Finite Group Databasebeta

← C11×#24625 #14601818

Subgroups — C11×#24625 #14601818

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3094C211yesmaximal, characteristic
2C2×C11×#482C211yesmaximal, characteristic
3C11×#2924C211yesmaximal, characteristic, complemented
4C11×#2911C211yesmaximal, characteristic, complemented
5C11×#2090C211yesmaximal, characteristic, complemented
6C11×#2089C211yesmaximal, characteristic, complemented
7C11×#2063C211yesmaximal, characteristic, complemented
8C11×#2063C211yesmaximal, characteristic, complemented
9C11×#1952C211yesmaximal, characteristic, complemented
10C11×#1951C211yesmaximal, characteristic, complemented
11C11×#1931C211yesmaximal, characteristic, complemented
12C11×#1931C211yesmaximal, characteristic, complemented
13C11×#1900C211yesmaximal, characteristic
14C11×#1855C211yesmaximal, characteristic, complemented
15C11×#1822C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C11×#482—21no—
21C11×#482—21no—
22C11×#482—21no—
23C11×#482—21no—
24C11×#482—21no—
25C11×#482—21no—
26C11×#481—21no—
27C11×#480—21no—
28C11×#433—21no—
29C11×#433—21no—
30C11×#432—21no—
31C11×#431—21no—
32C2×C11×#108C2211yescharacteristic
33C2×C11×#108C2211yescharacteristic
34C11×#428—21no—
35C11×#428—21no—
36C11×#428C2211yescharacteristic
37C11×#428C2211yescharacteristic
38C11×#428C2211yescharacteristic
39C11×#428C2211yescharacteristic
40C11×#428C2211yescharacteristic
41C11×#428C2211yescharacteristic
42C11×#427—21no—
43C11×#427—21no—
44C2×C11×#107C2211yescharacteristic
45C2×C11×#106C2211yescharacteristic
46C11×#424C2211yescharacteristic
47C11×#424C2211yescharacteristic
48C11×#418C2211yescharacteristic
49C11×#418C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#100C2211yescharacteristic
53C2×C11×#100C2211yescharacteristic
54C11×#407C2211yescharacteristic
55C11×#407C2211yescharacteristic
56C2×C11×C22⋊C8C2211yescharacteristic
57C11×#405C2211yescharacteristic
58C11×#405C2211yescharacteristic
59C11×#343C2211yescharacteristic
60C11×#343C2211yescharacteristic
61C11×#343C2211yescharacteristic
62C11×#343C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#341C2211yescharacteristic
66C11×#341C2211yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C2×C11×M16—21no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16C2311yescharacteristic
74C2×C11×M16C2311yescharacteristic
75C2×C11×M16C2311yescharacteristic
76C2×C11×M16C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C2×C11×M16C2311yescharacteristic
79C22×C8×C11—21no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#121—21no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#117—21no—
87C11×#117—21no—
88C11×#117—21no—
89C11×#117—21no—
90C11×#117—21no—
91C11×#117—21no—
92C11×#117D411yescharacteristic
93C11×#117D411yescharacteristic
94C11×#117C2311yescharacteristic
95C11×#117C2311yescharacteristic
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C42×C11—21no—
105C2×C42×C11—21no—
106C11×#108—22no—
107C11×#108—22no—
108C11×#107—21no—
109C11×#107—21no—
110C11×#107—21no—
111C11×#107—21no—
112C11×#107—21no—
113C11×#107—21no—
114C11×#107—21no—
115C11×#107—21no—
116C11×#106—21no—
117C11×#106—21no—
118C11×#106—21no—
119C11×#106—21no—
120C11×#106—21no—
121C11×#106—21no—
122C11×#106—21no—
123C11×#106—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—21no—
136C11×#100—22no—
137C11×#100—22no—
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8D411yescharacteristic
143C11×C22⋊C8D411yescharacteristic
144C11×C22⋊C8D411yescharacteristic
145C11×C22⋊C8D411yescharacteristic
146C11×#97—21no—
147C11×#97—21no—
148C4×C8×C11—21no—
149C4×C8×C11—21no—
150#24625C1111yesmaximal, characteristic, direct product factor, Sylow
151C24×C11—21no—
152C24×C11#4111yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—82no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11#4111yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C11×M16—24no—
178C11×M16—21no—
179C11×M16—21no—
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#4112yes—
189C11×M16#4112yes—
190C2×C8×C11—24no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
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×C11C2×D411yescharacteristic
202C2×C8×C11C2×D411yescharacteristic
203C2×C8×C11C2×D411yescharacteristic
204C2×C8×C11C2×D411yescharacteristic
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4C2×D411yescharacteristic
214C11×C4⋊C4C2×D411yescharacteristic
