Finite Group Databasebeta

← C11×#24147 #14601340

Subgroups — C11×#24147 #14601340

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3509C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic
4C11×#2546C211yesmaximal, characteristic, complemented
5C11×#2038C212yesmaximal
6C11×#2005C212yesmaximal
7C11×#1986C211yesmaximal, characteristic, complemented
8C11×#1966C211yesmaximal, characteristic, complemented
9C11×#1886C212yesmaximal, complemented
10C11×#1857C212yesmaximal, complemented
11C11×#1806C211yesmaximal, characteristic
12C2×C11×#137C2211yescharacteristic
13C11×#557—21no—
14C11×#557—21no—
15C11×#556—21no—
16C11×#556—21no—
17C11×#552—22no—
18C11×#552—22no—
19C11×#541—22no—
20C11×#536C2212yes—
21C11×#533—21no—
22C11×#533—21no—
23C11×#533C2211yescharacteristic
24C2×C11×C4⋊Q8C2212yes—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C11×#519C2212yes—
27C4×C11×#41C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C11×#479—22no—
30C11×#477—21no—
31C11×#475—21no—
32C11×#441—21no—
33C11×#440—21no—
34C4×C11×Q16—21no—
35C4×C11×SD16—21no—
36C11×#428C2211yescharacteristic
37C11×#428C2212yes—
38C11×#423C2211yescharacteristic
39C2×C11×#104C2212yes—
40C11×#419C2211yescharacteristic
41C11×#419C2212yes—
42C11×#417C2211yescharacteristic
43C2×C11×#101C2212yes—
44C2×C11×#101C2212yes—
45C4×C11×M16C2211yescharacteristic
46C11×#398—22no—
47C11×#391C2212yes—
48C11×#389—22no—
49C4×C11×C4⋊C4C2211yescharacteristic
50C11×#339C2212yes—
51C11×#339C2212yes—
52C11×#339C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11C2311yescharacteristic
55C22×Q8×C11C2312yes—
56C11×#137—22no—
57C11×#137—22no—
58C2×C11×Q16—21no—
59C2×C11×SD16—21no—
60C2×C11×M16C2311yescharacteristic
61C2×C11×M16C2312yes—
62C2×C11×M16C2311yescharacteristic
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8—24no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8—21no—
69C11×C4⋊Q8—42no—
70C11×C4⋊Q8D411yescharacteristic
71C11×C4⋊Q8D411yescharacteristic
72C11×#126—24no—
73C11×#126—24no—
74C11×#125—22no—
75C11×#125—22no—
76C11×#125—24no—
77C11×#125—24no—
78C11×#125D412yes—
79C11×#124—22no—
80C11×#123—24no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
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×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11D411yescharacteristic
100C4×Q8×C11D411yescharacteristic
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11D411yescharacteristic
104C4×D4×C11D411yescharacteristic
105C11×#117—22no—
106C11×#117—22no—
107C11×#117—24no—
108C11×#117—21no—
109C11×#117C2311yescharacteristic
110C11×#117C2312yes—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—24no—
114C2×C11×C4⋊C4D412yes—
115C2×C11×C4⋊C4D412yes—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C42×C11—21no—
118C2×C42×C11—21no—
119C2×C42×C11C2312yes—
120C2×C42×C11C2311yescharacteristic
121C11×#107—21no—
122C11×#107—22no—
123C11×#106—21no—
124C11×#106—22no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×#104—42no—
128C11×#103—21no—
129C11×#103—21no—
130C11×#103—21no—
131C11×#103—22no—
132C11×#103—22no—
133C11×#102—21no—
134C11×#101—24no—
135C11×#101—42no—
136C11×#97—21no—
137C4×C8×C11—21no—
138C11×#95—21no—
139C11×#95—24no—
140#24147C1111yesmaximal, characteristic, direct product factor, Sylow
141C11×#41—21no—
142C11×#41—21no—
143C11×#41—21no—
144C11×#41—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11C2×D411yescharacteristic
159C2×Q8×C11#4112yes—
160C2×D4×C11—21no—
161C2×D4×C11C2×D411yescharacteristic
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C11×Q16—24no—
173C11×SD16—24no—
174C11×M16—21no—
175C11×M16—22no—
176C11×M16—21no—
177C11×M16—22no—
178C11×M16—21no—
179C11×M16#4112yes—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—22no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—48no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D412yes—
