Finite Group Databasebeta

← C11×#24184 #14601377

Subgroups — C11×#24184 #14601377

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 630 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×C4×C11×D8C211yesmaximal, characteristic, complemented
4C11×#2538C211yesmaximal, characteristic, complemented
5C11×#2041C212yesmaximal, complemented
6C11×#2011C212yesmaximal, complemented
7C11×#1984C211yesmaximal, characteristic, complemented
8C11×#1957C211yesmaximal, characteristic, complemented
9C11×#1879C212yesmaximal, complemented
10C11×#1862C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C22×C11×D8C2211yescharacteristic
14C22×C11×D8C2212yes—
15C11×#550—24no—
16C11×#550—24no—
17C2×C11×#127C2212yes—
18C2×C11×#127C2211yescharacteristic
19C2×C11×C22⋊Q8—21no—
20C2×C11×#121—21no—
21C2×C11×#121—22no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2212yes—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#459—24no—
27C4×C11×D8—24no—
28C2×C11×#107C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#396—22no—
38C11×#390C2212yes—
39C11×#389C2212yes—
40C11×#384C2211yescharacteristic
41C11×#380—21no—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—44no—
47C2×C11×#41—44no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11C2312yes—
54C22×D4×C11C2311yescharacteristic
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—22no—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C2×C11×D8—22no—
60C2×C11×D8—22no—
61C2×C11×D8—24no—
62C2×C11×D8—24no—
63C2×C11×D8—22no—
64C2×C11×D8—42no—
65C22×C8×C11C2312yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#127—24no—
69C11×#127—24no—
70C11×#127—22no—
71C11×#127D414yes—
72C11×C22⋊Q8—44no—
73C11×#121—28no—
74C11×#121—216no—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×D4×C11—24no—
78C4×D4×C11—24no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11D414yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4D412yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C42×C11C2312yes—
97C2×C42×C11C2311yescharacteristic
98C11×#107—22no—
99C11×C4⋊C8—22no—
100C11×#102—22no—
101C11×#102—24no—
102C11×#102—24no—
103C11×#102—22no—
104C11×#102—42no—
105C11×#102—42no—
106C4×C8×C11—22no—
107C11×#95—22no—
108#24184C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—21no—
110C24×C11—22no—
111C24×C11—21no—
112C11×#41—432no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11D814yescomplemented
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11—44no—
136C2×D4×C11—44no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—81no—
140C2×D4×C11—81no—
141C2×D4×C11—82no—
142C2×D4×C11—82no—
143C2×D4×C11C2×D414yes—
144C2×D4×C11C2×D412yes—
145C2×D4×C11#4112yescomplemented
146C22×C4×C11—28no—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C11×D8—28no—
164C11×D8—48no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—22no—
168C2×C8×C11—21no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11—22no—
172C2×C8×C11—21no—
173C2×C8×C11#4112yescomplemented
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—44no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4C2×D412yes—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—82no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11C2×D412yes—
193C42×C11C2×D412yes—
194C2×#550C2×C1111yescharacteristic, complemented
195C2×#459C2×C1111yescharacteristic, complemented
196C2×C4×D8C2×C1111yescharacteristic, complemented
197#2538C2×C1111yescharacteristic, complemented
198#2041C2×C1112yescomplemented
199#2011C2×C1112yescomplemented
200#1984C2×C1111yescharacteristic, complemented
201#1957C2×C1111yescharacteristic, complemented
202#1879C2×C1112yescomplemented
203#1862C2×C1112yescomplemented
204#1802C2×C1111yescharacteristic, complemented
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—41no—