215C11×C4⋊C4C2×D411yescharacteristic
216C11×C4⋊C4C2×D411yescharacteristic
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—41no—
224C11×C22⋊C4—41no—
225C42×C11—21no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—41no—
230C42×C11—41no—
231#3094C2×C1111yescharacteristic
232C2×#482C2×C1111yescharacteristic
233#2924C2×C1111yescharacteristic, complemented
234#2911C2×C1111yescharacteristic, complemented
235#2090C2×C1111yescharacteristic, complemented
236#2089C2×C1111yescharacteristic, complemented
237#2063C2×C1111yescharacteristic, complemented
238#2063C2×C1111yescharacteristic, complemented
239#1952C2×C1111yescharacteristic, complemented
240#1951C2×C1111yescharacteristic, complemented
241#1931C2×C1111yescharacteristic, complemented
242#1931C2×C1111yescharacteristic, complemented
243#1900C2×C1111yescharacteristic
244#1855C2×C1111yescharacteristic, complemented
245#1822C2×C1111yescharacteristic, complemented
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—81no—
254C23×C11—81no—
255C23×C11#12111yescharacteristic
256C23×C11#12111yescharacteristic
257C23×C11C2×#4111yescharacteristic
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—82no—
263D4×C11—82no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—42no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—81no—
283C2×C4×C11—81no—
284C2×C4×C11—81no—
285C2×C4×C11—81no—
286C2×C4×C11#12111yescharacteristic
287C2×C4×C11#12111yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C112−1+411yescharacteristic
293C2×C4×C112−1+411yescharacteristic
294C8×C11—22no—
295C8×C11—22no—
296C8×C11—21no—
297C8×C11—21no—
298C8×C11—21no—
299C8×C11—21no—
300C8×C11—41no—
301C8×C11—41no—
302C8×C11—41no—
303C8×C11—41no—
304C22×M16C22×C1111yescharacteristic
305C2×#121C22×C1111yescharacteristic
306C2×#117C22×C1111yescharacteristic
307C2×#117C22×C1111yescharacteristic
308#482—21no—
309#482—21no—
310#482—21no—
311#482—21no—
312#482—21no—
313#482—21no—
314#481—21no—
315#480—21no—
316#433—21no—
317#433—21no—
318#432—21no—
319#431—21no—
320C2×#108C22×C1111yescharacteristic
321C2×#108C22×C1111yescharacteristic
322#428—21no—
323#428—21no—
324#428C22×C1111yescharacteristic
325#428C22×C1111yescharacteristic
326#428C22×C1111yescharacteristic
327#428C22×C1111yescharacteristic
328#428C22×C1111yescharacteristic
329#428C22×C1111yescharacteristic
330#427—21no—
331#427—21no—
332C2×#107C22×C1111yescharacteristic
333C2×#106C22×C1111yescharacteristic
334#424C22×C1111yescharacteristic
335#424C22×C1111yescharacteristic
336#418C22×C1111yescharacteristic
337#418C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×#102C22×C1111yescharacteristic
340C2×#100C22×C1111yescharacteristic
341C2×#100C22×C1111yescharacteristic
342#407C22×C1111yescharacteristic
343#407C22×C1111yescharacteristic
344C2×C22⋊C8C22×C1111yescharacteristic
345#405C22×C1111yescharacteristic
346#405C22×C1111yescharacteristic
347#343C22×C1111yescharacteristic
348#343C22×C1111yescharacteristic
349#343C22×C1111yescharacteristic
350#343C22×C1111yescharacteristic
351#343C22×C1111yescharacteristic
352#343C22×C1111yescharacteristic
353#341C22×C1111yescharacteristic
354#341C22×C1111yescharacteristic
355C22×C11—21no—
356C22×C11—21no—
357C22×C11—21no—
358C22×C11—21no—
359C22×C11—21no—
360C22×C11—21no—
361C22×C11—21no—
362C22×C11—21no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—161no—
369C22×C11—161no—
370C22×C11C2×#12111yescharacteristic
371C22×C11#55211yescharacteristic
372C22×C11#55211yescharacteristic
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11#52511yescharacteristic
383C4×C11#53611yescharacteristic
384C4×C11#54711yescharacteristic
385C4×C11#54711yescharacteristic
386C22×D4—21no—
387C22×D4C23×C1111yescharacteristic
388C23×C4C23×C1111yescharacteristic
389C2×M16—21no—
390C2×M16—22no—
391C2×M16—22no—
392C2×M16C23×C1111yescharacteristic
393C2×M16C23×C1111yescharacteristic
394C2×M16C23×C1111yescharacteristic
395C2×M16C23×C1111yescharacteristic
396C2×M16C23×C1111yescharacteristic
397C2×M16C23×C1111yescharacteristic
398C22×C8—21no—
399C22×C8C23×C1111yescharacteristic
400C22×C8C23×C1111yescharacteristic
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#117—21no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—21no—
410#117—21no—
411#117D4×C1111yescharacteristic
412#117D4×C1111yescharacteristic
413#117C23×C1111yescharacteristic
414#117C23×C1111yescharacteristic
415C2×C4⋊C4D4×C1111yescharacteristic