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D412yes—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C42×C11—24no—
214C42×C11—24no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—22no—
219C42×C11—22no—
220C42×C11—22no—
221C42×C11—41no—
222C42×C11—41no—
223C42×C11C2×D411yescharacteristic
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227#3509C2×C1111yescharacteristic
228#3078C2×C1111yescharacteristic, complemented
229C4×#137C2×C1111yescharacteristic
230#2546C2×C1111yescharacteristic, complemented
231#2038C2×C1112yes—
232#2005C2×C1112yes—
233#1986C2×C1111yescharacteristic, complemented
234#1966C2×C1111yescharacteristic, complemented
235#1886C2×C1112yescomplemented
236#1857C2×C1112yescomplemented
237#1806C2×C1111yescharacteristic
238C23×C11—21no—
239C23×C11C22×D411yescharacteristic
240Q8×C11—22no—
241Q8×C11—21no—
242Q8×C11—21no—
243Q8×C11—22no—
244Q8×C11—42no—
245Q8×C11—42no—
246Q8×C11—42no—
247Q8×C11—41no—
248Q8×C11—42no—
249Q8×C11—42no—
250Q8×C11—41no—
251Q8×C11—42no—
252D4×C11—21no—
253D4×C11—21no—
254D4×C11—41no—
255D4×C11—41no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—41no—
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11#12011yescharacteristic
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C8×C11—22no—
289C8×C11—41no—
290C8×C11—42no—
291C2×#137C22×C1111yescharacteristic
292#557—21no—
293#557—21no—
294#556—21no—
295#556—21no—
296#552—22no—
297#552—22no—
298#541—22no—
299#536C22×C1112yes—
300#533—21no—
301#533—21no—
302#533C22×C1111yescharacteristic
303C2×C4⋊Q8C22×C1112yes—
304C2×C4⋊Q8C22×C1111yescharacteristic
305#519C22×C1112yes—
306C4×#41C22×C1111yescharacteristic
307C2×C4×Q8C22×C1111yescharacteristic
308#479—22no—
309#477—21no—
310#475—21no—
311#441—21no—
312#440—21no—
313C4×Q16—21no—
314C4×SD16—21no—
315#428C22×C1112yes—
316#428C22×C1111yescharacteristic
317#423C22×C1111yescharacteristic
318C2×#104C22×C1112yes—
319#419C22×C1112yes—
320#419C22×C1111yescharacteristic
321#417C22×C1111yescharacteristic
322C2×#101C22×C1112yes—
323C2×#101C22×C1112yes—
324C4×M16C22×C1111yescharacteristic
325#398—22no—
326#391C22×C1112yes—
327#389—22no—
328C4×C4⋊C4C22×C1111yescharacteristic
329#339C22×C1112yes—
330#339C22×C1112yes—
331#339C22×C1112yes—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×#12011yescharacteristic
338C22×C11#54611yescharacteristic
339C22×C11#54711yescharacteristic
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—44no—
344C4×C11—44no—
345C4×C11—41no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—81no—
352C4×C11#45612yes—
353C4×C11#52511yescharacteristic
354C4×C11#53711yescharacteristic
355C4×C11#54811yescharacteristic
356C4×C11#55011yescharacteristic
357C2×#41C23×C1111yescharacteristic
358C22×Q8C23×C1111yescharacteristic
359C22×Q8C23×C1112yes—
360#137—22no—
361#137—22no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×M16C23×C1111yescharacteristic
365C2×M16C23×C1112yes—
366C2×M16C23×C1111yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8—24no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—42no—
374C4⋊Q8D4×C1111yescharacteristic
375C4⋊Q8D4×C1111yescharacteristic
376#126—24no—
377#126—24no—
378#125—22no—
379#125—22no—
380#125—24no—
381#125—24no—
382#125D4×C1112yes—
383#124—22no—
384#123—24no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—22no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8D4×C1111yescharacteristic
404C4×Q8D4×C1111yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4D4×C1111yescharacteristic
408C4×D4D4×C1111yescharacteristic
409#117—22no—
410#117—22no—
411#117—24no—
412#117—21no—
413#117C23×C1111yescharacteristic
414#117C23×C1112yes—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4D4×C1112yes—
