Finite Group Databasebeta

← C11×#18255 #14595448

Subgroups — C11×#18255 #14595448

Order 2816.

1260 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3537C211yesmaximal, characteristic
2C11×#3004C211yesmaximal, characteristic, complemented
3C2×C11×#448C211yesmaximal, characteristic, complemented
4C11×#2436C211yesmaximal, characteristic, complemented
5C11×#1606C214yesmaximal, complemented
6C11×#1601C214yesmaximal, complemented
7C11×#1507C211yesmaximal, characteristic, complemented
8C11×#1501C211yesmaximal, characteristic, complemented
9C11×#1471C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic, complemented
11C2×C11×#137—21no—
12C22×C11×SD16—21no—
13C11×#560—22no—
14C11×#553—21no—
15C11×#553—21no—
16D42×C11—22no—
17D42×C11—21no—
18D42×C11—21no—
19C11×#540—21no—
20C11×#538—21no—
21C11×#538C2212yes—
22C11×#535—21no—
23C11×#534—21no—
24C11×#534C2212yes—
25C2×C11×#124—21no—
26C11×#525C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C11×#451—21no—
30C11×#451C2212yescomplemented
31C11×#448—22no—
32C11×#448—21no—
33C11×#448C2214yescomplemented
34C11×#448C2212yescomplemented
35C11×#419—21no—
36C2×C11×#103—21no—
37C11×#407C2211yescharacteristic, complemented
38C2×C11×C22⋊C8C2211yescharacteristic, complemented
39C11×#393C2214yescomplemented
40C11×#391—21no—
41C11×#386—22no—
42C4×C11×C22⋊C4C2211yescharacteristic, complemented
43C11×#328C2212yescomplemented
44C11×#327C2212yescomplemented
45C11×#327C2214yescomplemented
46C11×#323C2214yescomplemented
47C2×C11×#41D411yescharacteristic
48C22×Q8×C11—21no—
49C22×Q8×C11—21no—
50C22×Q8×C11—21no—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×Q8×C11—44no—
54C22×Q8×C11C2312yes—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11D412yes—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11D411yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C11×#137—44no—
65C2×C11×Q16—22no—
66C2×C11×SD16—24no—
67C2×C11×SD16—22no—
68C2×C11×SD16—44no—
69C2×C11×M16—21no—
70C22×C8×C11—21no—
71C11×#127—22no—
72C11×#127—21no—
73C11×#126—22no—
74C11×#126—22no—
75C11×#125—21no—
76C11×#124—22no—
77C11×#124—44no—
78C11×#123—22no—
79C11×#123—21no—
80C11×#123—22no—
81C11×#123—22no—
82C11×#123—22no—
83C11×C22⋊Q8D411yescharacteristic
84C11×C22⋊Q8C2311yescharacteristic
85C11×#121—22no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121—21no—
95C11×#121—21no—
96C11×#121—21no—
97C11×#121—21no—
98C11×#121—22no—
99C11×#121D412yes—
100C11×#121D411yescharacteristic
101C11×#121C2312yes—
102C11×#121C2311yescharacteristic
103C11×#120—22no—
104C11×#120—22no—
105C11×#120—22no—
106C11×#120—21no—
107C11×#120—22no—
108C11×#120—22no—
109C11×#120—22no—
110C4×D4×C11—22no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11—21no—
115C4×D4×C11—22no—
116C11×#117—21no—
117C11×#117D411yescharacteristic
118C2×C11×C4⋊C4D411yescharacteristic
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4C2312yes—
124C2×C42×C11—21no—
125C11×#103—24no—
126C11×#103—22no—
127C11×#103—22no—
128C11×C22⋊C8—21no—
129C11×C22⋊C8—21no—
130C11×C22⋊C8C2312yes—
131C11×C22⋊C8C2312yes—
132C11×#95—24no—
133C11×#95C2312yes—
134#18255C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—22no—
136C24×C11—21no—
137C24×C11C2×D411yescharacteristic
138C24×C11C2×D412yes—
139C11×#41—42no—
