Finite Group Databasebeta

← C11×#24725 #14601918

Subgroups — C11×#24725 #14601918

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 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×#2925C211yesmaximal, characteristic
5C11×#2079C211yesmaximal, characteristic
6C11×#2078C211yesmaximal, characteristic
7C11×#2052C211yesmaximal, characteristic
8C11×#2052C211yesmaximal, characteristic
9C11×#1998C211yesmaximal, characteristic, complemented
10C11×#1952C211yesmaximal, characteristic, complemented
11C11×#1951C211yesmaximal, characteristic, complemented
12C11×#1950C211yesmaximal, characteristic, complemented
13C11×#1930C211yesmaximal, characteristic, complemented
14C11×#1930C211yesmaximal, characteristic, complemented
15C11×#1801C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C11×#479—21no—
21C11×#479—21no—
22C11×#479—21no—
23C11×#479—21no—
24C11×#479—21no—
25C11×#479—21no—
26C11×#478—21no—
27C11×#478—21no—
28C11×#441—21no—
29C11×#440—21no—
30C4×C11×Q16—21no—
31C4×C11×SD16—21no—
32C11×#433—21no—
33C11×#433—21no—
34C11×#432—21no—
35C11×#431—21no—
36C2×C11×#108C2211yescharacteristic
37C2×C11×#108C2211yescharacteristic
38C11×#428C2211yescharacteristic
39C11×#428C2211yescharacteristic
40C11×#428C2211yescharacteristic
41C2×C11×#107C2211yescharacteristic
42C2×C11×#106C2211yescharacteristic
43C11×#423C2211yescharacteristic
44C11×#423C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#419C2211yescharacteristic
47C11×#417C2211yescharacteristic
48C11×#417C2211yescharacteristic
49C11×#417C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×C11×#101C2211yescharacteristic
53C2×C11×#101C2211yescharacteristic
54C11×#408C2211yescharacteristic
55C11×#408C2211yescharacteristic
56C11×#405C2211yescharacteristic
57C11×#405C2211yescharacteristic
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×#137—22no—
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C2×C11×M16C2311yescharacteristic
74C2×C11×M16C2311yescharacteristic
75C2×C11×M16C2311yescharacteristic
76C2×C11×M16C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C2×C11×M16C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#125—21no—
82C11×#125—21no—
83C11×#125—21no—
84C11×#125—21no—
85C4×Q8×C11—21no—
86C4×Q8×C11—21no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11D411yescharacteristic
90C4×Q8×C11D411yescharacteristic
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11D411yescharacteristic
94C4×D4×C11D411yescharacteristic
95C11×#117—21no—
96C11×#117C2311yescharacteristic
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C11×#108—22no—
107C11×#108—22no—
108C11×#107—21no—
109C11×#107—21no—
110C11×#107—21no—
111C11×#107—21no—
112C11×#107—21no—
113C11×#106—21no—
114C11×#106—21no—
115C11×#106—21no—
116C11×#106—21no—
117C11×#106—21no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8D411yescharacteristic
123C11×C4⋊C8D411yescharacteristic
124C11×C4⋊C8D411yescharacteristic
125C11×C4⋊C8D411yescharacteristic
126C11×#103—21no—
127C11×#103—21no—
128C11×#103—21no—
129C11×#103—21no—
130C11×#103—21no—
131C11×#103—21no—
132C11×#103—21no—
133C11×#103—21no—
134C11×#103—21no—
135C11×#102—21no—
136C11×#102—21no—
137C11×#102—21no—
138C11×#101—22no—
139C11×#101—22no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×#97—21no—
145C11×#97—21no—
146C11×#97—21no—
147C4×C8×C11—21no—
148C4×C8×C11—21no—
149C4×C8×C11—21no—
150#24725C1111yesmaximal, characteristic, direct product factor, Sylow
151C11×#41—21no—
152C11×#41—21no—
153C11×#41—21no—
154C11×#41—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C2×D411yescharacteristic
161C2×Q8×C11#4112yes—
162C2×D4×C11—21no—
163C2×D4×C11C2×D411yescharacteristic
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×C11#4111yescharacteristic
172C22×C4×C11#4111yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C11×Q16—24no—
175C11×SD16—24no—
176C11×M16—21no—
177C11×M16—21no—
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#4112yes—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
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×C11C2×D411yescharacteristic
