Finite Group Databasebeta

← C11×#61469 #14638662

Subgroups — C11×#61469 #14638662

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3483C211yesmaximal, characteristic
2Q8×C11×#41C211yesmaximal, characteristic, complemented
3C11×#3392C211yesmaximal, characteristic, complemented
4Q8×C11×Q16C211yesmaximal, characteristic, complemented
5C11×#3363C211yesmaximal, characteristic, complemented
6C11×#3362C211yesmaximal, characteristic, complemented
7C11×#3357C213yesmaximal, complemented
8C11×#3333C213yesmaximal, complemented
9C11×#3329C213yesmaximal, complemented
10C11×#3278C213yesmaximal, complemented
11C11×#3182C213yesmaximal, complemented
12C11×#3116C213yesmaximal, complemented
13C11×#3112C213yesmaximal, complemented
14C11×#2971C211yesmaximal, characteristic, complemented
15C4×C11×#137C213yesmaximal, complemented
16C2×C11×#137C2213yes—
17Q82×C11C2211yescharacteristic
18Q82×C11C2211yescharacteristic
19C11×#557—21no—
20C11×#557C2211yescharacteristic
21C11×#555—23no—
22C11×#555C2213yes—
23C11×#554—23no—
24C11×#554C2213yes—
25C11×#550—21no—
26C11×#550C2213yes—
27C11×#550C2211yescharacteristic
28D4×Q8×C11C2213yes—
29C11×#533—23no—
30C11×#533C2213yes—
31C11×#532—23no—
32C11×#532C2213yes—
33C4×C11×#41—21no—
34C4×C11×#41—21no—
35C4×C11×#41C2213yes—
36C4×C11×#41C2211yescharacteristic
37C2×C4×Q8×C11C2213yes—
38C11×#500C2213yes—
39C11×#492C2213yes—
40C11×#487C2213yes—
41C11×#486C2213yes—
42C11×#485C2216yes—
43C11×#480C2216yes—
44C11×#477C2213yes—
45C11×#477C2213yes—
46C11×#477C2213yes—
47C11×#476C2213yes—
48C11×#468C2216yes—
49C11×#468C2216yes—
50C11×#462C2213yes—
51C11×#461C2213yes—
52C11×#460C2213yes—
53C11×#460C2213yes—
54C11×#452C2216yes—
55C11×#448C2216yes—
56C8×Q8×C11C2211yescharacteristic
57C8×Q8×C11C2211yescharacteristic
58C11×#441C2211yescharacteristic
59C11×#441C2213yes—
60C11×#440C2213yes—
61C11×#440C2216yes—
62C11×#440C2213yes—
63C4×C11×Q16C2213yes—
64C4×C11×Q16C2213yes—
65C4×C11×SD16C2213yes—
66C4×C11×SD16C2213yes—
67C11×#436C2213yes—
68C11×#436C2213yes—
69C11×#432C2213yes—
70C11×#428C2213yes—
71C11×#419C2213yes—
72C11×#417C2213yes—
73C4×C11×M16C2213yes—
74C2×C11×#41—21no—
75C2×C11×#41—23no—
76C2×C11×#41D411yescharacteristic
77C2×C11×#41C2313yes—
78C22×Q8×C11C2313yes—
79C11×#137—212no—
80C2×C11×Q16C2313yes—
81C2×C11×Q16C2311yescharacteristic
82C2×C11×SD16C2313yes—
83C2×C11×SD16C2313yes—
84C2×C11×SD16C2316yes—
85C2×C11×M16C2313yes—
86C2×C11×M16C2313yes—
87C11×C4⋊Q8—23no—
88C11×C4⋊Q8—23no—
89C11×C4⋊Q8—23no—
90C11×C4⋊Q8C2313yes—
91C11×C4⋊Q8C2313yes—
92C11×C4⋊Q8C2313yes—
93C11×#127—23no—
94C11×#127C2313yes—
95C11×#125—23no—
96C11×#125—23no—
97C11×#125—23no—
98C11×#124—26no—
99C11×#124—23no—
100C11×C22⋊Q8—23no—
101C11×C22⋊Q8—26no—
102C11×C22⋊Q8—26no—
103C11×C22⋊Q8C2316yes—
104C11×#121—23no—
105C11×#121—23no—
106C11×#121—23no—
107C11×#121—26no—
108C11×#121C2316yes—
109C4×Q8×C11—21no—
110C4×Q8×C11—21no—
111C4×Q8×C11—21no—
112C4×Q8×C11—23no—
113C4×Q8×C11—23no—
114C4×Q8×C11—23no—
115C4×Q8×C11D411yescharacteristic
