Finite Group Databasebeta

← C11×#61958 #14639151

Subgroups — C11×#61958 #14639151

Order 2816.

1922 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3517C211yesmaximal, characteristic, complemented
2C11×#3483C211yesmaximal, characteristic, complemented
3C11×#3392C211yesmaximal, characteristic, complemented
4C11×#3391C211yesmaximal, characteristic, complemented
5C11×#3363C211yesmaximal, characteristic, complemented
6C11×#3362C211yesmaximal, characteristic, complemented
7C11×#3305C213yesmaximal, complemented
8C11×#3303C213yesmaximal, complemented
9C11×#3287C213yesmaximal, complemented
10C11×#3284C213yesmaximal, complemented
11C11×#3247C213yesmaximal, complemented
12C11×#3207C213yesmaximal, complemented
13C11×#3102C213yesmaximal, complemented
14C11×#3035C213yesmaximal, complemented
15C11×#2988C211yesmaximal, characteristic, complemented
16C2×C11×#135C2216yes—
17Q82×C11C2211yescharacteristic
18C11×#557C2211yescharacteristic
19C11×#555—23no—
20C11×#555C2213yes—
21C11×#553—23no—
22C11×#550—21no—
23C11×#550—21no—
24C11×#550C2213yes—
25C11×#550C2213yes—
26C11×#550C2211yescharacteristic
27C11×#550C2211yescharacteristic
28C11×#547C2213yes—
29C11×#540—23no—
30C11×#532—23no—
31C11×#532C2213yes—
32C11×#532C2213yes—
33C11×#529C2213yes—
34C11×#520—21no—
35C4×C11×#41—21no—
36C4×C11×#41C2213yes—
37C4×C11×#41C2211yescharacteristic
38C11×#493C2213yes—
39C11×#492C2213yes—
40C11×#487C2213yes—
41C11×#486C2213yes—
42C11×#485C2213yes—
43C11×#482C2213yes—
44C11×#479C2211yescharacteristic
45C11×#478C2213yes—
46C11×#477C2213yes—
47C11×#476C2213yes—
48C11×#466C2216yes—
49C11×#465C2216yes—
50C11×#464C2213yes—
51C11×#463C2213yes—
52C11×#463C2216yes—
53C11×#462C2213yes—
54C11×#461C2213yes—
55C11×#460C2213yes—
56C11×#460C2213yes—
57C11×#459C2213yes—
58C11×#459C2213yes—
59C11×#452C2213yes—
60C11×#449C2216yes—
61C11×#449C2216yes—
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×#41—21no—
76C2×C11×#41—23no—
77C2×C11×#41D411yescharacteristic
78C2×C11×#41C2313yes—
79C2×C11×#41C2316yes—
80C11×#135—412no—
81C2×C11×Q16C2313yes—
82C2×C11×SD16C2313yes—
83C2×C11×SD16C2313yes—
84C2×C11×SD16C2316yes—
85C2×C11×D8C2313yes—
86C2×C11×D8C2316yes—
87C22×C8×C11C2316yes—
88C11×C4⋊Q8—23no—
89C11×C4⋊Q8C2313yes—
90C11×C4⋊Q8C2313yes—
91C11×#127—23no—
92C11×#127—23no—
93C11×#127C2313yes—
94C11×#127C2313yes—
95C11×#126—23no—
96C11×#125—23no—
97C11×#125C2311yescharacteristic
98C11×#124—26no—
99C11×#124—23no—
100C11×#124C2313yes—
101C11×#123—23no—
102C11×#123—26no—
103C11×C22⋊Q8C2313yes—
104C11×#121—23no—
105C11×#121—23no—
106C11×#121—23no—
107C11×#121—23no—
108C11×#121—23no—
109C11×#121—23no—
110C11×#121—23no—
111C11×#121—26no—
112C11×#121—26no—
113C11×#121C2313yes—
114C11×#121C2316yes—
115C4×Q8×C11—21no—
116C4×Q8×C11—21no—
117C4×Q8×C11D411yescharacteristic
118C4×Q8×C11C2311yescharacteristic
119C4×Q8×C11C2313yes—
120C4×Q8×C11C2313yes—
121C4×Q8×C11C2311yescharacteristic
122C4×D4×C11—23no—
