Finite Group Databasebeta

← C11×#61957 #14639150

Subgroups — C11×#61957 #14639150

Order 2816.

1868 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic, complemented
2C11×#3482C211yesmaximal, characteristic, complemented
3C11×#3395C211yesmaximal, characteristic, complemented
4C11×#3392C211yesmaximal, characteristic, complemented
5C11×#3359C211yesmaximal, characteristic, complemented
6C11×#3358C211yesmaximal, characteristic, complemented
7C11×#3304C213yesmaximal, complemented
8C11×#3302C213yesmaximal, complemented
9C11×#3284C213yesmaximal, complemented
10C11×#3283C213yesmaximal, complemented
11C11×#3248C213yesmaximal, complemented
12C11×#3210C213yesmaximal, complemented
13C11×#3102C213yesmaximal, complemented
14C11×#3035C213yesmaximal, complemented
15C11×#2988C211yesmaximal, characteristic, complemented
16C2×C11×#135C2216yes—
17C11×#557C2211yescharacteristic
18C11×#557C2211yescharacteristic
19C11×#556C2213yes—
20C11×#553—23no—
21C11×#552—23no—
22C11×#550—21no—
23C11×#550C2213yes—
24C11×#550C2211yescharacteristic
25D4×Q8×C11C2211yescharacteristic
26C11×#548—21no—
27C11×#547C2213yes—
28C11×#547C2213yes—
29C11×#540—23no—
30C11×#533C2213yes—
31C11×#532C2213yes—
32C11×#529—23no—
33C11×#529C2213yes—
34C11×#520—21no—
35C4×C11×#41C2213yes—
36C4×C11×#41C2211yescharacteristic
37C2×C4×Q8×C11—21no—
38C11×#494C2213yes—
39C11×#492C2213yes—
40C11×#487C2213yes—
41C11×#486C2213yes—
42C11×#485C2213yes—
43C11×#482C2213yes—
44C11×#479C2213yes—
45C11×#478C2211yescharacteristic
46C11×#475C2213yes—
47C11×#474C2213yes—
48C11×#467C2216yes—
49C11×#465C2216yes—
50C11×#464C2213yes—
51C11×#464C2216yes—
52C11×#463C2213yes—
53C11×#462C2213yes—
54C11×#462C2213yes—
55C11×#461C2213yes—
56C11×#461C2213yes—
57C11×#460C2213yes—
58C11×#459C2213yes—
59C11×#452C2216yes—
60C11×#452C2216yes—
61C11×#452C2213yes—
62C11×#449C2213yes—
63C8×Q8×C11C2211yescharacteristic
64C8×Q8×C11C2211yescharacteristic
65C4×C11×Q16C2213yes—
66C4×C11×SD16C2213yes—
67C4×C11×SD16C2213yes—
68C4×C11×D8C2213yes—
69C8×D4×C11C2213yes—
70C8×D4×C11C2213yes—
71C11×#431C2213yes—
72C2×C11×C4⋊C8C2213yes—
73C11×#416C2216yes—
74C2×C11×#41—21no—
75C2×C11×#41D411yescharacteristic
76C2×C11×#41C2313yes—
77C2×C11×#41C2316yes—
78C22×Q8×C11—21no—
79C11×#135—412no—
80C2×C11×Q16C2313yes—
81C2×C11×Q16C2316yes—
82C2×C11×SD16C2313yes—
83C2×C11×SD16C2313yes—
84C2×C11×SD16C2316yes—
85C2×C11×D8C2313yes—
86C22×C8×C11C2316yes—
87C11×C4⋊Q8C2313yes—
88C11×C4⋊Q8C2313yes—
89C11×C4⋊Q8C2313yes—
90C11×#127—23no—
91C11×#127C2313yes—
92C11×#126—26no—
93C11×#126—23no—
94C11×#125—23no—
95C11×#125—23no—
96C11×#125—23no—
97C11×#125C2311yescharacteristic
98C11×#124—23no—
99C11×#124C2313yes—
100C11×#123—23no—
101C11×#123—26no—
102C11×#123—26no—
103C11×C22⋊Q8—23no—
104C11×C22⋊Q8—23no—
105C11×C22⋊Q8C2313yes—
106C11×C22⋊Q8C2316yes—
107C11×#121—23no—
108C11×#121—23no—
109C11×#121—23no—
110C11×#121—23no—
111C11×#121—23no—
112C11×#121—26no—
113C11×#121C2313yes—
114C4×Q8×C11—21no—