116C4×Q8×C11C2311yescharacteristic
117C4×Q8×C11C2313yes—
118C4×Q8×C11C2313yes—
119C4×Q8×C11C2313yes—
120C4×Q8×C11C2311yescharacteristic
121C4×Q8×C11C2313yes—
122C4×Q8×C11C2311yescharacteristic
123C4×D4×C11—23no—
124C4×D4×C11—23no—
125C4×D4×C11—23no—
126C4×D4×C11—23no—
127C4×D4×C11—23no—
128C4×D4×C11—23no—
129C4×D4×C11D413yes—
130C4×D4×C11C2313yes—
131C4×D4×C11C2313yes—
132C4×D4×C11C2313yes—
133C11×#117—23no—
134C11×#117—23no—
135C11×#117—23no—
136C11×#117D413yes—
137C11×#117C2313yes—
138C2×C11×C4⋊C4—23no—
139C2×C11×C4⋊C4C2313yes—
140C2×C42×C11—23no—
141C2×C42×C11—23no—
142C2×C42×C11C2313yes—
143C11×#107C2313yes—
144C11×#107C2316yes—
145C11×#107C2313yes—
146C11×#106C2311yescharacteristic
147C11×#106C2313yes—
148C11×C4⋊C8C2313yes—
149C11×C4⋊C8C2313yes—
150C11×#103C2311yescharacteristic
151C11×#103C2313yes—
152C11×#103C2311yescharacteristic
153C11×#103C2313yes—
154C11×#103C2313yes—
155C11×#103C2313yes—
156C11×#103C2316yes—
157C11×#102C2313yes—
158C11×#102C2313yes—
159C11×#102C2316yes—
160C11×C22⋊C8C2316yes—
161C11×#97C2311yescharacteristic
162C11×#97C2313yes—
163C4×C8×C11C2313yes—
164C4×C8×C11C2313yes—
165#61469C1111yesmaximal, characteristic, direct product factor, Sylow
166C11×#41—24no—
167C11×#41—26no—
168C11×#41—43no—
169C11×#41—44no—
170C11×#41—86no—
171C2×Q8×C11—23no—
172C2×Q8×C11—23no—
173C2×Q8×C11—23no—
174C2×Q8×C11—26no—
175C2×Q8×C11—43no—
176C2×Q8×C11C2×D411yescharacteristic
177C2×Q8×C11C2413yes—
178C2×Q8×C11C2411yescharacteristic
179C2×Q8×C11C2411yescharacteristic
180C2×D4×C11—23no—
181C2×D4×C11—26no—
182C2×D4×C11—23no—
183C2×D4×C11—23no—
184C2×D4×C11C2×D413yes—
185C2×D4×C11C2413yes—
186C22×C4×C11—23no—
187C22×C4×C11—23no—
188C22×C4×C11—23no—
189C22×C4×C11—23no—
190C22×C4×C11—23no—
191C22×C4×C11C2×D413yes—
192C22×C4×C11C2×D413yes—
193C22×C4×C11C2413yes—
194C11×Q16—26no—
195C11×Q16#4114yescomplemented
196C11×SD16—26no—
197C11×SD16—26no—
198C11×SD16—46no—
199C11×M16—26no—
200C11×M16—43no—
201C2×C8×C11C2411yescharacteristic
202C2×C8×C11C2413yes—
203C2×C8×C11C2413yes—
204C2×C8×C11C2411yescharacteristic
205C11×C4⋊C4—21no—
206C11×C4⋊C4—23no—
207C11×C4⋊C4—23no—
208C11×C4⋊C4—23no—
209C11×C4⋊C4—23no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—23no—
212C11×C4⋊C4—23no—
213C11×C4⋊C4—23no—
214C11×C4⋊C4—23no—
215C11×C4⋊C4—23no—
216C11×C4⋊C4—26no—
217C11×C4⋊C4C2×D413yes—
218C11×C4⋊C4C2×D413yes—
219C11×C4⋊C4C2411yescharacteristic
220C11×C4⋊C4C2413yes—
221C11×C4⋊C4C2411yescharacteristic
222C11×C4⋊C4C2413yes—
223C11×C22⋊C4—26no—
224C11×C22⋊C4—23no—
225C11×C22⋊C4—26no—
226C11×C22⋊C4—23no—
227C11×C22⋊C4—23no—
228C11×C22⋊C4C2×D416yes—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—23no—
232C42×C11—23no—
233C42×C11—23no—
234C42×C11—23no—
235C42×C11—23no—
236C42×C11C2×D413yes—
237C42×C11C2×D413yes—
238C42×C11C2413yes—
239C42×C11C2411yescharacteristic
240#3483C2×C1111yescharacteristic
241Q8×#41C2×C1111yescharacteristic, complemented
242#3392C2×C1111yescharacteristic, complemented
