Finite Group Databasebeta

← #14755052

Subgroups — #14755052

Order 2816.

1842 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C2×#10622742C211yesmaximal, characteristic, complemented
5#13068935C212yesmaximal, complemented
6#13068930C212yesmaximal, complemented
7#13068925C212yesmaximal, complemented
8#13068920C212yesmaximal, complemented
9#13068336C211yesmaximal, characteristic, complemented
10C2×#10622167C211yesmaximal, characteristic, complemented
11C2×C11×#417C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16#10623364—24no—
17#10623364C418yescomplemented
18C2×#66999C2212yes—
19C2×#66992—22no—
20C2×#66991C2212yes—
21C2×#66983—21no—
22C2×C4×C22⋊D11—22no—
23C2×#66979C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C2×#66977—21no—
26C23×C11⋊C8C2211yescharacteristic
27#10623035—24no—
28#10623035—24no—
29C2×#66946—21no—
30C2×#66945C2212yes—
31C2×C4⋊C4×D11C2212yes—
32C2×#66940—21no—
33C11×#417—24no—
34C2×C11×#103C2212yes—
35C2×C11×#102C2212yes—
36#10622846—24no—
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41#10622742—24no—
42C2×(C2×D11)⋊C8C2212yes—
43C2×(C2×D11)⋊C8C2212yes—
44#10622189C2212yes—
45#10622189C2212yes—
46#10622167C2212yes—
47#10622167C2212yes—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41C2×C414yescomplemented
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—22no—
61C22×C22⋊D11D412yes—
62C23×Dic11—21no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339—22no—
67C2×#4339C2×C414yes—
68C2×#4339D414yes—
69C22×D44D411yescharacteristic
70C22×C4×D11—22no—
71C22×C4×D11C2312yes—
72C22×Dic22D411yescharacteristic
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C22×C8×C11C2312yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D414yescomplemented
80C2×C11×C4⋊C4C2312yes—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—22no—
83#66999—24no—
84#66999C2×C418yescomplemented
85#66992—216no—
86#66991—24no—
87#66991C2×C418yescomplemented
88#66983—28no—
89C4×C22⋊D11—216no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92#66979—22no—
93#66979D414yescomplemented
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11C2×C414yescomplemented
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100#66977—28no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—22no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—22no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110#66946—28no—
111#66945—24no—
112#66945—24no—
113C4⋊C4×D11—24no—
114C4⋊C4×D11—24no—
115#66940—28no—
116C11×#103—24no—
117C11×#102—24no—
118#66899—22no—
119#66899—22no—
120#66896—22no—
121#66896—22no—
122(C2×D11)⋊C8—24no—
123(C2×D11)⋊C8—24no—
124#20915—111nomaximal, Sylow
125C24×C11—21no—
126C24×C11C2×D411yescharacteristic
127C23×D11C2×D412yes—
128C11×#41—28no—
129C11×#41—28no—
130C11×#41—44no—
131C11×#41—44no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C22×C412yes—
138C2×D4×C11—24no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11C22×C412yes—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—81no—
154C22×C4×C11—81no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—24no—
164C2×C22⋊D11—24no—
165C2×C22⋊D11—28no—
166C2×C22⋊D11—82no—
167C2×C22⋊D11—82no—
168C2×C22⋊D11C22⋊C418yes—
169C22×Dic11—24no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—81no—
174C22×Dic11—81no—
175C22×Dic11C2×D412yes—
176#4339—28no—
177#4339—28no—
178#4339—28no—
179#4339—28no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44C22⋊C414yes—
183C2×C4×D11—28no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—22no—
188C2×C4×D11—82no—
189C2×C4×D11—82no—
190C2×C4×D11C22×C414yes—
191C2×C4×D11C2×D414yes—
192C2×Dic22—22no—
193C2×Dic22—22no—
194C2×Dic22C22⋊C414yes—
195C11×M16—44no—
196C2×C8×C11—22no—
197C2×C8×C11—22no—
198C2×C8×C11—22no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4C2×D414yes—
202C22⋊Dic11—28no—
203C22⋊Dic11—24no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—28no—
206C4⋊Dic11—24no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—22no—
210C4⋊Dic11C22×C414yes—
211C4⋊Dic11C2×D412yes—
212C4⋊Dic11C2×D412yes—
213Dic11⋊C4—28no—
214Dic11⋊C4—28no—
215C4×Dic11—28no—
216C4×Dic11—24no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—44no—
224C2×#537—111no—
225C2×#520—111no—
226C2×#417D1111yescharacteristic, complemented
227C2×#416—111no—
228C2×#408—111no—
229#1875—112no—
230#1874—112no—
231#1873—112no—
232#1872—112no—
233#1736—111no—