115C4×Q8×C11—21no—
116C4×Q8×C11—23no—
117C4×Q8×C11—23no—
118C4×Q8×C11D411yescharacteristic
119C4×Q8×C11C2313yes—
120C4×Q8×C11C2313yes—
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×C11C2311yescharacteristic
131C4×D4×C11C2313yes—
132C4×D4×C11C2313yes—
133C4×D4×C11C2313yes—
134C11×#117—23no—
135C11×#117—23no—
136C11×#117—23no—
137C11×#117D413yes—
138C11×#117C2313yes—
139C2×C11×C4⋊C4—23no—
140C2×C11×C4⋊C4—23no—
141C2×C42×C11—23no—
142C2×C42×C11C2313yes—
143C11×#107C2313yes—
144C11×#107C2311yescharacteristic
145C11×#106C2311yescharacteristic
146C11×#106C2313yes—
147C11×C4⋊C8C2313yes—
148C11×C4⋊C8C2313yes—
149C11×C4⋊C8C2313yes—
150C11×C4⋊C8C2311yescharacteristic
151C11×#103C2313yes—
152C11×#103C2316yes—
153C11×#103C2313yes—
154C11×#103C2313yes—
155C11×#103C2313yes—
156C11×#102C2313yes—
157C11×#102C2316yes—
158C11×#102C2311yescharacteristic
159C11×#102C2313yes—
160C11×#102C2311yescharacteristic
161C11×C22⋊C8C2313yes—
162C11×C22⋊C8C2313yes—
163C4×C8×C11C2313yes—
164C4×C8×C11C2313yes—
165#61957C1111yesmaximal, characteristic, direct product factor, Sylow
166C11×#41—24no—
167C11×#41—26no—
168C11×#41—43no—
169C11×#41—46no—
170C11×#41—46no—
171C11×#41—44no—
172C2×Q8×C11—23no—
173C2×Q8×C11—44no—
174C2×Q8×C11C2×D411yescharacteristic
175C2×Q8×C11C2413yes—
176C2×Q8×C11C2413yes—
177C2×D4×C11—23no—
178C2×D4×C11—23no—
179C2×D4×C11—26no—
180C2×D4×C11—23no—
181C2×D4×C11—23no—
182C2×D4×C11C2×D413yes—
183C2×D4×C11C2413yes—
184C2×D4×C11C2411yescharacteristic
185C22×C4×C11—21no—
186C22×C4×C11—23no—
187C22×C4×C11—23no—
188C22×C4×C11—23no—
189C22×C4×C11—26no—
190C22×C4×C11C2×D413yes—
191C22×C4×C11C2×D413yes—
192C22×C4×C11C2413yes—
193C11×Q16—43no—
194C11×Q16—46no—
195C11×SD16—26no—
196C11×SD16—43no—
197C11×SD16—46no—
198C11×D8—26no—
199C2×C8×C11—46no—
200C2×C8×C11C2411yescharacteristic
201C2×C8×C11C2411yescharacteristic
202C2×C8×C11C2413yes—
203C2×C8×C11C2413yes—
204C11×C4⋊C4—23no—
205C11×C4⋊C4—23no—
206C11×C4⋊C4—23no—
207C11×C4⋊C4—26no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—23no—
210C11×C4⋊C4—23no—
211C11×C4⋊C4—23no—
212C11×C4⋊C4—23no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—23no—
215C11×C4⋊C4—23no—
216C11×C4⋊C4C2×D413yes—
217C11×C4⋊C4C2×D413yes—
218C11×C4⋊C4C2411yescharacteristic
219C11×C4⋊C4C2413yes—
220C11×C4⋊C4C2411yescharacteristic
221C11×C4⋊C4C2411yescharacteristic
222C11×C22⋊C4—26no—
223C11×C22⋊C4—23no—
224C11×C22⋊C4—23no—
225C11×C22⋊C4—21no—
226C11×C22⋊C4—23no—
227C11×C22⋊C4—23no—
228C11×C22⋊C4—23no—
229C11×C22⋊C4—23no—
230C11×C22⋊C4—23no—
231C11×C22⋊C4C2×D416yes—
232C42×C11—23no—
233C42×C11—23no—
234C42×C11—23no—
235C42×C11—23no—
236C42×C11C2×D413yes—
237C42×C11C2×D413yes—
238C42×C11C2413yes—
239C42×C11C2411yescharacteristic
240#3517C2×C1111yescharacteristic, complemented
241#3482C2×C1111yescharacteristic, complemented
242#3395C2×C1111yescharacteristic, complemented
243#3392C2×C1111yescharacteristic, complemented
244#3359C2×C1111yescharacteristic, complemented
