Finite Group Databasebeta

← C11×#24051 #14601244

Subgroups — C11×#24051 #14601244

Order 2816.

1352 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#548C211yesmaximal, characteristic
2C2×C11×#484C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C11×#2486C211yesmaximal, characteristic, complemented
5C11×#2042C212yesmaximal, complemented
6C11×#2033C212yesmaximal, complemented
7C11×#1894C211yesmaximal, characteristic, complemented
8C11×#1870C211yesmaximal, characteristic, complemented
9C11×#1863C212yesmaximal, complemented
10C11×#1788C211yesmaximal, characteristic, complemented
11C11×#1787C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C11×#548—24no—
16C11×#548—24no—
17C2×C11×#124—21no—
18C2×C11×#124C2211yescharacteristic
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121—21no—
23C2×C11×#121C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C11×#484—24no—
29C2×C11×#107C2212yes—
30C11×#417—24no—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×#102C2212yes—
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2212yes—
39C11×#398—21no—
40C11×#397—21no—
41C11×#389C2212yes—
42C11×#381—21no—
43C11×#380C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—24no—
49C2×C11×#41—42no—
50C2×C11×#41D414yes—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11—21no—
54C22×Q8×C11—24no—
55C22×Q8×C11—42no—
56C22×Q8×C11C2311yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C2×C11×M16—22no—
68C2×C11×M16—42no—
69C22×C8×C11C2312yes—
70C22×C8×C11C2312yes—
71C11×#124—28no—
72C11×#124—22no—
73C11×#124—22no—
74C11×#123—44no—
75C11×C22⋊Q8—28no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8D414yes—
78C11×#121—28no—
79C11×#121—22no—
80C11×#121—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C11×#107—24no—
107C11×#103—24no—
108C11×#103—24no—
109C11×#103—24no—
110C11×#103—42no—
111C11×#102—24no—
112C11×#102—42no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—42no—
115C11×#95—22no—
116C11×#95—21no—
117C11×#95—22no—
118#24051C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C11×#41—28no—
123C11×#41—44no—
124C11×#41—48no—
125C2×Q8×C11—24no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C2×Q8×C11—48no—
133C2×Q8×C11—44no—
134C2×Q8×C11—44no—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11#4114yes—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—41no—
146C2×D4×C11—44no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11C2×D412yes—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—24no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—24no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—44no—
164C22×C4×C11—44no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2411yescharacteristic
175C11×M16—44no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—44no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4C2×D412yes—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—42no—
200C11×C22⋊C4—44no—
201C42×C11—24no—
202C42×C11—21no—
203C42×C11—21no—
204C2×#548C2×C1111yescharacteristic
205C2×#484C2×C1111yescharacteristic, complemented
206C2×#417C2×C1111yescharacteristic, complemented
207#2486C2×C1111yescharacteristic, complemented
208#2042C2×C1112yescomplemented
209#2033C2×C1112yescomplemented
210#1894C2×C1111yescharacteristic, complemented
211#1870C2×C1111yescharacteristic, complemented
212#1863C2×C1112yescomplemented
213#1788C2×C1111yescharacteristic, complemented
214#1787C2×C1112yescomplemented
215C23×C11—21no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—42no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—42no—
228C23×C11#12012yes—
229C23×C11AGL(1,ℤ/8)12yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—22no—
232Q8×C11—24no—
233Q8×C11—24no—
234Q8×C11—48no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11#12314yescomplemented
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—48no—
241D4×C11—44no—
242D4×C11—48no—
243D4×C11—42no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—48no—
260C2×C4×C11—48no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—84no—
274C2×C4×C11#12012yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4112yes—
278C2×C4×C11H(5,𝔽2)12yes—
279C8×C11—42no—
280C8×C11—42no—
281C22×#41C22×C1111yescharacteristic
282C23×Q8C22×C1111yescharacteristic
283C22×M16C22×C1111yescharacteristic
284#548—24no—
285#548—24no—
286C2×#124—21no—
287C2×#124C22×C1111yescharacteristic
288C2×#123—21no—
289C2×C22⋊Q8—21no—
290C2×C22⋊Q8C22×C1111yescharacteristic
291C2×#121—21no—
292C2×#121C22×C1111yescharacteristic
293C2×C4×Q8C22×C1111yescharacteristic
294C2×C4×D4—21no—
295C2×C4×D4C22×C1111yescharacteristic
296C22×C4⋊C4C22×C1111yescharacteristic
297#484—24no—
298C2×#107C22×C1112yes—
299#417—24no—
300C2×#103C22×C1112yes—
301C2×#103C22×C1112yes—
302C2×#103C22×C1112yes—
303C2×#103C22×C1112yes—
304C2×#102C22×C1112yes—
305C2×#102C22×C1112yes—
306C2×C22⋊C8C22×C1111yescharacteristic
307C2×C22⋊C8C22×C1112yes—
308#398—21no—
309#397—21no—
310#389C22×C1112yes—
311#381—21no—
312#380C22×C1111yescharacteristic
313#380C22×C1112yes—
314#340C22×C1112yes—
315#336C22×C1112yes—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—24no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—82no—
