Finite Group Databasebeta

← C11×#24170 #14601363

Subgroups — C11×#24170 #14601363

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3511C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C11×#2542C211yesmaximal, characteristic, complemented
5C11×#2039C212yesmaximal, complemented
6C11×#2006C212yesmaximal, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C11×#1980C211yesmaximal, characteristic, complemented
9C11×#1883C212yesmaximal, complemented
10C11×#1859C212yesmaximal, complemented
11C11×#1806C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
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
26C2×C11×C22⋊Q8—22no—
27C11×#520C2212yes—
28C4×C11×#41C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C11×#463—22no—
31C11×#461—21no—
32C11×#459—21no—
33C11×#442—21no—
34C11×#440—21no—
35C4×C11×SD16—21no—
36C4×C11×D8—21no—
37C11×#428C2211yescharacteristic
38C11×#423C2211yescharacteristic
39C2×C11×#104C2212yes—
40C2×C11×#104C2212yes—
41C2×C11×#104C2212yes—
42C11×#418C2211yescharacteristic
43C11×#417C2211yescharacteristic
44C11×#417C2212yes—
45C4×C11×M16C2211yescharacteristic
46C11×#399—22no—
47C11×#390C2212yes—
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×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C11×AGL(1,ℤ/8)—22no—
60C11×AGL(1,ℤ/8)—24no—
61C11×AGL(1,ℤ/8)—22no—
62C11×AGL(1,ℤ/8)—42no—
63C2×C11×SD16—21no—
64C2×C11×SD16—22no—
65C2×C11×D8—21no—
66C2×C11×D8—22no—
67C2×C11×M16C2312yes—
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8D411yescharacteristic
75C11×#127D411yescharacteristic
76C11×#126—24no—
77C11×#125—22no—
78C11×#124—22no—
79C11×#124—24no—
80C11×#124D412yes—
81C11×#123—24no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—48no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—24no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11D411yescharacteristic
96C4×Q8×C11D411yescharacteristic
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—24no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11D411yescharacteristic
109C4×D4×C11D411yescharacteristic
110C11×#117—22no—
111C11×#117—22no—
112C11×#117—21no—
113C11×#117C2311yescharacteristic
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—24no—
117C2×C11×C4⋊C4D412yes—
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—24no—
122C2×C42×C11—21no—
123C2×C42×C11C2312yes—
124C2×C42×C11C2311yescharacteristic
125C11×#107—21no—
126C11×#106—21no—
127C11×C4⋊C8—21no—
128C11×C4⋊C8—21no—
129C11×#104—24no—
130C11×#104—42no—
131C11×#104—42no—
132C11×#103—21no—
133C11×#103—22no—
134C11×#102—21no—
135C11×#102—22no—
136C11×#102—21no—
137C11×#102—21no—
138C11×#97—21no—
139C4×C8×C11—21no—
140C11×#95—21no—
141#24170C1111yesmaximal, characteristic, direct product factor, Sylow
142C24×C11—21no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—21no—
146C11×#41—21no—
147C11×#41—21no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—21no—
151C11×#41—84no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11—44no—
155C2×Q8×C11C2×D412yes—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—21no—
158C2×D4×C11—22no—
159C2×D4×C11—24no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11C2×D412yes—
168C2×D4×C11C2×D411yescharacteristic
169C2×D4×C11#4112yescomplemented
170C22×C4×C11—22no—
171C22×C4×C11—24no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11—21no—
177C22×C4×C11—44no—
178C22×C4×C11—41no—
179C22×C4×C11—41no—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D414yes—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C11×SD16—24no—
185C11×SD16—44no—
186C11×D8—24no—
187C11×D8—44no—
188C11×M16—21no—
189C11×M16—22no—
190C11×M16—21no—
191C11×M16—22no—
192C11×M16—21no—
193C11×M16#4112yescomplemented
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—22no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—48no—
211C11×C4⋊C4C2×D411yescharacteristic
212C11×C4⋊C4C2×D411yescharacteristic
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—48no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—41no—
224C42×C11—24no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—22no—
229C42×C11—22no—
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2×D411yescharacteristic
233C42×C11C2×D411yescharacteristic
234#3511C2×C1111yescharacteristic, complemented
235#3036C2×C1111yescharacteristic, complemented
236C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
237#2542C2×C1111yescharacteristic, complemented