140C2×Q8×C11—24no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—44no—
146C2×Q8×C11—42no—
147C2×Q8×C11—42no—
148C2×Q8×C11—42no—
149C2×Q8×C11—44no—
150C2×Q8×C11—44no—
151C2×Q8×C11—41no—
152C2×Q8×C11—41no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11—22no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—44no—
172C2×D4×C11—82no—
173C2×D4×C11—82no—
174C2×D4×C11—84no—
175C2×D4×C11—84no—
176C2×D4×C11C2×D411yescharacteristic
177C2×D4×C11C2×D412yes—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—22no—
184C22×C4×C11—42no—
185C22×C4×C11—44no—
186C22×C4×C11—41no—
187C22×C4×C11—41no—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C11×Q16—44no—
196C11×SD16—48no—
197C11×SD16—44no—
198C11×M16—42no—
199C2×C8×C11—22no—
200C2×C8×C11—22no—
201C2×C8×C11—42no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4C2×D412yes—
210C11×C4⋊C4C2×D411yescharacteristic
211C11×C4⋊C4C2×D411yescharacteristic
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—21no—
226C11×C22⋊C4—48no—
227C11×C22⋊C4—42no—
228C42×C11—22no—
229C42×C11—21no—
230C42×C11—42no—
231#3537C2×C1111yescharacteristic
232#3004C2×C1111yescharacteristic, complemented
233C2×#448C2×C1111yescharacteristic, complemented
234#2436C2×C1111yescharacteristic, complemented
235#1606C2×C1114yescomplemented
236#1601C2×C1114yescomplemented
237#1507C2×C1111yescharacteristic, complemented
238#1501C2×C1111yescharacteristic, complemented
239#1471C2×C1111yescharacteristic, complemented
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—21no—
245C23×C11—24no—
246C23×C11—41no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—81no—
251C23×C11—81no—
252C23×C11—82no—
253C23×C11—82no—
254C23×C11—82no—
255C23×C11#12011yescharacteristic
256C23×C11#12011yescharacteristic
257C23×C11C22×D411yescharacteristic
258Q8×C11—24no—
259Q8×C11—24no—
260Q8×C11—41no—
261Q8×C11—44no—
262Q8×C11—42no—
263Q8×C11—42no—
264Q8×C11—44no—
265D4×C11—42no—
266D4×C11—41no—
267D4×C11—44no—
268D4×C11—42no—
269D4×C11—44no—
270D4×C11—42no—
271D4×C11—42no—
272D4×C11—42no—
273D4×C11—81no—
274D4×C11—82no—
275D4×C11—82no—
276D4×C11—81no—
277D4×C11—82no—
278D4×C11—82no—
279D4×C11—82no—
280D4×C11—82no—
281D4×C11—82no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—44no—
296C2×C4×C11—44no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—81no—
304C2×C4×C11—82no—
305C2×C4×C11—82no—
306C2×C4×C11#12011yescharacteristic
307C2×C4×C11#12011yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C22×D411yescharacteristic
310C8×C11—42no—
311C8×C11—42no—
312C23×Q8C22×C1111yescharacteristic, complemented
313C2×#137—21no—
314C22×SD16—21no—
315#560—22no—
316#553—21no—
317#553—21no—
318D42—22no—
319D42—21no—
320D42—21no—
321#540—21no—
322#538—21no—
323#538C22×C1112yes—
324#535—21no—
325#534—21no—
326#534C22×C1112yes—
327C2×#124—21no—
328#525C22×C1111yescharacteristic
329C2×#121C22×C1111yescharacteristic
330C2×#121C22×C1111yescharacteristic
331#451—21no—
332#451C22×C1112yescomplemented
333#448—22no—
334#448—21no—
335#448C22×C1112yescomplemented
336#448C22×C1114yescomplemented
337#419—21no—
338C2×#103—21no—
339#407C22×C1111yescharacteristic, complemented
340C2×C22⋊C8C22×C1111yescharacteristic, complemented
341#393C22×C1114yescomplemented
342#391—21no—
343#386—22no—
344C4×C22⋊C4C22×C1111yescharacteristic, complemented