223C23×C11—42no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11C22×D411yescharacteristic
227Q8×C11—28no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—24no—
233D4×C11—24no—
234D4×C11—416no—
235D4×C11—42no—
236D4×C11—41no—
237D4×C11—42no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—48no—
242D4×C11—84no—
243D4×C11—88no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—416no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—48no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—84no—
263C2×C4×C11#12012yes—
264C2×C4×C11#12012yes—
265C2×C4×C11C2×D814yes—
266C2×C4×C11C2×D812yes—
267C2×C4×C11AGL(1,ℤ/8)12yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C8×C11—22no—
275C8×C11—41no—
276C8×C11—42no—
277C22×#41—21no—
278C22×D8C22×C1111yescharacteristic
279C22×D8C22×C1112yes—
280#550—24no—
281#550—24no—
282C2×#127C22×C1112yes—
283C2×#127C22×C1111yescharacteristic
284C2×C22⋊Q8—21no—
285C2×#121—21no—
286C2×#121—22no—
287C2×C4×Q8C22×C1111yescharacteristic
288C2×C4×D4C22×C1112yes—
289C2×C4×D4C22×C1111yescharacteristic
290C2×C4×D4C22×C1111yescharacteristic
291#459—24no—
292C4×D8—24no—
293C2×#107C22×C1111yescharacteristic
294C2×C4⋊C8C22×C1111yescharacteristic
295C2×#102C22×C1112yes—
296C2×#102C22×C1112yes—
297C2×#102C22×C1111yescharacteristic
298C2×#102C22×C1111yescharacteristic
299C2×#102C22×C1112yes—
300C2×#102C22×C1112yes—
301C2×C4×C8C22×C1111yescharacteristic
302#396—22no—
303#390C22×C1112yes—
304#389C22×C1112yes—
305#384C22×C1111yescharacteristic
306#380—21no—
307#340C22×C1112yes—
308#336C22×C1112yes—
309#336C22×C1112yes—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—42no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—81no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—82no—
325C22×C11—81no—
326C22×C11—82no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11C2×#12011yescharacteristic
332C22×C11#54811yescharacteristic
333C22×C11#55011yescharacteristic
334C22×C11C22×D811yescharacteristic
335C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C11#57611yescharacteristic
337C22×C11#57711yescharacteristic
338C4×C11—24no—
339C4×C11—22no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—82no—
343C4×C11—81no—
344C4×C11#44714yes—
345C4×C11#52511yescharacteristic
346C4×C11#53711yescharacteristic
347C4×C11#54611yescharacteristic
348C4×C11#54711yescharacteristic
349C2×#41—28no—
350C2×#41—44no—
351C2×#41—44no—
352C22×Q8D4×C1111yescharacteristic
353C22×D4—22no—
354C22×D4—21no—
355C22×D4—22no—
356C22×D4—21no—
357C22×D4C23×C1112yes—
358C22×D4C23×C1111yescharacteristic
359C22×D4C23×C1111yescharacteristic
360C23×C4—22no—
361C23×C4—21no—
362C23×C4—21no—
363C2×D8—22no—
364C2×D8—22no—
365C2×D8—24no—
366C2×D8—24no—
367C2×D8—22no—
368C2×D8—42no—
369C22×C8C23×C1112yes—
370C22×C8C23×C1111yescharacteristic
371C22×C8C23×C1111yescharacteristic
372#127—24no—
373#127—24no—
374#127—22no—
375#127D4×C1114yes—
376C22⋊Q8—44no—
377#121—28no—
378#121—216no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4D4×C1114yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C1111yescharacteristic
391C2×C4⋊C4D4×C1112yes—
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1112yes—
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C42C23×C1112yes—
401C2×C42C23×C1111yescharacteristic
402#107—22no—
403C4⋊C8—22no—
404#102—22no—
405#102—24no—
406#102—24no—
407#102—22no—
408#102—42no—
409#102—42no—
410C4×C8—22no—
411#95—22no—
412C2×C11—82no—
413C2×C11—82no—
414C2×C11—84no—
415C2×C11#240711yescharacteristic
416C2×C11C2×#44711yescharacteristic
417C2×C11#301211yescharacteristic
418C2×C11#335811yescharacteristic
419C2×C11#336611yescharacteristic
420C2×C11#339111yescharacteristic
421C2×C11#339711yescharacteristic
422C24—21no—
423C24—22no—
424C24—21no—
425#41—432no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8C11×D814yescomplemented
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—81no—
