Finite Group Databasebeta

← C11×#24173 #14601366

Subgroups — C11×#24173 #14601366

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3511C211yesmaximal, characteristic
2C11×#3037C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic, complemented
4C11×#2567C211yesmaximal, characteristic, complemented
5C11×#2039C212yesmaximal, complemented
6C11×#2007C212yesmaximal, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C11×#1980C211yesmaximal, characteristic, complemented
9C11×#1882C212yesmaximal, complemented
10C11×#1859C212yesmaximal, complemented
11C11×#1806C211yesmaximal, characteristic, complemented
12C2×C11×#137C2211yescharacteristic
13C2×C11×#137C2212yes—
14C11×#556—21no—
15C11×#555—21no—
16C11×#554—21no—
17C11×#553—22no—
18C11×#548—22no—
19C11×#547—21no—
20C11×#542—22no—
21C11×#537C2212yes—
22C11×#533—21no—
23C11×#532—21no—
24C11×#532C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic
26C11×#520C2212yes—
27C4×C11×#41C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C11×#464—22no—
30C11×#462—21no—
31C11×#460—21no—
32C11×#441—21no—
33C11×#440—21no—
34C4×C11×Q16—21no—
35C4×C11×SD16—21no—
36C11×#428C2211yescharacteristic
37C11×#423C2211yescharacteristic
38C2×C11×#104C2212yes—
39C2×C11×#104C2212yes—
40C2×C11×#104C2212yes—
41C11×#419C2211yescharacteristic
42C11×#417C2211yescharacteristic
43C11×#417C2212yes—
44C4×C11×M16C2211yescharacteristic
45C11×#395—22no—
46C11×#391C2212yes—
47C11×#389—22no—
48C11×#384C2212yes—
49C4×C11×C4⋊C4C2211yescharacteristic
50C11×#343C2212yes—
51C11×#343C2212yes—
52C11×#339C2212yes—
53C2×C11×#41—22no—
54C2×C11×#41C2311yescharacteristic
55C2×C11×#41C2312yes—
56C22×Q8×C11D412yes—
57C22×Q8×C11C2311yescharacteristic
58C11×#137—22no—
59C11×#137—24no—
60C11×#137—22no—
61C11×#137—42no—
62C2×C11×Q16—21no—
63C2×C11×Q16—22no—
64C2×C11×SD16—21no—
65C2×C11×SD16—22no—
66C2×C11×M16C2312yes—
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8D411yescharacteristic
74C11×#127D411yescharacteristic
75C11×#126—24no—
76C11×#125—22no—
77C11×#124—22no—
78C11×#124—24no—
79C11×#124D412yes—
80C11×#123—24no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×#121—22no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—24no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11D411yescharacteristic
98C4×Q8×C11D411yescharacteristic
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—24no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11D411yescharacteristic
107C4×D4×C11D411yescharacteristic
108C11×#117—22no—
109C11×#117—22no—
110C11×#117—21no—
111C11×#117C2311yescharacteristic
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—24no—
116C2×C11×C4⋊C4D412yes—
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2312yes—
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11C2312yes—
122C2×C42×C11C2311yescharacteristic
123C11×#107—21no—
124C11×#106—21no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×#104—24no—
128C11×#104—42no—
129C11×#104—42no—
130C11×#103—21no—
131C11×#103—22no—
132C11×#103—21no—
133C11×#103—21no—
134C11×#102—21no—
135C11×#102—22no—
136C11×#97—21no—
137C4×C8×C11—21no—
138C11×#95—21no—
139C11×#95—24no—
140#24173C1111yesmaximal, characteristic, direct product factor, Sylow
141C11×#41—22no—
142C11×#41—22no—
143C11×#41—21no—
144C11×#41—21no—
145C11×#41—21no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—21no—
149C11×#41—84no—
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—82no—
158C2×Q8×C11C2×D412yes—
159C2×Q8×C11C2×D411yescharacteristic
160C2×Q8×C11#4112yescomplemented
161C2×D4×C11—21no—
162C2×D4×C11—22no—
163C2×D4×C11—24no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11C2×D412yes—
167C2×D4×C11C2×D411yescharacteristic
168C22×C4×C11—21no—
169C22×C4×C11—22no—
170C22×C4×C11—24no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11—21no—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D414yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C11×Q16—24no—
181C11×Q16—44no—
182C11×SD16—24no—
183C11×SD16—44no—
184C11×M16—21no—
185C11×M16—22no—
186C11×M16—21no—
187C11×M16—22no—
188C11×M16—21no—
189C11×M16#4112yescomplemented
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—22no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—41no—
207C11×C4⋊C4—41no—
208C11×C4⋊C4—84no—
209C11×C4⋊C4C2×D411yescharacteristic