345#328C22×C1112yescomplemented
346#327C22×C1112yescomplemented
347#327C22×C1114yescomplemented
348#323C22×C1114yescomplemented
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—21no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—44no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—41no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—84no—
367C22×C11—162no—
368C22×C11—164no—
369C22×C11#45512yes—
370C22×C11C2×#12011yescharacteristic
371C22×C11#57712yes—
372C4×C11—21no—
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—42no—
376C4×C11—41no—
377C4×C11—42no—
378C4×C11—41no—
379C4×C11—44no—
380C4×C11—41no—
381C4×C11—82no—
382C4×C11B(4,𝔽2)12yes—
383C2×#41D4×C1111yescharacteristic
384C22×Q8—21no—
385C22×Q8—21no—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×Q8—44no—
390C22×Q8C23×C1112yes—
391C22×D4—22no—
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—22no—
395C22×D4D4×C1111yescharacteristic
396C22×D4D4×C1112yes—
397C22×D4D4×C1111yescharacteristic
398C23×C4—21no—
399C23×C4C23×C1111yescharacteristic
400#137—44no—
401C2×Q16—22no—
402C2×SD16—24no—
403C2×SD16—22no—
404C2×SD16—44no—
405C2×M16—21no—
406C22×C8—21no—
407#127—22no—
408#127—21no—
409#126—22no—
410#126—22no—
411#125—21no—
412#124—22no—
413#124—44no—
414#123—22no—
415#123—21no—
416#123—22no—
417#123—22no—
418#123—22no—
419C22⋊Q8D4×C1111yescharacteristic
420C22⋊Q8C23×C1111yescharacteristic
421#121—22no—
422#121—21no—
423#121—21no—
424#121—22no—
425#121—22no—
426#121—22no—
427#121—22no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121—22no—
435#121D4×C1112yes—
436#121D4×C1111yescharacteristic
437#121C23×C1112yes—
438#121C23×C1111yescharacteristic
439#120—22no—
440#120—22no—
441#120—22no—
442#120—21no—
443#120—22no—
444#120—22no—
445#120—22no—
446C4×D4—22no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—22no—
452#117—21no—
453#117D4×C1111yescharacteristic
454C2×C4⋊C4D4×C1111yescharacteristic
455C2×C4⋊C4D4×C1111yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4C23×C1112yes—
460C2×C42—21no—
461#103—24no—
462#103—22no—
463#103—22no—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8C23×C1112yes—
467C22⋊C8C23×C1112yes—
468#95—24no—
469#95C23×C1112yes—
470C2×C11—22no—
471C2×C11—22no—
472C2×C11—41no—
473C2×C11—82no—
474C2×C11—82no—
475C2×C11—81no—
476C2×C11#300911yescharacteristic
477C2×C11C2×#45511yescharacteristic
478C2×C11C2×B(4,𝔽2)11yescharacteristic
479C24—22no—
480C24—21no—
481C24C2×D4×C1111yescharacteristic
482C24C2×D4×C1112yes—
483#41—42no—
484C2×Q8—24no—
485C2×Q8—24no—
486C2×Q8—24no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—44no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8C2×D4×C1111yescharacteristic
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—44no—
516C2×D4—82no—
517C2×D4—82no—
518C2×D4—84no—
519C2×D4—84no—
520C2×D4C2×D4×C1111yescharacteristic
521C2×D4C2×D4×C1112yes—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—42no—
529C22×C4—44no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1112yes—
536C22×C4C2×D4×C1111yescharacteristic
537C22×C4C2×D4×C1111yescharacteristic
538C22×C4C24×C1111yescharacteristic
539Q16—44no—
540SD16—48no—
541SD16—44no—
542M16—42no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—42no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4C2×D4×C1112yes—
