Finite Group Databasebeta

← C11×#61470 #14638663

Subgroups — C11×#61470 #14638663

Order 2816.

1812 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3482C211yesmaximal, characteristic
2Q8×C11×#41C211yesmaximal, characteristic, complemented
3C11×#3395C211yesmaximal, characteristic, complemented
4Q8×C11×SD16C211yesmaximal, characteristic, complemented
5C11×#3363C211yesmaximal, characteristic, complemented
6C11×#3359C211yesmaximal, characteristic, complemented
7C11×#3356C213yesmaximal, complemented
8C11×#3331C213yesmaximal, complemented
9C11×#3328C213yesmaximal, complemented
10C11×#3276C213yesmaximal, complemented
11C11×#3185C213yesmaximal, complemented
12C11×#3116C213yesmaximal, complemented
13C11×#3113C213yesmaximal, complemented
14C11×#2971C211yesmaximal, characteristic, complemented
15C4×C11×#137C213yesmaximal, complemented
16C2×C11×#137C2213yes—
17Q82×C11C2211yescharacteristic
18C11×#557—21no—
19C11×#557C2211yescharacteristic
20C11×#557C2211yescharacteristic
21C11×#556C2213yes—
22C11×#554—23no—
23C11×#554C2213yes—
24C11×#552—23no—
25D4×Q8×C11C2213yes—
26D4×Q8×C11C2211yescharacteristic
27C11×#548—21no—
28C11×#547C2213yes—
29C11×#533—23no—
30C11×#533C2213yes—
31C11×#533C2213yes—
32C11×#529—23no—
33C4×C11×#41—21no—
34C4×C11×#41C2213yes—
35C4×C11×#41C2211yescharacteristic
36C2×C4×Q8×C11—21no—
37C2×C4×Q8×C11C2213yes—
38C11×#498C2213yes—
39C11×#494C2213yes—
40C11×#487C2213yes—
41C11×#487C2213yes—
42C11×#485C2216yes—
43C11×#483C2216yes—
44C11×#477C2213yes—
45C11×#476C2213yes—
46C11×#475C2213yes—
47C11×#475C2213yes—
48C11×#470C2216yes—
49C11×#470C2216yes—
50C11×#462C2213yes—
51C11×#462C2213yes—
52C11×#462C2213yes—
53C11×#461C2213yes—
54C11×#452C2216yes—
55C11×#451C2216yes—
56C8×Q8×C11C2211yescharacteristic
57C8×Q8×C11C2211yescharacteristic
58C11×#441C2213yes—
59C11×#441C2216yes—
60C11×#441C2213yes—
61C11×#440C2211yescharacteristic
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×#41D411yescharacteristic
75C2×C11×#41C2313yes—
76C22×Q8×C11—21no—
77C22×Q8×C11C2313yes—
78C11×#137—212no—
79C2×C11×Q16C2313yes—
80C2×C11×Q16C2313yes—
81C2×C11×Q16C2316yes—
82C2×C11×SD16C2313yes—
83C2×C11×SD16C2311yescharacteristic
84C2×C11×M16C2313yes—
85C2×C11×M16C2313yes—
86C11×C4⋊Q8—23no—
87C11×C4⋊Q8—23no—
88C11×C4⋊Q8C2313yes—
89C11×C4⋊Q8C2313yes—
90C11×C4⋊Q8C2313yes—
91C11×C4⋊Q8C2313yes—
92C11×#126—26no—
93C11×#125—23no—
94C11×#125—23no—
95C11×#125—23no—
96C11×#125—23no—
97C11×#125—23no—
98C11×#124—23no—
99C11×#123—26no—
100C11×C22⋊Q8—23no—
101C11×C22⋊Q8—23no—
102C11×C22⋊Q8—23no—
103C11×C22⋊Q8—26no—
104C11×C22⋊Q8—26no—
105C11×C22⋊Q8C2316yes—
106C11×C22⋊Q8C2316yes—
107C11×#121—23no—
108C4×Q8×C11—21no—
109C4×Q8×C11—21no—
110C4×Q8×C11—21no—
111C4×Q8×C11—23no—
112C4×Q8×C11—23no—
113C4×Q8×C11—23no—
114C4×Q8×C11—23no—
115C4×Q8×C11—23no—
116C4×Q8×C11D411yescharacteristic
117C4×Q8×C11C2311yescharacteristic
118C4×Q8×C11C2313yes—
119C4×Q8×C11C2313yes—