416C2×C4⋊C4D4×C1111yescharacteristic
417C2×C4⋊C4C23×C1111yescharacteristic
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42—21no—
424C2×C42—21no—
425#108—22no—
426#108—22no—
427#107—21no—
428#107—21no—
429#107—21no—
430#107—21no—
431#107—21no—
432#107—21no—
433#107—21no—
434#107—21no—
435#106—21no—
436#106—21no—
437#106—21no—
438#106—21no—
439#106—21no—
440#106—21no—
441#106—21no—
442#106—21no—
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447#102—21no—
448#102—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—21no—
454#102—21no—
455#100—22no—
456#100—22no—
457C22⋊C8—21no—
458C22⋊C8—21no—
459C22⋊C8—21no—
460C22⋊C8—21no—
461C22⋊C8D4×C1111yescharacteristic
462C22⋊C8D4×C1111yescharacteristic
463C22⋊C8D4×C1111yescharacteristic
464C22⋊C8D4×C1111yescharacteristic
465#97—21no—
466#97—21no—
467C4×C8—21no—
468C4×C8—21no—
469C2×C11—21no—
470C2×C11—21no—
471C2×C11—41no—
472C2×C11—41no—
473C2×C11—161no—
474C2×C11#241311yescharacteristic
475C2×C11#306711yescharacteristic
476C2×C11#306811yescharacteristic
477C24—21no—
478C24C11×#4111yescharacteristic
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—82no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4C2×D4×C1111yescharacteristic
498C22×C4C2×D4×C1111yescharacteristic
499C22×C4C2×D4×C1111yescharacteristic
500C22×C4C2×D4×C1111yescharacteristic
501C22×C4C11×#4111yescharacteristic
502C22×C4C24×C1111yescharacteristic
503M16—24no—
504M16—21no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16—21no—
509M16—21no—
510M16—21no—
511M16—21no—
512M16—21no—
513M16—21no—
514M16C11×#4112yes—
515M16C11×#4112yes—
516C2×C8—24no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8C2×D4×C1111yescharacteristic
528C2×C8C2×D4×C1111yescharacteristic
529C2×C8C2×D4×C1111yescharacteristic
530C2×C8C2×D4×C1111yescharacteristic
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4C2×D4×C1111yescharacteristic
540C4⋊C4C2×D4×C1111yescharacteristic
541C4⋊C4C2×D4×C1111yescharacteristic
542C4⋊C4C2×D4×C1111yescharacteristic
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—41no—
556C42—41no—
557C11#2462511yescharacteristic, direct product factor, Sylow
558C23—21no—
559C23—21no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—81no—
566C23—81no—
567C23C11×#12111yescharacteristic
568C23C11×#12111yescharacteristic
569C23C2×C11×#4111yescharacteristic
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574D4—82no—
575D4—82no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4C11×#12111yescharacteristic
599C2×C4C11×#12111yescharacteristic
600C2×C4C22×D4×C1111yescharacteristic
601C2×C4C22×D4×C1111yescharacteristic
602C2×C4C2×C11×#4111yescharacteristic
603C2×C4C2×C11×#4111yescharacteristic
604C2×C4C11×2−1+411yescharacteristic
605C2×C4C11×2−1+411yescharacteristic
606C8—22no—
607C8—22no—
608C8—21no—
609C8—21no—
610C8—21no—
611C8—21no—
612C8—41no—
613C8—41no—
614C8—41no—
615C8—41no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—161no—
630C22—161no—
631C22C2×C11×#12111yescharacteristic
632C22C11×#55211yescharacteristic
633C22C11×#55211yescharacteristic
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—81no—
643C4C11×#52511yescharacteristic
644C4C11×#53611yescharacteristic
645C4C11×#54711yescharacteristic
646C4C11×#54711yescharacteristic
647C2—21no—
648C2—21no—
649C2—41no—
650C2—41no—
651C2—161no—
652C2C11×#241311yescharacteristic
653C2C11×#306711yescharacteristic
654C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
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
3. C11×#2924C2semidirect
4. C11×#2911C2semidirect
5. C11×#2090C2semidirect
6. C11×#2089C2semidirect
7. C11×#2063C2semidirect
8. C11×#2063C2semidirect
9. C11×#1952C2semidirect
10. C11×#1951C2semidirect
11. C11×#1931C2semidirect
12. C11×#1931C2semidirect
14. C11×#1855C2semidirect
15. C11×#1822C2semidirect
150. #24625C11direct (N × H)
233. #2924C2×C11semidirect
234. #2911C2×C11semidirect
235. #2090C2×C11semidirect
236. #2089C2×C11semidirect
237. #2063C2×C11semidirect
238. #2063C2×C11semidirect
239. #1952C2×C11semidirect
240. #1951C2×C11semidirect
241. #1931C2×C11semidirect
242. #1931C2×C11semidirect
244. #1855C2×C11semidirect
245. #1822C2×C11semidirect
557. C11#24625direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30942
C2×C11×#4822
C11×#29242
C11×#29112
C11×#20902
C11×#20892
C11×#20632
C11×#19522
C11×#19512
C11×#19312
C11×#19002
C11×#18552
C11×#18222
#2462511