Finite Group Databasebeta

← #14781216

Subgroups — #14781216

Order 2816.

1164 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic, complemented
2C2×#10622619C211yesmaximal, characteristic
3C2×#10622619C211yesmaximal, characteristic
4C2×#10622619C211yesmaximal, characteristic
5#13069794C218yesmaximal, complemented
6#13068349C211yesmaximal, characteristic, complemented
7#13068348C211yesmaximal, characteristic, complemented
8C11×#1740C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16#10623050—22no—
17#10623050—22no—
18#10623048—22no—
19#10623048—22no—
20#10623031—22no—
21#10623014C2214yes—
22#10623001—22no—
23#10622619—22no—
24#10622619—22no—
25#10622619—22no—
26#10622619—22no—
27#10622619—22no—
28#10622619—22no—
29C2×#66870C2214yes—
30C2×#66870C2214yes—
31C2×#66870C2214yes—
32C11×#342C2214yes—
33#10622165C2214yes—
34#10622164C2214yes—
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11C2312yes—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339—21no—
48C2×#4339—21no—
49C22×D44Q811yescharacteristic, complemented
50C22×C4×D11Q812yescomplemented
51C22×Dic22Q811yescharacteristic, complemented
52C11×#117—21no—
53C11×#117—21no—
54C11×#117—21no—
55C11×#117—21no—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117—21no—
62C11×#117D412yes—
63C11×#117D412yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C22⋊C4C2312yes—
68C2×C11×C22⋊C4C2312yes—
69C2×C11×C22⋊C4C2312yes—
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C22⋊Dic11C2312yes—
74C2×C22⋊Dic11C2312yes—
75C2×C22⋊Dic11C2312yes—
76#66979—21no—
77#66979—21no—
78#66979—21no—
79#66979—21no—
80#66979—21no—
81#66979—21no—
82#66979—21no—
83#66979—21no—
84#66979D412yes—
85#66979D412yes—
86#66979D412yes—
87#66979D412yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91#66977—28no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95#66943—24no—
96#66943—24no—
97#66941—24no—
98#66941—24no—
99#66931—28no—
100#66931—28no—
101#66923—24no—
102#66922—24no—
103C4×Dic22—28no—
104#66870—28no—
105#66870—28no—
106#66870—28no—
107#23474—111nomaximal, Sylow
108C24×C11C2411yescharacteristic
109C23×D11C2×Q812yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×Q811yescharacteristic
120C22×C4×C11C2×Q811yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C2×C22⋊D11—22no—
128C2×C22⋊D11—22no—
129C2×C22⋊D11—22no—
130C2×C22⋊D11—22no—
131C2×C22⋊D11—22no—
132C2×C22⋊D11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11C2×Q812yes—
137#4339—41no—
138#4339—41no—
139#4339—41no—
140#4339—41no—
141#4339—41no—
142#4339—41no—
143#4339—41no—
144#4339—41no—
145#4339—41no—
146#4339—41no—
147#4339—41no—
148#4339—41no—
149#4339—41no—
150#4339—41no—
151#4339—41no—
152#4339—41no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×Dic22—28no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4C2×D414yes—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—41no—
187C42×C11—41no—
188C42×C11—41no—
189C42×C11—41no—
190C22⋊Dic11—22no—
191C22⋊Dic11—22no—
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194C22⋊Dic11C2×D414yes—
195C22⋊Dic11C2×D414yes—
196C4⋊Dic11—28no—
197C4⋊Dic11—22no—
198C4⋊Dic11—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—41no—
202C4⋊Dic11—41no—
203Dic11⋊C4—28no—
204Dic11⋊C4—28no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—41no—
210C4×Dic11—41no—
211#3458—111no—
212C2×#410—111no—
213C2×#410—111no—
214C2×#410—111no—
215#2032—118no—
216#1740—111no—
217#1740—111no—
218#1740D1111yescharacteristic, complemented
219C23×C11—81no—
220C23×C11C22×D411yescharacteristic
221C23×C11C22×D411yescharacteristic
222C23×C11C22×D411yescharacteristic
223C23×C11C22×Q811yescharacteristic
224C23×C11C2×#4111yescharacteristic
225C23×C11C2×#4111yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—82no—
231C2×C4×C11—24no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—82no—
235C2×C4×C11—82no—
236C2×C4×C11—82no—
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11C22⋊Q811yescharacteristic
