Finite Group Databasebeta

← C11×#24359 #14601552

Subgroups — C11×#24359 #14601552

Order 2816.

1624 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic, complemented
2C2×C11×#463C212yesmaximal, complemented
3C2×C11×#447C211yesmaximal, characteristic
4C11×#2436C211yesmaximal, characteristic, complemented
5D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#2012C212yesmaximal, complemented
8C11×#1893C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×SD16—24no—
15C22×C11×SD16—28no—
16C22×C11×SD16C2212yes—
17C22×C11×SD16C2212yes—
18C22×C11×D8C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C11×#124C2212yescomplemented
22C2×C11×#121C2211yescharacteristic
23C2×C4×D4×C11C2212yes—
24C22×C11×C22⋊C4—21no—
25C11×#463—28no—
26C11×#447—24no—
27C2×C11×C4⋊C8C2212yescomplemented
28C2×C11×#103C2212yescomplemented
29C2×C11×#103C2212yescomplemented
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2212yescomplemented
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#393—22no—
35C11×#391C2212yescomplemented
36C11×#390C2212yes—
37C11×#386—21no—
38C11×#386—21no—
39C11×#386—22no—
40C11×#380C2211yescharacteristic
41C11×#379—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
43C11×#340C2212yescomplemented
44C11×#336C2212yescomplemented
45C25×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—24no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—42no—
51C22×Q8×C11C2312yes—
52C22×D4×C11—24no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—42no—
57C22×D4×C11D414yes—
58C22×D4×C11C2311yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—22no—
63C23×C4×C11C2311yescharacteristic
64C2×C11×SD16—232no—
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16—24no—
70C2×C11×SD16D418yescomplemented
71C2×C11×D8—22no—
72C2×C11×D8—22no—
73C2×C11×D8—24no—
74C2×C11×D8—42no—
75C22×C8×C11—22no—
76C22×C8×C11—24no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2312yes—
80C11×#124—24no—
81C11×#124—42no—
82C11×#121—22no—
83C11×#121—22no—
84C4×D4×C11—24no—
85C4×D4×C11—42no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—44no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11C2312yes—
99C11×C4⋊C8—24no—
100C11×#103—24no—
101C11×#103—42no—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102—24no—
105C11×C22⋊C8—22no—
106C11×#95—21no—
107C11×#95—22no—
108C11×#95—22no—
109C11×#95D412yes—
110#24359C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—24no—
114C24×C11—21no—
115C24×C11—44no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11—82no—
119C24×C11C2×D411yescharacteristic
120C2×Q8×C11—22no—
121C2×Q8×C11—28no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—44no—
127C2×Q8×C11—48no—
128C2×Q8×C11—44no—
129C2×Q8×C11—42no—
130C2×Q8×C11C2×D414yes—
131C2×D4×C11—28no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—44no—
143C2×D4×C11—48no—
144C2×D4×C11—44no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11C2×D412yes—
149C2×D4×C11C2×D412yes—
150C2×D4×C11C2×D414yes—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—44no—
157C22×C4×C11—44no—
158C22×C4×C11—44no—
159C22×C4×C11—42no—
160C22×C4×C11—82no—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C11×SD16—216no—
168C11×SD16—216no—
169C11×D8—44no—
170C11×D8—44no—
171C2×C8×C11—28no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11C2×D414yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—44no—
186C11×C22⋊C4—44no—
187C11×C22⋊C4—44no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—82no—
192C42×C11—22no—
193C42×C11—22no—
194C23×SD16C2×C1111yescharacteristic, complemented
195C2×#463C2×C1112yescomplemented
196C2×#447C2×C1111yescharacteristic
197#2436C2×C1111yescharacteristic, complemented
198D4×C22⋊C4C2×C1111yescharacteristic, complemented
199#2055C2×C1112yescomplemented
200#2012C2×C1112yescomplemented
201#1893C2×C1111yescharacteristic, complemented
202#1877C2×C1112yescomplemented
203#1850C2×C1111yescharacteristic, complemented
204#1787C2×C1111yescharacteristic, complemented
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—48no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—48no—