243Q8×Q16C2×C1111yescharacteristic, complemented
244#3363C2×C1111yescharacteristic, complemented
245#3362C2×C1111yescharacteristic, complemented
246#3357C2×C1113yescomplemented
247#3333C2×C1113yescomplemented
248#3329C2×C1113yescomplemented
249#3278C2×C1113yescomplemented
250#3182C2×C1113yescomplemented
251#3116C2×C1113yescomplemented
252#3112C2×C1113yescomplemented
253#2971C2×C1111yescharacteristic, complemented
254C4×#137C2×C1113yescomplemented
255C23×C11—23no—
256C23×C11C22×D413yes—
257Q8×C11—21no—
258Q8×C11—21no—
259Q8×C11—23no—
260Q8×C11—23no—
261Q8×C11—46no—
262Q8×C11—83no—
263Q8×C11—83no—
264Q8×C11#13714yescomplemented
265Q8×C11C2×#4112yes—
266Q8×C11C2×#4112yes—
267D4×C11—26no—
268D4×C11—23no—
269D4×C11—23no—
270D4×C11—46no—
271D4×C11—46no—
272D4×C11—83no—
273D4×C11—86no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—26no—
277C2×C4×C11—23no—
278C2×C4×C11—23no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—23no—
282C2×C4×C11—23no—
283C2×C4×C11—23no—
284C2×C4×C11—43no—
285C2×C4×C11—46no—
286C2×C4×C11—46no—
287C2×C4×C11—46no—
288C2×C4×C11—46no—
289C2×C4×C11—83no—
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D413yes—
293C2×C4×C11C22×D413yes—
294C2×C4×C11C22×D413yes—
295C2×C4×C11C2511yescharacteristic
296C8×C11—23no—
297C8×C11—21no—
298C8×C11—23no—
299C8×C11C2×#4112yes—
300C2×#137C22×C1113yes—
301Q82C22×C1111yescharacteristic
302Q82C22×C1111yescharacteristic
303#557—21no—
304#557C22×C1111yescharacteristic
305#555—23no—
306#555C22×C1113yes—
307#554—23no—
308#554C22×C1113yes—
309#550—21no—
310#550C22×C1113yes—
311#550C22×C1111yescharacteristic
312D4×Q8C22×C1113yes—
313#533—23no—
314#533C22×C1113yes—
315#532—23no—
316#532C22×C1113yes—
317C4×#41—21no—
318C4×#41—21no—
319C4×#41C22×C1113yes—
320C4×#41C22×C1111yescharacteristic
321C2×C4×Q8C22×C1113yes—
322#500C22×C1113yes—
323#492C22×C1113yes—
324#487C22×C1113yes—
325#486C22×C1113yes—
326#485C22×C1116yes—
327#480C22×C1116yes—
328#477C22×C1113yes—
329#477C22×C1113yes—
330#477C22×C1113yes—
331#476C22×C1113yes—
332#468C22×C1116yes—
333#468C22×C1116yes—
334#462C22×C1113yes—
335#461C22×C1113yes—
336#460C22×C1113yes—
337#460C22×C1113yes—
338#452C22×C1116yes—
339#448C22×C1116yes—
340C8×Q8C22×C1111yescharacteristic
341C8×Q8C22×C1111yescharacteristic
342#441C22×C1113yes—
343#441C22×C1111yescharacteristic
344#440C22×C1113yes—
345#440C22×C1116yes—
346#440C22×C1113yes—
347C4×Q16C22×C1113yes—
348C4×Q16C22×C1113yes—
349C4×SD16C22×C1113yes—
350C4×SD16C22×C1113yes—
351#436C22×C1113yes—
352#436C22×C1113yes—
353#432C22×C1113yes—
354#428C22×C1113yes—
355#419C22×C1113yes—
356#417C22×C1113yes—
357C4×M16C22×C1113yes—
358C22×C11—23no—
359C22×C11—23no—
360C22×C11—23no—
361C22×C11—43no—
362C22×C11—43no—
363C22×C11—43no—
364C22×C11C23×D411yescharacteristic
365C4×C11—21no—
366C4×C11—23no—
367C4×C11—23no—
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—21no—
371C4×C11—43no—
372C4×C11—41no—
373C4×C11—43no—
374C4×C11—43no—
375C4×C11—41no—
376C4×C11C2×#13716yes—
