Finite Group Databasebeta

← C11×#18955 #14596148

Subgroups — C11×#18955 #14596148

Order 2816.

938 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
1C11×#3546C211yesmaximal, characteristic
2C11×#3238C211yesmaximal, characteristic, complemented
3C11×#3227C211yesmaximal, characteristic, complemented
4C11×#3206C211yesmaximal, characteristic, complemented
5C11×#1638C212yesmaximal, complemented
6C11×#1635C212yesmaximal, complemented
7C11×#1631C212yesmaximal, complemented
8C11×#1629C212yesmaximal, complemented
9C11×#1553C211yesmaximal, characteristic, complemented
10C11×#1496C211yesmaximal, characteristic, complemented
11C11×#1482C211yesmaximal, characteristic, complemented
12C11×#560—22no—
13C11×#556C2211yescharacteristic
14C11×#553—21no—
15C11×#550—21no—
16C11×#550C2211yescharacteristic
17C11×#547C2211yescharacteristic
18C11×#546—21no—
19C11×#546—21no—
20D42×C11C2211yescharacteristic
21C11×#542—21no—
22C11×#538—22no—
23C11×#537—21no—
24C11×#535—21no—
25C11×#535—21no—
26C11×#532C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic, complemented
29C11×#529C2211yescharacteristic
30C11×#501—21no—
31C11×#498—21no—
32C11×#492C2212yes—
33C11×#489—21no—
34C11×#487C2212yescomplemented
35C11×#486—21no—
36C11×#483—21no—
37C11×#481—21no—
38C11×#481—21no—
39C11×#480—21no—
40C11×#477C2212yescomplemented
41C11×#476C2212yes—
42C11×#476C2212yes—
43C11×#476C2212yescomplemented
44C11×#461—22no—
45C11×#448—22no—
46C11×#432C2211yescharacteristic, complemented
47C11×#431C2211yescharacteristic, complemented
48C11×#431C2211yescharacteristic, complemented
49C11×#332C2212yescomplemented
50C11×#331C2212yes—
51C11×Q8⋊C8C2212yescomplemented
52C11×D4⋊C8C2212yes—
53C11×D4⋊C8C2212yes—
54C11×D4⋊C8C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C22×Q8×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C2×C11×SD16—24no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8C2312yes—
68C11×C4⋊Q8C2311yescharacteristic
69C11×#127—22no—
70C11×#127—21no—
71C11×#127D411yescharacteristic
72C11×#127C2311yescharacteristic
73C11×#126—22no—
74C11×#126—22no—
75C11×#126—21no—
76C11×#125D411yescharacteristic
77C11×#124—22no—
78C11×#124—21no—
79C11×#124—21no—
80C11×#124—21no—
81C11×#124D411yescharacteristic
82C11×#123—22no—
83C11×#123—22no—
84C11×#123—21no—
85C11×#123—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8D411yescharacteristic
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—22no—
93C11×#121—22no—
94C11×#121—22no—
95C11×#121—21no—
96C11×#121—22no—
97C11×#121—21no—
98C11×#121—21no—
99C11×#121—21no—
100C11×#121—21no—
101C11×#121—21no—
102C11×#121D411yescharacteristic
103C11×#121D411yescharacteristic
104C11×#121D411yescharacteristic
105C11×#121D412yes—
106C11×#120—22no—
107C11×#120—22no—
108C11×#120—22no—
109C11×#120—22no—
110C4×Q8×C11—21no—
111C4×Q8×C11C2311yescharacteristic
112C4×D4×C11—22no—
113C4×D4×C11—21no—
114C4×D4×C11—21no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11D412yes—
118C4×D4×C11C2311yescharacteristic
119C4×D4×C11C2311yescharacteristic
120C4×D4×C11C2311yescharacteristic
121C11×#117—21no—
122C11×#117—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C22⋊C4—22no—
127C2×C42×C11C2311yescharacteristic
128C11×#107—22no—
129C11×#106—22no—
130C11×#106—22no—
131C11×#106—22no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#103—22no—
136C11×#103—24no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—22no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C4×C8×C11—21no—
145C4×C8×C11C2312yes—
146#18955C1111yesmaximal, characteristic, direct product factor, Sylow
147C24×C11—22no—
148C11×#41—82no—
149C11×#41—82no—
150C11×#41—82no—
151C11×#41—82no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—22no—
155C2×Q8×C11—41no—
156C2×Q8×C11—82no—
157C2×Q8×C11C2×D411yescharacteristic
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—21no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—82no—
172C2×D4×C11—82no—
173C2×D4×C11C2×D411yescharacteristic
174C2×D4×C11C2×D411yescharacteristic
175C2×D4×C11C2×D411yescharacteristic
176C2×D4×C11C2×D412yes—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—22no—