238#2039C2×C1112yescomplemented
239#2006C2×C1112yescomplemented
240#1997C2×C1111yescharacteristic, complemented
241#1980C2×C1111yescharacteristic, complemented
242#1883C2×C1112yescomplemented
243#1859C2×C1112yescomplemented
244#1806C2×C1111yescharacteristic, complemented
245C23×C11—21no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11C22×D411yescharacteristic
253Q8×C11—21no—
254Q8×C11—21no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—44no—
258Q8×C11—82no—
259D4×C11—21no—
260D4×C11—22no—
261D4×C11—21no—
262D4×C11—22no—
263D4×C11—22no—
264D4×C11—22no—
265D4×C11—42no—
266D4×C11—42no—
267D4×C11—41no—
268D4×C11—42no—
269D4×C11—41no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—42no—
273D4×C11—84no—
274C2×C4×C11—22no—
275C2×C4×C11—24no—
276C2×C4×C11—21no—
277C2×C4×C11—22no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—24no—
281C2×C4×C11—41no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—42no—
290C2×C4×C11—44no—
291C2×C4×C11—42no—
292C2×C4×C11—41no—
293C2×C4×C11—82no—
294C2×C4×C11—84no—
295C2×C4×C11—82no—
296C2×C4×C11#12011yescharacteristic
297C2×C4×C11#12011yescharacteristic
298C2×C4×C11#12011yescharacteristic
299C2×C4×C11#12011yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C2×C4×C112−1+411yescharacteristic
306C8×C11—22no—
307C8×C11—41no—
308C8×C11—42no—
309C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
310C2×AGL(1,ℤ/8)C22×C1112yes—
311#556—21no—
312#555—21no—
313#554—21no—
314#553—22no—
315#548—22no—
316#547—21no—
317#542—22no—
318#537C22×C1112yes—
319#533—21no—
320#532—21no—
321#532C22×C1111yescharacteristic
322C2×C4⋊Q8C22×C1111yescharacteristic
323C2×C22⋊Q8—22no—
324#520C22×C1112yes—
325C4×#41C22×C1111yescharacteristic
326C2×C4×D4C22×C1111yescharacteristic
327#463—22no—
328#461—21no—
329#459—21no—
330#442—21no—
331#440—21no—
332C4×SD16—21no—
333C4×D8—21no—
334#428C22×C1111yescharacteristic
335#423C22×C1111yescharacteristic
336C2×#104C22×C1112yes—
337C2×#104C22×C1112yes—
338C2×#104C22×C1112yes—
339#418C22×C1111yescharacteristic
340#417C22×C1112yes—
341#417C22×C1111yescharacteristic
342C4×M16C22×C1111yescharacteristic
343#399—22no—
344#390C22×C1112yes—
345#384C22×C1112yes—
346C4×C4⋊C4C22×C1111yescharacteristic
347#343C22×C1112yes—
348#343C22×C1112yes—
349#339C22×C1112yes—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—44no—
353C22×C11—42no—
354C22×C11—41no—
355C22×C11—42no—
356C22×C11—41no—
357C22×C11—42no—
358C22×C11—41no—
359C22×C11—42no—
360C22×C11—82no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11C2×#12011yescharacteristic
364C22×C11#54811yescharacteristic
365C22×C11#55011yescharacteristic
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—21no—
369C4×C11—44no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—44no—
374C4×C11—41no—
375C4×C11—81no—
376C4×C11#45312yes—
377C4×C11#52511yescharacteristic
378C4×C11#53711yescharacteristic
379C4×C11#54611yescharacteristic
380C4×C11#54711yescharacteristic
381C2×#41—22no—
382C2×#41C23×C1111yescharacteristic
383C2×#41C23×C1112yes—
384C22×Q8D4×C1112yes—
385C22×D4C23×C1111yescharacteristic
386C23×C4—21no—
387AGL(1,ℤ/8)—22no—
388AGL(1,ℤ/8)—24no—
389AGL(1,ℤ/8)—22no—
390AGL(1,ℤ/8)—42no—
391C2×SD16—21no—
392C2×SD16—22no—
393C2×D8—21no—
394C2×D8—22no—
395C2×M16C23×C1112yes—
396C2×M16C23×C1111yescharacteristic
397C2×M16C23×C1111yescharacteristic
398C4⋊Q8—21no—
399C4⋊Q8—21no—
400C4⋊Q8—21no—
401C4⋊Q8—21no—
402C4⋊Q8D4×C1111yescharacteristic
403#127D4×C1111yescharacteristic
404#126—24no—
405#125—22no—
406#124—22no—
407#124—24no—
408#124D4×C1112yes—
409#123—24no—
410C22⋊Q8—22no—
411C22⋊Q8—24no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—48no—
415#121—22no—
416#121—22no—
417#121—22no—
418#121—21no—
419#121—21no—
420#121—24no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×Q8D4×C1111yescharacteristic
424C4×Q8D4×C1111yescharacteristic
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—24no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4D4×C1111yescharacteristic
437C4×D4D4×C1111yescharacteristic
438#117—22no—
439#117—22no—
440#117—21no—
441#117C23×C1111yescharacteristic
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4D4×C1112yes—
446C2×C4⋊C4C23×C1111yescharacteristic
447C2×C4⋊C4C23×C1112yes—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—24no—
450C2×C42—21no—
451C2×C42C23×C1112yes—
452C2×C42C23×C1111yescharacteristic
453#107—21no—
454#106—21no—
455C4⋊C8—21no—
456C4⋊C8—21no—
