111yescharacteristic
291C2×#120—22no—
292C2×C4×D4C22×C1112yescomplemented
293#459—28no—
294#449—24no—
295C2×C4⋊C8C22×C1112yescomplemented
296C2×#103C22×C1111yescharacteristic, complemented
297C2×#102C22×C1112yes—
298C2×#102C22×C1112yes—
299C2×#102C22×C1111yescharacteristic, complemented
300C2×#102C22×C1112yescomplemented
301C2×C22⋊C8C22×C1111yescharacteristic
302#392—21no—
303#392—21no—
304#391C22×C1112yescomplemented
305#390C22×C1112yes—
306#386—22no—
307#381—21no—
308#380C22×C1111yescharacteristic
309C4×C22⋊C4C22×C1111yescharacteristic
310C2×#95—21no—
311#340C22×C1112yescomplemented
312#336C22×C1112yescomplemented
313C22×C11—22no—
314C22×C11—24no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—816no—
327C22×C11—82no—
328C22×C11—82no—
329C22×C11—82no—
330C22×C11—82no—
331C22×C11—81no—
332C22×C11—82no—
333C22×C11—82no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11C2×#12111yescharacteristic
337C22×C11D4212yes—
338C22×C11C2×AGL(1,ℤ/8)12yes—
339C22×C11#57611yescharacteristic
340C22×C11#57711yescharacteristic
341C4×C11—22no—
342C4×C11—24no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—82no—
346C4×C11—81no—
347C4×C11C2×#12011yescharacteristic
348C4×C11#53411yescharacteristic
349C4×C11#54612yes—
350C25—21no—
351C2×#41—22no—
352C2×#41—24no—
353C2×#41—42no—
354C2×#41D4×C1114yescomplemented
355C22×Q8C23×C1111yescharacteristic
356C22×D4—24no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—22no—
360C22×D4—21no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—42no—
365C22×D4C23×C1111yescharacteristic
366C22×D4C23×C1112yes—
367C22×D4C23×C1111yescharacteristic
368C23×C4—21no—
369C23×C4—22no—
370C23×C4C23×C1111yescharacteristic
371AGL(1,ℤ/8)—232no—
372C2×SD16—24no—
373C2×SD16—24no—
374C2×SD16—22no—
375C2×SD16—24no—
376C2×SD16—42no—
377C2×D8—24no—
378C2×D8—24no—
379C2×D8—22no—
380C2×D8—24no—
381C2×D8D4×C1118yescomplemented
382C2×M16—22no—
383C2×M16—24no—
384C22×C8C23×C1111yescharacteristic
385C22×C8C23×C1111yescharacteristic
386C22×C8C23×C1112yes—
387#127—24no—
388#127—42no—
389#121—22no—
390#121—22no—
391#120—48no—
392C4×D4—24no—
393C4×D4—42no—
394C2×C4⋊C4C23×C1112yes—
395C2×C4⋊C4C23×C1111yescharacteristic
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4D4×C1112yes—
402C2×C42C23×C1112yes—
403C4⋊C8—24no—
404#103—22no—
405#102—24no—
406#102—22no—
407#102—24no—
408#102—42no—
409C22⋊C8—22no—
410#95—21no—
411#95—22no—
412#95—22no—
413#95D4×C1111yescharacteristic
414#95D4×C1111yescharacteristic
415C2×C11—42no—
416C2×C11—44no—
417C2×C11—84no—
418C2×C11—161no—
419C2×C11#241011yescharacteristic
420C2×C11#303811yescharacteristic
421C2×C11#304511yescharacteristic
422C2×C11#326412yes—
423C2×C11#327212yes—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—44no—
428C24—44no—
429C24—42no—
430C24—81no—
431C24—81no—
432C24C2×D4×C1111yescharacteristic
433#41—28no—
434#41—44no—
435#41—48no—
436C2×Q8—21no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8C2×D4×C1112yes—
440C2×D4—28no—
441C2×D4—24no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—48no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—44no—
464C2×D4—82no—
465C2×D4—82no—
466C2×D4C2×D4×C1114yes—
467C2×D4C2×D4×C1112yes—
468C2×D4C2×D4×C1114yes—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—82no—
479C22×C4C2×D4×C1112yes—
480C22×C4C2×D4×C1111yescharacteristic
481C22×C4C2×D4×C1112yes—
482C22×C4C2×D4×C1112yes—
483C22×C4C11×#4112yes—
484C22×C4C24×C1111yescharacteristic
485SD16—216no—
486SD16—44no—
487D8—216no—
488D8—44no—
489M16—28no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8C2×D4×C1114yes—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—44no—