419C2×C4⋊C4D4×C1112yes—
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C42—21no—
422C2×C42—21no—
423C2×C42C23×C1112yes—
424C2×C42C23×C1111yescharacteristic
425#107—21no—
426#107—22no—
427#106—21no—
428#106—22no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431#104—42no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—22no—
436#103—22no—
437#102—21no—
438#101—24no—
439#101—42no—
440#97—21no—
441C4×C8—21no—
442#95—21no—
443#95—24no—
444C2×C11—21no—
445C2×C11—21no—
446C2×C11—81no—
447C2×C11#240711yescharacteristic
448C2×C11C2×#45611yescharacteristic
449C2×C11#302011yescharacteristic
450#41—21no—
451#41—21no—
452#41—21no—
453#41—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8C2×D4×C1111yescharacteristic
468C2×Q8C11×#4112yes—
469C2×D4—21no—
470C2×D4C2×D4×C1111yescharacteristic
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4C2×D4×C1114yes—
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C24×C1111yescharacteristic
481Q16—24no—
482SD16—24no—
483M16—21no—
484M16—22no—
485M16—21no—
486M16—22no—
487M16—21no—
488M16C11×#4112yes—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—22no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—48no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4C2×D4×C1111yescharacteristic
513C4⋊C4C2×D4×C1112yes—
514C4⋊C4C2×D4×C1111yescharacteristic
515C4⋊C4C2×D4×C1112yes—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—21no—
519C22⋊C4—22no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C42—24no—
523C42—24no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—41no—
531C42—41no—
532C42C2×D4×C1111yescharacteristic
533C42C2×D4×C1111yescharacteristic
534C42C2×D4×C1111yescharacteristic
535C42C2×D4×C1111yescharacteristic
536C11#2414711yescharacteristic, direct product factor, Sylow
537C23—21no—
538C23C22×D4×C1111yescharacteristic
539Q8—22no—
540Q8—21no—
541Q8—21no—
542Q8—22no—
543Q8—42no—
544Q8—42no—
545Q8—42no—
546Q8—41no—
547Q8—42no—
548Q8—42no—
549Q8—41no—
550Q8—42no—
551D4—21no—
552D4—21no—
553D4—41no—
554D4—41no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4C11×#12011yescharacteristic
578C2×C4C11×#12011yescharacteristic
579C2×C4C11×#12011yescharacteristic
580C2×C4C11×#12011yescharacteristic
581C2×C4C22×D4×C1111yescharacteristic
582C2×C4C22×D4×C1111yescharacteristic
583C2×C4C2×C11×#4111yescharacteristic
584C2×C4C2×C11×#4111yescharacteristic
585C2×C4C11×H(5,𝔽2)11yescharacteristic
586C2×C4C11×2−1+411yescharacteristic
587C8—22no—
588C8—41no—
589C8—42no—
590C22—21no—
591C22—21no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C2×C11×#12011yescharacteristic
596C22C11×#54611yescharacteristic
597C22C11×#54711yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—44no—
602C4—44no—
603C4—41no—
604C4—42no—
605C4—41no—
606C4—42no—
607C4—41no—
608C4—42no—
609C4—81no—
610C4C11×#45612yes—
611C4C11×#52511yescharacteristic
612C4C11×#53711yescharacteristic
613C4C11×#54811yescharacteristic
614C4C11×#55011yescharacteristic
615C2—21no—
616C2—21no—
617C2—81no—
618C2C11×#240711yescharacteristic
619C2C2×C11×#45611yescharacteristic
620C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#41C23
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×#3078C2semidirect
4. C11×#2546C2semidirect
7. C11×#1986C2semidirect
8. C11×#1966C2semidirect
9. C11×#1886C2semidirect
10. C11×#1857C2semidirect
140. #24147C11direct (N × H)
228. #3078C2×C11semidirect
230. #2546C2×C11semidirect
233. #1986C2×C11semidirect
234. #1966C2×C11semidirect
235. #1886C2×C11semidirect
236. #1857C2×C11semidirect
536. C11#24147direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35092
C11×#30782
C4×C11×#1372
C11×#25462
C11×#20382
C11×#20052
C11×#19862
C11×#19662
C11×#18862
C11×#18572
C11×#18062
#2414711