Finite Group Databasebeta

← C11×#24250 #14601443

Subgroups — C11×#24250 #14601443

Order 2816.

1540 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#550C211yesmaximal, characteristic, complemented
2C2×C11×#459C211yesmaximal, characteristic, complemented
3C2×C11×#449C212yesmaximal, complemented
4C2×C11×#440C211yesmaximal, characteristic, complemented
5C11×#2535C211yesmaximal, characteristic, complemented
6C11×#2033C212yesmaximal, complemented
7C11×#1999C212yesmaximal, complemented
8C11×#1961C211yesmaximal, characteristic, complemented
9C11×#1955C211yesmaximal, characteristic, complemented
10C11×#1805C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C22×C11×SD16C2211yescharacteristic
14C22×C11×D8C2212yes—
15C11×#550—24no—
16C11×#550—24no—
17C2×C11×#127—21no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#121—22no—
20C2×C11×#121C2212yes—
21C2×C11×#121C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#459—24no—
27C11×#449—28no—
28C11×#440—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×#102C2212yes—
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C11×#97C2211yescharacteristic
40C11×#397—21no—
41C11×#392—21no—
42C11×#386—22no—
43C11×#382C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11D411yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×D4×C11C2312yes—
61C23×C4×C11—22no—
62C23×C4×C11—21no—
63C23×C4×C11C2312yes—
64C2×C11×SD16—22no—
65C2×C11×SD16—22no—
66C2×C11×SD16D414yescomplemented
67C2×C11×D8—24no—
68C2×C11×D8—24no—
69C2×C11×D8—42no—
70C22×C8×C11C2312yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#127—28no—
74C11×#127—22no—
75C11×#127D414yescomplemented
76C11×#121—216no—
77C11×#121—24no—
78C11×#121—24no—
79C11×#121—24no—
80C11×#121—42no—
81C4×Q8×C11—22no—
82C4×Q8×C11D414yescomplemented
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D412yes—
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×#107—22no—
101C11×C4⋊C8—22no—
102C11×#103—22no—
103C11×#103—24no—
104C11×#102—24no—
105C11×#102—24no—
106C11×#102—22no—
107C11×#102—42no—
108C11×C22⋊C8—24no—
109C11×C22⋊C8—42no—
110C11×#97—22no—
111C11×#95—22no—
112C11×#95—21no—
113C11×#95—21no—
114#24250C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C24×C11—22no—
117C24×C11C2×D412yes—
118C11×#41—48no—
119C11×#41—48no—
120C11×#41—48no—
121C11×#41—48no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11C2×D412yes—
126C2×Q8×C11C2×D412yes—
127C2×Q8×C11#4112yes—
128C2×D4×C11—28no—
129C2×D4×C11—28no—
130C2×D4×C11—22no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—42no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—82no—
150C2×D4×C11—82no—
151C2×D4×C11—82no—
152C2×D4×C11—82no—
153C2×D4×C11C2×D414yes—
154C2×D4×C11C2×D412yes—
155C22×C4×C11—21no—
156C22×C4×C11—28no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—44no—
167C22×C4×C11—44no—
168C22×C4×C11—42no—
169C22×C4×C11—82no—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C11×SD16—28no—
175C11×D8—48no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—22no—
183C2×C8×C11—21no—
184C2×C8×C11C2×D412yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4C2×D412yes—
193C11×C22⋊C4—28no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—44no—
196C11×C22⋊C4—42no—
197C11×C22⋊C4—82no—
198C42×C11—24no—
199C42×C11C2×D412yes—
200C42×C11C2×D412yes—
201C2×#550C2×C1111yescharacteristic, complemented
202C2×#459C2×C1111yescharacteristic, complemented
203C2×#449C2×C1112yescomplemented
204C2×#440C2×C1111yescharacteristic, complemented
205#2535C2×C1111yescharacteristic, complemented
206#2033C2×C1112yescomplemented
207#1999C2×C1112yescomplemented
208#1961C2×C1111yescharacteristic, complemented
209#1955C2×C1111yescharacteristic, complemented
210#1805C2×C1111yescharacteristic, complemented
