Finite Group Databasebeta

← C11×#24082 #14601275

Subgroups — C11×#24082 #14601275

Order 2816.

1130 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3494C211yesmaximal, characteristic
2C11×#3092C211yesmaximal, characteristic, complemented
3C2×C11×#428C211yesmaximal, characteristic, complemented
4C11×#2501C211yesmaximal, characteristic, complemented
5C11×#2060C212yesmaximal, complemented
6C11×#2037C212yesmaximal, complemented
7C11×#1900C211yesmaximal, characteristic, complemented
8C11×#1871C211yesmaximal, characteristic, complemented
9C11×#1859C212yesmaximal, complemented
10C11×#1856C212yesmaximal, complemented
11C11×#1826C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C11×#555—21no—
14C11×#553—21no—
15C11×#553—21no—
16C11×#551—22no—
17C11×#547—21no—
18C11×#546—22no—
19C11×#544C2211yescharacteristic
20C11×#542—21no—
21C11×#540—21no—
22C11×#535C2211yescharacteristic
23C11×#532—21no—
24C11×#529—21no—
25C11×#525C2211yescharacteristic
26C2×C11×#123—22no—
27C2×C11×#121C2211yescharacteristic
28C11×#520C2211yescharacteristic
29C11×#518C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic
32C11×#484—21no—
33C11×#483—21no—
34C11×#481—21no—
35C11×#480—21no—
36C11×#428—21no—
37C11×#428—21no—
38C11×#428C2212yes—
39C11×#428C2212yes—
40C11×#428C2212yes—
41C2×C11×#107—21no—
42C2×C11×#106—21no—
43C2×C11×#104C2212yes—
44C11×#417C2212yes—
45C2×C11×#100C2212yes—
46C11×#407C2211yescharacteristic
47C11×#399—22no—
48C11×#390C2212yes—
49C11×#384C2212yes—
50C4×C11×C22⋊C4C2211yescharacteristic
51C11×#343C2212yes—
52C11×#339C2212yes—
53C11×#339C2212yes—
54C11×#339C2212yes—
55C2×C11×#41—22no—
56C2×C11×#41C2311yescharacteristic
57C22×D4×C11D412yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C2×C11×M16—21no—
62C2×C11×M16—24no—
63C2×C11×M16C2312yes—
64C2×C11×M16C2312yes—
65C22×C8×C11—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×#127—21no—
69C11×#126—22no—
70C11×#126—22no—
71C11×#125—21no—
72C11×#125—21no—
73C11×#124—22no—
74C11×#124—22no—
75C11×#124—21no—
76C11×#123—22no—
77C11×#123—22no—
78C11×#123—22no—
79C11×#123—22no—
80C11×#123—21no—
81C11×#123—48no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8D411yescharacteristic
85C11×C22⋊Q8D411yescharacteristic
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121—21no—
95C11×#121D411yescharacteristic
96C11×#121D411yescharacteristic
97C11×#120—21no—
98C11×#120—22no—
99C4×Q8×C11—21no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—21no—
103C4×D4×C11—22no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C11×#117—22no—
111C11×#117—21no—
112C11×#117—21no—
113C11×#117—21no—
114C11×#117D411yescharacteristic
115C11×#117D411yescharacteristic
116C11×#117C2311yescharacteristic
117C11×#117C2311yescharacteristic
118C11×#117C2311yescharacteristic
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—24no—
126C2×C11×C4⋊C4D411yescharacteristic
127C2×C11×C4⋊C4D411yescharacteristic
128C2×C11×C4⋊C4C2312yes—
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—22no—
133C2×C11×C22⋊C4—24no—
134C2×C11×C22⋊C4D412yes—
135C2×C42×C11—21no—
136C2×C42×C11C2312yes—
137C11×#107—22no—
138C11×#107—22no—
139C11×#107—22no—
140C11×#106—22no—
141C11×#106—22no—
142C11×#106—22no—
143C11×#104—24no—
144C11×#103—22no—
145C11×#102—22no—
146C11×#100—24no—
