Finite Group Databasebeta

← C11×#24860 #14602053

Subgroups — C11×#24860 #14602053

Order 2816.

704 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×#3080C211yesmaximal, characteristic
2C2×C11×#479C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic
4C11×#2906C211yesmaximal, characteristic
5C11×#2090C211yesmaximal, characteristic, complemented
6C11×#2089C211yesmaximal, characteristic, complemented
7C11×#2064C211yesmaximal, characteristic, complemented
8C11×#2064C211yesmaximal, characteristic, complemented
9C11×#1998C211yesmaximal, characteristic, complemented
10C11×#1950C211yesmaximal, characteristic, complemented
11C11×#1908C211yesmaximal, characteristic
12C11×#1908C211yesmaximal, characteristic
13C11×#1816C211yesmaximal, characteristic
14C11×#1815C211yesmaximal, characteristic
15C11×#1801C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C11×#479—21no—
23C11×#479—21no—
24C11×#479—21no—
25C11×#479—21no—
26C11×#479—21no—
27C11×#479—21no—
28C11×#478—21no—
29C11×#478—21no—
30C11×#441—21no—
31C11×#440—21no—
32C4×C11×Q16—21no—
33C4×C11×SD16—21no—
34C2×C11×#108C2211yescharacteristic
35C2×C11×#108C2211yescharacteristic
36C11×#428C2211yescharacteristic
37C11×#428C2211yescharacteristic
38C11×#428C2211yescharacteristic
39C2×C11×#107C2211yescharacteristic
40C2×C11×#106C2211yescharacteristic
41C11×#424—21no—
42C11×#424—21no—
43C11×#424C2211yescharacteristic
44C11×#424C2211yescharacteristic
45C11×#423—21no—
46C11×#423C2211yescharacteristic
47C11×#423C2211yescharacteristic
48C2×C11×C4⋊C8—21no—
49C2×C11×C4⋊C8C2211yescharacteristic
50C11×#419C2211yescharacteristic
51C11×#417C2211yescharacteristic
52C11×#417C2211yescharacteristic
53C11×#417C2211yescharacteristic
54C2×C11×#103C2211yescharacteristic
55C2×C11×#103C2211yescharacteristic
56C2×C11×#101C2211yescharacteristic
57C2×C11×#101C2211yescharacteristic
58C4×C11×M16C2211yescharacteristic
59C11×#343C2211yescharacteristic
60C11×#343C2211yescharacteristic
61C11×#343C2211yescharacteristic
62C11×#343C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#341C2211yescharacteristic
66C11×#341C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C11×#137—22no—
70C11×#137Q814yes—
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C11×#131—22no—
74C11×#131—22no—
75C11×#131—41no—
76C11×#131—41no—
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16C2311yescharacteristic
80C2×C11×M16C2311yescharacteristic
81C2×C11×M16C2311yescharacteristic
82C2×C11×M16C2311yescharacteristic
83C2×C11×M16C2311yescharacteristic
84C2×C11×M16C2311yescharacteristic
85C22×C8×C11—21no—
86C22×C8×C11—21no—
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×#125—21no—
90C11×#125—21no—
91C11×#125—21no—
92C11×#125—21no—
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—21no—
100C4×D4×C11—21no—
101C4×D4×C11D411yescharacteristic
102C4×D4×C11D411yescharacteristic
103C11×#117—21no—
104C11×#117C2311yescharacteristic
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C11×#108—41no—
115C11×#108—41no—
116C11×#107—21no—
117C11×#107—21no—
118C11×#107—21no—
119C11×#107—21no—
120C11×#107—21no—
121C11×#106—21no—
122C11×#106—21no—
123C11×#106—21no—
124C11×#106—21no—
125C11×#106—21no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×C4⋊C8—21no—
129C11×C4⋊C8—21no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8—21no—