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×C11—23no—
130C4×D4×C11D413yes—
131C4×D4×C11C2313yes—
132C4×D4×C11C2313yes—
133C4×D4×C11C2313yes—
134C4×D4×C11C2313yes—
135C11×#117—23no—
136C11×#117—23no—
137C11×#117—23no—
138C11×#117D413yes—
139C11×#117C2313yes—
140C2×C11×C4⋊C4—23no—
141C2×C42×C11—23no—
142C2×C42×C11C2313yes—
143C11×#107C2311yescharacteristic
144C11×#107C2313yes—
145C11×#106C2311yescharacteristic
146C11×#106C2313yes—
147C11×C4⋊C8C2313yes—
148C11×C4⋊C8C2313yes—
149C11×C4⋊C8C2313yes—
150C11×C4⋊C8C2311yescharacteristic
151C11×#103C2313yes—
152C11×#103C2316yes—
153C11×#103C2311yescharacteristic
154C11×#103C2311yescharacteristic
155C11×#103C2313yes—
156C11×#102C2313yes—
157C11×#102C2316yes—
158C11×#102C2313yes—
159C11×#102C2313yes—
160C11×#102C2313yes—
161C11×C22⋊C8C2313yes—
162C11×C22⋊C8C2313yes—
163C4×C8×C11C2313yes—
164C4×C8×C11C2313yes—
165#61958C1111yesmaximal, characteristic, direct product factor, Sylow
166C11×#41—24no—
167C11×#41—26no—
168C11×#41—43no—
169C11×#41—46no—
170C11×#41—46no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—86no—
174C2×Q8×C11—23no—
175C2×Q8×C11C2×D411yescharacteristic
176C2×Q8×C11C2413yes—
177C2×Q8×C11C2411yescharacteristic
178C2×D4×C11—23no—
179C2×D4×C11—23no—
180C2×D4×C11—26no—
181C2×D4×C11—26no—
182C2×D4×C11—23no—
183C2×D4×C11—23no—
184C2×D4×C11—23no—
185C2×D4×C11—23no—
186C2×D4×C11C2×D413yes—
187C2×D4×C11C2413yes—
188C2×D4×C11C2413yes—
189C22×C4×C11—23no—
190C22×C4×C11—23no—
191C22×C4×C11—23no—
192C22×C4×C11—23no—
193C22×C4×C11—26no—
194C22×C4×C11C2×D413yes—
195C22×C4×C11C2×D413yes—
196C22×C4×C11C2413yes—
197C11×Q16—26no—
198C11×SD16—26no—
199C11×SD16—43no—
200C11×SD16—46no—
201C11×D8—43no—
202C11×D8—46no—
203C2×C8×C11—46no—
204C2×C8×C11C2411yescharacteristic
205C2×C8×C11C2411yescharacteristic
206C2×C8×C11C2413yes—
207C2×C8×C11C2413yes—
208C11×C4⋊C4—23no—
209C11×C4⋊C4—23no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—23no—
213C11×C4⋊C4—23no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—23no—
216C11×C4⋊C4—23no—
217C11×C4⋊C4C2×D413yes—
218C11×C4⋊C4C2×D413yes—
219C11×C4⋊C4C2411yescharacteristic
220C11×C4⋊C4C2413yes—
221C11×C4⋊C4C2411yescharacteristic
222C11×C4⋊C4C2411yescharacteristic
223C11×C22⋊C4—23no—
224C11×C22⋊C4—23no—
225C11×C22⋊C4—23no—
226C11×C22⋊C4—23no—
227C11×C22⋊C4—26no—
228C11×C22⋊C4—23no—
229C11×C22⋊C4—23no—
230C11×C22⋊C4—23no—
231C11×C22⋊C4—23no—
232C11×C22⋊C4C2×D416yes—
233C42×C11—21no—
234C42×C11—23no—
235C42×C11—23no—
236C42×C11—23no—
237C42×C11C2×D413yes—
238C42×C11C2×D413yes—
239C42×C11C2413yes—
240C42×C11C2411yescharacteristic
241#3517C2×C1111yescharacteristic, complemented
242#3483C2×C1111yescharacteristic, complemented
243#3392C2×C1111yescharacteristic, complemented
244#3391C2×C1111yescharacteristic, complemented
245#3363C2×C1111yescharacteristic, complemented
246#3362C2×C1111yescharacteristic, complemented
247#3305C2×C1113yescomplemented
248#3303C2×C1113yescomplemented
249#3287C2×C1113yescomplemented
