Finite Group Databasebeta

← C11×#24356 #14601549

Subgroups — C11×#24356 #14601549

Order 2816.

1656 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic, complemented
2C2×C11×#460C212yesmaximal, complemented
3C2×C11×#448C211yesmaximal, characteristic, complemented
4C11×#2433C211yesmaximal, characteristic
5Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#2014C212yesmaximal, complemented
8C11×#1893C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal, complemented
10C11×#1850C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×SD16—24no—
15C22×C11×SD16—28no—
16C22×C11×SD16C2212yes—
17C22×C11×SD16C2212yes—
18C22×C11×SD16C2211yescharacteristic, complemented
19C22×C11×SD16C2211yescharacteristic, complemented
20C23×C8×C11C2211yescharacteristic
21C2×C11×#127C2212yes—
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120—21no—
24C2×C11×#120—21no—
25C2×C4×Q8×C11C2212yescomplemented
26C11×#460—28no—
27C11×#448—24no—
28C2×C11×C4⋊C8C2212yescomplemented
29C2×C11×#103C2211yescharacteristic, complemented
30C2×C11×#103C2211yescharacteristic, complemented
31C2×C11×#102C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yescomplemented
34C2×C11×C22⋊C8C2211yescharacteristic
35C11×#392—22no—
36C11×#391—22no—
37C11×#391C2212yescomplemented
38C11×#390C2212yes—
39C11×#380—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C22⋊C4—21no—
42C4×C11×C22⋊C4C2211yescharacteristic
43C11×#340C2212yescomplemented
44C11×#336C2212yescomplemented
45C25×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—24no—
49C22×Q8×C11—42no—
50C22×Q8×C11D414yescomplemented
51C22×Q8×C11C2311yescharacteristic
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—24no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—42no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2312yes—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C2×C11×SD16—232no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16—24no—
70C2×C11×SD16—22no—
71C2×C11×SD16—22no—
72C2×C11×SD16—24no—
73C2×C11×SD16—24no—
74C2×C11×SD16—42no—
75C2×C11×SD16D418yescomplemented
76C22×C8×C11—22no—
77C22×C8×C11—24no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2312yes—
81C11×#127—24no—
82C11×#127—42no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#120—44no—
86C11×#120—44no—
87C4×Q8×C11—24no—
88C4×Q8×C11—42no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11—22no—
99C2×C42×C11C2312yes—
100C11×C4⋊C8—24no—
101C11×#103—22no—
102C11×#103—22no—
103C11×#102—24no—
104C11×#102—24no—
105C11×#102—42no—
106C11×C22⋊C8—22no—
107C11×#95—22no—
108C11×#95—22no—
109C11×#95—21no—
110C11×#95D412yes—
111#24356C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—44no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11—82no—
119C24×C11C2×D411yescharacteristic
120C2×Q8×C11—24no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—28no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—44no—
128C2×Q8×C11—44no—
129C2×Q8×C11—48no—
130C2×Q8×C11C2×D412yes—
131C2×Q8×C11C2×D412yes—
132C2×Q8×C11C2×D414yes—
133C2×D4×C11—28no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—48no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11—44no—
154C2×D4×C11—82no—
155C2×D4×C11—82no—
156C2×D4×C11C2×D414yes—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—44no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11#4112yes—
170C22×C4×C11C2411yescharacteristic
171C11×SD16—216no—
172C11×SD16—216no—
173C11×SD16—44no—
174C11×SD16—44no—
175C2×C8×C11—28no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11C2×D414yes—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—44no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—44no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—44no—
193C11×C22⋊C4SD1614yescomplemented
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—44no—
197C23×SD16C2×C1111yescharacteristic, complemented
198C2×#460C2×C1112yescomplemented
199C2×#448C2×C1111yescharacteristic, complemented
200#2433C2×C1111yescharacteristic
201Q8×C22⋊C4C2×C1111yescharacteristic, complemented
202#2055C2×C1112yescomplemented
203#2014C2×C1112yescomplemented
204#1893C2×C1111yescharacteristic, complemented
205#1880C2×C1112yescomplemented
206#1850C2×C1111yescharacteristic, complemented
207#1786C2×C1111yescharacteristic, complemented