245#3358C2×C1111yescharacteristic, complemented
246#3304C2×C1113yescomplemented
247#3302C2×C1113yescomplemented
248#3284C2×C1113yescomplemented
249#3283C2×C1113yescomplemented
250#3248C2×C1113yescomplemented
251#3210C2×C1113yescomplemented
252#3102C2×C1113yescomplemented
253#3035C2×C1113yescomplemented
254#2988C2×C1111yescharacteristic, complemented
255C23×C11—21no—
256C23×C11—23no—
257C23×C11C22×D413yes—
258Q8×C11—23no—
259Q8×C11—23no—
260Q8×C11—23no—
261Q8×C11—23no—
262Q8×C11—46no—
263Q8×C11#13514yescomplemented
264D4×C11—26no—
265D4×C11—23no—
266D4×C11—21no—
267D4×C11—23no—
268D4×C11—46no—
269D4×C11—46no—
270D4×C11—83no—
271D4×C11—83no—
272D4×C11—86no—
273D4×C11H(5,𝔽2)12yes—
274C2×C4×C11—26no—
275C2×C4×C11—23no—
276C2×C4×C11—23no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—23no—
280C2×C4×C11—23no—
281C2×C4×C11—23no—
282C2×C4×C11—21no—
283C2×C4×C11—43no—
284C2×C4×C11—46no—
285C2×C4×C11—42no—
286C2×C4×C11—46no—
287C2×C4×C11—46no—
288C2×C4×C11—86no—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D413yes—
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D413yes—
293C2×C4×C11C22×D413yes—
294C2×C4×C11C2511yescharacteristic
295C8×C11—23no—
296C8×C11—23no—
297C8×C11—21no—
298C8×C11—21no—
299C2×#135C22×C1116yes—
300#557C22×C1111yescharacteristic
301#557C22×C1111yescharacteristic
302#556C22×C1113yes—
303#553—23no—
304#552—23no—
305#550—21no—
306#550C22×C1113yes—
307#550C22×C1111yescharacteristic
308D4×Q8C22×C1111yescharacteristic
309#548—21no—
310#547C22×C1113yes—
311#547C22×C1113yes—
312#540—23no—
313#533C22×C1113yes—
314#532C22×C1113yes—
315#529—23no—
316#529C22×C1113yes—
317#520—21no—
318C4×#41C22×C1113yes—
319C4×#41C22×C1111yescharacteristic
320C2×C4×Q8—21no—
321#494C22×C1113yes—
322#492C22×C1113yes—
323#487C22×C1113yes—
324#486C22×C1113yes—
325#485C22×C1113yes—
326#482C22×C1113yes—
327#479C22×C1113yes—
328#478C22×C1111yescharacteristic
329#475C22×C1113yes—
330#474C22×C1113yes—
331#467C22×C1116yes—
332#465C22×C1116yes—
333#464C22×C1113yes—
334#464C22×C1116yes—
335#463C22×C1113yes—
336#462C22×C1113yes—
337#462C22×C1113yes—
338#461C22×C1113yes—
339#461C22×C1113yes—
340#460C22×C1113yes—
341#459C22×C1113yes—
342#452C22×C1113yes—
343#452C22×C1116yes—
344#452C22×C1116yes—
345#449C22×C1113yes—
346C8×Q8C22×C1111yescharacteristic
347C8×Q8C22×C1111yescharacteristic
348C4×Q16C22×C1113yes—
349C4×SD16C22×C1113yes—
350C4×SD16C22×C1113yes—
351C4×D8C22×C1113yes—
352C8×D4C22×C1113yes—
353C8×D4C22×C1113yes—
354#431C22×C1113yes—
355C2×C4⋊C8C22×C1113yes—
356#416C22×C1116yes—
357C22×C11—23no—
358C22×C11—23no—
359C22×C11—22no—
360C22×C11—23no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—43no—
364C22×C11—43no—
365C22×C11—43no—
366C22×C11C23×D411yescharacteristic
367C4×C11—21no—
368C4×C11—23no—
369C4×C11—23no—
370C4×C11—21no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—43no—
374C4×C11—43no—
375C4×C11—41no—
376C4×C11—43no—
377C4×C11C2×#13516yes—
378C4×C11C2×H(5,𝔽2)11yescharacteristic