250#3284C2×C1113yescomplemented
251#3247C2×C1113yescomplemented
252#3207C2×C1113yescomplemented
253#3102C2×C1113yescomplemented
254#3035C2×C1113yescomplemented
255#2988C2×C1111yescharacteristic, complemented
256C23×C11—23no—
257C23×C11—23no—
258C23×C11C22×D413yes—
259Q8×C11—21no—
260Q8×C11—23no—
261Q8×C11—23no—
262Q8×C11—83no—
263Q8×C11#13514yescomplemented
264Q8×C11H(5,𝔽2)12yes—
265D4×C11—26no—
266D4×C11—23no—
267D4×C11—23no—
268D4×C11—23no—
269D4×C11—23no—
270D4×C11—46no—
271D4×C11—46no—
272D4×C11—46no—
273D4×C11—83no—
274D4×C11—83no—
275D4×C11—83no—
276D4×C11—86no—
277D4×C11—86no—
278C2×C4×C11—21no—
279C2×C4×C11—26no—
280C2×C4×C11—23no—
281C2×C4×C11—23no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—23no—
285C2×C4×C11—23no—
286C2×C4×C11—21no—
287C2×C4×C11—43no—
288C2×C4×C11—46no—
289C2×C4×C11—46no—
290C2×C4×C11—46no—
291C2×C4×C11—46no—
292C2×C4×C11—86no—
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D413yes—
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C22×D413yes—
297C2×C4×C11C22×D413yes—
298C2×C4×C11C2511yescharacteristic
299C8×C11—23no—
300C8×C11—23no—
301C8×C11—21no—
302C8×C11—21no—
303C2×#135C22×C1116yes—
304Q82C22×C1111yescharacteristic
305#557C22×C1111yescharacteristic
306#555—23no—
307#555C22×C1113yes—
308#553—23no—
309#550—21no—
310#550—21no—
311#550C22×C1113yes—
312#550C22×C1113yes—
313#550C22×C1111yescharacteristic
314#550C22×C1111yescharacteristic
315#547C22×C1113yes—
316#540—23no—
317#532—23no—
318#532C22×C1113yes—
319#532C22×C1113yes—
320#529C22×C1113yes—
321#520—21no—
322C4×#41—21no—
323C4×#41C22×C1113yes—
324C4×#41C22×C1111yescharacteristic
325#493C22×C1113yes—
326#492C22×C1113yes—
327#487C22×C1113yes—
328#486C22×C1113yes—
329#485C22×C1113yes—
330#482C22×C1113yes—
331#479C22×C1111yescharacteristic
332#478C22×C1113yes—
333#477C22×C1113yes—
334#476C22×C1113yes—
335#466C22×C1116yes—
336#465C22×C1116yes—
337#464C22×C1113yes—
338#463C22×C1113yes—
339#463C22×C1116yes—
340#462C22×C1113yes—
341#461C22×C1113yes—
342#460C22×C1113yes—
343#460C22×C1113yes—
344#459C22×C1113yes—
345#459C22×C1113yes—
346#452C22×C1113yes—
347#449C22×C1113yes—
348#449C22×C1116yes—
349#449C22×C1116yes—
350C8×Q8C22×C1111yescharacteristic
351C8×Q8C22×C1111yescharacteristic
352C4×Q16C22×C1113yes—
353C4×SD16C22×C1113yes—
354C4×SD16C22×C1113yes—
355C4×D8C22×C1113yes—
356C8×D4C22×C1113yes—
357C8×D4C22×C1113yes—
358#431C22×C1113yes—
359C2×C4⋊C8C22×C1113yes—
360#416C22×C1116yes—
361C22×C11—23no—
362C22×C11—23no—
363C22×C11—23no—
364C22×C11—43no—
365C22×C11—43no—
366C22×C11—43no—
367C22×C11—43no—
368C22×C11—43no—
369C22×C11—43no—
370C22×C11C23×D411yescharacteristic
371C4×C11—21no—
372C4×C11—23no—
373C4×C11—23no—
374C4×C11—22no—
375C4×C11—21no—
376C4×C11—43no—
377C4×C11—41no—
378C4×C11—43no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11C2×#13516yes—
382C4×C11C2×H(5,𝔽2)11yescharacteristic
383C4×C11#58511yescharacteristic
384C2×#41—21no—
385C2×#41—21no—
