Finite Group Databasebeta

← #14755282

Subgroups — #14755282

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081819C211yesmaximal, characteristic, complemented
2C22×#66901C211yesmaximal, characteristic, complemented
3#13077135C211yesmaximal, characteristic, complemented
4#13071107C211yesmaximal, characteristic, complemented
5#13068994C214yesmaximal, complemented
6#13068987C214yesmaximal, complemented
7#13068354C211yesmaximal, characteristic, complemented
8C2×#10622193C211yesmaximal, characteristic, complemented
9C2×C11×#575C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C11×#575—24no—
13C11×#575C418yescomplemented
14C2×C11×#137—21no—
15C2×C11×#137C2212yes—
16C2×C11×AGL(1,ℤ/8)—21no—
17C2×C11×AGL(1,ℤ/8)C2212yes—
18C2×C11×#135—22no—
19C22×C11×M16C2211yescharacteristic
20#10623358—22no—
21#10623358C2214yes—
22#41×Dic11—22no—
23#41×Dic11—22no—
24#10623343—21no—
25#10623329—21no—
26#10623329—22no—
27C2×#66979—22no—
28C2×#66979C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C2×#66901—24no—
33C2×#66901C2214yes—
34#10622846—22no—
35#10622845—22no—
36#10622843C2212yescomplemented
37#10622838C2212yescomplemented
38#10622834C2212yescomplemented
39#10622833—22no—
40#10622828C2212yescomplemented
41C4×C22⋊Dic11—22no—
42#10622193C2214yescomplemented
43#10622192C2214yescomplemented
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41C2×C414yes—
56C2×C11×#41C2×C414yescomplemented
57C2×C11×#41D414yes—
58C2×C11×#41D412yes—
59C2×C11×#41C2312yes—
60C22×Q8×C11D411yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×Dic11—21no—
70C11×#137—24no—
71C11×#137—28no—
72C11×#137C2×C418yescomplemented
73C11×AGL(1,ℤ/8)—24no—
74C11×AGL(1,ℤ/8)—28no—
75C11×AGL(1,ℤ/8)C2×C418yescomplemented
76C11×#135—216no—
77C2×C11×Q16—22no—
78C2×C11×SD16—22no—
79C2×C11×SD16—22no—
80C2×C11×D8—22no—
81C2×C11×M16—21no—
82C2×C11×M16—22no—
83C2×C11×M16C2×C414yescomplemented
84C2×C11×M16C2312yes—
85C22×C8×C11—21no—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11D412yes—
90Q8×Dic11—24no—
91Q8×Dic11—24no—
92D4×Dic11—28no—
93D4×Dic11—24no—
94D4×Dic11—24no—
95D4×Dic11—28no—
96#66979—24no—
97#66979—24no—
98#66979—21no—
99#66979—21no—
100#66979—21no—
101#66979—21no—
102#66979—21no—
103#66979—21no—
104#66979—24no—
105#66979D412yes—
106#66979C2312yes—
107C2×C4⋊Dic11—24no—
108C2×C4⋊Dic11D412yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11D412yes—
116C2×C4×Dic11C2312yes—
117C2×#4318—21no—
118C2×#4318—22no—
119C2×#4318—22no—
120C2×#4318C2312yes—
121C22×C11⋊C8—21no—
122#66901—28no—
123#66899—24no—
124#66896—24no—
125C11⋊#95—24no—
126#20942—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C11×#41—24no—
131C11×#41—24no—
132C11×#41—24no—
133C11×#41—24no—
134C11×#41—24no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—24no—
138C11×#41—24no—
139C11×#41—24no—
140C11×#41—24no—
141C11×#41—42no—
142C11×#41—42no—
143C11×#41—42no—
144C11×#41—42no—
145C11×#41C22⋊C418yescomplemented
146C11×#41C22×C414yes—
147C11×#41C2×D414yes—
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11C22⋊C414yescomplemented
156C2×Q8×C11C22×C412yes—
157C2×Q8×C11C2×D412yes—
158C2×D4×C11—24no—
159C2×D4×C11—22no—
160C2×D4×C11—24no—
161C2×D4×C11—22no—
162C2×D4×C11—24no—
163C2×D4×C11—21no—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—41no—
171C2×D4×C11—41no—
172C2×D4×C11—42no—
173C2×D4×C11C22⋊C414yescomplemented
174C2×D4×C11C22×C412yes—
175C2×D4×C11C2×D412yes—
176C22×C4×C11—21no—
177C22×C4×C11—24no—
178C22×C4×C11—22no—
179C22×C4×C11—24no—
180C22×C4×C11—22no—