219C23×C11—41no—
220C23×C11—42no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—42no—
224C23×C11—84no—
225C23×C11—88no—
226C23×C11—88no—
227C23×C11#12112yes—
228C23×C11#13512yes—
229C23×C11AGL(1,ℤ/8)12yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—24no—
232Q8×C11—24no—
233Q8×C11—48no—
234Q8×C11—42no—
235Q8×C11—42no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—24no—
240D4×C11—48no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—84no—
246D4×C11#12014yes—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—48no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—88no—
268C2×C4×C11#12112yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D412yes—
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)12yes—
273C8×C11—24no—
274C8×C11—41no—
275C8×C11—41no—
276C23×Q8C22×C1111yescharacteristic
277C23×D4C22×C1111yescharacteristic
278C22×SD16—24no—
279C22×SD16—28no—
280C22×SD16C22×C1112yes—
281C22×SD16C22×C1112yes—
282C22×D8C22×C1111yescharacteristic
283C22×D8C22×C1111yescharacteristic
284C23×C8C22×C1111yescharacteristic
285C2×#124C22×C1112yescomplemented
286C2×#121C22×C1111yescharacteristic
287C2×C4×D4C22×C1112yes—
288C22×C22⋊C4—21no—
289#463—28no—
290#447—24no—
291C2×C4⋊C8C22×C1112yescomplemented
292C2×#103C22×C1112yescomplemented
293C2×#103C22×C1112yescomplemented
294C2×#102C22×C1111yescharacteristic
295C2×#102C22×C1111yescharacteristic
296C2×#102C22×C1112yescomplemented
297C2×C22⋊C8C22×C1111yescharacteristic
298#393—22no—
299#391C22×C1112yescomplemented
300#390C22×C1112yes—
301#386—21no—
302#386—21no—
303#386—22no—
304#380C22×C1111yescharacteristic
305#379—21no—
306C4×C22⋊C4C22×C1111yescharacteristic
307#340C22×C1112yescomplemented
308#336C22×C1112yescomplemented
309C22×C11—22no—
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—22no—
313C22×C11—24no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—816no—
322C22×C11—82no—
323C22×C11—82no—
324C22×C11—81no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11#46314yescomplemented
330C22×C11C2×#12111yescharacteristic
331C22×C11D4212yes—
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C11#57712yes—
335C4×C11—22no—
336C4×C11—44no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11—82no—
340C4×C11—81no—
341C4×C11C2×#12011yescharacteristic
342C4×C11#53411yescharacteristic
343C4×C11#54612yes—
344C25—21no—
345C22×Q8—21no—
346C22×Q8—24no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—42no—
350C22×Q8C23×C1112yes—
351C22×D4—24no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4—22no—
355C22×D4—42no—
356C22×D4D4×C1114yes—
357C22×D4C23×C1111yescharacteristic
358C22×D4C23×C1111yescharacteristic
359C22×D4C23×C1111yescharacteristic
360C23×C4—21no—
361C23×C4—22no—
362C23×C4C23×C1111yescharacteristic
363C2×SD16—232no—
364C2×SD16—24no—
365C2×SD16—24no—
366C2×SD16—24no—
367C2×SD16—24no—
368C2×SD16—24no—
369C2×SD16D4×C1118yescomplemented
370C2×D8—22no—
371C2×D8—22no—
372C2×D8—24no—
373C2×D8—42no—
374C22×C8—22no—
375C22×C8—24no—
376C22×C8C23×C1111yescharacteristic
377C22×C8C23×C1111yescharacteristic
378C22×C8C23×C1112yes—
379#124—24no—
380#124—42no—
381#121—22no—
382#121—22no—
383C4×D4—24no—
384C4×D4—42no—
385C2×C4⋊C4C23×C1112yes—
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4D4×C1111yescharacteristic
396C2×C22⋊C4D4×C1111yescharacteristic
397C2×C42C23×C1112yes—
398C4⋊C8—24no—
399#103—24no—
400#103—42no—
401#102—22no—
402#102—22no—
403#102—24no—
404C22⋊C8—22no—
405#95—21no—
406#95—22no—
407#95—22no—
408#95D4×C1112yes—
409C2×C11—24no—
410C2×C11—44no—
411C2×C11—82no—
412C2×C11—161no—
413C2×C11#241011yescharacteristic
414C2×C11C2×#46311yescharacteristic
415C2×C11#304211yescharacteristic
416C2×C11#326512yes—
417C2×C11#328212yes—
418C24—21no—
419C24—21no—
420C24—24no—
421C24—21no—
422C24—44no—
423C24—42no—
424C24—42no—
425C24—82no—
426C24C2×D4×C1111yescharacteristic
427C2×Q8—22no—
428C2×Q8—28no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—44no—
434C2×Q8—48no—
435C2×Q8—44no—
436C2×Q8—42no—