242C2×C4×C11C22⋊Q811yescharacteristic
243C2×C4×C11C22⋊Q811yescharacteristic
244C2×C4×C11C22⋊Q811yescharacteristic
245C2×C4×C11C22⋊Q811yescharacteristic
246C2×C4×C11C22⋊Q811yescharacteristic
247C2×C4×C11C22⋊Q811yescharacteristic
248C2×C4×C11C22⋊Q811yescharacteristic
249C2×C4×C11C22⋊Q811yescharacteristic
250C2×C4×C11C22⋊Q811yescharacteristic
251C2×C4×C11C22⋊Q811yescharacteristic
252C2×C4×C11C22⋊Q811yescharacteristic
253C2×C4×C11#12411yescharacteristic
254C2×C4×C11#12411yescharacteristic
255C2×C4×C11#12411yescharacteristic
256C2×C4×C11#12411yescharacteristic
257C2×C4×C11#12411yescharacteristic
258C2×C4×C11#12411yescharacteristic
259C2×C4×C11#12411yescharacteristic
260C2×C4×C11#12411yescharacteristic
261C2×C4×C11#12411yescharacteristic
262C2×C4×C11#12411yescharacteristic
263C2×C4×C11#12411yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C22⋊D11—42no—
266C22⋊D11—42no—
267C22⋊D11—42no—
268C22⋊D11—42no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—42no—
275C2×Dic11—82no—
276C2×Dic11—82no—
277C2×Dic11—82no—
278D44—41no—
279D44—41no—
280D44—41no—
281D44—41no—
282C4×D11—42no—
283C4×D11—42no—
284C4×D11—42no—
285C4×D11—42no—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—88no—
291C22×#41—111no—
292#544—222no—
293#544—222no—
294#544—222no—
295#543—114no—
296#533—222no—
297#533—222no—
298#533—222no—
299C2×#117—111no—
300C2×#117—111no—
301C2×#117—111no—
302C2×#117C2×D1111yescharacteristic
303C2×#117C2×D1111yescharacteristic
304C2×#117C2×D1111yescharacteristic
305#410—222no—
306#410—222no—
307#410—222no—
308#410—222no—
309#410—222no—
310#410—222no—
311C2×#99—114no—
312C2×#99—114no—
313C2×#99—114no—
314#342—114no—
315#342—114no—
316#342C2×D1114yes—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×C22⋊Q811yescharacteristic
326C22×C11C2×C22⋊Q811yescharacteristic
327C22×C11C2×C22⋊Q811yescharacteristic
328C22×C11C2×#12411yescharacteristic
329C22×C11C2×#12411yescharacteristic
330C22×C11C2×#12411yescharacteristic
331C2×D11—42no—
332C2×D11—82no—
333C2×D11—82no—
334C2×D11—82no—
335C4×C11—44no—
336C4×C11—82no—
337C4×C11—82no—
338C4×C11#39311yescharacteristic
339C4×C11#39311yescharacteristic
340C4×C11#39311yescharacteristic
341C4×C11#39311yescharacteristic
342C4×C11#39311yescharacteristic
343C4×C11#39311yescharacteristic
344C4×C11#39311yescharacteristic
345C4×C11#39311yescharacteristic
346Dic11—44no—
347Dic11—44no—
348Dic11—42no—
349Dic11—82no—
350C2×#41—221no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—221no—
354C2×#41—221no—
355C2×#41—221no—
356C2×#41—221no—
357C2×#41—221no—
358C2×#41—221no—
359C2×#41—221no—
360C2×#41—221no—
361C2×#41—221no—
362C22×Q8—111no—
363C22×D4—112no—
364C22×D4—111no—
365C23×C4—112no—
366C23×C4C22×D1111yescharacteristic
367C4⋊Q8—224no—
368C4⋊Q8—224no—
369C4⋊Q8—224no—
370#125—224no—
371#125—224no—
372#125—224no—
373C22⋊Q8—228no—
374C22⋊Q8—228no—
375C22⋊Q8—228no—
376C4×Q8—228no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—112no—
388#117—112no—
389#117—112no—
390#117—112no—
391#117—221no—
392#117—221no—
393#117—221no—
394#117—221no—
395#117—221no—
396#117—221no—
397#117—221no—
398#117—221no—
399#117D4412yes—
400#117D4412yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C22⋊C4—112no—
408C2×C22⋊C4—112no—
409C2×C22⋊C4—112no—
410C2×C22⋊C4C22×D1112yes—
411C2×C22⋊C4C22×D1112yes—
412C2×C22⋊C4C22×D1112yes—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42—221no—
419#99—228no—
420#99—228no—
421#99—228no—
422C2×C11—21no—
423C2×C11—21no—
424C2×C11—21no—
425C2×C11—21no—
426C2×C11—21no—
427C2×C11—21no—
428C2×C11—21no—
429C2×C11C2×#39311yescharacteristic
430D11—82no—
431C24—112no—
432C24C23×D1111yescharacteristic
433#41—441no—
434#41—441no—
435#41—441no—
436#41—441no—
437#41—441no—
438#41—441no—
439#41—441no—
440#41—441no—
441#41—441no—
442#41—441no—
443#41—441no—
444#41—441no—
445#41—441no—
446#41—441no—
447#41—441no—
448#41—441no—
449C2×Q8—228no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—222no—