199C2×C8×C11C2×D411yescharacteristic
200C2×C8×C11C2×D411yescharacteristic
201C2×C8×C11C2×D411yescharacteristic
202C11×C4⋊C4—21no—
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—21no—
210C11×C4⋊C4—41no—
211C11×C4⋊C4—41no—
212C11×C4⋊C4—41no—
213C11×C4⋊C4—41no—
214C11×C4⋊C4—41no—
215C11×C4⋊C4—41no—
216C11×C4⋊C4C2×D411yescharacteristic
217C11×C4⋊C4C2×D411yescharacteristic
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—41no—
225C42×C11—41no—
226C42×C11C2×D411yescharacteristic
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230#3080C2×C1111yescharacteristic
231C2×#479C2×C1111yescharacteristic, complemented
232C4×#137C2×C1111yescharacteristic
233#2925C2×C1111yescharacteristic
234#2079C2×C1111yescharacteristic
235#2078C2×C1111yescharacteristic
236#2052C2×C1111yescharacteristic
237#2052C2×C1111yescharacteristic
238#1998C2×C1111yescharacteristic, complemented
239#1952C2×C1111yescharacteristic, complemented
240#1951C2×C1111yescharacteristic, complemented
241#1950C2×C1111yescharacteristic, complemented
242#1930C2×C1111yescharacteristic, complemented
243#1930C2×C1111yescharacteristic, complemented
244#1801C2×C1111yescharacteristic, complemented
245C23×C11—21no—
246C23×C11C2×#4111yescharacteristic
247Q8×C11—22no—
248Q8×C11—21no—
249Q8×C11—21no—
250Q8×C11—22no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—21no—
254D4×C11—21no—
255D4×C11—41no—
256D4×C11—41no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—81no—
272C2×C4×C11—81no—
273C2×C4×C11—81no—
274C2×C4×C11—81no—
275C2×C4×C11#12111yescharacteristic
276C2×C4×C11#12111yescharacteristic
277C2×C4×C11#12111yescharacteristic
278C2×C4×C11#12111yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C8×C11—22no—
286C8×C11—21no—
287C8×C11—21no—
288C8×C11—21no—
289C8×C11—21no—
290C8×C11—41no—
291C8×C11—41no—
292C8×C11—41no—
293C8×C11—41no—
294C8×C11—41no—
295C2×#137C22×C1111yescharacteristic
296C2×#125C22×C1111yescharacteristic
297C4×#41C22×C1111yescharacteristic
298C2×C4×Q8C22×C1111yescharacteristic
299#479—21no—
300#479—21no—
301#479—21no—
302#479—21no—
303#479—21no—
304#479—21no—
305#478—21no—
306#478—21no—
307#441—21no—
308#440—21no—
309C4×Q16—21no—
310C4×SD16—21no—
311#433—21no—
312#433—21no—
313#432—21no—
314#431—21no—
315C2×#108C22×C1111yescharacteristic
316C2×#108C22×C1111yescharacteristic
317#428C22×C1111yescharacteristic
318#428C22×C1111yescharacteristic
319#428C22×C1111yescharacteristic
320C2×#107C22×C1111yescharacteristic
321C2×#106C22×C1111yescharacteristic
322#423C22×C1111yescharacteristic
323#423C22×C1111yescharacteristic
324C2×C4⋊C8C22×C1111yescharacteristic
325#419C22×C1111yescharacteristic
326#417C22×C1111yescharacteristic
327#417C22×C1111yescharacteristic
328#417C22×C1111yescharacteristic
329C2×#103C22×C1111yescharacteristic
330C2×#103C22×C1111yescharacteristic
331C2×#101C22×C1111yescharacteristic
332C2×#101C22×C1111yescharacteristic
333#408C22×C1111yescharacteristic
334#408C22×C1111yescharacteristic
335#405C22×C1111yescharacteristic
336#405C22×C1111yescharacteristic
337C4×M16C22×C1111yescharacteristic
338#343C22×C1111yescharacteristic
339#343C22×C1111yescharacteristic
340#343C22×C1111yescharacteristic
341#343C22×C1111yescharacteristic
342#343C22×C1111yescharacteristic
343#343C22×C1111yescharacteristic
344#341C22×C1111yescharacteristic
345#341C22×C1111yescharacteristic
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11C2×#12111yescharacteristic
352C22×C11#55211yescharacteristic
353C22×C11#55611yescharacteristic
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—81no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11#52511yescharacteristic
366C4×C11#53611yescharacteristic
367C4×C11#54711yescharacteristic
368C4×C11#54811yescharacteristic
369C2×#41C23×C1111yescharacteristic
370C22×Q8C23×C1111yescharacteristic
371#137—22no—
372#137—22no—
373C2×Q16—21no—
374C2×SD16—21no—
375C2×M16C23×C1111yescharacteristic
376C2×M16C23×C1111yescharacteristic
377C2×M16C23×C1111yescharacteristic
378C2×M16C23×C1111yescharacteristic