377C4×C11C22×#4111yescharacteristic
378C4×C11#58511yescharacteristic
379C2×#41—21no—
380C2×#41—23no—
381C2×#41D4×C1111yescharacteristic
382C2×#41C23×C1113yes—
383C22×Q8C23×C1113yes—
384#137—212no—
385C2×Q16C23×C1113yes—
386C2×Q16C23×C1111yescharacteristic
387C2×SD16C23×C1113yes—
388C2×SD16C23×C1113yes—
389C2×SD16C23×C1116yes—
390C2×M16C23×C1113yes—
391C2×M16C23×C1113yes—
392C4⋊Q8—23no—
393C4⋊Q8—23no—
394C4⋊Q8—23no—
395C4⋊Q8C23×C1113yes—
396C4⋊Q8C23×C1113yes—
397C4⋊Q8C23×C1113yes—
398#127—23no—
399#127C23×C1113yes—
400#125—23no—
401#125—23no—
402#125—23no—
403#124—26no—
404#124—23no—
405C22⋊Q8—23no—
406C22⋊Q8—26no—
407C22⋊Q8—26no—
408C22⋊Q8C23×C1116yes—
409#121—23no—
410#121—23no—
411#121—23no—
412#121—26no—
413#121C23×C1116yes—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—23no—
418C4×Q8—23no—
419C4×Q8—23no—
420C4×Q8D4×C1111yescharacteristic
421C4×Q8C23×C1111yescharacteristic
422C4×Q8C23×C1113yes—
423C4×Q8C23×C1113yes—
424C4×Q8C23×C1113yes—
425C4×Q8C23×C1111yescharacteristic
426C4×Q8C23×C1113yes—
427C4×Q8C23×C1111yescharacteristic
428C4×D4—23no—
429C4×D4—23no—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4D4×C1113yes—
435C4×D4C23×C1113yes—
436C4×D4C23×C1113yes—
437C4×D4C23×C1113yes—
438#117—23no—
439#117—23no—
440#117—23no—
441#117D4×C1113yes—
442#117C23×C1113yes—
443C2×C4⋊C4—23no—
444C2×C4⋊C4C23×C1113yes—
445C2×C42—23no—
446C2×C42—23no—
447C2×C42C23×C1113yes—
448#107C23×C1113yes—
449#107C23×C1113yes—
450#107C23×C1116yes—
451#106C23×C1111yescharacteristic
452#106C23×C1113yes—
453C4⋊C8C23×C1113yes—
454C4⋊C8C23×C1113yes—
455#103C23×C1111yescharacteristic
456#103C23×C1113yes—
457#103C23×C1111yescharacteristic
458#103C23×C1113yes—
459#103C23×C1113yes—
460#103C23×C1113yes—
461#103C23×C1116yes—
462#102C23×C1113yes—
463#102C23×C1113yes—
464#102C23×C1116yes—
465C22⋊C8C23×C1116yes—
466#97C23×C1111yescharacteristic
467#97C23×C1113yes—
468C4×C8C23×C1113yes—
469C4×C8C23×C1113yes—
470C2×C11—43no—
471C2×C11—83no—
472C2×C11D4×#4111yescharacteristic
473C2×C11C22×#13711yescharacteristic
474C2×C11#358511yescharacteristic
475#41—24no—
476#41—26no—
477#41—43no—
478#41—44no—
479#41—86no—
480C2×Q8—23no—
481C2×Q8—23no—
482C2×Q8—23no—
483C2×Q8—26no—
484C2×Q8—43no—
485C2×Q8C2×D4×C1111yescharacteristic
486C2×Q8C24×C1113yes—
487C2×Q8C24×C1111yescharacteristic
488C2×Q8C24×C1111yescharacteristic
489C2×D4—23no—
490C2×D4—26no—
491C2×D4—23no—
492C2×D4—23no—
493C2×D4C2×D4×C1113yes—
494C2×D4C24×C1113yes—
495C22×C4—23no—
496C22×C4—23no—
497C22×C4—23no—
498C22×C4—23no—
499C22×C4—23no—
500C22×C4C2×D4×C1113yes—
501C22×C4C2×D4×C1113yes—
502C22×C4C24×C1113yes—
503Q16—26no—
504Q16C11×#4114yescomplemented
505SD16—26no—
506SD16—26no—
507SD16—46no—
508M16—26no—
509M16—43no—
510C2×C8C24×C1111yescharacteristic
511C2×C8C24×C1113yes—
512C2×C8C24×C1113yes—
513C2×C8C24×C1111yescharacteristic
514C4⋊C4—21no—
515C4⋊C4—23no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—21no—
520C4⋊C4—23no—
521C4⋊C4—23no—
522C4⋊C4—23no—
523C4⋊C4—23no—
524C4⋊C4—23no—
