Finite Group Databasebeta

← D11×#2041 #14781437

Subgroups — D11×#2041 #14781437

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#127C211yesmaximal, characteristic
2C2×D11×#102C212yesmaximal, complemented
3C2×D11×#102C212yesmaximal, complemented
4D11×#389C211yesmaximal, characteristic, complemented
5#13069851C211yesmaximal, characteristic, complemented
6#13069850C211yesmaximal, characteristic, complemented
7#13069849C212yesmaximal, complemented
8#13069848C212yesmaximal, complemented
9#13069847C211yesmaximal, characteristic, complemented
10D11×#336C211yesmaximal, characteristic, complemented
11C11×#2041C211yesmaximal, characteristic, complemented
12C22×D4×D11—21no—
13C22×D4×D11—21no—
14C22×D4×D11C2212yes—
15C2×C11×#127C2211yescharacteristic
16C2×#66993—21no—
17C2×#66993—21no—
18C2×#66993C2212yes—
19C22×C8×D11C2212yes—
20D11×#127—28no—
21C2×C4⋊C4×D11—21no—
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×#66927C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×C11×#102C2212yescomplemented
27C2×C11×#102C2212yescomplemented
28C11×#389C2211yescharacteristic, complemented
29C2×#66896C2212yescomplemented
30C2×#66896C2212yescomplemented
31C2×#66885C2212yescomplemented
32C2×#66885C2212yescomplemented
33#10622598C2211yescharacteristic, complemented
34#10622586C2211yescharacteristic, complemented
35#10622585—21no—
36C2×#66873C2212yescomplemented
37C2×#66873C2212yescomplemented
38#10622541C2211yescharacteristic, complemented
39D11×#102—28no—
40D11×#102—28no—
41D11×#95—21no—
42#10622260—21no—
43C11×#336C2211yescharacteristic, complemented
44#10622188C2212yescomplemented
45#10622162C2211yescharacteristic, complemented
46C24×D11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2312yes—
50C22×C22⋊D11—22no—
51C22×C22⋊D11—22no—
52C22×C22⋊D11—22no—
53C2×D4×D11—28no—
54C2×D4×D11—28no—
55C2×D4×D11—24no—
56C2×D4×D11—24no—
57C2×D4×D11—24no—
58C2×D4×D11—24no—
59C2×D4×D11—24no—
60C2×D4×D11—44no—
61C2×D4×D11—44no—
62C2×D4×D11—44no—
63C2×D4×D11—44no—
64C2×D4×D11D418yes—
65C22×D44—21no—
66C22×D44—21no—
67C22×D44C2312yes—
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11D411yescharacteristic
71C22×C4×D11D411yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×C8×C11C2312yes—
74C11×#127—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79#66993—28no—
80#66993—28no—
81#66993—24no—
82#66993—24no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2312yes—
94C2×C8×D11—24no—
95C2×C8×D11—24no—
96C2×C8×D11—24no—
97C4⋊C4×D11—22no—
98C4⋊C4×D11—24no—
99C4⋊C4×D11—44no—
100C4⋊C4×D11D414yescomplemented
101#66927—24no—
102C42×D11—24no—
103C11×#102—24no—
104C11×#102—24no—
105C11×#95—21no—
106#66896—24no—
107#66896—24no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111#66885—24no—
112#66885—24no—
113#66873—24no—
114#66873—24no—
115C2×#2041—111nomaximal, Sylow
116C24×C11—22no—
117C23×D11—22no—
118C23×D11—28no—
119C23×D11—44no—
120C23×D11—44no—
121C23×D11—44no—
122C23×D11—44no—
123C23×D11—44no—
124C23×D11—44no—
125C23×D11C2×D411yescharacteristic
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11C2×D414yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—28no—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—28no—
146C2×C22⋊D11—44no—
147C2×C22⋊D11—44no—
148C2×C22⋊D11—44no—
149C2×C22⋊D11—44no—
150C2×C22⋊D11—44no—
151C2×C22⋊D11—44no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157D4×D11—216no—