211#1788C2×C1112yescomplemented
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—41no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11C22×D411yescharacteristic
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11#12114yes—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—24no—
239D4×C11—24no—
240D4×C11—44no—
241D4×C11—48no—
242D4×C11—416no—
243D4×C11—42no—
244D4×C11—41no—
245D4×C11—42no—
246D4×C11—41no—
247D4×C11—84no—
248D4×C11—88no—
249D4×C11—88no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—416no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—84no—
271C2×C4×C11#12012yes—
272C2×C4×C11#12012yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C8×C11—22no—
280C8×C11—41no—
281C8×C11—42no—
282C22×#41C22×C1112yes—
283C22×SD16C22×C1111yescharacteristic
284C22×D8C22×C1112yes—
285#550—24no—
286#550—24no—
287C2×#127—21no—
288C2×#127C22×C1111yescharacteristic
289C2×#121—22no—
290C2×#121C22×C1112yes—
291C2×#121C22×C1112yes—
292C2×C4×Q8C22×C1111yescharacteristic
293C2×C4×D4—21no—
294C2×C4×D4C22×C1111yescharacteristic
295C2×C4×D4C22×C1111yescharacteristic
296#459—24no—
297#449—28no—
298#440—24no—
299C2×#107C22×C1111yescharacteristic
300C2×C4⋊C8C22×C1111yescharacteristic
301C2×#103C22×C1112yes—
302C2×#103C22×C1111yescharacteristic
303C2×#102C22×C1111yescharacteristic
304C2×#102C22×C1112yes—
305C2×#102C22×C1112yes—
306C2×#102C22×C1112yes—
307C2×C22⋊C8C22×C1112yes—
308C2×C22⋊C8C22×C1112yes—
309C2×#97C22×C1111yescharacteristic
310#397—21no—
311#392—21no—
312#386—22no—
313#382C22×C1111yescharacteristic
314#380C22×C1112yes—
315#340C22×C1112yes—
316C22×C11—44no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—82no—
331C22×C11—82no—
332C22×C11—82no—
333C22×C11—82no—
334C22×C11—82no—
335C22×C11C2×#12011yescharacteristic
336C22×C11D4211yescharacteristic
337C22×C11#54611yescharacteristic
338C22×C11#57512yes—
339C22×C11#57612yes—
340C4×C11—24no—
341C4×C11—22no—
342C4×C11—22no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—81no—
346C4×C11—82no—
347C4×C11C2×#12111yescharacteristic
348C4×C11#53511yescharacteristic
349C4×C11D4211yescharacteristic
350C4×C11#54611yescharacteristic
351C2×#41—24no—
352C2×#41—24no—
353C2×#41—24no—
354C2×#41—24no—
355C2×#41—42no—
356C2×#41—42no—
357C22×Q8C23×C1111yescharacteristic
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—21no—
362C22×D4—21no—
363C22×D4D4×C1111yescharacteristic
364C22×D4C23×C1111yescharacteristic
365C22×D4C23×C1112yes—
366C23×C4—22no—
367C23×C4—21no—
368C23×C4C23×C1112yes—
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16D4×C1114yescomplemented
372C2×D8—24no—
373C2×D8—24no—
374C2×D8—42no—
375C22×C8C23×C1112yes—
376C22×C8C23×C1111yescharacteristic
377C22×C8C23×C1111yescharacteristic
378#127—28no—
379#127—22no—
380#127D4×C1114yescomplemented
381#121—216no—
382#121—24no—
383#121—24no—
384#121—24no—
385#121—42no—
386C4×Q8—22no—
387C4×Q8D4×C1114yescomplemented
388C4×D4—28no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4D4×C1111yescharacteristic
395C2×C4⋊C4C23×C1111yescharacteristic
396C2×C4⋊C4C23×C1112yes—
397C2×C4⋊C4C23×C1111yescharacteristic
398C2×C22⋊C4—22no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4D4×C1112yes—
403C2×C42—21no—
404C2×C42C23×C1111yescharacteristic
405#107—22no—
406C4⋊C8—22no—
407#103—22no—
408#103—24no—
409#102—24no—
410#102—24no—
411#102—22no—
412#102—42no—
413C22⋊C8—24no—
414C22⋊C8—42no—
415#97—22no—
416#95—22no—
417#95—21no—
418#95—21no—
419C2×C11—82no—
420C2×C11—84no—
421C2×C11—82no—
422C2×C11#240811yescharacteristic
423C2×C11#300511yescharacteristic
424C2×C11#300811yescharacteristic
425C2×C11#326812yes—
426C2×C11#330912yes—
427C24—21no—
428C24—22no—
429C24C2×D4×C1112yes—
430#41—48no—