379C4×C11#58511yescharacteristic
380C2×#41—21no—
381C2×#41D4×C1111yescharacteristic
382C2×#41C23×C1113yes—
383C2×#41C23×C1116yes—
384C22×Q8—21no—
385#135—412no—
386C2×Q16C23×C1116yes—
387C2×Q16C23×C1113yes—
388C2×SD16C23×C1113yes—
389C2×SD16C23×C1116yes—
390C2×SD16C23×C1113yes—
391C2×D8C23×C1113yes—
392C22×C8C23×C1116yes—
393C4⋊Q8C23×C1113yes—
394C4⋊Q8C23×C1113yes—
395C4⋊Q8C23×C1113yes—
396#127—23no—
397#127C23×C1113yes—
398#126—26no—
399#126—23no—
400#125—23no—
401#125—23no—
402#125—23no—
403#125C23×C1111yescharacteristic
404#124—23no—
405#124C23×C1113yes—
406#123—23no—
407#123—26no—
408#123—26no—
409C22⋊Q8—23no—
410C22⋊Q8—23no—
411C22⋊Q8C23×C1113yes—
412C22⋊Q8C23×C1116yes—
413#121—23no—
414#121—23no—
415#121—23no—
416#121—23no—
417#121—23no—
418#121—26no—
419#121C23×C1113yes—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—23no—
423C4×Q8—23no—
424C4×Q8D4×C1111yescharacteristic
425C4×Q8C23×C1113yes—
426C4×Q8C23×C1113yes—
427C4×Q8C23×C1113yes—
428C4×Q8C23×C1111yescharacteristic
429C4×D4—23no—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—23no—
435C4×D4D4×C1113yes—
436C4×D4C23×C1111yescharacteristic
437C4×D4C23×C1113yes—
438C4×D4C23×C1113yes—
439C4×D4C23×C1113yes—
440#117—23no—
441#117—23no—
442#117—23no—
443#117D4×C1113yes—
444#117C23×C1113yes—
445C2×C4⋊C4—23no—
446C2×C4⋊C4—23no—
447C2×C42—23no—
448C2×C42C23×C1113yes—
449#107C23×C1113yes—
450#107C23×C1111yescharacteristic
451#106C23×C1111yescharacteristic
452#106C23×C1113yes—
453C4⋊C8C23×C1113yes—
454C4⋊C8C23×C1113yes—
455C4⋊C8C23×C1113yes—
456C4⋊C8C23×C1111yescharacteristic
457#103C23×C1113yes—
458#103C23×C1116yes—
459#103C23×C1113yes—
460#103C23×C1113yes—
461#103C23×C1113yes—
462#102C23×C1113yes—
463#102C23×C1116yes—
464#102C23×C1111yescharacteristic
465#102C23×C1113yes—
466#102C23×C1111yescharacteristic
467C22⋊C8C23×C1113yes—
468C22⋊C8C23×C1113yes—
469C4×C8C23×C1113yes—
470C4×C8C23×C1113yes—
471C2×C11—43no—
472C2×C11—42no—
473C2×C11—83no—
474C2×C11#348811yescharacteristic
475C2×C11C22×#13511yescharacteristic
476C2×C11#358611yescharacteristic
477#41—24no—
478#41—26no—
479#41—43no—
480#41—46no—
481#41—46no—
482#41—44no—
483C2×Q8—23no—
484C2×Q8—44no—
485C2×Q8C2×D4×C1111yescharacteristic
486C2×Q8C24×C1113yes—
487C2×Q8C24×C1113yes—
488C2×D4—23no—
489C2×D4—23no—
490C2×D4—26no—
491C2×D4—23no—
492C2×D4—23no—
493C2×D4C2×D4×C1113yes—
494C2×D4C24×C1113yes—
495C2×D4C24×C1111yescharacteristic
496C22×C4—21no—
497C22×C4—23no—
498C22×C4—23no—
499C22×C4—23no—
500C22×C4—26no—
501C22×C4C2×D4×C1113yes—
502C22×C4C2×D4×C1113yes—
503C22×C4C24×C1113yes—
504Q16—46no—
505Q16—43no—
506SD16—26no—
507SD16—46no—
508SD16—43no—
509D8—26no—
510C2×C8—46no—
511C2×C8C24×C1111yescharacteristic
512C2×C8C24×C1111yescharacteristic
513C2×C8C24×C1113yes—
514C2×C8C24×C1113yes—
515C4⋊C4—23no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—26no—
519C4⋊C4—21no—
520C4⋊C4—23no—
521C4⋊C4—23no—
522C4⋊C4—23no—
523C4⋊C4—23no—
524C4⋊C4—21no—