147C11×C22⋊C8—21no—
148C11×C22⋊C8—21no—
149C11×#95—21no—
150#24082C1111yesmaximal, characteristic, direct product factor, Sylow
151C24×C11C2×D411yescharacteristic
152C24×C11C2×D412yes—
153C11×#41—22no—
154C11×#41—22no—
155C11×#41—84no—
156C2×Q8×C11—22no—
157C2×Q8×C11C2×D411yescharacteristic
158C2×D4×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—44no—
170C2×D4×C11C2×D411yescharacteristic
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—22no—
181C22×C4×C11—44no—
182C22×C4×C11—41no—
183C22×C4×C11—41no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2411yescharacteristic
191C11×M16—24no—
192C11×M16—22no—
193C11×M16—22no—
194C11×M16—22no—
195C11×M16#4114yescomplemented
196C2×C8×C11—24no—
197C2×C8×C11—22no—
198C2×C8×C11—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—48no—
212C11×C4⋊C4—41no—
213C11×C4⋊C4—41no—
214C11×C4⋊C4C2×D411yescharacteristic
215C11×C4⋊C4C2×D411yescharacteristic
216C11×C4⋊C4C2×D411yescharacteristic
217C11×C4⋊C4C2×D411yescharacteristic
218C11×C4⋊C4C2×D411yescharacteristic
219C11×C4⋊C4C2×D411yescharacteristic
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—24no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—21no—
227C11×C22⋊C4—21no—
228C11×C22⋊C4—21no—
229C11×C22⋊C4—21no—
230C11×C22⋊C4—21no—
231C11×C22⋊C4—21no—
232C11×C22⋊C4—21no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—21no—
236C11×C22⋊C4—21no—
237C11×C22⋊C4—48no—
238C42×C11—22no—
239C42×C11—21no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—22no—
245C42×C11—22no—
246#3494C2×C1111yescharacteristic
247#3092C2×C1111yescharacteristic, complemented
248C2×#428C2×C1111yescharacteristic, complemented
249#2501C2×C1111yescharacteristic, complemented
250#2060C2×C1112yescomplemented
251#2037C2×C1112yescomplemented
252#1900C2×C1111yescharacteristic, complemented
253#1871C2×C1111yescharacteristic, complemented
254#1859C2×C1112yescomplemented
255#1856C2×C1112yescomplemented
256#1826C2×C1111yescharacteristic, complemented
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—21no—
261C23×C11—24no—
262C23×C11—41no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11#12011yescharacteristic
266C23×C11#12011yescharacteristic
267C23×C11C22×D411yescharacteristic
268Q8×C11—22no—
269Q8×C11—82no—
270D4×C11—22no—
271D4×C11—42no—
272D4×C11—44no—
273D4×C11—42no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—42no—
277D4×C11—81no—
278D4×C11—82no—
279D4×C11—82no—
280D4×C11—82no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—42no—
303C2×C4×C11—44no—
304C2×C4×C11—42no—
305C2×C4×C11—81no—
306C2×C4×C11—82no—
307C2×C4×C11—82no—
308C2×C4×C11—82no—
309C2×C4×C11—82no—
310C2×C4×C11—82no—
311C2×C4×C11#12011yescharacteristic
312C2×C4×C11#12011yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C2×#4112yes—
316C2×C4×C112−1+412yes—
317C8×C11—24no—
318C8×C11—42no—
319C22×M16C22×C1111yescharacteristic
320#555—21no—
321#553—21no—
322#553—21no—
323#551—22no—
324#547—21no—
325#546—22no—
326#544C22×C1111yescharacteristic
327#542—21no—
328#540—21no—
329#535C22×C1111yescharacteristic
330#532—21no—
331#529—21no—
332#525C22×C1111yescharacteristic
333C2×#123—22no—
334C2×#121C22×C1111yescharacteristic
335#520C22×C1111yescharacteristic
336#518C22×C1111yescharacteristic
337C2×#117C22×C1111yescharacteristic