181C22×C4×C11—21no—
182C22×C4×C11—24no—
183C22×C4×C11—41no—
184C22×C4×C11—41no—
185C22×C4×C11—42no—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11#4112yes—
194C22×C4×C11#4112yes—
195C22×C4×C11C2411yescharacteristic
196C22×Dic11—28no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—44no—
200C22×Dic11—42no—
201C22×Dic11C2×D414yes—
202C11×Q16—28no—
203C11×SD16—28no—
204C11×SD16—28no—
205C11×D8—28no—
206C11×M16—24no—
207C11×M16—22no—
208C11×M16C22×C414yes—
209C2×C8×C11—24no—
210C2×C8×C11—22no—
211C22⋊Dic11—28no—
212C22⋊Dic11—22no—
213C22⋊Dic11—22no—
214C22⋊Dic11—22no—
215C22⋊Dic11—22no—
216C22⋊Dic11—48no—
217C4⋊Dic11—28no—
218C4⋊Dic11—22no—
219C4⋊Dic11—22no—
220C4⋊Dic11—22no—
221C4⋊Dic11C2×D414yes—
222C4×Dic11—28no—
223C4×Dic11—22no—
224C4×Dic11—22no—
225C4×Dic11—22no—
226C4×Dic11—22no—
227C4×Dic11—22no—
228C4×Dic11—22no—
229C4×Dic11—42no—
230#4318—22no—
231#4318—22no—
232#4318—42no—
233C2×C11⋊C8—22no—
234C2×C11⋊C8—42no—
235C2×#575D1111yescharacteristic
236#3428—111no—
237C22×#104—111no—
238#2896—111no—
239#2297—111no—
240#1883—114no—
241#1882—114no—
242#1742—111no—
243C2×#339—111no—
244C23×C11—22no—
245C23×C11—24no—
246C23×C11—22no—
247C23×C11—42no—
248C23×C11—44no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—82no—
252C23×C11C4×D412yes—
253C23×C11#12011yescharacteristic
254C23×C11#12011yescharacteristic
255C23×C11#12112yes—
256C23×C11C22×D411yescharacteristic
257Q8×C11—22no—
258Q8×C11—24no—
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—41no—
262Q8×C11—41no—
263Q8×C11C2×C22⋊C414yes—
264D4×C11—24no—
265D4×C11—24no—
266D4×C11—28no—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—24no—
271D4×C11—44no—
272D4×C11—44no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11C2×C22⋊C414yes—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—28no—
281C2×C4×C11—22no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—44no—
285C2×C4×C11—44no—
286C2×C4×C11C2×C22⋊C412yes—
287C2×C4×C11C2×C22⋊C412yes—
288C2×C4×C11C4×D412yes—
289C2×C4×C11C4×D412yes—
290C2×C4×C11C4×D412yes—
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12011yescharacteristic
293C2×C4×C11#12112yes—
294C2×C4×C11#12112yes—
295C2×C4×C11#12112yes—
296C2×C4×C11#12312yes—
297C2×C4×C11#12312yes—
298C2×C4×C11C23×C411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—42no—
308C2×Dic11—48no—
309C2×Dic11—42no—
310C2×Dic11—44no—
311C2×Dic11—82no—
312C2×Dic11—88no—
313C8×C11—24no—
314C11⋊C8—42no—
315C22×#41C2×D1111yescharacteristic
316C22×#41C2×D1111yescharacteristic
317#575—24no—
318#575Dic1118yescomplemented
319C2×#137—21no—
320C2×#137C2×D1112yes—
321C2×AGL(1,ℤ/8)—21no—
322C2×AGL(1,ℤ/8)C2×D1112yes—
323C2×#135—22no—
324C22×M16—111no—
325C22×M16C2×D1111yescharacteristic
326#520—114no—
327#520—222no—
328#519—221no—
329#518—222no—
330#518—221no—
331C4×#41—222no—
332C4×#41—222no—
333C2×#117—111no—
334C2×#117—111no—
335C2×#117—222no—
336C22×C42—111no—
337C2×#104—114no—
338C2×#104—224no—
339#419—112no—
340#418—112no—
341#417—222no—
342#416—222no—
343#391—112no—
344#390—112no—
345#386—222no—
346C4×C22⋊C4—222no—
347#343—114no—
348#339—114no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—24no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—44no—
356C22×C11—44no—
357C22×C11—42no—
358C22×C11—84no—
359C22×C11—82no—
360C22×C11—82no—
361C22×C11#38612yes—
362C22×C11#38612yes—
363C22×C11C2×C4×D411yescharacteristic
364C22×C11C2×#12011yescharacteristic
365C22×C11C2×#12111yescharacteristic
366C4×C11—24no—
367C4×C11—42no—