379C2×M16C23×C1111yescharacteristic
380C2×M16C23×C1111yescharacteristic
381C22×C8C23×C1111yescharacteristic
382C22×C8C23×C1111yescharacteristic
383#125—21no—
384#125—21no—
385#125—21no—
386#125—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8D4×C1111yescharacteristic
392C4×Q8D4×C1111yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4D4×C1111yescharacteristic
396C4×D4D4×C1111yescharacteristic
397#117—21no—
398#117C23×C1111yescharacteristic
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4C23×C1111yescharacteristic
403C2×C4⋊C4C23×C1111yescharacteristic
404C2×C4⋊C4C23×C1111yescharacteristic
405C2×C42—21no—
406C2×C42—21no—
407C2×C42C23×C1111yescharacteristic
408#108—22no—
409#108—22no—
410#107—21no—
411#107—21no—
412#107—21no—
413#107—21no—
414#107—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—21no—
419#106—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8D4×C1111yescharacteristic
425C4⋊C8D4×C1111yescharacteristic
426C4⋊C8D4×C1111yescharacteristic
427C4⋊C8D4×C1111yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—21no—
436#103—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#101—22no—
441#101—22no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446#97—21no—
447#97—21no—
448#97—21no—
449C4×C8—21no—
450C4×C8—21no—
451C4×C8—21no—
452C2×C11—21no—
453C2×C11—21no—
454C2×C11—81no—
455C2×C11#241511yescharacteristic
456C2×C11#306711yescharacteristic
457C2×C11#306911yescharacteristic
458#41—21no—
459#41—21no—
460#41—21no—
461#41—21no—
462C2×Q8—21no—
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—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4C11×#4111yescharacteristic
479C22×C4C11×#4111yescharacteristic
480C22×C4C24×C1111yescharacteristic
481Q16—24no—
482SD16—24no—
483M16—21no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16C11×#4112yes—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8C2×D4×C1111yescharacteristic
506C2×C8C2×D4×C1111yescharacteristic
507C2×C8C2×D4×C1111yescharacteristic
508C2×C8C2×D4×C1111yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4C2×D4×C1111yescharacteristic
524C4⋊C4C2×D4×C1111yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—41no—
532C42—41no—
533C42C2×D4×C1111yescharacteristic
534C42C2×D4×C1111yescharacteristic
535C42C2×D4×C1111yescharacteristic
536C42C2×D4×C1111yescharacteristic
537C11#2472511yescharacteristic, direct product factor, Sylow
538C23—21no—
539C23C2×C11×#4111yescharacteristic
540Q8—22no—
541Q8—21no—
542Q8—21no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4C11×#12111yescharacteristic
569C2×C4C11×#12111yescharacteristic
570C2×C4C11×#12111yescharacteristic
571C2×C4C11×#12111yescharacteristic
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C22×D4×C1111yescharacteristic
574C2×C4C2×C11×#4111yescharacteristic
575C2×C4C2×C11×#4111yescharacteristic
576C2×C4C11×2−1+411yescharacteristic
577C2×C4C11×2−1+411yescharacteristic
578C8—22no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×C11×#12111yescharacteristic
594C22C11×#55211yescharacteristic
595C22C11×#55611yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C11×#52511yescharacteristic
608C4C11×#53611yescharacteristic
609C4C11×#54711yescharacteristic
610C4C11×#54811yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2C11×#241511yescharacteristic
615C2C11×#306711yescharacteristic
616C2C11×#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
9. C11×#1998C2semidirect
10. C11×#1952C2semidirect
11. C11×#1951C2semidirect
12. C11×#1950C2semidirect
13. C11×#1930C2semidirect
14. C11×#1930C2semidirect
15. C11×#1801C2semidirect
150. #24725C11direct (N × H)
231. C2×#479C2×C11semidirect
238. #1998C2×C11semidirect
239. #1952C2×C11semidirect
240. #1951C2×C11semidirect
241. #1950C2×C11semidirect
242. #1930C2×C11semidirect
243. #1930C2×C11semidirect
244. #1801C2×C11semidirect
537. C11#24725direct (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×#29252
C11×#20792
C11×#20782
C11×#20522
C11×#19982
C11×#19522
C11×#19512
C11×#19502
C11×#19302
C11×#18012
#2472511