120C4×Q8×C11C2313yes—
121C4×Q8×C11C2313yes—
122C4×Q8×C11C2313yes—
123C4×Q8×C11C2311yescharacteristic
124C4×D4×C11—23no—
125C4×D4×C11—23no—
126C4×D4×C11—23no—
127C4×D4×C11—23no—
128C4×D4×C11D413yes—
129C4×D4×C11C2311yescharacteristic
130C4×D4×C11C2313yes—
131C4×D4×C11C2313yes—
132C11×#117—23no—
133C11×#117—23no—
134C11×#117—23no—
135C11×#117D413yes—
136C11×#117C2313yes—
137C2×C11×C4⋊C4—23no—
138C2×C11×C4⋊C4—23no—
139C2×C11×C4⋊C4C2313yes—
140C2×C42×C11—23no—
141C2×C42×C11—23no—
142C2×C42×C11C2313yes—
143C11×#107C2311yescharacteristic
144C11×#107C2313yes—
145C11×#106C2313yes—
146C11×#106C2316yes—
147C11×#106C2313yes—
148C11×C4⋊C8C2313yes—
149C11×C4⋊C8C2313yes—
150C11×#103C2313yes—
151C11×#103C2313yes—
152C11×#103C2311yescharacteristic
153C11×#103C2313yes—
154C11×#103C2313yes—
155C11×#103C2313yes—
156C11×#103C2316yes—
157C11×#103C2316yes—
158C11×#102C2311yescharacteristic
159C11×#102C2313yes—
160C11×C22⋊C8C2316yes—
161C11×#97C2311yescharacteristic
162C11×#97C2313yes—
163C4×C8×C11C2313yes—
164C4×C8×C11C2313yes—
165#61470C1111yesmaximal, characteristic, direct product factor, Sylow
166C11×#41—24no—
167C11×#41—26no—
168C11×#41—43no—
169C2×Q8×C11—23no—
170C2×Q8×C11—23no—
171C2×Q8×C11—23no—
172C2×Q8×C11—26no—
173C2×Q8×C11—43no—
174C2×Q8×C11—44no—
175C2×Q8×C11C2×D411yescharacteristic
176C2×Q8×C11C2413yes—
177C2×Q8×C11C2413yes—
178C2×Q8×C11C2411yescharacteristic
179C2×D4×C11—23no—
180C2×D4×C11C2×D413yes—
181C2×D4×C11C2411yescharacteristic
182C22×C4×C11—23no—
183C22×C4×C11—23no—
184C22×C4×C11—21no—
185C22×C4×C11—23no—
186C22×C4×C11—23no—
187C22×C4×C11C2×D413yes—
188C22×C4×C11C2×D413yes—
189C22×C4×C11C2413yes—
190C11×Q16—26no—
191C11×Q16—26no—
192C11×Q16—46no—
193C11×SD16—26no—
194C11×SD16#4114yescomplemented
195C11×M16—26no—
196C11×M16—43no—
197C2×C8×C11C2411yescharacteristic
198C2×C8×C11C2413yes—
199C2×C8×C11C2413yes—
200C2×C8×C11C2411yescharacteristic
201C11×C4⋊C4—21no—
202C11×C4⋊C4—23no—
203C11×C4⋊C4—26no—
204C11×C4⋊C4—23no—
205C11×C4⋊C4—23no—
206C11×C4⋊C4—23no—
207C11×C4⋊C4—23no—
208C11×C4⋊C4—23no—
209C11×C4⋊C4—23no—
210C11×C4⋊C4—23no—
211C11×C4⋊C4—23no—
212C11×C4⋊C4—23no—
213C11×C4⋊C4—23no—
214C11×C4⋊C4—23no—
215C11×C4⋊C4—26no—
216C11×C4⋊C4C2×D413yes—
217C11×C4⋊C4C2×D413yes—
218C11×C4⋊C4C2411yescharacteristic
219C11×C4⋊C4C2413yes—
220C11×C4⋊C4C2413yes—
221C11×C4⋊C4C2411yescharacteristic
222C11×C22⋊C4—26no—
223C11×C22⋊C4—26no—
224C11×C22⋊C4—23no—
225C11×C22⋊C4—21no—
226C11×C22⋊C4—23no—
227C11×C22⋊C4C2×D416yes—
228C42×C11—21no—
229C42×C11—23no—
230C42×C11—23no—
231C42×C11—23no—
232C42×C11—23no—
233C42×C11—23no—
234C42×C11—23no—
235C42×C11C2×D413yes—
236C42×C11C2×D413yes—
237C42×C11C2413yes—
238C42×C11C2411yescharacteristic
239#3482C2×C1111yescharacteristic
240Q8×#41C2×C1111yescharacteristic, complemented
241#3395C2×C1111yescharacteristic, complemented
242Q8×SD16C2×C1111yescharacteristic, complemented
243#3363C2×C1111yescharacteristic, complemented