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—48no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—41no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—42no—
223C23×C11—88no—
224C23×C11—88no—
225C23×C11—84no—
226C23×C11—84no—
227C23×C11#12112yes—
228C23×C11C2×SD1612yes—
229C23×C11AGL(1,ℤ/8)12yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—22no—
232Q8×C11—24no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—48no—
236Q8×C11—42no—
237Q8×C11#12014yescomplemented
238D4×C11—24no—
239D4×C11—24no—
240D4×C11—48no—
241D4×C11—41no—
242D4×C11—42no—
243D4×C11—41no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—88no—
247D4×C11—88no—
248D4×C11—84no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—48no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11#12112yes—
270C2×C4×C11C2×SD1614yescomplemented
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D412yes—
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)12yes—
275C8×C11—24no—
276C8×C11—41no—
277C8×C11—41no—
278C23×Q8C22×C1111yescharacteristic
279C23×D4C22×C1111yescharacteristic
280C22×SD16—24no—
281C22×SD16—28no—
282C22×SD16C22×C1112yes—
283C22×SD16C22×C1112yes—
284C22×SD16C22×C1111yescharacteristic, complemented
285C22×SD16C22×C1111yescharacteristic, complemented
286C23×C8C22×C1111yescharacteristic
287C2×#127C22×C1112yes—
288C2×#121C22×C1111yescharacteristic
289C2×#120—21no—
290C2×#120—21no—
291C2×C4×Q8C22×C1112yescomplemented
292#460—28no—
293#448—24no—
294C2×C4⋊C8C22×C1112yescomplemented
295C2×#103C22×C1111yescharacteristic, complemented
296C2×#103C22×C1111yescharacteristic, complemented
297C2×#102C22×C1112yes—
298C2×#102C22×C1112yes—
299C2×#102C22×C1112yescomplemented
300C2×C22⋊C8C22×C1111yescharacteristic
301#392—22no—
302#391—22no—
303#391C22×C1112yescomplemented
304#390C22×C1112yes—
305#380—21no—
306#380C22×C1111yescharacteristic
307C4×C22⋊C4—21no—
308C4×C22⋊C4C22×C1111yescharacteristic
309#340C22×C1112yescomplemented
310#336C22×C1112yescomplemented
311C22×C11—22no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—22no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—816no—
319C22×C11—82no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11—82no—
323C22×C11—81no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11#46014yescomplemented
329C22×C11C2×#12111yescharacteristic
330C22×C11D4212yes—
331C22×C11C22×SD1611yescharacteristic
332C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C11#57712yes—
334C4×C11—22no—
335C4×C11—24no—
336C4×C11—24no—
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—22no—
347C22×Q8—24no—
348C22×Q8—42no—
349C22×Q8D4×C1114yescomplemented
350C22×Q8C23×C1111yescharacteristic
351C22×Q8C23×C1111yescharacteristic
352C22×D4—24no—
353C22×D4—21no—
354C22×D4—22no—
355C22×D4—21no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—42no—
360C22×D4C23×C1111yescharacteristic
361C22×D4C23×C1112yes—
362C23×C4—21no—
363C23×C4C23×C1111yescharacteristic
364C2×SD16—232no—
365C2×SD16—24no—
366C2×SD16—24no—
367C2×SD16—24no—
368C2×SD16—24no—
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16—24no—
372C2×SD16—24no—
373C2×SD16—42no—
374C2×SD16D4×C1118yescomplemented
375C22×C8—22no—
376C22×C8—24no—
377C22×C8C23×C1111yescharacteristic
378C22×C8C23×C1111yescharacteristic
379C22×C8C23×C1112yes—
380#127—24no—
381#127—42no—
382#121—22no—
383#121—22no—
384#120—44no—
385#120—44no—
386C4×Q8—24no—
387C4×Q8—42no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4C23×C1112yes—
390C2×C4⋊C4C23×C1111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4D4×C1111yescharacteristic
396C2×C22⋊C4D4×C1111yescharacteristic
397C2×C42—22no—
398C2×C42C23×C1112yes—
399C4⋊C8—24no—
400#103—22no—
401#103—22no—
402#102—24no—
403#102—24no—
404#102—42no—
405C22⋊C8—22no—
406#95—22no—
407#95—22no—
408#95—21no—
409#95D4×C1112yes—
410C2×C11—24no—
411C2×C11—84no—
412C2×C11—161no—
413C2×C11#241011yescharacteristic
414C2×C11C2×#46011yescharacteristic
415C2×C11#304311yescharacteristic
416C2×C11#326512yes—
417C2×C11D4×SD1612yes—
418C24—22no—
419C24—21no—
420C24—44no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—82no—
425C24C2×D4×C1111yescharacteristic
426C2×Q8—24no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—28no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—48no—
436C2×Q8C2×D4×C1112yes—
437C2×Q8C2×D4×C1112yes—
438C2×Q8C2×D4×C1114yes—
