Finite Group Databasebeta

← #14755046

Subgroups — #14755046

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×#10623041C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4C2×#10622726C211yesmaximal, characteristic, complemented
5C2×#10622723C211yesmaximal, characteristic, complemented
6#13068937C212yesmaximal, complemented
7#13068932C212yesmaximal, complemented
8#13068927C212yesmaximal, complemented
9#13068922C212yesmaximal, complemented
10#13068335C211yesmaximal, characteristic, complemented
11C2×C11×#340C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66983—22no—
18C2×C4×C22⋊D11—22no—
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21#10623041—24no—
22#10623041C418yescomplemented
23C2×#66950—21no—
24C2×#66950C2212yes—
25C2×#66948—21no—
26C2×#66948C2212yes—
27#10623035—24no—
28#10623035—24no—
29C2×#66946—21no—
30C2×#66945C2212yes—
31C2×C4⋊C4×D11C2212yes—
32C2×#66940—21no—
33#10622726—24no—
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36#10622723—24no—
37C2×(C2×D11)⋊C8C2212yes—
38C2×(C2×D11)⋊C8C2212yes—
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66874C2212yes—
42#10622579—24no—
43C2×#66873C2212yes—
44C11×#340C2212yes—
45C11×#340C2212yes—
46#10622167C2212yes—
47#10622167C2212yes—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C22×C22⋊D11D412yes—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C2×#4339—22no—
59C2×#4339—22no—
60C2×#4339—22no—
61C2×#4339—22no—
62C2×#4339C2×C414yes—
63C2×#4339C2×C414yescomplemented
64C2×#4339D414yes—
65C22×D44—22no—
66C22×D44D411yescharacteristic
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11—22no—
70C22×C4×D11C2312yes—
71C22×Dic22D411yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4C2×C414yescomplemented
83C2×C11×C4⋊C4D414yescomplemented
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C22⋊Dic11—21no—
87#66983—216no—
88C4×C22⋊D11—216no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92#66979—22no—
93#66979D414yescomplemented
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—22no—
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318—22no—
103C22×C11⋊C8C2312yes—
104#66950—24no—
105#66950—28no—
106#66950C2×C418yescomplemented
107#66948—28no—
108#66948—24no—
109#66948C2×C418yescomplemented
110#66946—28no—
111#66945—24no—
112#66945—24no—
113C4⋊C4×D11—24no—
114C4⋊C4×D11—24no—
115#66940—28no—
116#66885—22no—
117#66885—22no—
118(C2×D11)⋊C8—24no—
119(C2×D11)⋊C8—24no—
120#66880—22no—
121#66880—22no—
122#66874—24no—
123#66873—24no—
124#20915—111nomaximal, Sylow
125C24×C11C2×D411yescharacteristic
126C23×D11—21no—
127C23×D11C2×D412yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—81no—
133C22×C4×C11—81no—
134C22×C4×C11—81no—
135C22×C4×C11—81no—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4112yes—
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—24no—
146C2×C22⋊D11—24no—
147C2×C22⋊D11—42no—
148C2×C22⋊D11—42no—
149C2×C22⋊D11C22⋊C418yes—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D412yes—
154#4339—28no—
155#4339—28no—
156#4339—28no—
157#4339—28no—
158#4339—28no—
159#4339—28no—
160#4339—44no—
161#4339—44no—
162C2×D44—28no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—82no—
171C2×D44—82no—
172C2×D44C22⋊C414yes—
173C2×D44C22×C412yes—
174C2×C4×D11—28no—
175C2×C4×D11—24no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
182C2×C4×D11—82no—
183C2×C4×D11—82no—
184C2×C4×D11C22×C414yes—
185C2×C4×D11C2×D414yes—
186C2×Dic22—22no—
187C2×Dic22—22no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22C22⋊C414yes—
194C2×Dic22C22×C412yes—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—44no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4C22×C414yes—
207C11×C4⋊C4C2×D414yes—
208C22⋊Dic11—24no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—28no—
212C4⋊Dic11—28no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11C2×D412yes—
216C4⋊Dic11C2×D412yes—
217Dic11⋊C4—28no—
218C4×Dic11—28no—
219C4×Dic11—24no—
220#4318—44no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—22no—
223C2×C11⋊C8—22no—
224C2×#537—111no—