244#3359C2×C1111yescharacteristic, complemented
245#3356C2×C1113yescomplemented
246#3331C2×C1113yescomplemented
247#3328C2×C1113yescomplemented
248#3276C2×C1113yescomplemented
249#3185C2×C1113yescomplemented
250#3116C2×C1113yescomplemented
251#3113C2×C1113yescomplemented
252#2971C2×C1111yescharacteristic, complemented
253C4×#137C2×C1113yescomplemented
254C23×C11—21no—
255C23×C11C22×D413yes—
256Q8×C11—21no—
257Q8×C11—23no—
258Q8×C11—23no—
259Q8×C11—23no—
260Q8×C11—23no—
261Q8×C11—46no—
262Q8×C11—46no—
263Q8×C11—83no—
264Q8×C11#13714yescomplemented
265Q8×C11C2×#4112yes—
266D4×C11—26no—
267D4×C11—21no—
268D4×C11—46no—
269D4×C11C2×#4112yes—
270C2×C4×C11—21no—
271C2×C4×C11—26no—
272C2×C4×C11—23no—
273C2×C4×C11—23no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—23no—
277C2×C4×C11—23no—
278C2×C4×C11—23no—
279C2×C4×C11—23no—
280C2×C4×C11—43no—
281C2×C4×C11—46no—
282C2×C4×C11—46no—
283C2×C4×C11—42no—
284C2×C4×C11—46no—
285C2×C4×C11—83no—
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D413yes—
289C2×C4×C11C22×D413yes—
290C2×C4×C11C22×D413yes—
291C2×C4×C11C2511yescharacteristic
292C8×C11—23no—
293C8×C11—21no—
294C8×C11—23no—
295C8×C11C2×#4112yes—
296C2×#137C22×C1113yes—
297Q82C22×C1111yescharacteristic
298#557—21no—
299#557C22×C1111yescharacteristic
300#557C22×C1111yescharacteristic
301#556C22×C1113yes—
302#554—23no—
303#554C22×C1113yes—
304#552—23no—
305D4×Q8C22×C1113yes—
306D4×Q8C22×C1111yescharacteristic
307#548—21no—
308#547C22×C1113yes—
309#533—23no—
310#533C22×C1113yes—
311#533C22×C1113yes—
312#529—23no—
313C4×#41—21no—
314C4×#41C22×C1113yes—
315C4×#41C22×C1111yescharacteristic
316C2×C4×Q8—21no—
317C2×C4×Q8C22×C1113yes—
318#498C22×C1113yes—
319#494C22×C1113yes—
320#487C22×C1113yes—
321#487C22×C1113yes—
322#485C22×C1116yes—
323#483C22×C1116yes—
324#477C22×C1113yes—
325#476C22×C1113yes—
326#475C22×C1113yes—
327#475C22×C1113yes—
328#470C22×C1116yes—
329#470C22×C1116yes—
330#462C22×C1113yes—
331#462C22×C1113yes—
332#462C22×C1113yes—
333#461C22×C1113yes—
334#452C22×C1116yes—
335#451C22×C1116yes—
336C8×Q8C22×C1111yescharacteristic
337C8×Q8C22×C1111yescharacteristic
338#441C22×C1113yes—
339#441C22×C1116yes—
340#441C22×C1113yes—
341#440C22×C1113yes—
342#440C22×C1111yescharacteristic
343C4×Q16C22×C1113yes—
344C4×Q16C22×C1113yes—
345C4×SD16C22×C1113yes—
346C4×SD16C22×C1113yes—
347#436C22×C1113yes—
348#436C22×C1113yes—
349#432C22×C1113yes—
350#428C22×C1113yes—
351#419C22×C1113yes—
352#417C22×C1113yes—
353C4×M16C22×C1113yes—
354C22×C11—23no—
355C22×C11—23no—
356C22×C11—22no—
357C22×C11—23no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11C23×D411yescharacteristic
361C4×C11—21no—
362C4×C11—23no—
363C4×C11—23no—
364C4×C11—22no—
365C4×C11—21no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—43no—
369C4×C11—43no—
370C4×C11—43no—
371C4×C11—43no—
372C4×C11C2×#13716yes—
373C4×C11C22×#4111yescharacteristic