183C22×C4×C11—41no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C11×SD16—84no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4C2×D412yes—
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—21no—
224C42×C11—22no—
225C42×C11—21no—
226C42×C11C2×D411yescharacteristic
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2411yescharacteristic
230#3546C2×C1111yescharacteristic
231#3238C2×C1111yescharacteristic, complemented
232#3227C2×C1111yescharacteristic, complemented
233#3206C2×C1111yescharacteristic, complemented
234#1638C2×C1112yescomplemented
235#1635C2×C1112yescomplemented
236#1631C2×C1112yescomplemented
237#1629C2×C1112yescomplemented
238#1553C2×C1111yescharacteristic, complemented
239#1496C2×C1111yescharacteristic, complemented
240#1482C2×C1111yescharacteristic, complemented
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—22no—
244C23×C11—21no—
245C23×C11—82no—
246C23×C11—82no—
247C23×C11—82no—
248C23×C11#12011yescharacteristic
249Q8×C11—22no—
250Q8×C11—44no—
251Q8×C11—42no—
252Q8×C11—81no—
253Q8×C11—82no—
254D4×C11—22no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—42no—
258D4×C11—42no—
259D4×C11—42no—
260D4×C11—81no—
261D4×C11—81no—
262D4×C11—81no—
263D4×C11—81no—
264D4×C11—81no—
265D4×C11—82no—
266D4×C11—82no—
267D4×C11—82no—
268D4×C11—82no—
269D4×C11—82no—
270D4×C11—82no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—41no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—82no—
285C2×C4×C11—82no—
286C2×C4×C11—82no—
287C2×C4×C11—82no—
288C2×C4×C11#12011yescharacteristic
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C8×C11—42no—
295C8×C11—42no—
296C8×C11—42no—
297#560—22no—
298#556C22×C1111yescharacteristic
299#553—21no—
300#550—21no—
301#550C22×C1111yescharacteristic
302#547C22×C1111yescharacteristic
303#546—21no—
304#546—21no—
305D42C22×C1111yescharacteristic
306#542—21no—
307#538—22no—
308#537—21no—
309#535—21no—
310#535—21no—
311#532C22×C1111yescharacteristic
312#532C22×C1111yescharacteristic
313C2×C4⋊Q8C22×C1111yescharacteristic, complemented
314#529C22×C1111yescharacteristic
315#501—21no—
316#498—21no—
317#492C22×C1112yes—
318#489—21no—
319#487C22×C1112yescomplemented
320#486—21no—
321#483—21no—
322#481—21no—
323#481—21no—
324#480—21no—
325#477C22×C1112yescomplemented
326#476C22×C1112yes—
327#476C22×C1112yes—
328#476C22×C1112yescomplemented
329#461—22no—
330#448—22no—
331#432C22×C1111yescharacteristic, complemented
332#431C22×C1111yescharacteristic, complemented
333#431C22×C1111yescharacteristic, complemented
334#332C22×C1112yescomplemented
335#331C22×C1112yes—
336Q8⋊C8C22×C1112yescomplemented
337D4⋊C8C22×C1112yes—
338D4⋊C8C22×C1112yes—
339D4⋊C8C22×C1112yescomplemented
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—42no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—164no—
356C22×C11C2×#12011yescharacteristic
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—82no—
368C4×C11#57712yes—
369C4×C11#57712yes—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374C22×Q8—21no—
375C22×D4—21no—
376C22×D4—21no—
377C2×SD16—24no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8D4×C1111yescharacteristic
382C4⋊Q8C23×C1112yes—
383C4⋊Q8C23×C1111yescharacteristic
384#127—22no—
385#127—21no—
386#127D4×C1111yescharacteristic
387#127C23×C1111yescharacteristic
388#126—22no—
389#126—22no—
390#126—21no—
391#125D4×C1111yescharacteristic
392#124—22no—
393#124—21no—
394#124—21no—
395#124—21no—
396#124D4×C1111yescharacteristic
397#123—22no—
398#123—22no—
399#123—21no—
400#123—22no—
401C22⋊Q8—22no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8D4×C1111yescharacteristic
405#121—22no—
406#121—22no—
407#121—22no—
408#121—22no—
409#121—22no—
410#121—21no—
411#121—22no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121—21no—
417#121D4×C1111yescharacteristic
418#121D4×C1111yescharacteristic
419#121D4×C1111yescharacteristic
420#121D4×C1112yes—
421#120—22no—
422#120—22no—
423#120—22no—
424#120—22no—
425C4×Q8—21no—
426C4×Q8C23×C1111yescharacteristic
427C4×D4—22no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4D4×C1112yes—
433C4×D4C23×C1111yescharacteristic
434C4×D4C23×C1111yescharacteristic