368C4×C11#38612yes—
369C4×C11#38612yes—
370C4×C11C22×C22⋊C411yescharacteristic
371C4×C11C2×C4×D411yescharacteristic
372C4×C11C2×#12111yescharacteristic
373C4×C11C2×#12311yescharacteristic
374Dic11—44no—
375Dic11—44no—
376Dic11—44no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—22no—
382C2×#41—21no—
383C2×#41—21no—
384C2×#41—22no—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—22no—
388C2×#41C2×Dic1114yes—
389C2×#41C2×Dic1114yescomplemented
390C2×#41C22⋊D1114yes—
391C2×#41C22⋊D1112yes—
392C2×#41C22×D1112yes—
393C22×Q8C22⋊D1111yescharacteristic
394C22×Q8C22×D1111yescharacteristic
395C22×D4—21no—
396C22×D4—21no—
397C22×D4C22⋊D1111yescharacteristic
398C22×D4C22×D1111yescharacteristic
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—221no—
402C23×C4C22×D1111yescharacteristic
403#137—24no—
404#137—28no—
405#137C2×Dic1118yescomplemented
406AGL(1,ℤ/8)—24no—
407AGL(1,ℤ/8)—28no—
408AGL(1,ℤ/8)C2×Dic1118yescomplemented
409#135—216no—
410C2×Q16—22no—
411C2×SD16—22no—
412C2×SD16—22no—
413C2×D8—22no—
414C2×M16—21no—
415C2×M16—22no—
416C2×M16—112no—
417C2×M16—221no—
418C2×M16—222no—
419C2×M16—222no—
420C2×M16C2×Dic1114yescomplemented
421C2×M16C22×D1112yes—
422C22×C8—21no—
423C22×C8—221no—
424C4×Q8—224no—
425C4×Q8—224no—
426C4×D4—228no—
427C4×D4—228no—
428C4×D4—224no—
429C4×D4—224no—
430#117—112no—
431#117—112no—
432#117—224no—
433#117—224no—
434#117—224no—
435#117—221no—
436#117—221no—
437#117—221no—
438#117—221no—
439#117—221no—
440#117—221no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—112no—
443C2×C4⋊C4—224no—
444C2×C22⋊C4—112no—
445C2×C22⋊C4—224no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—224no—
448C2×C42—112no—
449C2×C42—112no—
450C2×C42—224no—
451C2×C42—221no—
452C2×C42—222no—
453C2×C42—222no—
454C2×C42—221no—
455#104—228no—
456#103—224no—
457#102—224no—
458#95—224no—
459C2×C11—21no—
460C2×C11—21no—
461C2×C11—22no—
462C2×C11—22no—
463C2×C11—44no—
464C2×C11—82no—
465C2×C11C2×#38611yescharacteristic
466C2×C11#301812yes—
467C24—21no—
468C24—21no—
469C24D4×D1111yescharacteristic
470#41—24no—
471#41—24no—
472#41—24no—
473#41—24no—
474#41—24no—
475#41—22no—
476#41—22no—
477#41—24no—
478#41—24no—
479#41—24no—
480#41—24no—
481#41—42no—
482#41—42no—
483#41—42no—
484#41—42no—
485#41C22⋊Dic1118yescomplemented
486#41C22×Dic1114yes—
487#41C2×C22⋊D1114yes—
488C2×Q8—22no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C22⋊Dic1114yescomplemented
496C2×Q8C22×Dic1112yes—
497C2×Q8C2×C22⋊D1112yes—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—24no—
501C2×D4—22no—
502C2×D4—24no—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—42no—
513C2×D4C22⋊Dic1114yescomplemented
514C2×D4C22×Dic1112yes—
515C2×D4C2×C22⋊D1112yes—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—42no—
526C22×C4—114no—
527C22×C4—222no—
528C22×C4—228no—
529C22×C4—222no—
530C22×C4—444no—
531C22×C4—442no—
532C22×C4D4×D1111yescharacteristic
533C22×C4D4×D1111yescharacteristic
534C22×C4D4×D1111yescharacteristic
535C22×C4#434112yes—
536C22×C4#434112yes—
537C22×C4C22×Dic1112yes—
538C22×C4C2×C22⋊D1111yescharacteristic
539C22×C4C2×C22⋊D1111yescharacteristic
540C22×C4C2×C22⋊D1112yes—
541C22×C4C23×D1111yescharacteristic
542Q16—28no—
543SD16—28no—
544SD16—28no—
545D8—28no—
546M16—24no—
547M16—22no—
548M16—222no—
549M16—222no—
550M16—442no—
551M16C22×Dic1114yes—
552C2×C8—24no—
553C2×C8—22no—
554C2×C8—222no—
555C2×C8—442no—
556C4⋊C4—114no—
557C4⋊C4—228no—
558C4⋊C4—222no—
559C4⋊C4—222no—
560C4⋊C4—222no—
561C22⋊C4—228no—
562C22⋊C4—222no—