134C11×C4⋊C8D411yescharacteristic
135C11×C4⋊C8D411yescharacteristic
136C11×C4⋊C8D411yescharacteristic
137C11×C4⋊C8D411yescharacteristic
138C11×#103—21no—
139C11×#103—21no—
140C11×#103—21no—
141C11×#103—21no—
142C11×#103—21no—
143C11×#103—21no—
144C11×#103—21no—
145C11×#103—21no—
146C11×#103—21no—
147C11×#102—21no—
148C11×#102—21no—
149C11×#102—21no—
150C11×#101—41no—
151C11×#101—41no—
152C11×#97—21no—
153C4×C8×C11—21no—
154#24860C1111yesmaximal, characteristic, direct product factor, Sylow
155C11×#41—21no—
156C11×#41—21no—
157C11×#41C2×Q812yes—
158C11×#41#4112yes—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11C2×D411yescharacteristic
165C2×Q8×C11C2×Q812yes—
166C2×D4×C11—21no—
167C2×D4×C11C2×D411yescharacteristic
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11#4111yescharacteristic
176C22×C4×C11#4111yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C11×Q16—24no—
179C11×SD16—24no—
180C11×M16—21no—
181C11×M16—21no—
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C11×M16—21no—
187C11×M16—21no—
188C11×M16—21no—
189C11×M16—21no—
190C11×M16—21no—
191C11×M16—42no—
192C11×M16—42no—
193C11×M16C2×Q812yes—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—42no—
205C2×C8×C11—42no—
206C2×C8×C11C2×D411yescharacteristic
207C2×C8×C11C2×D411yescharacteristic
208C2×C8×C11C2×D411yescharacteristic
209C2×C8×C11C2×D411yescharacteristic
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—41no—
219C11×C4⋊C4—41no—
220C11×C4⋊C4—41no—
221C11×C4⋊C4—41no—
222C11×C4⋊C4—41no—
223C11×C4⋊C4—41no—
224C11×C4⋊C4C2×D411yescharacteristic
225C11×C4⋊C4C2×D411yescharacteristic
226C11×C22⋊C4—21no—
227C11×C22⋊C4—21no—
228C11×C22⋊C4—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—41no—
233C42×C11—41no—
234C42×C11C2×D411yescharacteristic
235C42×C11C2×D411yescharacteristic
236C42×C11C2×D411yescharacteristic
237C42×C11C2×D411yescharacteristic
238#3080C2×C1111yescharacteristic
239C2×#479C2×C1111yescharacteristic, complemented
240C4×#137C2×C1111yescharacteristic
241#2906C2×C1111yescharacteristic
242#2090C2×C1111yescharacteristic, complemented
243#2089C2×C1111yescharacteristic, complemented
244#2064C2×C1111yescharacteristic, complemented
245#2064C2×C1111yescharacteristic, complemented
246#1998C2×C1111yescharacteristic, complemented
247#1950C2×C1111yescharacteristic, complemented
248#1908C2×C1111yescharacteristic
249#1908C2×C1111yescharacteristic
250#1816C2×C1111yescharacteristic
251#1815C2×C1111yescharacteristic
252#1801C2×C1111yescharacteristic, complemented
253C23×C11—21no—
254C23×C11C2×#4111yescharacteristic
255Q8×C11—21no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—41no—
259Q8×C11—41no—
260Q8×C11C22⋊Q812yes—
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—21no—
264D4×C11C22⋊Q812yes—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—81no—
280C2×C4×C11—81no—
281C2×C4×C11—81no—
282C2×C4×C11—81no—
283C2×C4×C11#12111yescharacteristic
284C2×C4×C11#12111yescharacteristic
285C2×C4×C11#12111yescharacteristic
286C2×C4×C11#12111yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×Q811yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C112−1+411yescharacteristic
293C8×C11—22no—
294C8×C11—21no—
295C8×C11—21no—
296C8×C11—21no—
297C8×C11—21no—
298C8×C11—41no—
299C8×C11—41no—
300C8×C11—41no—
301C8×C11—41no—
302C8×C11—41no—
303C2×#137C22×C1111yescharacteristic