437C2×Q8C2×D4×C1114yes—
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—44no—
450C2×D4—48no—
451C2×D4—44no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4C2×D4×C1112yes—
456C2×D4C2×D4×C1112yes—
457C2×D4C2×D4×C1114yes—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—42no—
467C22×C4—82no—
468C22×C4C2×D4×C1112yes—
469C22×C4C2×D4×C1112yes—
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1112yes—
472C22×C4C11×#4112yes—
473C22×C4C24×C1111yescharacteristic
474SD16—216no—
475SD16—216no—
476D8—44no—
477D8—44no—
478C2×C8—28no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8C2×D4×C1114yes—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—44no—
493C22⋊C4—44no—
494C22⋊C4—44no—
495C22⋊C4—44no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—82no—
499C42—22no—
500C42—22no—
501C11#2435911yescharacteristic, direct product factor, Sylow
502C23—22no—
503C23—22no—
504C23—22no—
505C23—24no—
506C23—22no—
507C23—48no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23—48no—
516C23—41no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—84no—
522C23—88no—
523C23—88no—
524C23C11×#12112yes—
525C23C11×#13512yes—
526C23C11×AGL(1,ℤ/8)12yes—
527C23C22×D4×C1111yescharacteristic
528Q8—24no—
529Q8—24no—
530Q8—48no—
531Q8—42no—
532Q8—42no—
533D4—22no—
534D4—22no—
535D4—22no—
536D4—24no—
537D4—48no—
538D4—41no—
539D4—41no—
540D4—42no—
541D4—42no—
542D4—84no—
543D4C11×#12014yes—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—48no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—88no—
565C2×C4C11×#12112yes—
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C22×D4×C1112yes—
568C2×C4C2×C11×#4111yescharacteristic
569C2×C4C11×H(5,𝔽2)12yes—
570C8—24no—
571C8—41no—
572C8—41no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—22no—
577C22—24no—
578C22—44no—
579C22—44no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—816no—
586C22—82no—
587C22—82no—
588C22—81no—
589C22—82no—
590C22—82no—
591C22—81no—
592C22—81no—
593C22C11×#46314yescomplemented
594C22C2×C11×#12111yescharacteristic
595C22D42×C1112yes—
596C22C2×C11×#13511yescharacteristic
597C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
598C22C11×#57712yes—
599C4—22no—
600C4—44no—
601C4—42no—
602C4—42no—
603C4—82no—
604C4—81no—
605C4C2×C11×#12011yescharacteristic
606C4C11×#53411yescharacteristic
607C4C11×#54612yes—
608C2—24no—
609C2—44no—
610C2—82no—
611C2—161no—
612C2C11×#241011yescharacteristic
613C2C2×C11×#46311yescharacteristic
614C2C11×#304211yescharacteristic
615C2C11×#326512yes—
616C2C11×#328212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
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. C23×C11×SD16C2semidirect
2. C2×C11×#463C2semidirect
4. C11×#2436C2semidirect
5. D4×C11×C22⋊C4C2semidirect
6. C11×#2055C2semidirect
7. C11×#2012C2semidirect
8. C11×#1893C2semidirect
9. C11×#1877C2semidirect
10. C11×#1850C2semidirect
11. C11×#1787C2semidirect
21. C2×C11×#124C22semidirect
27. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#103C22semidirect
32. C2×C11×#102C22semidirect
35. C11×#391C22semidirect
43. C11×#340C22semidirect
44. C11×#336C22semidirect
70. C2×C11×SD16D4semidirect
110. #24359C11direct (N × H)
194. C23×SD16C2×C11semidirect
195. C2×#463C2×C11semidirect
197. #2436C2×C11semidirect
198. D4×C22⋊C4C2×C11semidirect
199. #2055C2×C11semidirect
200. #2012C2×C11semidirect
201. #1893C2×C11semidirect
202. #1877C2×C11semidirect
203. #1850C2×C11semidirect
204. #1787C2×C11semidirect
285. C2×#124C22×C11semidirect
291. C2×C4⋊C8C22×C11semidirect
292. C2×#103C22×C11semidirect
293. C2×#103C22×C11semidirect
296. C2×#102C22×C11semidirect
299. #391C22×C11semidirect
307. #340C22×C11semidirect
308. #336C22×C11semidirect
329. C22×C11#463semidirect
369. C2×SD16D4×C11semidirect
501. C11#24359direct (N × H)
593. C22C11×#463semidirect

Maximal subgroups

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

subgroupindex
C23×C11×SD162
C2×C11×#4632
C2×C11×#4472
C11×#24362
D4×C11×C22⋊C42
C11×#20552
C11×#20122
C11×#18932
C11×#18772
C11×#18502
C11×#17872
#2435911