225C2×#520—111no—
226C2×#417—111no—
227C2×#416—111no—
228C2×#408—111no—
229#1875—112no—
230#1874—112no—
231#1873—112no—
232#1872—112no—
233#1736—111no—
234C2×#340D1111yescharacteristic, complemented
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11C2×C22⋊C412yes—
240C23×C11#12012yes—
241C23×C11#12312yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11C2×C22⋊C414yes—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—84no—
264C2×C4×C11—84no—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C4×D414yes—
267C2×C4×C11C4×D414yes—
268C2×C4×C11#12012yes—
269C2×C4×C11#12114yes—
270C2×C4×C11#12114yes—
271C2×C4×C11#12312yes—
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C22⋊D11—216no—
279C22⋊D11—48no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11C2×C22⋊C414yes—
292D44—22no—
293D44—22no—
294D44—28no—
295D44—41no—
296D44—41no—
297D44—88no—
298C4×D11—24no—
299C4×D11—24no—
300C4×D11—24no—
301C4×D11—24no—
302C4×D11—48no—
303C4×D11—88no—
304Dic22—28no—
305Dic22—22no—
306Dic22—22no—
307Dic22—41no—
308Dic22—41no—
309C8×C11—41no—
310C8×C11—41no—
311C11⋊C8—42no—
312C22×#41—111no—
313C22×#41—111no—
314C22×M16—111no—
315C23×C8C2×D1111yescharacteristic
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—112no—
331C22×C4⋊C4C2×D1111yescharacteristic
332C22×C4⋊C4C2×D1111yescharacteristic
333#417—224no—
334#416—224no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—112no—
338C2×#102—111no—
339C2×#102—111no—
340C2×#102—112no—
341#408—224no—
342C2×C22⋊C8—112no—
343C2×C22⋊C8—112no—
344#340—112no—
345#340—112no—
346#340C2×D1112yes—
347#340C2×D1112yes—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11#38614yes—
355C22×C11C22×C22⋊C411yescharacteristic
356C22×C11C2×#12011yescharacteristic
357C22×C11C2×#12311yescharacteristic
358C22×C11#57611yescharacteristic
359C22×C11#57711yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57811yescharacteristic
362C2×D11—24no—
363C2×D11—24no—
364C2×D11—24no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C4×C11—44no—
377C4×C11—44no—
378C4×C11#38614yes—
379C4×C11C2×C4×D411yescharacteristic
380C4×C11C2×C4×D411yescharacteristic
381C4×C11C2×#12111yescharacteristic
382C4×C11C2×#12111yescharacteristic
383Dic11—24no—
384Dic11—42no—
385Dic11—42no—
386Dic11—42no—
387C2×#41—114no—
388C2×#41—114no—
389C2×#41—114no—
390C2×#41—222no—
391C2×#41—222no—
392C2×#41—222no—
393C2×#41—222no—
394C2×#41—222no—
395C2×#41—222no—
396C2×#41—222no—
397C2×#41—222no—
398C2×#41—222no—
399C22×Q8—111no—
400C22×Q8—111no—
401C22×D4—112no—
402C22×D4—111no—
403C22×D4—111no—
404C22×D4—222no—
405C22×D4—221no—
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—112no—
409C23×C4—222no—
410C23×C4—221no—
411C23×C4C22×D1111yescharacteristic
412C2×M16—222no—
413C2×M16—222no—
414C2×M16—222no—
415C22×C8—22no—
416C22×C8—22no—
417C22×C8—22no—
418C22×C8—112no—
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421C22⋊Q8—118no—
422C22⋊Q8—224no—
423C22⋊Q8—228no—
424#121—118no—
425#121—224no—
426#121—228no—
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—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—224no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—222no—
444C2×C4⋊C4—224no—
445C2×C4⋊C4C4×D1114yescomplemented
446C2×C4⋊C4D4414yescomplemented
447C2×C4⋊C4C22×D1112yes—
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—222no—
456#103—222no—
457#103—224no—
458#102—222no—
459#102—222no—
460#102—224no—
461C22⋊C8—224no—
462C22⋊C8—224no—
463C2×C11—24no—
464C2×C11C2×#38611yescharacteristic
465C2×C11#289711yescharacteristic
466C2×C11#289811yescharacteristic
467C2×C11#301211yescharacteristic
468C2×C11#301311yescharacteristic
469C2×C11#309811yescharacteristic
470C2×C11#309911yescharacteristic
471D11—44no—
472D11—82no—
473C24—112no—
474C24—221no—
475C24D4×D1111yescharacteristic
476#41—228no—
477#41—228no—
478#41—228no—
479#41—228no—
480#41—228no—
481#41—228no—
482#41—444no—
483#41—444no—
484C2×Q8—114no—
485C2×Q8—112no—
486C2×Q8—222no—
487C2×Q8—222no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×D4—118no—
