Finite Group Databasebeta

← C11×#24266 #14601459

Subgroups — C11×#24266 #14601459

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic, complemented
2C2×C11×#467C211yesmaximal, characteristic, complemented
3C2×C11×#466C211yesmaximal, characteristic, complemented
4C2×C8×D4×C11C211yesmaximal, characteristic, complemented
5C11×#2407C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1970C211yesmaximal, characteristic, complemented
9C11×#1969C211yesmaximal, characteristic, complemented
10C11×#1808C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C2×C11×#135—24no—
14C2×C11×#135—24no—
15C2×C11×#135—24no—
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2212yes—
18C22×C11×D8C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×#121C2212yes—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#467—24no—
25C11×#466—24no—
26C8×D4×C11—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C4×C8×C11C2211yescharacteristic
37C11×#394—22no—
38C11×#392—22no—
39C11×#391C2212yes—
40C11×#390C2212yes—
41C11×#386—22no—
42C11×#385—22no—
43C11×#380C2212yes—
44C11×#340C2212yes—
45C2×C11×#41—24no—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—42no—
50C2×C11×#41—42no—
51C22×Q8×C11C2312yes—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11D411yescharacteristic
55C22×D4×C11C2312yes—
56C23×C4×C11—22no—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C11×#135—232no—
60C2×C11×Q16—22no—
61C2×C11×Q16—22no—
62C2×C11×Q16D414yescomplemented
63C2×C11×SD16—24no—
64C2×C11×SD16—24no—
65C2×C11×SD16—24no—
66C2×C11×D8—22no—
67C2×C11×D8—22no—
68C2×C11×D8D414yescomplemented
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11D414yescomplemented
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8—42no—
81C11×#121—24no—
82C11×#121—42no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C11×#107—22no—
98C11×#107—22no—
99C11×C4⋊C8—22no—
100C11×#103—24no—
101C11×#103—42no—
102C11×#102—24no—
103C11×#102—42no—
104C11×C22⋊C8—22no—
105C11×C22⋊C8—22no—
106C4×C8×C11—22no—
107C11×#95—22no—
108C11×#95—22no—
109C11×#95—22no—
110#24266C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—22no—
112C24×C11C2×D411yescharacteristic
113C24×C11C2×D411yescharacteristic
114C11×#41—216no—
115C11×#41—48no—
116C11×#41—48no—
117C11×#41—48no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11C2×D414yes—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—44no—
137C2×D4×C11—82no—
138C2×D4×C11C2×D414yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C11×Q16—28no—
163C11×SD16—216no—
164C11×D8—28no—
165C2×C8×C11—28no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—44no—
175C2×C8×C11C2×D412yes—
176C2×C8×C11C2×D412yes—
177C2×C8×C11C2×D412yes—
178C2×C8×C11C2×D412yes—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—44no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—44no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—44no—
190C11×C22⋊C4—82no—
191C11×C22⋊C4—82no—
192C42×C11—21no—
193C42×C11—21no—
194C22×#135C2×C1111yescharacteristic, complemented
195C2×#467C2×C1111yescharacteristic, complemented
196C2×#466C2×C1111yescharacteristic, complemented
197C2×C8×D4C2×C1111yescharacteristic, complemented
198#2407C2×C1112yescomplemented
199#2055C2×C1112yescomplemented
200#2000C2×C1112yescomplemented
201#1970C2×C1111yescharacteristic, complemented
202#1969C2×C1111yescharacteristic, complemented
203#1808C2×C1111yescharacteristic, complemented
204#1788C2×C1112yescomplemented
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—24no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11#12112yes—
225C23×C11#13512yescomplemented
226C23×C11C22×D411yescharacteristic
227Q8×C11—24no—