234C2×#340—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C2×C22⋊C412yes—
247C23×C11#12012yes—
248C23×C11#12312yes—
249C23×C11C22×D411yescharacteristic
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11C2×C22⋊C414yes—
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11—41no—
260Q8×C11—41no—
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—48no—
264D4×C11—41no—
265D4×C11—41no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—48no—
273C2×C4×C11—84no—
274C2×C4×C11C2×C22⋊C412yes—
275C2×C4×C11C4×D414yes—
276C2×C4×C11C4×D414yes—
277C2×C4×C11#12012yes—
278C2×C4×C11#12114yes—
279C2×C4×C11#12114yes—
280C2×C4×C11#12312yes—
281C2×C4×C11C23×C411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C22⋊D11—216no—
288C22⋊D11—88no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—24no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—41no—
295C2×Dic11—42no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—42no—
299C2×Dic11—41no—
300C2×Dic11—84no—
301C2×Dic11C2×C22⋊C414yes—
302D44—28no—
303C4×D11—24no—
304C4×D11—24no—
305C4×D11—24no—
306C4×D11—24no—
307C4×D11—88no—
308Dic22—28no—
309C8×C11—42no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C22×#41—111no—
313C22×#41C2×D1111yescharacteristic
314C22×M16C2×D1111yescharacteristic
315C23×C8—111no—
316#537—118no—
317#537—224no—
318C2×C22⋊Q8—112no—
319C2×C22⋊Q8—221no—
320C2×#121—112no—
321C2×#121—221no—
322C2×#121—222no—
323#520—224no—
324#520—224no—
325C2×C4×Q8—221no—
326C2×C4×D4—221no—
327C2×C4×D4—222no—
328C2×#117—111no—
329C2×#117—112no—
330C22×C4⋊C4—111no—
331C22×C4⋊C4—112no—
332C22×C4⋊C4C2×D1111yescharacteristic
333#417—24no—
334#416—224no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103C2×D1112yes—
338C2×#102—111no—
339C2×#102—111no—
340C2×#102C2×D1112yes—
341#408—224no—
342C2×C22⋊C8—112no—
343C2×C22⋊C8—112no—
344#340—112no—
345#340—112no—
346#340—112no—
347#340—112no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11#38614yes—
362C22×C11C22×C22⋊C411yescharacteristic
363C22×C11C2×#12011yescharacteristic
364C22×C11C2×#12311yescharacteristic
365C22×C11#57611yescharacteristic
366C22×C11#57711yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57811yescharacteristic
369C2×D11—24no—
370C2×D11—24no—
371C2×D11—24no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—42no—
376C4×C11—44no—
377C4×C11—42no—
378C4×C11#38614yes—
379C4×C11C2×C4×D411yescharacteristic
380C4×C11C2×C4×D411yescharacteristic
381C4×C11C2×#12111yescharacteristic
382C4×C11C2×#12111yescharacteristic
383Dic11—24no—
384Dic11—44no—
385Dic11—42no—
386Dic11—42no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41—22no—
390C2×#41—22no—
391C2×#41—22no—
392C2×#41—114no—
393C2×#41—114no—
394C2×#41—222no—
395C2×#41—222no—
396C2×#41—222no—
397C2×#41—222no—
398C2×#41C4×D1114yescomplemented
399C22×Q8—111no—
400C22×Q8C22×D1111yescharacteristic
401C22×D4—21no—
402C22×D4—112no—
403C22×D4—111no—
404C22×D4—222no—
405C22×D4C22×D1111yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—112no—
409C23×C4—222no—
410C23×C4—221no—
411C23×C4C22×D1111yescharacteristic
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—22no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8—222no—
418C22×C8—222no—
419C22×C8—222no—
420C22×C8C22×D1112yes—
421C22⋊Q8—118no—
422C22⋊Q8—228no—
423C22⋊Q8—224no—
424#121—118no—
425#121—228no—
426#121—224no—
427#121—2216no—
428C4×Q8—228no—
429C4×D4—228no—
430C4×D4—2216no—
431#117—114no—
432#117—224no—
433#117—222no—
434#117—224no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—112no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—224no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—222no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4—222no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4C22⋊D1114yescomplemented
448C2×C4⋊C4C22×D1112yes—
449C2×C22⋊C4—222no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—221no—
453C2×C42—222no—
454C2×C42—221no—
455#103—24no—
456#103—222no—
457#103—222no—
458#102—24no—
459#102—222no—
460#102—222no—
461C22⋊C8—224no—
462C22⋊C8—224no—
463C2×C11—24no—
464C2×C11—82no—
465C2×C11C2×#38611yescharacteristic
466C2×C11#289711yescharacteristic
467C2×C11#289811yescharacteristic
468C2×C11#301211yescharacteristic
469C2×C11#301311yescharacteristic
470C2×C11#309811yescharacteristic
471C2×C11#309911yescharacteristic
472D11—44no—
473C24—21no—
474C24—112no—
475C24D4×D1111yescharacteristic
476#41—28no—