210C11×C4⋊C4C2×D411yescharacteristic
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C42×C11—24no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—22no—
224C42×C11—22no—
225C42×C11—41no—
226C42×C11—41no—
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231#3511C2×C1111yescharacteristic
232#3037C2×C1111yescharacteristic, complemented
233C4×#137C2×C1111yescharacteristic, complemented
234#2567C2×C1111yescharacteristic, complemented
235#2039C2×C1112yescomplemented
236#2007C2×C1112yescomplemented
237#1997C2×C1111yescharacteristic, complemented
238#1980C2×C1111yescharacteristic, complemented
239#1882C2×C1112yescomplemented
240#1859C2×C1112yescomplemented
241#1806C2×C1111yescharacteristic, complemented
242C23×C11—21no—
243C23×C11—22no—
244C23×C11C22×D411yescharacteristic
245Q8×C11—22no—
246Q8×C11—21no—
247Q8×C11—21no—
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—44no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—82no—
255D4×C11—21no—
256D4×C11—21no—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—42no—
260D4×C11—42no—
261D4×C11—41no—
262D4×C11—42no—
263D4×C11—41no—
264D4×C11—42no—
265D4×C11—84no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—41no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—41no—
278C2×C4×C11—42no—
279C2×C4×C11—41no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—42no—
285C2×C4×C11—44no—
286C2×C4×C11—42no—
287C2×C4×C11—41no—
288C2×C4×C11—84no—
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12011yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11H(5,𝔽2)11yescharacteristic
298C2×C4×C112−1+411yescharacteristic
299C8×C11—22no—
300C8×C11—41no—
301C8×C11—42no—
302C2×#137C22×C1111yescharacteristic
303C2×#137C22×C1112yes—
304#556—21no—
305#555—21no—
306#554—21no—
307#553—22no—
308#548—22no—
309#547—21no—
310#542—22no—
311#537C22×C1112yes—
312#533—21no—
313#532—21no—
314#532C22×C1111yescharacteristic
315C2×C4⋊Q8C22×C1111yescharacteristic
316#520C22×C1112yes—
317C4×#41C22×C1111yescharacteristic
318C2×C4×Q8C22×C1111yescharacteristic
319#464—22no—
320#462—21no—
321#460—21no—
322#441—21no—
323#440—21no—
324C4×Q16—21no—
325C4×SD16—21no—
326#428C22×C1111yescharacteristic
327#423C22×C1111yescharacteristic
328C2×#104C22×C1112yes—
329C2×#104C22×C1112yes—
330C2×#104C22×C1112yes—
331#419C22×C1111yescharacteristic
332#417C22×C1112yes—
333#417C22×C1111yescharacteristic
334C4×M16C22×C1111yescharacteristic
335#395—22no—
336#391C22×C1112yes—
337#389—22no—
338#384C22×C1112yes—
339C4×C4⋊C4C22×C1111yescharacteristic
340#343C22×C1112yes—
341#343C22×C1112yes—
342#339C22×C1112yes—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—42no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—42no—
349C22×C11—41no—
350C22×C11—42no—
351C22×C11C2×#12011yescharacteristic
352C22×C11#54811yescharacteristic
353C22×C11#55011yescharacteristic
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—44no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—44no—
364C4×C11—81no—
365C4×C11#45612yes—
366C4×C11#52511yescharacteristic
367C4×C11#53711yescharacteristic
368C4×C11#54611yescharacteristic
369C4×C11#54711yescharacteristic
370C2×#41—22no—
371C2×#41C23×C1111yescharacteristic
372C2×#41C23×C1112yes—
373C22×Q8D4×C1112yes—
374C22×Q8C23×C1111yescharacteristic
375#137—22no—
376#137—24no—
377#137—22no—
378#137—42no—
379C2×Q16—21no—
380C2×Q16—22no—
381C2×SD16—21no—
382C2×SD16—22no—
383C2×M16C23×C1112yes—
384C2×M16C23×C1111yescharacteristic
385C2×M16C23×C1111yescharacteristic
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8D4×C1111yescharacteristic
391#127D4×C1111yescharacteristic
392#126—24no—
393#125—22no—
394#124—22no—
395#124—24no—
396#124D4×C1112yes—
397#123—24no—
398C22⋊Q8—22no—
399C22⋊Q8—24no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402#121—22no—
403#121—22no—
404#121—22no—
405#121—21no—
406#121—21no—
407#121—24no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8D4×C1111yescharacteristic
415C4×Q8D4×C1111yescharacteristic
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—24no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4D4×C1111yescharacteristic
424C4×D4D4×C1111yescharacteristic
425#117—22no—
426#117—22no—
427#117—21no—
428#117C23×C1111yescharacteristic
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4D4×C1112yes—