431#41—48no—
432#41—48no—
433#41—48no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×D4×C1112yes—
438C2×Q8C2×D4×C1112yes—
439C2×Q8C11×#4112yes—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—22no—
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—42no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—82no—
462C2×D4—82no—
463C2×D4—82no—
464C2×D4—82no—
465C2×D4C2×D4×C1114yes—
466C2×D4C2×D4×C1112yes—
467C22×C4—21no—
468C22×C4—28no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—42no—
481C22×C4—82no—
482C22×C4C2×D4×C1112yes—
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C24×C1111yescharacteristic
486SD16—28no—
487D8—48no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—21no—
494C2×C8—22no—
495C2×C8—21no—
496C2×C8C2×D4×C1112yes—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4C2×D4×C1112yes—
505C22⋊C4—28no—
506C22⋊C4—24no—
507C22⋊C4—44no—
508C22⋊C4—42no—
509C22⋊C4—82no—
510C42—24no—
511C42C2×D4×C1112yes—
512C42C2×D4×C1112yes—
513C11#2425011yescharacteristic, direct product factor, Sylow
514C23—22no—
515C23—24no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—41no—
524C23—42no—
525C23—42no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23C22×D4×C1111yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8C11×#12114yes—
538D4—22no—
539D4—22no—
540D4—24no—
541D4—24no—
542D4—44no—
543D4—48no—
544D4—416no—
545D4—42no—
546D4—41no—
547D4—42no—
548D4—41no—
549D4—84no—
550D4—88no—
551D4—88no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—416no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—84no—
573C2×C4C11×#12012yes—
574C2×C4C11×#12012yes—
575C2×C4C22×D4×C1111yescharacteristic
576C2×C4C22×D4×C1111yescharacteristic
577C2×C4C22×D4×C1111yescharacteristic
578C2×C4C2×C11×#4111yescharacteristic
579C2×C4C11×H(5,𝔽2)11yescharacteristic
580C2×C4C11×H(5,𝔽2)11yescharacteristic
581C8—22no—
582C8—41no—
583C8—42no—
584C22—44no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—44no—
589C22—42no—
590C22—44no—
591C22—42no—
592C22—44no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—81no—
597C22—81no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22C2×C11×#12011yescharacteristic
604C22D42×C1111yescharacteristic
605C22C11×#54611yescharacteristic
606C22C11×#57512yes—
607C22C11×#57612yes—
608C4—24no—
609C4—22no—
610C4—22no—
611C4—42no—
612C4—42no—
613C4—81no—
614C4—82no—
615C4C2×C11×#12111yescharacteristic
616C4C11×#53511yescharacteristic
617C4D42×C1111yescharacteristic
618C4C11×#54611yescharacteristic
619C2—82no—
620C2—84no—
621C2—82no—
622C2C11×#240811yescharacteristic
623C2C11×#300511yescharacteristic
624C2C11×#300811yescharacteristic
625C2C11×#326812yes—
626C2C11×#330912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#550C2semidirect
2. C2×C11×#459C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#440C2semidirect
5. C11×#2535C2semidirect
6. C11×#2033C2semidirect
7. C11×#1999C2semidirect
8. C11×#1961C2semidirect
9. C11×#1955C2semidirect
10. C11×#1805C2semidirect
11. C11×#1788C2semidirect
66. C2×C11×SD16D4semidirect
75. C11×#127D4semidirect
82. C4×Q8×C11D4semidirect
114. #24250C11direct (N × H)
201. C2×#550C2×C11semidirect
202. C2×#459C2×C11semidirect
203. C2×#449C2×C11semidirect
204. C2×#440C2×C11semidirect
205. #2535C2×C11semidirect
206. #2033C2×C11semidirect
207. #1999C2×C11semidirect
208. #1961C2×C11semidirect
209. #1955C2×C11semidirect
210. #1805C2×C11semidirect
211. #1788C2×C11semidirect
371. C2×SD16D4×C11semidirect
380. #127D4×C11semidirect
387. C4×Q8D4×C11semidirect
513. C11#24250direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5502
C2×C11×#4592
C2×C11×#4492
C2×C11×#4402
C11×#25352
C11×#20332
C11×#19992
C11×#19612
C11×#19552
C11×#18052
C11×#17882
#2425011