338C22×C4⋊C4C22×C1111yescharacteristic
339#484—21no—
340#483—21no—
341#481—21no—
342#480—21no—
343#428—21no—
344#428—21no—
345#428C22×C1112yes—
346#428C22×C1112yes—
347#428C22×C1112yes—
348C2×#107—21no—
349C2×#106—21no—
350C2×#104C22×C1112yes—
351#417C22×C1112yes—
352C2×#100C22×C1112yes—
353#407C22×C1111yescharacteristic
354#399—22no—
355#390C22×C1112yes—
356#384C22×C1112yes—
357C4×C22⋊C4C22×C1111yescharacteristic
358#343C22×C1112yes—
359#339C22×C1112yes—
360#339C22×C1112yes—
361#339C22×C1112yes—
362C22×C11—21no—
363C22×C11—21no—
364C22×C11—21no—
365C22×C11—21no—
366C22×C11—21no—
367C22×C11—21no—
368C22×C11—21no—
369C22×C11—44no—
370C22×C11—41no—
371C22×C11—42no—
372C22×C11—41no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—41no—
376C22×C11—84no—
377C22×C11#45312yes—
378C22×C11C2×#12011yescharacteristic
379C22×C11#54712yes—
380C4×C11—21no—
381C4×C11—21no—
382C4×C11—44no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—42no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11—82no—
392C4×C11#52511yescharacteristic
393C4×C11#53611yescharacteristic
394C4×C11#54712yes—
395C2×#41—22no—
396C2×#41C23×C1111yescharacteristic
397C22×D4D4×C1112yes—
398C22×D4C23×C1111yescharacteristic
399C23×C4—21no—
400C23×C4C23×C1111yescharacteristic
401C2×M16—21no—
402C2×M16—24no—
403C2×M16C23×C1112yes—
404C2×M16C23×C1112yes—
405C22×C8—21no—
406C4⋊Q8—21no—
407C4⋊Q8—21no—
408#127—21no—
409#126—22no—
410#126—22no—
411#125—21no—
412#125—21no—
413#124—22no—
414#124—22no—
415#124—21no—
416#123—22no—
417#123—22no—
418#123—22no—
419#123—22no—
420#123—21no—
421#123—48no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8D4×C1111yescharacteristic
425C22⋊Q8D4×C1111yescharacteristic
426#121—22no—
427#121—22no—
428#121—22no—
429#121—21no—
430#121—21no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121—21no—
435#121D4×C1111yescharacteristic
436#121D4×C1111yescharacteristic
437#120—21no—
438#120—22no—
439C4×Q8—21no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—21no—
443C4×D4—22no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450#117—22no—
451#117—21no—
452#117—21no—
453#117—21no—
454#117D4×C1111yescharacteristic
455#117D4×C1111yescharacteristic
456#117C23×C1111yescharacteristic
457#117C23×C1111yescharacteristic
458#117C23×C1111yescharacteristic
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4D4×C1111yescharacteristic
467C2×C4⋊C4D4×C1111yescharacteristic
468C2×C4⋊C4C23×C1112yes—
469C2×C4⋊C4C23×C1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4D4×C1112yes—
475C2×C42—21no—
476C2×C42C23×C1112yes—
477#107—22no—
478#107—22no—
479#107—22no—
480#106—22no—
481#106—22no—
482#106—22no—
483#104—24no—
484#103—22no—
485#102—22no—
486#100—24no—
487C22⋊C8—21no—
488C22⋊C8—21no—
489#95—21no—
490C2×C11—22no—
491C2×C11—22no—
492C2×C11—41no—
493C2×C11—81no—
494C2×C11—82no—
495C2×C11#240611yescharacteristic
496C2×C11C2×#45311yescharacteristic
497C2×C11#302211yescharacteristic
498C24C2×D4×C1111yescharacteristic
499C24C2×D4×C1112yes—
500#41—22no—
501#41—22no—
502#41—84no—
503C2×Q8—22no—
504C2×Q8C2×D4×C1111yescharacteristic
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—21no—
511C2×D4—22no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—44no—
517C2×D4C2×D4×C1111yescharacteristic