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1112yes—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42C23×C1112yes—
439C2×C42C23×C1111yescharacteristic
440#107—21no—
441#106—21no—
442C4⋊C8—21no—
443C4⋊C8—21no—
444#104—24no—
445#104—42no—
446#104—42no—
447#103—21no—
448#103—22no—
449#103—21no—
450#103—21no—
451#102—21no—
452#102—22no—
453#97—21no—
454C4×C8—21no—
455#95—21no—
456#95—24no—
457C2×C11—21no—
458C2×C11—21no—
459C2×C11—81no—
460C2×C11—82no—
461C2×C11#240711yescharacteristic
462C2×C11C2×#45611yescharacteristic
463C2×C11#301911yescharacteristic
464#41—22no—
465#41—22no—
466#41—21no—
467#41—21no—
468#41—21no—
469#41—22no—
470#41—22no—
471#41—21no—
472#41—84no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—82no—
481C2×Q8C2×D4×C1112yes—
482C2×Q8C2×D4×C1111yescharacteristic
483C2×Q8C11×#4112yescomplemented
484C2×D4—21no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4C2×D4×C1112yes—
490C2×D4C2×D4×C1111yescharacteristic
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4C2×D4×C1111yescharacteristic
500C22×C4C2×D4×C1114yes—
501C22×C4C2×D4×C1111yescharacteristic
502C22×C4C24×C1111yescharacteristic
503Q16—24no—
504Q16—44no—
505SD16—24no—
506SD16—44no—
507M16—21no—
508M16—22no—
509M16—21no—
510M16—22no—
511M16—21no—
512M16C11×#4112yescomplemented
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—22no—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—84no—
532C4⋊C4C2×D4×C1111yescharacteristic
533C4⋊C4C2×D4×C1111yescharacteristic
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—24no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C42—24no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—22no—
547C42—22no—
548C42—41no—
549C42—41no—
550C42C2×D4×C1111yescharacteristic
551C42C2×D4×C1111yescharacteristic
552C42C2×D4×C1111yescharacteristic
553C42C2×D4×C1111yescharacteristic
554C11#2417311yescharacteristic, direct product factor, Sylow
555C23—21no—
556C23—22no—
557C23C22×D4×C1111yescharacteristic
558Q8—22no—
559Q8—21no—
560Q8—21no—
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—44no—
565Q8—41no—
566Q8—41no—
567Q8—82no—
568D4—21no—
569D4—21no—
570D4—22no—
571D4—22no—
572D4—42no—
573D4—42no—
574D4—41no—
575D4—42no—
576D4—41no—
577D4—42no—
578D4—84no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—84no—
602C2×C4C11×#12011yescharacteristic
603C2×C4C11×#12011yescharacteristic
604C2×C4C11×#12011yescharacteristic
605C2×C4C11×#12011yescharacteristic
606C2×C4C22×D4×C1111yescharacteristic
607C2×C4C22×D4×C1111yescharacteristic
608C2×C4C2×C11×#4111yescharacteristic
609C2×C4C2×C11×#4111yescharacteristic
610C2×C4C11×H(5,𝔽2)11yescharacteristic
611C2×C4C11×2−1+411yescharacteristic
612C8—22no—
613C8—41no—
614C8—42no—
615C22—21no—
616C22—21no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—41no—
622C22—42no—
623C22C2×C11×#12011yescharacteristic
624C22C11×#54811yescharacteristic
625C22C11×#55011yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—44no—
630C4—42no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—41no—
635C4—44no—
636C4—81no—
637C4C11×#45612yes—
638C4C11×#52511yescharacteristic
639C4C11×#53711yescharacteristic
640C4C11×#54611yescharacteristic
641C4C11×#54711yescharacteristic
642C2—21no—
643C2—21no—
644C2—81no—
645C2—82no—
646C2C11×#240711yescharacteristic
647C2C2×C11×#45611yescharacteristic
648C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3511C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3037C2semidirect
3. C4×C11×#137C2semidirect
4. C11×#2567C2semidirect
5. C11×#2039C2semidirect
6. C11×#2007C2semidirect
7. C11×#1997C2semidirect
8. C11×#1980C2semidirect
9. C11×#1882C2semidirect
10. C11×#1859C2semidirect
11. C11×#1806C2semidirect
140. #24173C11direct (N × H)
160. C2×Q8×C11#41semidirect
189. C11×M16#41semidirect
232. #3037C2×C11semidirect
233. C4×#137C2×C11semidirect
234. #2567C2×C11semidirect
235. #2039C2×C11semidirect
236. #2007C2×C11semidirect
237. #1997C2×C11semidirect
238. #1980C2×C11semidirect
239. #1882C2×C11semidirect
240. #1859C2×C11semidirect
241. #1806C2×C11semidirect
483. C2×Q8C11×#41semidirect
512. M16C11×#41semidirect
554. C11#24173direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35112
C11×#30372
C4×C11×#1372
C11×#25672
C11×#20392
C11×#20072
C11×#19972
C11×#19802
C11×#18822
C11×#18592
C11×#18062
#2417311