525C4⋊C4—26no—
526C4⋊C4C2×D4×C1113yes—
527C4⋊C4C2×D4×C1113yes—
528C4⋊C4C24×C1111yescharacteristic
529C4⋊C4C24×C1113yes—
530C4⋊C4C24×C1111yescharacteristic
531C4⋊C4C24×C1113yes—
532C22⋊C4—26no—
533C22⋊C4—23no—
534C22⋊C4—26no—
535C22⋊C4—23no—
536C22⋊C4—23no—
537C22⋊C4C2×D4×C1116yes—
538C42—21no—
539C42—21no—
540C42—23no—
541C42—23no—
542C42—23no—
543C42—23no—
544C42—23no—
545C42C2×D4×C1113yes—
546C42C2×D4×C1113yes—
547C42C24×C1113yes—
548C42C24×C1111yescharacteristic
549C11#6146911yescharacteristic, direct product factor, Sylow
550C23—23no—
551C23C22×D4×C1113yes—
552Q8—21no—
553Q8—21no—
554Q8—23no—
555Q8—23no—
556Q8—46no—
557Q8—83no—
558Q8—83no—
559Q8C11×#13714yescomplemented
560Q8C2×C11×#4112yes—
561Q8C2×C11×#4112yes—
562D4—26no—
563D4—23no—
564D4—23no—
565D4—46no—
566D4—46no—
567D4—83no—
568D4—86no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—26no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—23no—
577C2×C4—23no—
578C2×C4—23no—
579C2×C4—43no—
580C2×C4—46no—
581C2×C4—46no—
582C2×C4—46no—
583C2×C4—46no—
584C2×C4—83no—
585C2×C4C22×D4×C1111yescharacteristic
586C2×C4C22×D4×C1111yescharacteristic
587C2×C4C22×D4×C1113yes—
588C2×C4C22×D4×C1113yes—
589C2×C4C22×D4×C1113yes—
590C2×C4C25×C1111yescharacteristic
591C8—23no—
592C8—21no—
593C8—23no—
594C8C2×C11×#4112yes—
595C22—23no—
596C22—23no—
597C22—23no—
598C22—43no—
599C22—43no—
600C22—43no—
601C22C23×D4×C1111yescharacteristic
602C4—23no—
603C4—22no—
604C4—22no—
605C4—21no—
606C4—21no—
607C4—23no—
608C4—43no—
609C4—41no—
610C4—43no—
611C4—41no—
612C4—43no—
613C4C2×C11×#13716yes—
614C4C22×C11×#4111yescharacteristic
615C4C11×#58511yescharacteristic
616C2—43no—
617C2—83no—
618C2D4×C11×#4111yescharacteristic
619C2C22×C11×#13711yescharacteristic
620C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3483C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C11×#41C2semidirect
3. C11×#3392C2semidirect
4. Q8×C11×Q16C2semidirect
5. C11×#3363C2semidirect
6. C11×#3362C2semidirect
7. C11×#3357C2semidirect
8. C11×#3333C2semidirect
9. C11×#3329C2semidirect
10. C11×#3278C2semidirect
11. C11×#3182C2semidirect
12. C11×#3116C2semidirect
13. C11×#3112C2semidirect
14. C11×#2971C2semidirect
15. C4×C11×#137C2semidirect
165. #61469C11direct (N × H)
195. C11×Q16#41semidirect
241. Q8×#41C2×C11semidirect
242. #3392C2×C11semidirect
243. Q8×Q16C2×C11semidirect
244. #3363C2×C11semidirect
245. #3362C2×C11semidirect
246. #3357C2×C11semidirect
247. #3333C2×C11semidirect
248. #3329C2×C11semidirect
249. #3278C2×C11semidirect
250. #3182C2×C11semidirect
251. #3116C2×C11semidirect
252. #3112C2×C11semidirect
253. #2971C2×C11semidirect
254. C4×#137C2×C11semidirect
264. Q8×C11#137semidirect
504. Q16C11×#41semidirect
549. C11#61469direct (N × H)
559. Q8C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#34832
Q8×C11×#412
C11×#33922
Q8×C11×Q162
C11×#33632
C11×#33622
C11×#33572
C11×#33332
C11×#33292
C11×#32782
C11×#31822
C11×#31162
C11×#31122
C11×#29712
C4×C11×#1372
#6146911