386C2×#41—23no—
387C2×#41D4×C1111yescharacteristic
388C2×#41C23×C1113yes—
389C2×#41C23×C1116yes—
390#135—412no—
391C2×Q16C23×C1113yes—
392C2×SD16C23×C1113yes—
393C2×SD16C23×C1116yes—
394C2×SD16C23×C1113yes—
395C2×D8C23×C1116yes—
396C2×D8C23×C1113yes—
397C22×C8C23×C1116yes—
398C4⋊Q8—23no—
399C4⋊Q8C23×C1113yes—
400C4⋊Q8C23×C1113yes—
401#127—23no—
402#127—23no—
403#127C23×C1113yes—
404#127C23×C1113yes—
405#126—23no—
406#125—23no—
407#125C23×C1111yescharacteristic
408#124—26no—
409#124—23no—
410#124C23×C1113yes—
411#123—23no—
412#123—26no—
413C22⋊Q8C23×C1113yes—
414#121—23no—
415#121—23no—
416#121—23no—
417#121—23no—
418#121—23no—
419#121—23no—
420#121—23no—
421#121—26no—
422#121—26no—
423#121C23×C1113yes—
424#121C23×C1116yes—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8D4×C1111yescharacteristic
428C4×Q8C23×C1111yescharacteristic
429C4×Q8C23×C1113yes—
430C4×Q8C23×C1113yes—
431C4×Q8C23×C1111yescharacteristic
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—23no—
435C4×D4—23no—
436C4×D4—23no—
437C4×D4—23no—
438C4×D4—23no—
439C4×D4—23no—
440C4×D4D4×C1113yes—
441C4×D4C23×C1113yes—
442C4×D4C23×C1113yes—
443C4×D4C23×C1113yes—
444C4×D4C23×C1113yes—
445#117—23no—
446#117—23no—
447#117—23no—
448#117D4×C1113yes—
449#117C23×C1113yes—
450C2×C4⋊C4—23no—
451C2×C42—23no—
452C2×C42C23×C1113yes—
453#107C23×C1111yescharacteristic
454#107C23×C1113yes—
455#106C23×C1111yescharacteristic
456#106C23×C1113yes—
457C4⋊C8C23×C1113yes—
458C4⋊C8C23×C1113yes—
459C4⋊C8C23×C1113yes—
460C4⋊C8C23×C1111yescharacteristic
461#103C23×C1113yes—
462#103C23×C1116yes—
463#103C23×C1111yescharacteristic
464#103C23×C1111yescharacteristic
465#103C23×C1113yes—
466#102C23×C1113yes—
467#102C23×C1116yes—
468#102C23×C1113yes—
469#102C23×C1113yes—
470#102C23×C1113yes—
471C22⋊C8C23×C1113yes—
472C22⋊C8C23×C1113yes—
473C4×C8C23×C1113yes—
474C4×C8C23×C1113yes—
475C2×C11—43no—
476C2×C11—83no—
477C2×C11—83no—
478C2×C11#348811yescharacteristic
479C2×C11C22×#13511yescharacteristic
480C2×C11#358511yescharacteristic
481#41—24no—
482#41—26no—
483#41—43no—
484#41—46no—
485#41—46no—
486#41—44no—
487#41—44no—
488#41—86no—
489C2×Q8—23no—
490C2×Q8C2×D4×C1111yescharacteristic
491C2×Q8C24×C1113yes—
492C2×Q8C24×C1111yescharacteristic
493C2×D4—23no—
494C2×D4—23no—
495C2×D4—26no—
496C2×D4—26no—
497C2×D4—23no—
498C2×D4—23no—
499C2×D4—23no—
500C2×D4—23no—
501C2×D4C2×D4×C1113yes—
502C2×D4C24×C1113yes—
503C2×D4C24×C1113yes—
504C22×C4—23no—
505C22×C4—23no—
506C22×C4—23no—
507C22×C4—23no—
508C22×C4—26no—
509C22×C4C2×D4×C1113yes—
510C22×C4C2×D4×C1113yes—
511C22×C4C24×C1113yes—
512Q16—26no—
513SD16—26no—
514SD16—46no—
515SD16—43no—
516D8—46no—
517D8—43no—
518C2×C8—46no—
519C2×C8C24×C1111yescharacteristic
520C2×C8C24×C1111yescharacteristic
521C2×C8C24×C1113yes—
522C2×C8C24×C1113yes—
523C4⋊C4—23no—
524C4⋊C4—23no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—23no—
528C4⋊C4—23no—
529C4⋊C4—21no—
530C4⋊C4—23no—
531C4⋊C4—23no—