503C22⋊C4—44no—
504C22⋊C4—42no—
505C22⋊C4—44no—
506C22⋊C4—81no—
507C42—22no—
508C42—22no—
509C11#2437211yescharacteristic, direct product factor, Sylow
510C23—22no—
511C23—24no—
512C23—22no—
513C23—22no—
514C23—21no—
515C23—21no—
516C23—24no—
517C23—48no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—41no—
528C23—42no—
529C23—42no—
530C23—41no—
531C23—41no—
532C23—84no—
533C23—84no—
534C23—88no—
535C23—88no—
536C23C11×#12112yes—
537C23C22×D4×C1111yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—42no—
541D4—24no—
542D4—22no—
543D4—24no—
544D4—24no—
545D4—48no—
546D4—48no—
547D4—41no—
548D4—42no—
549D4—41no—
550D4—42no—
551D4—42no—
552D4—88no—
553D4—88no—
554D4—84no—
555D4C11×#12014yescomplemented
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—48no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—88no—
574C2×C4C11×#12112yes—
575C2×C4C11×AGL(1,ℤ/8)14yescomplemented
576C2×C4C22×D4×C1111yescharacteristic
577C2×C4C22×D4×C1112yes—
578C2×C4C2×C11×#4111yescharacteristic
579C2×C4C11×H(5,𝔽2)12yes—
580C8—24no—
581C8—41no—
582C8—41no—
583C22—22no—
584C22—24no—
585C22—22no—
586C22—22no—
587C22—44no—
588C22—42no—
589C22—42no—
590C22—44no—
591C22—42no—
592C22—42no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—816no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—81no—
602C22—82no—
603C22—82no—
604C22—81no—
605C22—81no—
606C22C2×C11×#12111yescharacteristic
607C22D42×C1112yes—
608C22C2×C11×AGL(1,ℤ/8)12yes—
609C22C11×#57611yescharacteristic
610C22C11×#57711yescharacteristic
611C4—22no—
612C4—24no—
613C4—42no—
614C4—42no—
615C4—82no—
616C4—81no—
617C4C2×C11×#12011yescharacteristic
618C4C11×#53411yescharacteristic
619C4C11×#54612yes—
620C2—42no—
621C2—44no—
622C2—84no—
623C2—161no—
624C2C11×#241011yescharacteristic
625C2C11×#303811yescharacteristic
626C2C11×#304511yescharacteristic
627C2C11×#326412yes—
628C2C11×#327212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×AGL(1,ℤ/8)C2semidirect
2. C2×C11×#459C2semidirect
3. C2×C11×#449C2semidirect
4. C11×#2433C2semidirect
5. C11×#2339C2semidirect
6. C11×#2055C2semidirect
7. C11×#2014C2semidirect
8. C11×#1895C2semidirect
9. C11×#1879C2semidirect
10. C11×#1851C2semidirect
11. C11×#1786C2semidirect
17. C22×C11×SD16C22semidirect
19. C22×C11×D8C22semidirect
24. C2×C4×D4×C11C22semidirect
27. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#103C22semidirect
31. C2×C11×#102C22semidirect
32. C2×C11×#102C22semidirect
36. C11×#391C22semidirect
43. C11×#340C22semidirect
44. C11×#336C22semidirect
49. C2×C11×#41D4semidirect
76. C2×C11×D8D4semidirect
110. #24372C11direct (N × H)
196. C22×AGL(1,ℤ/8)C2×C11semidirect
197. C2×#459C2×C11semidirect
198. C2×#449C2×C11semidirect
199. #2433C2×C11semidirect
200. #2339C2×C11semidirect
201. #2055C2×C11semidirect
202. #2014C2×C11semidirect
203. #1895C2×C11semidirect
204. #1879C2×C11semidirect
205. #1851C2×C11semidirect
206. #1786C2×C11semidirect
252. D4×C11#120semidirect
272. C2×C4×C11AGL(1,ℤ/8)semidirect
285. C22×SD16C22×C11semidirect
287. C22×D8C22×C11semidirect
292. C2×C4×D4C22×C11semidirect
295. C2×C4⋊C8C22×C11semidirect
296. C2×#103C22×C11semidirect
299. C2×#102C22×C11semidirect
300. C2×#102C22×C11semidirect
304. #391C22×C11semidirect
311. #340C22×C11semidirect
312. #336C22×C11semidirect
354. C2×#41D4×C11semidirect
381. C2×D8D4×C11semidirect
509. C11#24372direct (N × H)
555. D4C11×#120semidirect
575. C2×C4C11×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C22×C11×AGL(1,ℤ/8)2
C2×C11×#4592
C2×C11×#4492
C11×#24332
C11×#23392
C11×#20552
C11×#20142
C11×#18952
C11×#18792
C11×#18512
C11×#17862
#2437211