158D4×D11—216no—
159D4×D11—432no—
160D4×D11—432no—
161D4×D11—48no—
162D4×D11—48no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—42no—
171C2×D44—42no—
172C2×D44—42no—
173C2×D44—42no—
174C2×D44C2×D414yes—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—24no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
182C2×C4×D11—42no—
183C2×C4×D11—42no—
184C2×C4×D11—42no—
185C2×C4×D11D814yes—
186C2×C4×D11SD1614yes—
187C2×C4×D11C2×D414yes—
188C2×C4×D11C2×D412yes—
189C2×C4×D11#4112yes—
190C2×C4×D11#4114yes—
191C2×C8×C11—22no—
192C2×C8×C11—22no—
193C2×C8×C11—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4C2×D412yescomplemented
198C42×C11—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11C2×D412yescomplemented
203Dic11⋊C4—24no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—22no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C8×D11—48no—
214C22×#127—111no—
215C22×#102—112no—
216C22×#102—112no—
217C2×#389—111no—
218#2041—112no—
219#2041—112no—
220#2041—111no—
221#2041—111no—
222#2041—111no—
223#2041D1111yescharacteristic, direct product factor
224C2×#336—111no—
225C23×C11—24no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11C22×D411yescharacteristic
233C22×D11—24no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—416no—
241C22×D11—416no—
242C22×D11—416no—
243C22×D11—88no—
244C22×D11—88no—
245C22×D11—88no—
246C22×D11—88no—
247C22×D11#12012yes—
248C22×D11#12112yes—
249C22×D11#12412yes—
250C22×D11C2×D812yes—
251C22×D11C2×SD1612yes—
252C22×D11AGL(1,ℤ/8)12yes—
253C22×D11AGL(1,ℤ/8)12yes—
254D4×C11—24no—
255D4×C11—24no—
256D4×C11—48no—
257D4×C11—48no—
258D4×C11—42no—
259D4×C11—42no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11C2×D812yes—
271C2×C4×C11C2×SD1612yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D412yes—
274C2×C4×C11C2×#4112yes—
275C2×C4×C11C2×#4111yescharacteristic
276C22⋊D11—416no—
277C22⋊D11—416no—
278C22⋊D11—416no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11#12012yes—
290C2×Dic11#12112yes—
291C2×Dic11#12412yes—
292C2×Dic11C2×D812yes—
293C2×Dic11C2×SD1612yes—
294D44—24no—
295D44—24no—
296D44—48no—
297D44—48no—
298D44—42no—
299D44—42no—
300C4×D11—28no—
301C4×D11—28no—
302C4×D11—48no—
303C4×D11—84no—
304C4×D11#12118yes—
305C4×D11#12318yes—
306C8×C11—42no—
307C11⋊C8—42no—
308C23×D4—112no—
309C23×D4—221no—
310C23×D4—221no—
311C23×C8—112no—
312C2×#127—112no—
313C2×#127—111no—
314C2×#127—221no—
315C2×#127—221no—
316C2×#127—228no—
317C2×#127C2×D1111yescharacteristic
318C22×C4⋊C4—111no—
319C22×C4⋊C4—111no—
320C22×C4⋊C4—221no—
321C22×C42—111no—
322C2×#102—112no—
323C2×#102—112no—
324C2×#102—112no—
325C2×#102—112no—
326C2×#102—112no—
327C2×#102—112no—
328C2×#102—228no—
329C2×#102—228no—
330C2×#102C2×D1112yescomplemented
331C2×#102C2×D1112yescomplemented
332#389—111no—
333#389—111no—
334#389—111no—
335#389—221no—
336#389—221no—
337#389C2×D1111yescharacteristic, complemented
338C2×#95—221no—
339#336—112no—
340#336—111no—
341#336C2×D1111yescharacteristic, complemented
342C22×C11—44no—
343C22×C11—44no—
344C22×C11—44no—
345C22×C11—82no—
346C22×C11—82no—
347C22×C11—82no—
348C22×C11—82no—
349C22×C11C2×#12011yescharacteristic
350C22×C11C2×#12111yescharacteristic
351C22×C11C2×#12411yescharacteristic
352C22×C11C22×D811yescharacteristic
353C22×C11C22×SD1611yescharacteristic
354C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—44no—
359C2×D11—82no—