453C2×D4—81no—
454C2×D4—82no—
455C2×D4—82no—
456C2×D4C2×D4×C1114yes—
457C2×D4C2×D4×C1112yes—
458C2×D4C11×#4112yescomplemented
459C22×C4—28no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4C2×D4×C1112yes—
472C22×C4C2×D4×C1111yescharacteristic
473C22×C4C2×D4×C1112yes—
474C22×C4C2×D4×C1111yescharacteristic
475C22×C4C24×C1111yescharacteristic
476D8—28no—
477D8—48no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—21no—
486C2×C8C11×#4112yescomplemented
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—42no—
495C4⋊C4—44no—
496C4⋊C4—81no—
497C4⋊C4C2×D4×C1112yes—
498C22⋊C4—28no—
499C22⋊C4—24no—
500C22⋊C4—42no—
501C22⋊C4—44no—
502C22⋊C4—82no—
503C42—22no—
504C42—22no—
505C42C2×D4×C1112yes—
506C42C2×D4×C1112yes—
507C11#2418411yescharacteristic, direct product factor, Sylow
508C23—24no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—42no—
519C23—41no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—42no—
525C23—41no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23C22×D4×C1111yescharacteristic
530Q8—28no—
531D4—22no—
532D4—22no—
533D4—22no—
534D4—22no—
535D4—24no—
536D4—24no—
537D4—416no—
538D4—42no—
539D4—41no—
540D4—42no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—48no—
545D4—84no—
546D4—88no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—416no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—48no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—84no—
566C2×C4C11×#12012yes—
567C2×C4C11×#12012yes—
568C2×C4C2×C11×D814yes—
569C2×C4C2×C11×D812yes—
570C2×C4C11×AGL(1,ℤ/8)12yes—
571C2×C4C22×D4×C1111yescharacteristic
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C2×C11×#4111yescharacteristic
574C2×C4C2×C11×#4111yescharacteristic
575C2×C4C11×H(5,𝔽2)11yescharacteristic
576C2×C4C11×2−1+411yescharacteristic
577C8—22no—
578C8—41no—
579C8—42no—
580C22—42no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—42no—
585C22—44no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—82no—
597C22—81no—
598C22—82no—
599C22—81no—
600C22—81no—
601C22C2×C11×#12011yescharacteristic
602C22C11×#54811yescharacteristic
603C22C11×#55011yescharacteristic
604C22C22×C11×D811yescharacteristic
605C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
606C22C11×#57611yescharacteristic
607C22C11×#57711yescharacteristic
608C4—24no—
609C4—22no—
610C4—42no—
611C4—42no—
612C4—81no—
613C4—82no—
614C4C11×#44714yes—
615C4C11×#52511yescharacteristic
616C4C11×#53711yescharacteristic
617C4C11×#54611yescharacteristic
618C4C11×#54711yescharacteristic
619C2—82no—
620C2—84no—
621C2—82no—
622C2C11×#240711yescharacteristic
623C2C2×C11×#44711yescharacteristic
624C2C11×#301211yescharacteristic
625C2C11×#335811yescharacteristic
626C2C11×#336611yescharacteristic
627C2C11×#339111yescharacteristic
628C2C11×#339711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×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×C4×C11×D8C2semidirect
4. C11×#2538C2semidirect
5. C11×#2041C2semidirect
6. C11×#2011C2semidirect
7. C11×#1984C2semidirect
8. C11×#1957C2semidirect
9. C11×#1879C2semidirect
10. C11×#1862C2semidirect
11. C11×#1802C2semidirect
108. #24184C11direct (N × H)
115. C2×Q8×C11D8semidirect
145. C2×D4×C11#41semidirect
173. C2×C8×C11#41semidirect
194. C2×#550C2×C11semidirect
195. C2×#459C2×C11semidirect
196. C2×C4×D8C2×C11semidirect
197. #2538C2×C11semidirect
198. #2041C2×C11semidirect
199. #2011C2×C11semidirect
200. #1984C2×C11semidirect
201. #1957C2×C11semidirect
202. #1879C2×C11semidirect
203. #1862C2×C11semidirect
204. #1802C2×C11semidirect
428. C2×Q8C11×D8semidirect
458. C2×D4C11×#41semidirect
486. C2×C8C11×#41semidirect
507. C11#24184direct (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×C4×C11×D82
C11×#25382
C11×#20412
C11×#20112
C11×#19842
C11×#19572
C11×#18792
C11×#18622
C11×#18022
#2418411