228Q8×C11—24no—
229Q8×C11—42no—
230Q8×C11—42no—
231D4×C11—28no—
232D4×C11—24no—
233D4×C11—24no—
234D4×C11—416no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—88no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—24no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—416no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11#12112yes—
267C2×C4×C11#13512yescomplemented
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C8×C11—22no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11#12014yes—
278C22×#41C22×C1112yes—
279C2×#135—24no—
280C2×#135—24no—
281C2×#135—24no—
282C22×Q16C22×C1111yescharacteristic
283C22×SD16C22×C1112yes—
284C22×D8C22×C1111yescharacteristic
285C23×C8C22×C1111yescharacteristic
286C23×C8C22×C1111yescharacteristic
287C2×C22⋊Q8C22×C1112yes—
288C2×#121C22×C1112yes—
289C2×C4×D4C22×C1111yescharacteristic
290#467—24no—
291#466—24no—
292C8×D4—24no—
293C2×#107C22×C1111yescharacteristic
294C2×#107C22×C1111yescharacteristic
295C2×C4⋊C8C22×C1111yescharacteristic
296C2×#103C22×C1112yes—
297C2×#103C22×C1112yes—
298C2×#102C22×C1112yes—
299C2×#102C22×C1112yes—
300C2×C22⋊C8C22×C1111yescharacteristic
301C2×C22⋊C8C22×C1111yescharacteristic
302C2×C4×C8C22×C1111yescharacteristic
303#394—22no—
304#392—22no—
305#391C22×C1112yes—
306#390C22×C1112yes—
307#386—22no—
308#385—22no—
309#380C22×C1112yes—
310#340C22×C1112yes—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—82no—
329C22×C11—82no—
330C22×C11—82no—
331C22×C11—82no—
332C22×C11C2×#12111yescharacteristic
333C22×C11D4211yescharacteristic
334C22×C11D4211yescharacteristic
335C22×C11C2×#13511yescharacteristic
336C22×C11C2×#13511yescharacteristic
337C22×C11#57611yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—41no—
342C4×C11—44no—
343C4×C11—41no—
344C4×C11—82no—
345C4×C11—82no—
346C4×C11C2×#12011yescharacteristic
347C4×C11#53511yescharacteristic
348C4×C11#54611yescharacteristic
349C4×C11#54611yescharacteristic
350C2×#41—24no—
351C2×#41—24no—
352C2×#41—24no—
353C2×#41—24no—
354C2×#41—42no—
355C2×#41—42no—
356C22×Q8C23×C1112yes—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4D4×C1111yescharacteristic
360C22×D4C23×C1112yes—
361C23×C4—22no—
362C23×C4C23×C1111yescharacteristic
363C23×C4C23×C1111yescharacteristic
364#135—232no—
365C2×Q16—22no—
366C2×Q16—22no—
367C2×Q16D4×C1114yescomplemented
368C2×SD16—24no—
369C2×SD16—24no—
370C2×SD16—24no—
371C2×D8—22no—
372C2×D8—22no—
373C2×D8D4×C1114yescomplemented
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—22no—
379C22×C8D4×C1114yescomplemented
380C22×C8C23×C1111yescharacteristic
381C22×C8C23×C1111yescharacteristic
382C22×C8C23×C1111yescharacteristic
383C22×C8C23×C1111yescharacteristic
384C22⋊Q8—24no—
385C22⋊Q8—42no—
386#121—24no—
387#121—42no—
388C4×D4—22no—
389C4×D4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4D4×C1111yescharacteristic
392C2×C4⋊C4C23×C1112yes—
393C2×C4⋊C4C23×C1112yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4D4×C1111yescharacteristic
400C2×C22⋊C4D4×C1111yescharacteristic
401C2×C42C23×C1111yescharacteristic
402#107—22no—
403#107—22no—
404C4⋊C8—22no—
405#103—24no—
406#103—42no—
407#102—24no—
408#102—42no—
409C22⋊C8—22no—
410C22⋊C8—22no—
411C4×C8—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415C2×C11—42no—
416C2×C11—42no—
417C2×C11—84no—
418C2×C11#240811yescharacteristic
419C2×C11#305011yescharacteristic
420C2×C11#306111yescharacteristic
421C2×C11#328011yescharacteristic
422C2×C11#328311yescharacteristic
423C2×C11#328511yescharacteristic
424C2×C11#328711yescharacteristic
425C24—22no—
426C24C2×D4×C1111yescharacteristic
427C24C2×D4×C1111yescharacteristic
428#41—216no—
429#41—48no—