360C2×D11—82no—
361C2×D11—82no—
362C2×D11—82no—
363C2×D11—832no—
364C2×D11#39414yes—
365C2×D11#44714yes—
366C2×D11#45014yes—
367C2×D11#45914yes—
368C2×D11#46014yes—
369C2×D11#48614yes—
370C2×D11#49014yes—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—42no—
374C4×C11—81no—
375C4×C11C2×#12112yes—
376C4×C11C2×#12312yes—
377Dic11—22no—
378Dic11—22no—
379Dic11—42no—
380Dic11—81no—
381Dic11#39414yes—
382C25—222no—
383C22×D4—21no—
384C22×D4—21no—
385C22×D4—118no—
386C22×D4—112no—
387C22×D4—224no—
388C22×D4—224no—
389C22×D4—224no—
390C22×D4—224no—
391C22×D4—224no—
392C22×D4—222no—
393C22×D4—222no—
394C22×D4—222no—
395C22×D4—228no—
396C22×D4—228no—
397C22×D4—221no—
398C22×D4—221no—
399C22×D4—444no—
400C22×D4—444no—
401C22×D4—444no—
402C22×D4—444no—
403C22×D4C22×D1112yes—
404C23×C4—111no—
405C23×C4—111no—
406C23×C4—111no—
407C23×C4—221no—
408C23×C4—221no—
409C22×C8—112no—
410C22×C8—224no—
411C22×C8—224no—
412C22×C8—224no—
413C22×C8C22×D1112yes—
414#127—24no—
415#127—224no—
416#127—224no—
417#127—228no—
418#127—228no—
419#127—224no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—114no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4—224no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—444no—
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42—224no—
438C2×C42C22×D1111yescharacteristic
439#102—24no—
440#102—24no—
441#102—224no—
442#102—224no—
443#102—224no—
444#102—224no—
445#102—224no—
446#102—224no—
447#95—21no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11—84no—
452C2×C11C2×#39411yescharacteristic
453C2×C11C2×#44711yescharacteristic
454C2×C11C2×#45011yescharacteristic
455C2×C11C2×#45911yescharacteristic
456C2×C11C2×#46011yescharacteristic
457C2×C11C2×#48611yescharacteristic
458C2×C11C2×#49011yescharacteristic
459D11—84no—
460D11#204118yesdirect product factor
461C24—22no—
462C24—111no—
463C24—228no—
464C24—222no—
465C24—444no—
466C24—444no—
467C24—444no—
468C24—444no—
469C24—444no—
470C24—444no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—114no—
483C2×D4—224no—
484C2×D4—224no—
485C2×D4—2216no—
486C2×D4—2216no—
487C2×D4—228no—
488C2×D4—228no—
489C2×D4—228no—
490C2×D4—222no—
491C2×D4—222no—
492C2×D4—222no—
493C2×D4—222no—
494C2×D4—222no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4—448no—
498C2×D4—448no—
499C2×D4—444no—
500C2×D4—444no—
501C2×D4—444no—
502C2×D4—444no—
503C2×D4—4432no—
504C2×D4—4432no—
505C2×D4—444no—
506C2×D4—444no—
507C2×D4—442no—
508C2×D4—442no—
509C2×D4D4×D1114yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—111no—
513C22×C4—114no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—114no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—114no—
520C22×C4—114no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—224no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—442no—
529C22×C4—442no—
530C22×C4—442no—
531C22×C4—442no—
532C22×C4—442no—
533C22×C4D4×D1111yescharacteristic
534C22×C4D4×D1111yescharacteristic
535C22×C4C23×D1111yescharacteristic
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—222no—
540C2×C8—222no—
541C2×C8—222no—
542C2×C8—448no—
543C4⋊C4—21no—
544C4⋊C4—22no—
545C4⋊C4—42no—
546C4⋊C4—112no—
547C4⋊C4—224no—
548C4⋊C4—221no—
549C4⋊C4—222no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4D4×D1112yescomplemented
555C42—22no—
556C42—222no—
557C42—222no—
558C42—222no—
559C11C2×#204111yescharacteristic, complemented, Sylow