374C4×C11#58511yescharacteristic
375C2×#41D4×C1111yescharacteristic
376C2×#41C23×C1113yes—
377C22×Q8—21no—
378C22×Q8C23×C1113yes—
379#137—212no—
380C2×Q16C23×C1113yes—
381C2×Q16C23×C1113yes—
382C2×Q16C23×C1116yes—
383C2×SD16C23×C1113yes—
384C2×SD16C23×C1111yescharacteristic
385C2×M16C23×C1113yes—
386C2×M16C23×C1113yes—
387C4⋊Q8—23no—
388C4⋊Q8—23no—
389C4⋊Q8C23×C1113yes—
390C4⋊Q8C23×C1113yes—
391C4⋊Q8C23×C1113yes—
392C4⋊Q8C23×C1113yes—
393#126—26no—
394#125—23no—
395#125—23no—
396#125—23no—
397#125—23no—
398#125—23no—
399#124—23no—
400#123—26no—
401C22⋊Q8—23no—
402C22⋊Q8—23no—
403C22⋊Q8—23no—
404C22⋊Q8—26no—
405C22⋊Q8—26no—
406C22⋊Q8C23×C1116yes—
407C22⋊Q8C23×C1116yes—
408#121—23no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—23no—
413C4×Q8—23no—
414C4×Q8—23no—
415C4×Q8—23no—
416C4×Q8—23no—
417C4×Q8D4×C1111yescharacteristic
418C4×Q8C23×C1111yescharacteristic
419C4×Q8C23×C1113yes—
420C4×Q8C23×C1113yes—
421C4×Q8C23×C1113yes—
422C4×Q8C23×C1113yes—
423C4×Q8C23×C1113yes—
424C4×Q8C23×C1111yescharacteristic
425C4×D4—23no—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4—23no—
429C4×D4D4×C1113yes—
430C4×D4C23×C1111yescharacteristic
431C4×D4C23×C1113yes—
432C4×D4C23×C1113yes—
433#117—23no—
434#117—23no—
435#117—23no—
436#117D4×C1113yes—
437#117C23×C1113yes—
438C2×C4⋊C4—23no—
439C2×C4⋊C4—23no—
440C2×C4⋊C4C23×C1113yes—
441C2×C42—23no—
442C2×C42—23no—
443C2×C42C23×C1113yes—
444#107C23×C1111yescharacteristic
445#107C23×C1113yes—
446#106C23×C1113yes—
447#106C23×C1113yes—
448#106C23×C1116yes—
449C4⋊C8C23×C1113yes—
450C4⋊C8C23×C1113yes—
451#103C23×C1113yes—
452#103C23×C1113yes—
453#103C23×C1111yescharacteristic
454#103C23×C1113yes—
455#103C23×C1113yes—
456#103C23×C1113yes—
457#103C23×C1116yes—
458#103C23×C1116yes—
459#102C23×C1111yescharacteristic
460#102C23×C1113yes—
461C22⋊C8C23×C1116yes—
462#97C23×C1111yescharacteristic
463#97C23×C1113yes—
464C4×C8C23×C1113yes—
465C4×C8C23×C1113yes—
466C2×C11—43no—
467C2×C11—42no—
468C2×C11D4×#4111yescharacteristic
469C2×C11C22×#13711yescharacteristic
470C2×C11#358611yescharacteristic
471#41—24no—
472#41—26no—
473#41—43no—
474C2×Q8—23no—
475C2×Q8—23no—
476C2×Q8—23no—
477C2×Q8—26no—
478C2×Q8—43no—
479C2×Q8—44no—
480C2×Q8C2×D4×C1111yescharacteristic
481C2×Q8C24×C1113yes—
482C2×Q8C24×C1113yes—
483C2×Q8C24×C1111yescharacteristic
484C2×D4—23no—
485C2×D4C2×D4×C1113yes—
486C2×D4C24×C1111yescharacteristic
487C22×C4—23no—
488C22×C4—23no—
489C22×C4—21no—
490C22×C4—23no—
491C22×C4—23no—
492C22×C4C2×D4×C1113yes—
493C22×C4C2×D4×C1113yes—
494C22×C4C24×C1113yes—
495Q16—26no—
496Q16—26no—
497Q16—46no—
498SD16—26no—
499SD16C11×#4114yescomplemented
500M16—26no—
501M16—43no—
502C2×C8C24×C1111yescharacteristic
503C2×C8C24×C1113yes—
504C2×C8C24×C1113yes—
505C2×C8C24×C1111yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—23no—
508C4⋊C4—26no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—23no—