439C2×D4—28no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—48no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—44no—
460C2×D4—82no—
461C2×D4—82no—
462C2×D4C2×D4×C1114yes—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—44no—
471C22×C4C2×D4×C1112yes—
472C22×C4C2×D4×C1111yescharacteristic
473C22×C4C2×D4×C1112yes—
474C22×C4C2×D4×C1112yes—
475C22×C4C11×#4112yes—
476C22×C4C24×C1111yescharacteristic
477SD16—216no—
478SD16—216no—
479SD16—44no—
480SD16—44no—
481C2×C8—28no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8C2×D4×C1114yes—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—44no—
494C22⋊C4—22no—
495C22⋊C4—44no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—44no—
499C22⋊C4C11×SD1614yescomplemented
500C42—22no—
501C42—22no—
502C42—44no—
503C11#2435611yescharacteristic, direct product factor, Sylow
504C23—22no—
505C23—22no—
506C23—24no—
507C23—48no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—41no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—42no—
519C23—88no—
520C23—88no—
521C23—84no—
522C23—84no—
523C23C11×#12112yes—
524C23C2×C11×SD1612yes—
525C23C11×AGL(1,ℤ/8)12yes—
526C23C22×D4×C1111yescharacteristic
527Q8—22no—
528Q8—24no—
529Q8—22no—
530Q8—22no—
531Q8—48no—
532Q8—42no—
533Q8C11×#12014yescomplemented
534D4—24no—
535D4—24no—
536D4—48no—
537D4—41no—
538D4—42no—
539D4—41no—
540D4—42no—
541D4—42no—
542D4—88no—
543D4—88no—
544D4—84no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—48no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4C11×#12112yes—
566C2×C4C2×C11×SD1614yescomplemented
567C2×C4C22×D4×C1111yescharacteristic
568C2×C4C22×D4×C1112yes—
569C2×C4C2×C11×#4111yescharacteristic
570C2×C4C11×H(5,𝔽2)12yes—
571C8—24no—
572C8—41no—
573C8—41no—
574C22—22no—
575C22—24no—
576C22—24no—
577C22—22no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—816no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22—81no—
587C22—82no—
588C22—82no—
589C22—81no—
590C22—81no—
591C22C11×#46014yescomplemented
592C22C2×C11×#12111yescharacteristic
593C22D42×C1112yes—
594C22C22×C11×SD1611yescharacteristic
595C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
596C22C11×#57712yes—
597C4—22no—
598C4—24no—
599C4—24no—
600C4—42no—
601C4—42no—
602C4—82no—
603C4—81no—
604C4C2×C11×#12011yescharacteristic
605C4C11×#53411yescharacteristic
606C4C11×#54612yes—
607C2—24no—
608C2—84no—
609C2—161no—
610C2C11×#241011yescharacteristic
611C2C2×C11×#46011yescharacteristic
612C2C11×#304311yescharacteristic
613C2C11×#326512yes—
614C2D4×C11×SD1612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2433C2
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×#460C2semidirect
3. C2×C11×#448C2semidirect
5. Q8×C11×C22⋊C4C2semidirect
6. C11×#2055C2semidirect
7. C11×#2014C2semidirect
8. C11×#1893C2semidirect
9. C11×#1880C2semidirect
10. C11×#1850C2semidirect
11. C11×#1786C2semidirect
18. C22×C11×SD16C22semidirect
19. C22×C11×SD16C22semidirect
25. C2×C4×Q8×C11C22semidirect
28. C2×C11×C4⋊C8C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#103C22semidirect
33. C2×C11×#102C22semidirect
37. C11×#391C22semidirect
43. C11×#340C22semidirect
44. C11×#336C22semidirect
50. C22×Q8×C11D4semidirect
75. C2×C11×SD16D4semidirect
111. #24356C11direct (N × H)
193. C11×C22⋊C4SD16semidirect
197. C23×SD16C2×C11semidirect
198. C2×#460C2×C11semidirect
199. C2×#448C2×C11semidirect
201. Q8×C22⋊C4C2×C11semidirect
202. #2055C2×C11semidirect
203. #2014C2×C11semidirect
204. #1893C2×C11semidirect
205. #1880C2×C11semidirect
206. #1850C2×C11semidirect
207. #1786C2×C11semidirect
237. Q8×C11#120semidirect
270. C2×C4×C11C2×SD16semidirect
284. C22×SD16C22×C11semidirect
285. C22×SD16C22×C11semidirect
291. C2×C4×Q8C22×C11semidirect
294. C2×C4⋊C8C22×C11semidirect
295. C2×#103C22×C11semidirect
296. C2×#103C22×C11semidirect
299. C2×#102C22×C11semidirect
303. #391C22×C11semidirect
309. #340C22×C11semidirect
310. #336C22×C11semidirect
328. C22×C11#460semidirect
349. C22×Q8D4×C11semidirect
374. C2×SD16D4×C11semidirect
499. C22⋊C4C11×SD16semidirect
503. C11#24356direct (N × H)
533. Q8C11×#120semidirect
566. C2×C4C2×C11×SD16semidirect
591. C22C11×#460semidirect

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×#4602
C2×C11×#4482
C11×#24332
Q8×C11×C22⋊C42
C11×#20552
C11×#20142
C11×#18932
C11×#18802
C11×#18502
C11×#17862
#2435611