554C4⋊C4C2×D4×C1111yescharacteristic
555C4⋊C4C2×D4×C1111yescharacteristic
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—21no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—21no—
570C22⋊C4—48no—
571C22⋊C4—42no—
572C42—22no—
573C42—21no—
574C42—42no—
575C11#1825511yescharacteristic, direct product factor, Sylow
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—21no—
581C23—24no—
582C23—41no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—81no—
587C23—81no—
588C23—82no—
589C23—82no—
590C23—82no—
591C23C11×#12011yescharacteristic
592C23C11×#12011yescharacteristic
593C23C22×D4×C1111yescharacteristic
594Q8—24no—
595Q8—24no—
596Q8—41no—
597Q8—42no—
598Q8—42no—
599Q8—44no—
600Q8—44no—
601D4—42no—
602D4—41no—
603D4—44no—
604D4—42no—
605D4—44no—
606D4—42no—
607D4—42no—
608D4—42no—
609D4—81no—
610D4—82no—
611D4—82no—
612D4—81no—
613D4—82no—
614D4—82no—
615D4—82no—
616D4—82no—
617D4—82no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—44no—
632C2×C4—44no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—81no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4C11×#12011yescharacteristic
643C2×C4C11×#12011yescharacteristic
644C2×C4C22×D4×C1111yescharacteristic
645C2×C4C22×D4×C1111yescharacteristic
646C8—42no—
647C8—42no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—44no—
656C22—42no—
657C22—42no—
658C22—41no—
659C22—42no—
660C22—42no—
661C22—41no—
662C22—41no—
663C22—42no—
664C22—42no—
665C22—84no—
666C22—162no—
667C22—164no—
668C22C11×#45512yes—
669C22C2×C11×#12011yescharacteristic
670C22C11×#57712yes—
671C4—21no—
672C4—21no—
673C4—21no—
674C4—42no—
675C4—41no—
676C4—42no—
677C4—41no—
678C4—44no—
679C4—41no—
680C4—82no—
681C4C11×B(4,𝔽2)12yes—
682C2—22no—
683C2—22no—
684C2—41no—
685C2—82no—
686C2—82no—
687C2—81no—
688C2C11×#300911yescharacteristic
689C2C2×C11×#45511yescharacteristic
690C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3537C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3004C2semidirect
3. C2×C11×#448C2semidirect
4. C11×#2436C2semidirect
5. C11×#1606C2semidirect
6. C11×#1601C2semidirect
7. C11×#1507C2semidirect
8. C11×#1501C2semidirect
9. C11×#1471C2semidirect
10. C23×Q8×C11C22semidirect
30. C11×#451C22semidirect
33. C11×#448C22semidirect
34. C11×#448C22semidirect
37. C11×#407C22semidirect
38. C2×C11×C22⋊C8C22semidirect
39. C11×#393C22semidirect
42. C4×C11×C22⋊C4C22semidirect
43. C11×#328C22semidirect
44. C11×#327C22semidirect
45. C11×#327C22semidirect
46. C11×#323C22semidirect
134. #18255C11direct (N × H)
232. #3004C2×C11semidirect
233. C2×#448C2×C11semidirect
234. #2436C2×C11semidirect
235. #1606C2×C11semidirect
236. #1601C2×C11semidirect
237. #1507C2×C11semidirect
238. #1501C2×C11semidirect
239. #1471C2×C11semidirect
312. C23×Q8C22×C11semidirect
332. #451C22×C11semidirect
335. #448C22×C11semidirect
336. #448C22×C11semidirect
339. #407C22×C11semidirect
340. C2×C22⋊C8C22×C11semidirect
341. #393C22×C11semidirect
344. C4×C22⋊C4C22×C11semidirect
345. #328C22×C11semidirect
346. #327C22×C11semidirect
347. #327C22×C11semidirect
348. #323C22×C11semidirect
575. C11#18255direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35372
C11×#30042
C2×C11×#4482
C11×#24362
C11×#16062
C11×#16012
C11×#15072
C11×#15012
C11×#14712
#1825511