515C4⋊C4—23no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—23no—
520C4⋊C4—26no—
521C4⋊C4C2×D4×C1113yes—
522C4⋊C4C2×D4×C1113yes—
523C4⋊C4C24×C1111yescharacteristic
524C4⋊C4C24×C1113yes—
525C4⋊C4C24×C1113yes—
526C4⋊C4C24×C1111yescharacteristic
527C22⋊C4—26no—
528C22⋊C4—26no—
529C22⋊C4—23no—
530C22⋊C4—21no—
531C22⋊C4—23no—
532C22⋊C4C2×D4×C1116yes—
533C42—21no—
534C42—23no—
535C42—23no—
536C42—23no—
537C42—23no—
538C42—23no—
539C42—23no—
540C42C2×D4×C1113yes—
541C42C2×D4×C1113yes—
542C42C24×C1113yes—
543C42C24×C1111yescharacteristic
544C11#6147011yescharacteristic, direct product factor, Sylow
545C23—21no—
546C23C22×D4×C1113yes—
547Q8—21no—
548Q8—23no—
549Q8—23no—
550Q8—23no—
551Q8—23no—
552Q8—46no—
553Q8—46no—
554Q8—83no—
555Q8C11×#13714yescomplemented
556Q8C2×C11×#4112yes—
557D4—26no—
558D4—21no—
559D4—46no—
560D4C2×C11×#4112yes—
561C2×C4—21no—
562C2×C4—26no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—23no—
571C2×C4—43no—
572C2×C4—46no—
573C2×C4—46no—
574C2×C4—42no—
575C2×C4—46no—
576C2×C4—83no—
577C2×C4C22×D4×C1111yescharacteristic
578C2×C4C22×D4×C1111yescharacteristic
579C2×C4C22×D4×C1113yes—
580C2×C4C22×D4×C1113yes—
581C2×C4C22×D4×C1113yes—
582C2×C4C25×C1111yescharacteristic
583C8—23no—
584C8—21no—
585C8—23no—
586C8C2×C11×#4112yes—
587C22—23no—
588C22—22no—
589C22—23no—
590C22—23no—
591C22—41no—
592C22—41no—
593C22C23×D4×C1111yescharacteristic
594C4—23no—
595C4—22no—
596C4—21no—
597C4—21no—
598C4—23no—
599C4—43no—
600C4—43no—
601C4—43no—
602C4—41no—
603C4—41no—
604C4—43no—
605C4C2×C11×#13716yes—
606C4C22×C11×#4111yescharacteristic
607C4C11×#58511yescharacteristic
608C2—43no—
609C2—42no—
610C2D4×C11×#4111yescharacteristic
611C2C22×C11×#13711yescharacteristic
612C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3482C2
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×#3395C2semidirect
4. Q8×C11×SD16C2semidirect
5. C11×#3363C2semidirect
6. C11×#3359C2semidirect
7. C11×#3356C2semidirect
8. C11×#3331C2semidirect
9. C11×#3328C2semidirect
10. C11×#3276C2semidirect
11. C11×#3185C2semidirect
12. C11×#3116C2semidirect
13. C11×#3113C2semidirect
14. C11×#2971C2semidirect
15. C4×C11×#137C2semidirect
165. #61470C11direct (N × H)
194. C11×SD16#41semidirect
240. Q8×#41C2×C11semidirect
241. #3395C2×C11semidirect
242. Q8×SD16C2×C11semidirect
243. #3363C2×C11semidirect
244. #3359C2×C11semidirect
245. #3356C2×C11semidirect
246. #3331C2×C11semidirect
247. #3328C2×C11semidirect
248. #3276C2×C11semidirect
249. #3185C2×C11semidirect
250. #3116C2×C11semidirect
251. #3113C2×C11semidirect
252. #2971C2×C11semidirect
253. C4×#137C2×C11semidirect
264. Q8×C11#137semidirect
499. SD16C11×#41semidirect
544. C11#61470direct (N × H)
555. Q8C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#34822
Q8×C11×#412
C11×#33952
Q8×C11×SD162
C11×#33632
C11×#33592
C11×#33562
C11×#33312
C11×#33282
C11×#32762
C11×#31852
C11×#31162
C11×#31132
C11×#29712
C4×C11×#1372
#6147011