Finite Group Databasebeta

← C11×#24039 #14601232

Subgroups — C11×#24039 #14601232

Order 2816.

1484 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#546C211yesmaximal, characteristic
2C2×C11×#484C211yesmaximal, characteristic, complemented
3C22×C11×#102C211yesmaximal, characteristic, complemented
4C11×#2487C211yesmaximal, characteristic, complemented
5C11×#2042C212yesmaximal, complemented
6C11×#2033C212yesmaximal, complemented
7C11×#1892C211yesmaximal, characteristic, complemented
8C11×#1869C211yesmaximal, characteristic, complemented
9C11×#1862C212yesmaximal, complemented
10C11×#1788C212yesmaximal, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C11×#546—24no—
16C11×#546—24no—
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121—21no—
21C2×C11×#121C2211yescharacteristic
22C2×C11×#120—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4—21no—
27C11×#484—24no—
28C2×C11×#107C2212yescomplemented
29C2×C11×#103C2212yescomplemented
30C2×C11×#103C2212yescomplemented
31C2×C11×#102—24no—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yescomplemented
38C11×#400—21no—
39C11×#399—21no—
40C11×#389C2212yescomplemented
41C11×#386—21no—
42C11×#385—21no—
43C11×#380C2211yescharacteristic
44C11×#380C2212yescomplemented
45C11×#340C2212yescomplemented
46C11×#336C2212yescomplemented
47C25×C11—21no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—24no—
51C2×C11×#41—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—24no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—42no—
59C22×D4×C11D411yescharacteristic
60C22×D4×C11D414yes—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C8×C11—22no—
69C22×C8×C11—42no—
70C22×C8×C11C2312yes—
71C22×C8×C11C2312yes—
72C11×#124—22no—
73C11×#124—22no—
74C11×#123—28no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8D414yes—
77C11×#121—28no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#120—28no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—28no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C11×#107—24no—
106C11×#103—24no—
107C11×#103—42no—
108C11×#102—24no—
109C11×#102—24no—
110C11×#102—24no—
111C11×#102—42no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—42no—
114C11×#95—21no—
115C11×#95—22no—
116C11×#95—22no—
117#24039C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—21no—
119C24×C11—21no—
120C24×C11—24no—
121C24×C11—44no—
122C24×C11—42no—
123C24×C11—42no—
124C24×C11—82no—
125C24×C11C2×D411yescharacteristic
126C24×C11C2×D411yescharacteristic
127C11×#41—48no—
128C11×#41—44no—
129C11×#41—44no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—28no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—44no—
147C2×D4×C11—48no—
148C2×D4×C11—44no—
149C2×D4×C11—44no—
150C2×D4×C11—82no—
151C2×D4×C11C2×D412yes—
152C2×D4×C11C2×D412yes—
153C2×D4×C11#4114yes—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—24no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—44no—
167C22×C4×C11—42no—
168C22×C4×C11—82no—
169C22×C4×C11—82no—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2411yescharacteristic
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—44no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4—82no—
193C11×C4⋊C4C2×D412yes—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—82no—
203C42×C11—21no—
204C42×C11—21no—
205C2×#546C2×C1111yescharacteristic
206C2×#484C2×C1111yescharacteristic, complemented
207C22×#102C2×C1111yescharacteristic, complemented
208#2487C2×C1111yescharacteristic, complemented
209#2042C2×C1112yescomplemented
210#2033C2×C1112yescomplemented
211#1892C2×C1111yescharacteristic, complemented
212#1869C2×C1111yescharacteristic, complemented
213#1862C2×C1112yescomplemented
214#1788C2×C1112yescomplemented
215#1786C2×C1111yescharacteristic, complemented
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—21no—
222C23×C11—22no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—22no—