330C22×C11—82no—
331C22×C11C2×#12011yescharacteristic
332C22×C11#54612yes—
333C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C11#57511yescharacteristic
335C22×C11#57812yes—
336C4×C11—22no—
337C4×C11—24no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—41no—
343C4×C11—82no—
344C4×C11—82no—
345C4×C11C2×#12311yescharacteristic
346C4×C11#53411yescharacteristic
347C4×C11#54612yes—
348C2×#41—22no—
349C2×#41—24no—
350C2×#41—42no—
351C2×#41D4×C1114yes—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—21no—
355C22×Q8—24no—
356C22×Q8—42no—
357C22×Q8C23×C1111yescharacteristic
358C22×Q8C23×C1111yescharacteristic
359C22×D4—21no—
360C22×D4—21no—
361C22×D4D4×C1111yescharacteristic
362C22×D4C23×C1111yescharacteristic
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4C23×C1111yescharacteristic
367C23×C4C23×C1111yescharacteristic
368C2×M16—22no—
369C2×M16—42no—
370C22×C8C23×C1112yes—
371C22×C8C23×C1112yes—
372#124—28no—
373#124—22no—
374#124—22no—
375#123—44no—
376C22⋊Q8—28no—
377C22⋊Q8—22no—
378C22⋊Q8D4×C1114yes—
379#121—28no—
380#121—22no—
381#121—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×D4—28no—
385C4×D4—22no—
386C4×D4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4D4×C1111yescharacteristic
394C2×C4⋊C4C23×C1112yes—
395C2×C4⋊C4C23×C1112yes—
396C2×C4⋊C4C23×C1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4D4×C1111yescharacteristic
404C2×C22⋊C4D4×C1111yescharacteristic
405C2×C42—21no—
406C2×C42C23×C1111yescharacteristic
407#107—24no—
408#103—24no—
409#103—24no—
410#103—24no—
411#103—42no—
412#102—24no—
413#102—42no—
414C22⋊C8—22no—
415C22⋊C8—42no—
416#95—22no—
417#95—21no—
418#95—22no—
419C2×C11—42no—
420C2×C11—42no—
421C2×C11—82no—
422C2×C11#240511yescharacteristic
423C2×C11#300611yescharacteristic
424C2×C11#301111yescharacteristic
425C2×C11#330812yes—
426C2×C11#332712yes—
427C24—21no—
428C24C2×D4×C1111yescharacteristic
429C24C2×D4×C1111yescharacteristic
430#41—28no—
431#41—44no—
432#41—48no—
433C2×Q8—24no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—44no—
440C2×Q8—48no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8C2×D4×C1112yes—
444C2×Q8C2×D4×C1112yes—
445C2×Q8C11×#4114yes—
446C2×D4—24no—
447C2×D4—22no—
448C2×D4—24no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—41no—
454C2×D4—44no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4C2×D4×C1112yes—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1112yes—
481C22×C4C2×D4×C1112yes—
482C22×C4C24×C1111yescharacteristic
483M16—44no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C4⋊C4—24no—
491C4⋊C4—24no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—44no—
499C4⋊C4—42no—
500C4⋊C4C2×D4×C1112yes—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—42no—
508C22⋊C4—44no—
509C42—24no—
510C42—21no—
511C42—21no—
512C11#2405111yescharacteristic, direct product factor, Sylow
513C23—21no—
514C23—22no—
515C23—22no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—42no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23C11×#12012yes—
527C23C11×AGL(1,ℤ/8)12yes—
528C23C22×D4×C1111yescharacteristic
529Q8—22no—
530Q8—24no—
531Q8—24no—
532Q8—48no—
533Q8—41no—
534Q8—41no—
535Q8C11×#12314yescomplemented
536D4—22no—
537D4—22no—
538D4—48no—
539D4—44no—
540D4—48no—
541D4—42no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—48no—
558C2×C4—48no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—84no—
572C2×C4C11×#12012yes—
573C2×C4C22×D4×C1111yescharacteristic
574C2×C4C22×D4×C1111yescharacteristic
575C2×C4C2×C11×#4112yes—
576C2×C4C11×H(5,𝔽2)12yes—
577C8—42no—
578C8—42no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—24no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22C2×C11×#12011yescharacteristic
595C22C11×#54612yes—
596C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
597C22C11×#57511yescharacteristic
598C22C11×#57812yes—
599C4—22no—
600C4—24no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—42no—
605C4—41no—
606C4—82no—
607C4—82no—
608C4C2×C11×#12311yescharacteristic
609C4C11×#53411yescharacteristic
610C4C11×#54612yes—
611C2—42no—
612C2—42no—
613C2—82no—
614C2C11×#240511yescharacteristic
615C2C11×#300611yescharacteristic
616C2C11×#301111yescharacteristic
617C2C11×#330812yes—
618C2C11×#332712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#548C2
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
2. C2×C11×#484C2semidirect
3. C2×C11×#417C2semidirect
4. C11×#2486C2semidirect
5. C11×#2042C2semidirect
6. C11×#2033C2semidirect
7. C11×#1894C2semidirect
8. C11×#1870C2semidirect
9. C11×#1863C2semidirect
10. C11×#1788C2semidirect
11. C11×#1787C2semidirect
118. #24051C11direct (N × H)
205. C2×#484C2×C11semidirect
206. C2×#417C2×C11semidirect
207. #2486C2×C11semidirect
208. #2042C2×C11semidirect
209. #2033C2×C11semidirect
210. #1894C2×C11semidirect
211. #1870C2×C11semidirect
212. #1863C2×C11semidirect
213. #1788C2×C11semidirect
214. #1787C2×C11semidirect
237. Q8×C11#123semidirect
512. C11#24051direct (N × H)
535. Q8C11×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5482
C2×C11×#4842
C2×C11×#4172
C11×#24862
C11×#20422
C11×#20332
C11×#18942
C11×#18702
C11×#18632
C11×#17882
C11×#17872
#2405111