435C4×D4C23×C1111yescharacteristic
436#117—21no—
437#117—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C22⋊C4—22no—
442C2×C42C23×C1111yescharacteristic
443#107—22no—
444#106—22no—
445#106—22no—
446#106—22no—
447C4⋊C8—21no—
448C4⋊C8C23×C1112yes—
449C4⋊C8C23×C1112yes—
450#103—22no—
451#103—24no—
452#102—22no—
453#102—22no—
454#102—22no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457C22⋊C8—21no—
458#97—21no—
459C4×C8—21no—
460C4×C8C23×C1112yes—
461C2×C11—41no—
462C2×C11—81no—
463C2×C11—82no—
464C2×C11—81no—
465C2×C11—81no—
466C2×C11#300911yescharacteristic
467C2×C11#300911yescharacteristic
468C2×C11#302111yescharacteristic
469C24—22no—
470#41—82no—
471#41—82no—
472#41—82no—
473#41—82no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—22no—
477C2×Q8—41no—
478C2×Q8—82no—
479C2×Q8C2×D4×C1111yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—82no—
494C2×D4—82no—
495C2×D4C2×D4×C1111yescharacteristic
496C2×D4C2×D4×C1111yescharacteristic
497C2×D4C2×D4×C1111yescharacteristic
498C2×D4C2×D4×C1112yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—41no—
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C2×D4×C1111yescharacteristic
508C22×C4C2×D4×C1111yescharacteristic
509SD16—84no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4C2×D4×C1112yes—
526C4⋊C4C2×D4×C1111yescharacteristic
527C4⋊C4C2×D4×C1111yescharacteristic
528C4⋊C4C2×D4×C1111yescharacteristic
529C4⋊C4C2×D4×C1111yescharacteristic
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C42—22no—
547C42—21no—
548C42C2×D4×C1111yescharacteristic
549C42C2×D4×C1111yescharacteristic
550C42C2×D4×C1111yescharacteristic
551C42C24×C1111yescharacteristic
552C11#1895511yescharacteristic, direct product factor, Sylow
553C23—21no—
554C23—21no—
555C23—22no—
556C23—21no—
557C23—82no—
558C23—82no—
559C23—82no—
560C23C11×#12011yescharacteristic
561Q8—22no—
562Q8—44no—
563Q8—42no—
564Q8—81no—
565Q8—82no—
566D4—22no—
567D4—22no—
568D4—22no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—81no—
573D4—81no—
574D4—81no—
575D4—81no—
576D4—81no—
577D4—82no—
578D4—82no—
579D4—82no—
580D4—82no—
581D4—82no—
582D4—82no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4C11×#12011yescharacteristic
601C2×C4C11×#12011yescharacteristic
602C2×C4C11×#12011yescharacteristic
603C2×C4C22×D4×C1111yescharacteristic
604C2×C4C22×D4×C1111yescharacteristic
605C2×C4C22×D4×C1111yescharacteristic
606C8—42no—
607C8—42no—
608C8—42no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—164no—
625C22C2×C11×#12011yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—82no—
637C4C11×#57712yes—
638C4C11×#57712yes—
639C2—41no—
640C2—81no—
641C2—81no—
642C2—82no—
643C2—81no—
644C2C11×#300911yescharacteristic
645C2C11×#300911yescharacteristic
646C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3546C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3238C2semidirect
3. C11×#3227C2semidirect
4. C11×#3206C2semidirect
5. C11×#1638C2semidirect
6. C11×#1635C2semidirect
7. C11×#1631C2semidirect
8. C11×#1629C2semidirect
9. C11×#1553C2semidirect
10. C11×#1496C2semidirect
11. C11×#1482C2semidirect
28. C2×C11×C4⋊Q8C22semidirect
34. C11×#487C22semidirect
40. C11×#477C22semidirect
43. C11×#476C22semidirect
46. C11×#432C22semidirect
47. C11×#431C22semidirect
48. C11×#431C22semidirect
49. C11×#332C22semidirect
51. C11×Q8⋊C8C22semidirect
54. C11×D4⋊C8C22semidirect
146. #18955C11direct (N × H)
231. #3238C2×C11semidirect
232. #3227C2×C11semidirect
233. #3206C2×C11semidirect
234. #1638C2×C11semidirect
235. #1635C2×C11semidirect
236. #1631C2×C11semidirect
237. #1629C2×C11semidirect
238. #1553C2×C11semidirect
239. #1496C2×C11semidirect
240. #1482C2×C11semidirect
313. C2×C4⋊Q8C22×C11semidirect
319. #487C22×C11semidirect
325. #477C22×C11semidirect
328. #476C22×C11semidirect
331. #432C22×C11semidirect
332. #431C22×C11semidirect
333. #431C22×C11semidirect
334. #332C22×C11semidirect
336. Q8⋊C8C22×C11semidirect
339. D4⋊C8C22×C11semidirect
552. C11#18955direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35462
C11×#32382
C11×#32272
C11×#32062
C11×#16382
C11×#16352
C11×#16312
C11×#16292
C11×#15532
C11×#14962
C11×#14822
#1895511