226C23×C11—48no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—48no—
235C23×C11—84no—
236C23×C11—88no—
237C23×C11—88no—
238C23×C11#12012yes—
239C23×C11#13512yes—
240C23×C11#13712yes—
241C23×C11C22×D411yescharacteristic
242Q8×C11—24no—
243Q8×C11—41no—
244Q8×C11—41no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—24no—
249D4×C11—48no—
250D4×C11—48no—
251D4×C11—44no—
252D4×C11—42no—
253D4×C11—84no—
254D4×C11#12314yes—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—48no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—84no—
281C2×C4×C11—84no—
282C2×C4×C11#12012yes—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C2×#4112yes—
286C2×C4×C11H(5,𝔽2)12yes—
287C8×C11—42no—
288C8×C11—42no—
289C22×#41C22×C1111yescharacteristic
290C23×D4C22×C1111yescharacteristic
291C23×C8C22×C1111yescharacteristic
292#546—24no—
293#546—24no—
294C2×#124C22×C1111yescharacteristic
295C2×#123—21no—
296C2×C22⋊Q8C22×C1111yescharacteristic
297C2×#121—21no—
298C2×#121C22×C1111yescharacteristic
299C2×#120—21no—
300C2×C4×D4C22×C1111yescharacteristic
301C2×C4×D4C22×C1111yescharacteristic
302C22×C4⋊C4C22×C1111yescharacteristic
303C22×C22⋊C4—21no—
304#484—24no—
305C2×#107C22×C1112yescomplemented
306C2×#103C22×C1112yescomplemented
307C2×#103C22×C1112yescomplemented
308C2×#102—24no—
309C2×#102C22×C1112yes—
310C2×#102C22×C1112yes—
311C2×#102C22×C1112yes—
312C2×#102C22×C1112yes—
313C2×C22⋊C8C22×C1111yescharacteristic
314C2×C22⋊C8C22×C1112yescomplemented
315#400—21no—
316#399—21no—
317#389C22×C1112yescomplemented
318#386—21no—
319#385—21no—
320#380C22×C1111yescharacteristic
321#380C22×C1112yescomplemented
322#340C22×C1112yescomplemented
323#336C22×C1112yescomplemented
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—24no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—41no—
334C22×C11—42no—
335C22×C11—41no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—816no—
342C22×C11—82no—
343C22×C11—82no—
344C22×C11#45214yes—
345C22×C11C2×#12011yescharacteristic
346C22×C11#54612yes—
347C22×C11C2×#13511yescharacteristic
348C22×C11C2×#13711yescharacteristic
349C22×C11#57612yes—
350C4×C11—22no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—82no—
357C4×C11—82no—
358C4×C11C2×#12311yescharacteristic
359C4×C11#53411yescharacteristic
360C4×C11#54612yes—
361C25—21no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—24no—
365C2×#41—42no—
366C22×Q8C23×C1111yescharacteristic
367C22×D4—24no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—22no—
372C22×D4—42no—
373C22×D4D4×C1111yescharacteristic
374C22×D4D4×C1114yes—
375C22×D4C23×C1111yescharacteristic
376C22×D4C23×C1111yescharacteristic
377C23×C4—21no—
378C23×C4—21no—
379C23×C4—21no—
380C23×C4C23×C1111yescharacteristic
381C23×C4C23×C1111yescharacteristic
382C22×C8—22no—
383C22×C8—42no—
384C22×C8C23×C1112yes—
385C22×C8C23×C1112yes—
386#124—22no—
387#124—22no—
388#123—28no—
389C22⋊Q8—22no—
390C22⋊Q8D4×C1114yes—
391#121—28no—
392#121—22no—
393#121—22no—
394#120—28no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4D4×C1111yescharacteristic
405C2×C4⋊C4C23×C1112yes—
406C2×C4⋊C4C23×C1112yes—
407C2×C4⋊C4C23×C1111yescharacteristic
408C2×C22⋊C4—28no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4D4×C1111yescharacteristic
417C2×C22⋊C4D4×C1111yescharacteristic
418C2×C42C23×C1111yescharacteristic
419#107—24no—
420#103—24no—
421#103—42no—
422#102—24no—
423#102—24no—
424#102—24no—
425#102—42no—
426C22⋊C8—22no—
427C22⋊C8—42no—
428#95—21no—
429#95—22no—
430#95—22no—
431C2×C11—24no—
432C2×C11—44no—
433C2×C11—81no—
434C2×C11—82no—
435C2×C11#240511yescharacteristic
436C2×C11C2×#45211yescharacteristic
437C2×C11#300811yescharacteristic
438C2×C11#329712yes—
439C2×C11#331412yes—
440C24—21no—
441C24—21no—
442C24—24no—
443C24—44no—
444C24—42no—
445C24—42no—
446C24—82no—
447C24C2×D4×C1111yescharacteristic
448C24C2×D4×C1111yescharacteristic