304C2×#131C22×C1111yescharacteristic
305C2×#131C22×C1111yescharacteristic
306C2×#125C22×C1111yescharacteristic
307C4×#41C22×C1111yescharacteristic
308C2×C4×Q8C22×C1111yescharacteristic
309#479—21no—
310#479—21no—
311#479—21no—
312#479—21no—
313#479—21no—
314#479—21no—
315#478—21no—
316#478—21no—
317#441—21no—
318#440—21no—
319C4×Q16—21no—
320C4×SD16—21no—
321C2×#108C22×C1111yescharacteristic
322C2×#108C22×C1111yescharacteristic
323#428C22×C1111yescharacteristic
324#428C22×C1111yescharacteristic
325#428C22×C1111yescharacteristic
326C2×#107C22×C1111yescharacteristic
327C2×#106C22×C1111yescharacteristic
328#424—21no—
329#424—21no—
330#424C22×C1111yescharacteristic
331#424C22×C1111yescharacteristic
332#423—21no—
333#423C22×C1111yescharacteristic
334#423C22×C1111yescharacteristic
335C2×C4⋊C8—21no—
336C2×C4⋊C8C22×C1111yescharacteristic
337#419C22×C1111yescharacteristic
338#417C22×C1111yescharacteristic
339#417C22×C1111yescharacteristic
340#417C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#101C22×C1111yescharacteristic
344C2×#101C22×C1111yescharacteristic
345C4×M16C22×C1111yescharacteristic
346#343C22×C1111yescharacteristic
347#343C22×C1111yescharacteristic
348#343C22×C1111yescharacteristic
349#343C22×C1111yescharacteristic
350#343C22×C1111yescharacteristic
351#343C22×C1111yescharacteristic
352#341C22×C1111yescharacteristic
353#341C22×C1111yescharacteristic
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11C2×#12111yescharacteristic
360C22×C11#55211yescharacteristic
361C22×C11#55411yescharacteristic
362C4×C11—22no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11C2×C22⋊Q811yescharacteristic
374C4×C11#53711yescharacteristic
375C4×C11#54611yescharacteristic
376C4×C11D4×Q811yescharacteristic
377C2×#41C23×C1111yescharacteristic
378C22×Q8C23×C1111yescharacteristic
379#137—22no—
380#137Q8×C1114yes—
381C2×Q16—21no—
382C2×SD16—21no—
383#131—22no—
384#131—22no—
385#131—41no—
386#131—41no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16C23×C1111yescharacteristic
390C2×M16C23×C1111yescharacteristic
391C2×M16C23×C1111yescharacteristic
392C2×M16C23×C1111yescharacteristic
393C2×M16C23×C1111yescharacteristic
394C2×M16C23×C1111yescharacteristic
395C22×C8—21no—
396C22×C8—21no—
397C22×C8C23×C1111yescharacteristic
398C22×C8C23×C1111yescharacteristic
399#125—21no—
400#125—21no—
401#125—21no—
402#125—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8D4×C1111yescharacteristic
408C4×Q8D4×C1111yescharacteristic
409C4×D4—21no—
410C4×D4—21no—
411C4×D4D4×C1111yescharacteristic
412C4×D4D4×C1111yescharacteristic
413#117—21no—
414#117C23×C1111yescharacteristic
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C42—21no—
422C2×C42—21no—
423C2×C42C23×C1111yescharacteristic
424#108—41no—
425#108—41no—
426#107—21no—
427#107—21no—
428#107—21no—
429#107—21no—
430#107—21no—
431#106—21no—
432#106—21no—
433#106—21no—
434#106—21no—
435#106—21no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—21no—
443C4⋊C8—21no—
444C4⋊C8D4×C1111yescharacteristic
445C4⋊C8D4×C1111yescharacteristic
446C4⋊C8D4×C1111yescharacteristic
447C4⋊C8D4×C1111yescharacteristic
448#103—21no—
449#103—21no—
450#103—21no—
451#103—21no—
452#103—21no—
453#103—21no—
454#103—21no—
455#103—21no—
456#103—21no—
457#102—21no—
458#102—21no—
459#102—21no—
460#101—41no—
461#101—41no—