457#104—24no—
458#104—42no—
459#104—42no—
460#103—21no—
461#103—22no—
462#102—21no—
463#102—22no—
464#102—21no—
465#102—21no—
466#97—21no—
467C4×C8—21no—
468#95—21no—
469C2×C11—21no—
470C2×C11—21no—
471C2×C11—81no—
472C2×C11—82no—
473C2×C11—82no—
474C2×C11#240711yescharacteristic
475C2×C11C2×#45311yescharacteristic
476C2×C11#302011yescharacteristic
477C24—21no—
478#41—22no—
479#41—22no—
480#41—21no—
481#41—21no—
482#41—21no—
483#41—22no—
484#41—22no—
485#41—21no—
486#41—84no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—44no—
490C2×Q8C2×D4×C1112yes—
491C2×Q8C2×D4×C1111yescharacteristic
492C2×D4—21no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4C2×D4×C1112yes—
503C2×D4C2×D4×C1111yescharacteristic
504C2×D4C11×#4112yescomplemented
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—44no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4C2×D4×C1111yescharacteristic
516C22×C4C2×D4×C1114yes—
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C24×C1111yescharacteristic
519SD16—24no—
520SD16—44no—
521D8—24no—
522D8—44no—
523M16—21no—
524M16—22no—
525M16—21no—
526M16—22no—
527M16—21no—
528M16C11×#4112yescomplemented
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—22no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—48no—
546C4⋊C4C2×D4×C1111yescharacteristic
547C4⋊C4C2×D4×C1111yescharacteristic
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—48no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C42—24no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—22no—
564C42—22no—
565C42C2×D4×C1111yescharacteristic
566C42C2×D4×C1111yescharacteristic
567C42C2×D4×C1111yescharacteristic
568C42C2×D4×C1111yescharacteristic
569C11#2417011yescharacteristic, direct product factor, Sylow
570C23—21no—
571C23—22no—
572C23—22no—
573C23—42no—
574C23—42no—
575C23—41no—
576C23—41no—
577C23C22×D4×C1111yescharacteristic
578Q8—21no—
579Q8—21no—
580Q8—22no—
581Q8—22no—
582Q8—44no—
583Q8—82no—
584D4—21no—
585D4—22no—
586D4—21no—
587D4—22no—
588D4—22no—
589D4—22no—
590D4—42no—
591D4—42no—
592D4—41no—
593D4—42no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—42no—
598D4—84no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—24no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—44no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—82no—
619C2×C4—84no—
620C2×C4—82no—
621C2×C4C11×#12011yescharacteristic
622C2×C4C11×#12011yescharacteristic
623C2×C4C11×#12011yescharacteristic
624C2×C4C11×#12011yescharacteristic
625C2×C4C22×D4×C1111yescharacteristic
626C2×C4C22×D4×C1111yescharacteristic
627C2×C4C2×C11×#4111yescharacteristic
628C2×C4C2×C11×#4111yescharacteristic
629C2×C4C11×H(5,𝔽2)11yescharacteristic
630C2×C4C11×2−1+411yescharacteristic
631C8—22no—
632C8—41no—
633C8—42no—
634C22—21no—
635C22—21no—
636C22—44no—
637C22—42no—
638C22—41no—
639C22—42no—
640C22—41no—
641C22—42no—
642C22—41no—
643C22—42no—
644C22—82no—
645C22—81no—
646C22—81no—
647C22C2×C11×#12011yescharacteristic
648C22C11×#54811yescharacteristic
649C22C11×#55011yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—44no—
654C4—42no—
655C4—41no—
656C4—41no—
657C4—44no—
658C4—41no—
659C4—81no—
660C4C11×#45312yes—
661C4C11×#52511yescharacteristic
662C4C11×#53711yescharacteristic
663C4C11×#54611yescharacteristic
664C4C11×#54711yescharacteristic
665C2—21no—
666C2—21no—
667C2—82no—
668C2—81no—
669C2—82no—
670C2C11×#240711yescharacteristic
671C2C2×C11×#45311yescharacteristic
672C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C11×#3511C2semidirect
2. C11×#3036C2semidirect
3. C4×C11×AGL(1,ℤ/8)C2semidirect
4. C11×#2542C2semidirect
5. C11×#2039C2semidirect
6. C11×#2006C2semidirect
7. C11×#1997C2semidirect
8. C11×#1980C2semidirect
9. C11×#1883C2semidirect
10. C11×#1859C2semidirect
11. C11×#1806C2semidirect
141. #24170C11direct (N × H)
169. C2×D4×C11#41semidirect
193. C11×M16#41semidirect
234. #3511C2×C11semidirect
235. #3036C2×C11semidirect
236. C4×AGL(1,ℤ/8)C2×C11semidirect
237. #2542C2×C11semidirect
238. #2039C2×C11semidirect
239. #2006C2×C11semidirect
240. #1997C2×C11semidirect
241. #1980C2×C11semidirect
242. #1883C2×C11semidirect
243. #1859C2×C11semidirect
244. #1806C2×C11semidirect
504. C2×D4C11×#41semidirect
528. M16C11×#41semidirect
569. C11#24170direct (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×#30362
C4×C11×AGL(1,ℤ/8)2
C11×#25422
C11×#20392
C11×#20062
C11×#19972
C11×#19802
C11×#18832
C11×#18592
C11×#18062
#2417011