525C4⋊C4—23no—
526C4⋊C4—23no—
527C4⋊C4C2×D4×C1113yes—
528C4⋊C4C2×D4×C1113yes—
529C4⋊C4C24×C1111yescharacteristic
530C4⋊C4C24×C1113yes—
531C4⋊C4C24×C1111yescharacteristic
532C4⋊C4C24×C1111yescharacteristic
533C22⋊C4—26no—
534C22⋊C4—23no—
535C22⋊C4—23no—
536C22⋊C4—21no—
537C22⋊C4—23no—
538C22⋊C4—23no—
539C22⋊C4—23no—
540C22⋊C4—23no—
541C22⋊C4—23no—
542C22⋊C4C2×D4×C1116yes—
543C42—23no—
544C42—23no—
545C42—23no—
546C42—23no—
547C42C2×D4×C1113yes—
548C42C2×D4×C1113yes—
549C42C24×C1113yes—
550C42C24×C1111yescharacteristic
551C11#6195711yescharacteristic, direct product factor, Sylow
552C23—21no—
553C23—23no—
554C23C22×D4×C1113yes—
555Q8—23no—
556Q8—23no—
557Q8—23no—
558Q8—23no—
559Q8—46no—
560Q8C11×#13514yescomplemented
561D4—26no—
562D4—23no—
563D4—21no—
564D4—23no—
565D4—46no—
566D4—46no—
567D4—83no—
568D4—83no—
569D4—86no—
570D4C11×H(5,𝔽2)12yes—
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—21no—
580C2×C4—43no—
581C2×C4—46no—
582C2×C4—42no—
583C2×C4—46no—
584C2×C4—46no—
585C2×C4—86no—
586C2×C4C22×D4×C1111yescharacteristic
587C2×C4C22×D4×C1113yes—
588C2×C4C22×D4×C1111yescharacteristic
589C2×C4C22×D4×C1113yes—
590C2×C4C22×D4×C1113yes—
591C2×C4C25×C1111yescharacteristic
592C8—23no—
593C8—23no—
594C8—21no—
595C8—21no—
596C22—23no—
597C22—22no—
598C22—23no—
599C22—23no—
600C22—41no—
601C22—41no—
602C22—43no—
603C22—43no—
604C22—43no—
605C22C23×D4×C1111yescharacteristic
606C4—23no—
607C4—21no—
608C4—21no—
609C4—23no—
610C4—43no—
611C4—43no—
612C4—41no—
613C4—43no—
614C4—41no—
615C4—41no—
616C4C2×C11×#13516yes—
617C4C2×C11×H(5,𝔽2)11yescharacteristic
618C4C11×#58511yescharacteristic
619C2—43no—
620C2—42no—
621C2—83no—
622C2C11×#348811yescharacteristic
623C2C22×C11×#13511yescharacteristic
624C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
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
1. C11×#3517C2semidirect
2. C11×#3482C2semidirect
3. C11×#3395C2semidirect
4. C11×#3392C2semidirect
5. C11×#3359C2semidirect
6. C11×#3358C2semidirect
7. C11×#3304C2semidirect
8. C11×#3302C2semidirect
9. C11×#3284C2semidirect
10. C11×#3283C2semidirect
11. C11×#3248C2semidirect
12. C11×#3210C2semidirect
13. C11×#3102C2semidirect
14. C11×#3035C2semidirect
15. C11×#2988C2semidirect
165. #61957C11direct (N × H)
240. #3517C2×C11semidirect
241. #3482C2×C11semidirect
242. #3395C2×C11semidirect
243. #3392C2×C11semidirect
244. #3359C2×C11semidirect
245. #3358C2×C11semidirect
246. #3304C2×C11semidirect
247. #3302C2×C11semidirect
248. #3284C2×C11semidirect
249. #3283C2×C11semidirect
250. #3248C2×C11semidirect
251. #3210C2×C11semidirect
252. #3102C2×C11semidirect
253. #3035C2×C11semidirect
254. #2988C2×C11semidirect
263. Q8×C11#135semidirect
551. C11#61957direct (N × H)
560. Q8C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#35172
C11×#34822
C11×#33952
C11×#33922
C11×#33592
C11×#33582
C11×#33042
C11×#33022
C11×#32842
C11×#32832
C11×#32482
C11×#32102
C11×#31022
C11×#30352
C11×#29882
#6195711