462#97—21no—
463C4×C8—21no—
464C2×C11—21no—
465C2×C11—21no—
466C2×C11—42no—
467C2×C11#241711yescharacteristic
468C2×C11#306711yescharacteristic
469C2×C11#306911yescharacteristic
470#41—21no—
471#41—21no—
472#41C2×Q8×C1112yes—
473#41C11×#4112yes—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C2×D4×C1111yescharacteristic
480C2×Q8C2×Q8×C1112yes—
481C2×D4—21no—
482C2×D4C2×D4×C1111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4C11×#4111yescharacteristic
491C22×C4C11×#4111yescharacteristic
492C22×C4C24×C1111yescharacteristic
493Q16—24no—
494SD16—24no—
495M16—21no—
496M16—21no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—21no—
502M16—21no—
503M16—21no—
504M16—21no—
505M16—21no—
506M16—42no—
507M16—42no—
508M16C2×Q8×C1112yes—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—42no—
520C2×C8—42no—
521C2×C8C2×D4×C1111yescharacteristic
522C2×C8C2×D4×C1111yescharacteristic
523C2×C8C2×D4×C1111yescharacteristic
524C2×C8C2×D4×C1111yescharacteristic
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4C2×D4×C1111yescharacteristic
540C4⋊C4C2×D4×C1111yescharacteristic
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—41no—
548C42—41no—
549C42C2×D4×C1111yescharacteristic
550C42C2×D4×C1111yescharacteristic
551C42C2×D4×C1111yescharacteristic
552C42C2×D4×C1111yescharacteristic
553C11#2486011yescharacteristic, direct product factor, Sylow
554C23—21no—
555C23C2×C11×#4111yescharacteristic
556Q8—21no—
557Q8—22no—
558Q8—22no—
559Q8—41no—
560Q8—41no—
561Q8C11×C22⋊Q812yes—
562D4—22no—
563D4—22no—
564D4—21no—
565D4C11×C22⋊Q812yes—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4C11×#12111yescharacteristic
585C2×C4C11×#12111yescharacteristic
586C2×C4C11×#12111yescharacteristic
587C2×C4C11×#12111yescharacteristic
588C2×C4C22×D4×C1111yescharacteristic
589C2×C4C22×D4×C1111yescharacteristic
590C2×C4C22×Q8×C1111yescharacteristic
591C2×C4C2×C11×#4111yescharacteristic
592C2×C4C11×H(5,𝔽2)11yescharacteristic
593C2×C4C11×2−1+411yescharacteristic
594C8—22no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—41no—
600C8—41no—
601C8—41no—
602C8—41no—
603C8—41no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C2×C11×#12111yescharacteristic
610C22C11×#55211yescharacteristic
611C22C11×#55411yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4C2×C11×C22⋊Q811yescharacteristic
624C4C11×#53711yescharacteristic
625C4C11×#54611yescharacteristic
626C4D4×Q8×C1111yescharacteristic
627C2—21no—
628C2—21no—
629C2—42no—
630C2C11×#241711yescharacteristic
631C2C11×#306711yescharacteristic
632C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
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. C2×C11×#479C2semidirect
5. C11×#2090C2semidirect
6. C11×#2089C2semidirect
7. C11×#2064C2semidirect
8. C11×#2064C2semidirect
9. C11×#1998C2semidirect
10. C11×#1950C2semidirect
15. C11×#1801C2semidirect
154. #24860C11direct (N × H)
239. C2×#479C2×C11semidirect
242. #2090C2×C11semidirect
243. #2089C2×C11semidirect
244. #2064C2×C11semidirect
245. #2064C2×C11semidirect
246. #1998C2×C11semidirect
247. #1950C2×C11semidirect
252. #1801C2×C11semidirect
553. C11#24860direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30802
C2×C11×#4792
C4×C11×#1372
C11×#29062
C11×#20902
C11×#20892
C11×#20642
C11×#19982
C11×#19502
C11×#19082
C11×#18162
C11×#18152
C11×#18012
#2486011