560C23—24no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—112no—
568C23—112no—
569C23—112no—
570C23—112no—
571C23—112no—
572C23—112no—
573C23—112no—
574C23—224no—
575C23—4416no—
576C23—4416no—
577C23—4416no—
578C23—442no—
579C23—442no—
580C23—442no—
581C23—442no—
582C23—442no—
583C23—442no—
584C23—888no—
585C23—888no—
586C23—888no—
587C23—888no—
588C23C2×D4×D1111yescharacteristic
589D4—24no—
590D4—24no—
591D4—48no—
592D4—48no—
593D4—42no—
594D4—42no—
595D4—224no—
596D4—224no—
597D4—448no—
598D4—448no—
599D4—4416no—
600D4—4416no—
601D4—4416no—
602D4—442no—
603D4—442no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—118no—
618C2×C4—118no—
619C2×C4—112no—
620C2×C4—112no—
621C2×C4—228no—
622C2×C4—228no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—222no—
628C2×C4—448no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—884no—
635C2×C4D8×D1112yes—
636C2×C4SD16×D1112yes—
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4C2×D4×D1112yes—
639C2×C4#41×D1112yes—
640C2×C4#41×D1111yescharacteristic
641C8—42no—
642C8—442no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—82no—
647C22—82no—
648C22—82no—
649C22—82no—
650C22—114no—
651C22—114no—
652C22—114no—
653C22—114no—
654C22—114no—
655C22—114no—
656C22—114no—
657C22—444no—
658C22—444no—
659C22—444no—
660C22—8832no—
661C22—882no—
662C22—882no—
663C22—882no—
664C22—882no—
665C22D11×#12011yescharacteristic
666C22D11×#12111yescharacteristic
667C22D11×#12411yescharacteristic
668C22C2×D8×D1111yescharacteristic
669C22C2×SD16×D1111yescharacteristic
670C22D11×AGL(1,ℤ/8)11yescharacteristic
671C22D11×AGL(1,ℤ/8)11yescharacteristic
672C4—22no—
673C4—22no—
674C4—42no—
675C4—81no—
676C4—114no—
677C4—222no—
678C4—222no—
679C4—442no—
680C4—881no—
681C4D11×#12112yes—
682C4D11×#12312yes—
683C2—84no—
684C2—118no—
685C2—884no—
686C2D11×#39411yescharacteristic
687C2D11×#44711yescharacteristic
688C2D11×#45011yescharacteristic
689C2D11×#45911yescharacteristic
690C2D11×#46011yescharacteristic
691C2D11×#48611yescharacteristic
692C2D11×#49011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2041C2
socleC23×C11C22×D4
prime radicalC2×D11×#127C2
hypercenter#2041D11
hypocenterC11C2×#2041
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
2. C2×D11×#102C2semidirect
3. C2×D11×#102C2semidirect
4. D11×#389C2semidirect
5. #13069851C2semidirect
6. #13069850C2semidirect
7. #13069849C2semidirect
8. #13069848C2semidirect
9. #13069847C2semidirect
10. D11×#336C2semidirect
11. C11×#2041C2semidirect
26. C2×C11×#102C22semidirect
27. C2×C11×#102C22semidirect
28. C11×#389C22semidirect
29. C2×#66896C22semidirect
30. C2×#66896C22semidirect
31. C2×#66885C22semidirect
32. C2×#66885C22semidirect
33. #10622598C22semidirect
34. #10622586C22semidirect
36. C2×#66873C22semidirect
37. C2×#66873C22semidirect
38. #10622541C22semidirect
43. C11×#336C22semidirect
44. #10622188C22semidirect
45. #10622162C22semidirect
100. C4⋊C4×D11D4semidirect
197. C11×C4⋊C4C2×D4semidirect
202. C4⋊Dic11C2×D4semidirect
223. #2041D11direct (N × H)
330. C2×#102C2×D11semidirect
331. C2×#102C2×D11semidirect
337. #389C2×D11semidirect
341. #336C2×D11semidirect
460. D11#2041direct (N × H)
554. C4⋊C4D4×D11semidirect
559. C11C2×#2041semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1272
C2×D11×#1022
D11×#3892
#130698512
#130698502
#130698492
#130698482
#130698472
D11×#3362
C11×#20412
C2×#204111