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—44no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4C2×D4×C1111yescharacteristic
532C22×C4C2×D4×C1111yescharacteristic
533C22×C4C2×D4×C1111yescharacteristic
534C22×C4C2×D4×C1111yescharacteristic
535C22×C4C2×D4×C1111yescharacteristic
536C22×C4C2×D4×C1112yes—
537C22×C4C24×C1111yescharacteristic
538M16—24no—
539M16—22no—
540M16—22no—
541M16—22no—
542M16C11×#4114yescomplemented
543C2×C8—24no—
544C2×C8—22no—
545C2×C8—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—48no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4C2×D4×C1111yescharacteristic
562C4⋊C4C2×D4×C1111yescharacteristic
563C4⋊C4C2×D4×C1111yescharacteristic
564C4⋊C4C2×D4×C1111yescharacteristic
565C4⋊C4C2×D4×C1111yescharacteristic
566C4⋊C4C2×D4×C1111yescharacteristic
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—24no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—48no—
585C42—22no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—22no—
592C42—22no—
593C11#2408211yescharacteristic, direct product factor, Sylow
594C23—22no—
595C23—22no—
596C23—22no—
597C23—21no—
598C23—24no—
599C23—41no—
600C23—42no—
601C23—42no—
602C23C11×#12011yescharacteristic
603C23C11×#12011yescharacteristic
604C23C22×D4×C1111yescharacteristic
605Q8—22no—
606Q8—82no—
607D4—22no—
608D4—42no—
609D4—44no—
610D4—42no—
611D4—41no—
612D4—41no—
613D4—42no—
614D4—81no—
615D4—82no—
616D4—82no—
617D4—82no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—44no—
641C2×C4—42no—
642C2×C4—81no—
643C2×C4—82no—
644C2×C4—82no—
645C2×C4—82no—
646C2×C4—82no—
647C2×C4—82no—
648C2×C4C11×#12011yescharacteristic
649C2×C4C11×#12011yescharacteristic
650C2×C4C22×D4×C1111yescharacteristic
651C2×C4C22×D4×C1111yescharacteristic
652C2×C4C2×C11×#4112yes—
653C2×C4C11×2−1+412yes—
654C8—24no—
655C8—42no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—44no—
664C22—41no—
665C22—42no—
666C22—41no—
667C22—42no—
668C22—42no—
669C22—41no—
670C22—84no—
671C22C11×#45312yes—
672C22C2×C11×#12011yescharacteristic
673C22C11×#54712yes—
674C4—21no—
675C4—21no—
676C4—44no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—82no—
686C4C11×#52511yescharacteristic
687C4C11×#53611yescharacteristic
688C4C11×#54712yes—
689C2—22no—
690C2—22no—
691C2—41no—
692C2—82no—
693C2—81no—
694C2C11×#240611yescharacteristic
695C2C2×C11×#45311yescharacteristic
696C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3494C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3092C2semidirect
3. C2×C11×#428C2semidirect
4. C11×#2501C2semidirect
5. C11×#2060C2semidirect
6. C11×#2037C2semidirect
7. C11×#1900C2semidirect
8. C11×#1871C2semidirect
9. C11×#1859C2semidirect
10. C11×#1856C2semidirect
11. C11×#1826C2semidirect
150. #24082C11direct (N × H)
195. C11×M16#41semidirect
247. #3092C2×C11semidirect
248. C2×#428C2×C11semidirect
249. #2501C2×C11semidirect
250. #2060C2×C11semidirect
251. #2037C2×C11semidirect
252. #1900C2×C11semidirect
253. #1871C2×C11semidirect
254. #1859C2×C11semidirect
255. #1856C2×C11semidirect
256. #1826C2×C11semidirect
542. M16C11×#41semidirect
593. C11#24082direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34942
C11×#30922
C2×C11×#4282
C11×#25012
C11×#20602
C11×#20372
C11×#19002
C11×#18712
C11×#18592
C11×#18562
C11×#18262
#2408211