494C2×D4—114no—
495C2×D4—112no—
496C2×D4—228no—
497C2×D4—224no—
498C2×D4—224no—
499C2×D4—224no—
500C2×D4—222no—
501C2×D4—222no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4—221no—
506C2×D4—221no—
507C2×D4—442no—
508C2×D4—442no—
509C2×D4—882no—
510C2×D4—882no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—81no—
516C22×C4—81no—
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—221no—
530C22×C4—224no—
531C22×C4—442no—
532C22×C4—442no—
533C22×C4—882no—
534C22×C4—882no—
535C22×C4C2×C4×D1112yes—
536C22×C4C2×D4412yes—
537C22×C4#433912yes—
538C22×C4D4×D1111yescharacteristic
539C22×C4D4×D1112yes—
540C22×C4D4×D1112yes—
541C22×C4#434312yes—
542C22×C4C23×D1111yescharacteristic
543M16—444no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—44no—
551C2×C8—222no—
552C2×C8—222no—
553C2×C8—222no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—112no—
559C4⋊C4—112no—
560C4⋊C4—228no—
561C4⋊C4—228no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4C2×C4×D1114yes—
565C4⋊C4C2×D4414yes—
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—114no—
578C23—222no—
579C23—222no—
580C23—222no—
581C23—222no—
582C23—222no—
583C23—222no—
584C23—222no—
585C23—441no—
586C23—441no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23C22⋊C4×D1112yes—
592C23#6693512yes—
593C23#6694712yes—
594C23C2×D4×D1111yescharacteristic
595Q8—228no—
596Q8—222no—
597Q8—222no—
598Q8—441no—
599Q8—441no—
600D4—2216no—
601D4—222no—
602D4—222no—
603D4—228no—
604D4—448no—
605D4—441no—
606D4—441no—
607D4—888no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—84no—
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—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—448no—
633C2×C4—888no—
634C2×C4C4×D4414yes—
635C2×C4C22⋊C4×D1112yes—
636C2×C4#6693512yes—
637C2×C4#6693714yes—
638C2×C4#6694614yes—
639C2×C4#6694712yes—
640C2×C4#6694814yes—
641C2×C4C22×C4×D1111yescharacteristic
642C2×C4C22×D4411yescharacteristic
643C2×C4C2×#433911yescharacteristic
644C2×C4C2×D4×D1111yescharacteristic
645C2×C4C2×D4×D1111yescharacteristic
646C2×C4C2×#434311yescharacteristic
647C8—41no—
648C8—41no—
649C8—442no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—224no—
657C22—224no—
658C22—224no—
659C22—442no—
660C22—442no—
661C22—442no—
662C22—442no—
663C22—442no—
664C22—442no—
665C22—442no—
666C22—881no—
667C22—881no—
668C22—881no—
669C22—881no—
670C22#1062227814yes—
671C22C2×C22⋊C4×D1111yescharacteristic
672C22C2×#6693511yescharacteristic
673C22C2×#6694711yescharacteristic
674C22#1062328811yescharacteristic
675C22#1062329311yescharacteristic
676C22#1062329311yescharacteristic
677C22#1062329711yescharacteristic
678C4—44no—
679C4—44no—
680C4—224no—
681C4—442no—
682C4—442no—
683C4—442no—
684C4#1062227814yes—
685C4C2×C4×D4411yescharacteristic
686C4C2×#6693711yescharacteristic
687C4C2×#6694611yescharacteristic
688C4C2×#6694811yescharacteristic
689C2—24no—
690C2—444no—
691C2—882no—
692C2C2×#1062227811yescharacteristic
693C2#1307713711yescharacteristic
694C2#1307714411yescharacteristic
695C2#1307792511yescharacteristic
696C2#1307793611yescharacteristic
697C2#1307859911yescharacteristic
698C2#1307861011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC2×#10623041C2
cosocleC22×C4×C11C24
hypercenterC2×#340D11
hypocenterC11#20915
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. C2×#10622579C2semidirect
4. C2×#10622726C2semidirect
5. C2×#10622723C2semidirect
6. #13068937C2semidirect
7. #13068932C2semidirect
8. #13068927C2semidirect
9. #13068922C2semidirect
10. #13068335C2semidirect
11. C2×C11×#340C2semidirect
22. #10623041C4semidirect
63. C2×#4339C2×C4semidirect
82. C2×C11×C4⋊C4C2×C4semidirect
83. C2×C11×C4⋊C4D4semidirect
93. #66979D4semidirect
106. #66950C2×C4semidirect
109. #66948C2×C4semidirect
234. C2×#340D11semidirect
445. C2×C4⋊C4C4×D11semidirect
446. C2×C4⋊C4D44semidirect
572. C11#20915semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
C2×#106230352
C2×#106225792
C2×#106227262
C2×#106227232
#130689372
#130689322
#130689272
#130689222
#130683352
C2×C11×#3402
#2091511