449#41—48no—
450#41—44no—
451#41—44no—
452C2×Q8—21no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8C2×D4×C1112yes—
456C2×D4—28no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—44no—
469C2×D4—48no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—82no—
473C2×D4C2×D4×C1112yes—
474C2×D4C2×D4×C1112yes—
475C2×D4C11×#4114yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—44no—
489C22×C4—42no—
490C22×C4—82no—
491C22×C4—82no—
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C2×D4×C1112yes—
497C22×C4C2×D4×C1112yes—
498C22×C4C24×C1111yescharacteristic
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—44no—
506C4⋊C4—24no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—42no—
514C4⋊C4—82no—
515C4⋊C4C2×D4×C1112yes—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—22no—
521C22⋊C4—24no—
522C22⋊C4—22no—
523C22⋊C4—42no—
524C22⋊C4—82no—
525C42—21no—
526C42—21no—
527C11#2403911yescharacteristic, direct product factor, Sylow
528C23—22no—
529C23—22no—
530C23—22no—
531C23—24no—
532C23—22no—
533C23—21no—
534C23—22no—
535C23—21no—
536C23—21no—
537C23—22no—
538C23—48no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—41no—
545C23—42no—
546C23—48no—
547C23—84no—
548C23—88no—
549C23—88no—
550C23C11×#12012yes—
551C23C11×#13512yes—
552C23C11×#13712yes—
553C23C22×D4×C1111yescharacteristic
554Q8—24no—
555Q8—41no—
556Q8—41no—
557D4—22no—
558D4—22no—
559D4—22no—
560D4—24no—
561D4—48no—
562D4—48no—
563D4—44no—
564D4—42no—
565D4—84no—
566D4C11×#12314yes—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—48no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—84no—
593C2×C4—84no—
594C2×C4C11×#12012yes—
595C2×C4C22×D4×C1111yescharacteristic
596C2×C4C22×D4×C1111yescharacteristic
597C2×C4C2×C11×#4112yes—
598C2×C4C11×H(5,𝔽2)12yes—
599C8—42no—
600C8—42no—
601C22—22no—
602C22—22no—
603C22—24no—
604C22—24no—
605C22—24no—
606C22—42no—
607C22—42no—
608C22—44no—
609C22—44no—
610C22—41no—
611C22—42no—
612C22—41no—
613C22—42no—
614C22—41no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—816no—
619C22—82no—
620C22—82no—
621C22C11×#45214yes—
622C22C2×C11×#12011yescharacteristic
623C22C11×#54612yes—
624C22C2×C11×#13511yescharacteristic
625C22C2×C11×#13711yescharacteristic
626C22C11×#57612yes—
627C4—22no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—82no—
634C4—82no—
635C4C2×C11×#12311yescharacteristic
636C4C11×#53411yescharacteristic
637C4C11×#54612yes—
638C2—24no—
639C2—44no—
640C2—81no—
641C2—82no—
642C2C11×#240511yescharacteristic
643C2C2×C11×#45211yescharacteristic
644C2C11×#300811yescharacteristic
645C2C11×#329712yes—
646C2C11×#331412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#484C2semidirect
3. C22×C11×#102C2semidirect
4. C11×#2487C2semidirect
5. C11×#2042C2semidirect
6. C11×#2033C2semidirect
7. C11×#1892C2semidirect
8. C11×#1869C2semidirect
9. C11×#1862C2semidirect
10. C11×#1788C2semidirect
11. C11×#1786C2semidirect
28. C2×C11×#107C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#103C22semidirect
37. C2×C11×C22⋊C8C22semidirect
40. C11×#389C22semidirect
44. C11×#380C22semidirect
45. C11×#340C22semidirect
46. C11×#336C22semidirect
117. #24039C11direct (N × H)
206. C2×#484C2×C11semidirect
207. C22×#102C2×C11semidirect
208. #2487C2×C11semidirect
209. #2042C2×C11semidirect
210. #2033C2×C11semidirect
211. #1892C2×C11semidirect
212. #1869C2×C11semidirect
213. #1862C2×C11semidirect
214. #1788C2×C11semidirect
215. #1786C2×C11semidirect
305. C2×#107C22×C11semidirect
306. C2×#103C22×C11semidirect
307. C2×#103C22×C11semidirect
314. C2×C22⋊C8C22×C11semidirect
317. #389C22×C11semidirect
321. #380C22×C11semidirect
322. #340C22×C11semidirect
323. #336C22×C11semidirect
527. C11#24039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5462
C2×C11×#4842
C22×C11×#1022
C11×#24872
C11×#20422
C11×#20332
C11×#18922
C11×#18692
C11×#18622
C11×#17882
C11×#17862
#2403911