563C22⋊C4—222no—
564C22⋊C4—222no—
565C22⋊C4—222no—
566C22⋊C4—448no—
567C42—228no—
568C42—222no—
569C42—222no—
570C42—222no—
571C42—222no—
572C42—222no—
573C42—222no—
574C42—442no—
575C11#2094211yescharacteristic, complemented, Sylow
576C23—22no—
577C23—24no—
578C23—22no—
579C23—42no—
580C23—44no—
581C23—41no—
582C23—41no—
583C23—82no—
584C23D4×Dic1112yes—
585C23#6699011yescharacteristic
586C23#6699011yescharacteristic
587C23#6699212yes—
588C23C2×D4×D1111yescharacteristic
589Q8—22no—
590Q8—24no—
591Q8—22no—
592Q8—22no—
593Q8—41no—
594Q8—41no—
595Q8C2×C22⋊Dic1114yes—
596D4—24no—
597D4—24no—
598D4—28no—
599D4—22no—
600D4—22no—
601D4—24no—
602D4—22no—
603D4—44no—
604D4—44no—
605D4—41no—
606D4—41no—
607D4C2×C22⋊Dic1114yes—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—28no—
613C2×C4—22no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—442no—
622C2×C4—448no—
623C2×C4—442no—
624C2×C4—444no—
625C2×C4—882no—
626C2×C4—888no—
627C2×C4D4×Dic1112yes—
628C2×C4D4×Dic1112yes—
629C2×C4D4×Dic1112yes—
630C2×C4#6698812yes—
631C2×C4#6698812yes—
632C2×C4#6699011yescharacteristic
633C2×C4#6699011yescharacteristic
634C2×C4#6699212yes—
635C2×C4#6699212yes—
636C2×C4#6699212yes—
637C2×C4C2×C22⋊Dic1112yes—
638C2×C4C2×C22⋊Dic1112yes—
639C2×C4C2×D4×D1111yescharacteristic
640C2×C4C2×#434111yescharacteristic
641C2×C4C2×#434111yescharacteristic
642C2×C4C23×Dic1111yescharacteristic
643C2×C4C22×C22⋊D1111yescharacteristic
644C2×C4C22×C22⋊D1111yescharacteristic
645C8—24no—
646C8—442no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—24no—
651C22—42no—
652C22—42no—
653C22—44no—
654C22—44no—
655C22—42no—
656C22—84no—
657C22—82no—
658C22—82no—
659C22#1062283312yes—
660C22#1062283312yes—
661C22C2×D4×Dic1111yescharacteristic
662C22C2×#6699011yescharacteristic
663C22C2×#6699211yescharacteristic
664C4—24no—
665C4—42no—
666C4—444no—
667C4—444no—
668C4—444no—
669C4#1062283312yes—
670C4#1062283312yes—
671C4C2×D4×Dic1111yescharacteristic
672C4C2×#6698811yescharacteristic
673C4C2×#6699211yescharacteristic
674C4C22×C22⋊Dic1111yescharacteristic
675C2—21no—
676C2—21no—
677C2—22no—
678C2—22no—
679C2—44no—
680C2—82no—
681C2C2×#1062283311yescharacteristic
682C2#1307796212yes—
subgroupG/H
centerC2×C4#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#575C2
socleC22×C11C2×#120
cosocleC22×C4×C11C24
hypercenterC2×#575D11
hypocenterC11#20942
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. #13081819C2semidirect
2. C22×#66901C2semidirect
3. #13077135C2semidirect
4. #13071107C2semidirect
5. #13068994C2semidirect
6. #13068987C2semidirect
7. #13068354C2semidirect
8. C2×#10622193C2semidirect
13. C11×#575C4semidirect
36. #10622843C22semidirect
37. #10622838C22semidirect
38. #10622834C22semidirect
40. #10622828C22semidirect
42. #10622193C22semidirect
43. #10622192C22semidirect
56. C2×C11×#41C2×C4semidirect
72. C11×#137C2×C4semidirect
75. C11×AGL(1,ℤ/8)C2×C4semidirect
83. C2×C11×M16C2×C4semidirect
145. C11×#41C22⋊C4semidirect
155. C2×Q8×C11C22⋊C4semidirect
173. C2×D4×C11C22⋊C4semidirect
318. #575Dic11semidirect
389. C2×#41C2×Dic11semidirect
405. #137C2×Dic11semidirect
408. AGL(1,ℤ/8)C2×Dic11semidirect
420. C2×M16C2×Dic11semidirect
485. #41C22⋊Dic11semidirect
495. C2×Q8C22⋊Dic11semidirect
513. C2×D4C22⋊Dic11semidirect
575. C11#20942semidirect

Maximal subgroups

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

subgroupindex
#130818192
C22×#669012
#130771352
#130711072
#130689942
#130689872
#130683542
C2×#106221932
C2×C11×#5752
#2094211