430#41—48no—
431#41—48no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8C2×D4×C1114yes—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—82no—
452C2×D4C2×D4×C1114yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C2×D4×C1112yes—
473C22×C4C2×D4×C1111yescharacteristic
474C22×C4C11×#4112yes—
475C22×C4C24×C1111yescharacteristic
476Q16—28no—
477SD16—216no—
478D8—28no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—28no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—44no—
489C2×C8C2×D4×C1112yes—
490C2×C8C2×D4×C1112yes—
491C2×C8C2×D4×C1112yes—
492C2×C8C2×D4×C1112yes—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—44no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—44no—
502C22⋊C4—44no—
503C22⋊C4—44no—
504C22⋊C4—82no—
505C22⋊C4—82no—
506C42—21no—
507C42—21no—
508C11#2426611yescharacteristic, direct product factor, Sylow
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—24no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C11×#12112yes—
529C23C11×#13512yescomplemented
530C23C22×D4×C1111yescharacteristic
531Q8—24no—
532Q8—24no—
533Q8—42no—
534Q8—42no—
535D4—28no—
536D4—24no—
537D4—24no—
538D4—416no—
539D4—42no—
540D4—42no—
541D4—88no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—24no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—416no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4C11×#12112yes—
571C2×C4C11×#13512yescomplemented
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C22×D4×C1111yescharacteristic
574C2×C4C22×D4×C1111yescharacteristic
575C2×C4C2×C11×#4111yescharacteristic
576C2×C4C11×H(5,𝔽2)11yescharacteristic
577C2×C4C11×H(5,𝔽2)11yescharacteristic
578C8—22no—
579C8—41no—
580C8—41no—
581C8C11×#12014yes—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22C2×C11×#12111yescharacteristic
604C22D42×C1111yescharacteristic
605C22D42×C1111yescharacteristic
606C22C2×C11×#13511yescharacteristic
607C22C2×C11×#13511yescharacteristic
608C22C11×#57611yescharacteristic
609C22C11×#57811yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—44no—
614C4—41no—
615C4—82no—
616C4—82no—
617C4C2×C11×#12011yescharacteristic
618C4C11×#53511yescharacteristic
619C4C11×#54611yescharacteristic
620C4C11×#54611yescharacteristic
621C2—42no—
622C2—42no—
623C2—84no—
624C2C11×#240811yescharacteristic
625C2C11×#305011yescharacteristic
626C2C11×#306111yescharacteristic
627C2C11×#328011yescharacteristic
628C2C11×#328311yescharacteristic
629C2C11×#328511yescharacteristic
630C2C11×#328711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C22×C11×#135C2semidirect
2. C2×C11×#467C2semidirect
3. C2×C11×#466C2semidirect
4. C2×C8×D4×C11C2semidirect
5. C11×#2407C2semidirect
6. C11×#2055C2semidirect
7. C11×#2000C2semidirect
8. C11×#1970C2semidirect
9. C11×#1969C2semidirect
10. C11×#1808C2semidirect
11. C11×#1788C2semidirect
62. C2×C11×Q16D4semidirect
68. C2×C11×D8D4semidirect
74. C22×C8×C11D4semidirect
110. #24266C11direct (N × H)
194. C22×#135C2×C11semidirect
195. C2×#467C2×C11semidirect
196. C2×#466C2×C11semidirect
197. C2×C8×D4C2×C11semidirect
198. #2407C2×C11semidirect
199. #2055C2×C11semidirect
200. #2000C2×C11semidirect
201. #1970C2×C11semidirect
202. #1969C2×C11semidirect
203. #1808C2×C11semidirect
204. #1788C2×C11semidirect
225. C23×C11#135semidirect
267. C2×C4×C11#135semidirect
367. C2×Q16D4×C11semidirect
373. C2×D8D4×C11semidirect
379. C22×C8D4×C11semidirect
508. C11#24266direct (N × H)
529. C23C11×#135semidirect
571. C2×C4C11×#135semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C2×C11×#4672
C2×C11×#4662
C2×C8×D4×C112
C11×#24072
C11×#20552
C11×#20002
C11×#19702
C11×#19692
C11×#18082
C11×#17882
#2426611