477#41—28no—
478#41—44no—
479#41—44no—
480#41—228no—
481#41—228no—
482#41—228no—
483#41—228no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—114no—
490C2×Q8—222no—
491C2×Q8—222no—
492C2×Q8C2×C4×D1112yes—
493C2×D4—24no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—118no—
502C2×D4—114no—
503C2×D4—224no—
504C2×D4—224no—
505C2×D4—228no—
506C2×D4—222no—
507C2×D4—222no—
508C2×D4—882no—
509C2×D4—882no—
510C2×D4C2×C4×D1112yes—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4—112no—
520C22×C4—114no—
521C22×C4—114no—
522C22×C4—228no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—222no—
530C22×C4—224no—
531C22×C4—882no—
532C22×C4—882no—
533C22×C4—881no—
534C22×C4—881no—
535C22×C4C2×C4×D1112yes—
536C22×C4#433912yes—
537C22×C4D4×D1111yescharacteristic
538C22×C4D4×D1112yes—
539C22×C4D4×D1112yes—
540C22×C4#434112yes—
541C22×C4C2×C22⋊D1112yes—
542C22×C4C23×D1111yescharacteristic
543M16—44no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—444no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—114no—
557C4⋊C4—112no—
558C4⋊C4—112no—
559C4⋊C4—228no—
560C4⋊C4—228no—
561C4⋊C4—224no—
562C4⋊C4—222no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4C2×C22⋊D1114yes—
566C22⋊C4—228no—
567C22⋊C4—228no—
568C22⋊C4—228no—
569C22⋊C4—224no—
570C42—228no—
571C42—224no—
572C11#2091511yescharacteristic, complemented, Sylow
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—22no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—114no—
585C23—222no—
586C23—222no—
587C23—222no—
588C23—222no—
589C23—222no—
590C23—222no—
591C23C22⋊C4×D1112yes—
592C23#6693612yes—
593C23#6699012yes—
594C23C2×D4×D1111yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—41no—
598Q8—41no—
599Q8—228no—
600D4—22no—
601D4—22no—
602D4—48no—
603D4—41no—
604D4—41no—
605D4—2216no—
606D4—228no—
607D4—888no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—48no—
615C2×C4—84no—
616C2×C4—114no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—441no—
627C2×C4—442no—
628C2×C4—441no—
629C2×C4—442no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—888no—
633C2×C4—884no—
634C2×C4C22⋊C4×D1112yes—
635C2×C4(C22⋊D11)⋊C414yes—
636C2×C4#6693612yes—
637C2×C4#6693714yes—
638C2×C4C4×C22⋊D1114yes—
639C2×C4#6699012yes—
640C2×C4#6699114yes—
641C2×C4C22×C4×D1111yescharacteristic
642C2×C4C2×#433911yescharacteristic
643C2×C4C2×D4×D1111yescharacteristic
644C2×C4C2×D4×D1111yescharacteristic
645C2×C4C2×#434111yescharacteristic
646C2×C4C22×C22⋊D1111yescharacteristic
647C8—42no—
648C8—441no—
649C8—441no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—224no—
664C22—224no—
665C22—224no—
666C22—442no—
667C22—442no—
668C22—442no—
669C22—442no—
670C22#1062256914yes—
671C22C2×C22⋊C4×D1111yescharacteristic
672C22C2×#6693611yescharacteristic
673C22#1062330511yescharacteristic
674C22#1062330611yescharacteristic
675C22#1062330911yescharacteristic
676C22#1062331011yescharacteristic
677C22C2×#6699011yescharacteristic
678C4—44no—
679C4—42no—
680C4—224no—
681C4—444no—
682C4—442no—
683C4—442no—
684C4#1062256914yes—
685C4C2×(C22⋊D11)⋊C411yescharacteristic
686C4C2×#6693711yescharacteristic
687C4C2×C4×C22⋊D1111yescharacteristic
688C4C2×#6699111yescharacteristic
689C2—24no—
690C2—82no—
691C2—444no—
692C2C2×#1062256911yescharacteristic
693C2#1307714011yescharacteristic
694C2#1307714711yescharacteristic
695C2#1307791911yescharacteristic
696C2#1307793011yescharacteristic
697C2#1307859311yescharacteristic
698C2#1307860411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
cosocleC22×C4×C11C24
hypercenterC2×#417D11
hypocenterC11#20915
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. C2×#10622846C2semidirect
4. C2×#10622742C2semidirect
5. #13068935C2semidirect
6. #13068930C2semidirect
7. #13068925C2semidirect
8. #13068920C2semidirect
9. #13068336C2semidirect
10. C2×#10622167C2semidirect
11. C2×C11×#417C2semidirect
17. #10623364C4semidirect
53. C2×C11×#41C2×C4semidirect
79. C2×C11×C4⋊C4D4semidirect
84. #66999C2×C4semidirect
87. #66991C2×C4semidirect
93. #66979D4semidirect
96. C2×C4⋊Dic11C2×C4semidirect
226. C2×#417D11semidirect
398. C2×#41C4×D11semidirect
447. C2×C4⋊C4C22⋊D11semidirect
572. C11#20915semidirect

Maximal subgroups

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

subgroupindex
C2×#106233642
C2×#106230352
C2×#106228462
C2×#106227422
#130689352
#130689302
#130689252
#130689202
#130683362
C2×#106221672
C2×C11×#4172
#2091511