532C4⋊C4C2×D4×C1113yes—
533C4⋊C4C2×D4×C1113yes—
534C4⋊C4C24×C1111yescharacteristic
535C4⋊C4C24×C1113yes—
536C4⋊C4C24×C1111yescharacteristic
537C4⋊C4C24×C1111yescharacteristic
538C22⋊C4—23no—
539C22⋊C4—23no—
540C22⋊C4—23no—
541C22⋊C4—23no—
542C22⋊C4—26no—
543C22⋊C4—23no—
544C22⋊C4—23no—
545C22⋊C4—23no—
546C22⋊C4—23no—
547C22⋊C4C2×D4×C1116yes—
548C42—21no—
549C42—23no—
550C42—23no—
551C42—23no—
552C42C2×D4×C1113yes—
553C42C2×D4×C1113yes—
554C42C24×C1113yes—
555C42C24×C1111yescharacteristic
556C11#6195811yescharacteristic, direct product factor, Sylow
557C23—23no—
558C23—23no—
559C23C22×D4×C1113yes—
560Q8—21no—
561Q8—23no—
562Q8—23no—
563Q8—83no—
564Q8C11×#13514yescomplemented
565Q8C11×H(5,𝔽2)12yes—
566D4—26no—
567D4—23no—
568D4—23no—
569D4—23no—
570D4—23no—
571D4—46no—
572D4—46no—
573D4—46no—
574D4—83no—
575D4—83no—
576D4—83no—
577D4—86no—
578D4—86no—
579C2×C4—21no—
580C2×C4—26no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—23no—
586C2×C4—23no—
587C2×C4—21no—
588C2×C4—43no—
589C2×C4—46no—
590C2×C4—46no—
591C2×C4—46no—
592C2×C4—46no—
593C2×C4—86no—
594C2×C4C22×D4×C1111yescharacteristic
595C2×C4C22×D4×C1113yes—
596C2×C4C22×D4×C1111yescharacteristic
597C2×C4C22×D4×C1113yes—
598C2×C4C22×D4×C1113yes—
599C2×C4C25×C1111yescharacteristic
600C8—23no—
601C8—23no—
602C8—21no—
603C8—21no—
604C22—23no—
605C22—23no—
606C22—23no—
607C22—43no—
608C22—43no—
609C22—43no—
610C22—43no—
611C22—43no—
612C22—43no—
613C22C23×D4×C1111yescharacteristic
614C4—23no—
615C4—22no—
616C4—21no—
617C4—21no—
618C4—23no—
619C4—43no—
620C4—41no—
621C4—41no—
622C4—43no—
623C4—41no—
624C4C2×C11×#13516yes—
625C4C2×C11×H(5,𝔽2)11yescharacteristic
626C4C11×#58511yescharacteristic
627C2—43no—
628C2—83no—
629C2—83no—
630C2C11×#348811yescharacteristic
631C2C22×C11×#13511yescharacteristic
632C2C11×#358511yescharacteristic
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×#3483C2semidirect
3. C11×#3392C2semidirect
4. C11×#3391C2semidirect
5. C11×#3363C2semidirect
6. C11×#3362C2semidirect
7. C11×#3305C2semidirect
8. C11×#3303C2semidirect
9. C11×#3287C2semidirect
10. C11×#3284C2semidirect
11. C11×#3247C2semidirect
12. C11×#3207C2semidirect
13. C11×#3102C2semidirect
14. C11×#3035C2semidirect
15. C11×#2988C2semidirect
165. #61958C11direct (N × H)
241. #3517C2×C11semidirect
242. #3483C2×C11semidirect
243. #3392C2×C11semidirect
244. #3391C2×C11semidirect
245. #3363C2×C11semidirect
246. #3362C2×C11semidirect
247. #3305C2×C11semidirect
248. #3303C2×C11semidirect
249. #3287C2×C11semidirect
250. #3284C2×C11semidirect
251. #3247C2×C11semidirect
252. #3207C2×C11semidirect
253. #3102C2×C11semidirect
254. #3035C2×C11semidirect
255. #2988C2×C11semidirect
263. Q8×C11#135semidirect
556. C11#61958direct (N × H)
564. 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×#34832
C11×#33922
C11×#33912
C11×#33632
C11×#33622
C11×#33052
C11×#33032
C11×#32872
C11×#32842
C11×#32472
C11×#32072
C11×#31022
C11×#30352
C11×#29882
#6195811