461C2×D4—222no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—112no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4C2×D4411yescharacteristic
482C22×C4C2×D4411yescharacteristic
483C22×C4#433911yescharacteristic
484C22×C4#433911yescharacteristic
485C22×C4#433911yescharacteristic
486C22×C4#433911yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4D4×D1111yescharacteristic
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491C22×C4#434111yescharacteristic
492C22×C4#434111yescharacteristic
493C22×C4Q8×D1111yescharacteristic
494C22×C4Q8×D1111yescharacteristic
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—228no—
502C4⋊C4—228no—
503C4⋊C4—228no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—441no—
509C4⋊C4—441no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—114no—
516C22⋊C4—114no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4C2×D4414yes—
522C42—22no—
523C42—22no—
524C42—41no—
525C42—41no—
526C42—41no—
527C42—41no—
528C42—222no—
529C42—222no—
530C42—222no—
531C42—222no—
532C42—441no—
533C42—441no—
534C11#2347411yescharacteristic, complemented, Sylow
535C23—81no—
536C23—222no—
537C23—222no—
538C23—222no—
539C23—882no—
540C23C22×D4411yescharacteristic
541C23C2×#433911yescharacteristic
542C23C2×#433911yescharacteristic
543C23C2×D4×D1111yescharacteristic
544C23C2×D4×D1111yescharacteristic
545C23C2×#434111yescharacteristic
546C23C2×Q8×D1111yescharacteristic
547Q8—441no—
548Q8—441no—
549Q8—441no—
550Q8—441no—
551Q8—888no—
552D4—442no—
553D4—442no—
554D4—442no—
555D4—442no—
556D4—441no—
557D4—441no—
558D4—441no—
559D4—441no—
560C2×C4—24no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—882no—
577C2×C4—882no—
578C2×C4—882no—
579C2×C4#6692811yescharacteristic
580C2×C4#6692811yescharacteristic
581C2×C4#6692811yescharacteristic
582C2×C4#6692811yescharacteristic
583C2×C4#6693511yescharacteristic
584C2×C4#6693511yescharacteristic
585C2×C4#6693511yescharacteristic
586C2×C4#6693511yescharacteristic
587C2×C4#6693811yescharacteristic
588C2×C4#6693811yescharacteristic
589C2×C4#6693811yescharacteristic
590C2×C4#6693811yescharacteristic
591C2×C4#6693811yescharacteristic
592C2×C4#6693811yescharacteristic
593C2×C4#6693811yescharacteristic
594C2×C4#6693811yescharacteristic
595C2×C4#6694911yescharacteristic
596C2×C4#6694911yescharacteristic
597C2×C4#6694911yescharacteristic
598C2×C4#6694911yescharacteristic
599C2×C4#6694911yescharacteristic
600C2×C4#6694911yescharacteristic
601C2×C4#6694911yescharacteristic
602C2×C4#6694911yescharacteristic
603C2×C4#6695011yescharacteristic
604C2×C4#6695011yescharacteristic
605C2×C4#6695011yescharacteristic
606C2×C4#6695011yescharacteristic
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—442no—
615C22—882no—
616C22—882no—
617C22—882no—
618C22C2×#6692811yescharacteristic
619C22C2×#6693511yescharacteristic
620C22C2×#6693811yescharacteristic
621C22C2×#6693811yescharacteristic
622C22C2×#6694911yescharacteristic
623C22C2×#6694911yescharacteristic
624C22C2×#6695011yescharacteristic
625C4—44no—
626C4—82no—
627C4—82no—
628C4—444no—
629C4—444no—
630C4—442no—
631C4—882no—
632C4#1062228611yescharacteristic
633C4#1062228611yescharacteristic
634C4#1062228611yescharacteristic
635C4#1062228611yescharacteristic
636C4#1062228611yescharacteristic
637C4#1062228611yescharacteristic
638C4#1062228611yescharacteristic
639C4#1062228611yescharacteristic
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—21no—
647C2—882no—
648C2C2×#1062228611yescharacteristic
subgroupG/H
centerC4#10622286
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#1740C2
socleC2×C11C2×#393
prime radicalC22×#4339C22
hypercenter#1740D11
hypocenterC11#23474
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
5. #13069794C2semidirect
6. #13068349C2semidirect
7. #13068348C2semidirect
8. C11×#1740C2semidirect
49. C22×D44Q8semidirect
50. C22×C4×D11Q8semidirect
51. C22×Dic22Q8semidirect
218. #1740D11semidirect
534. C11#23474semidirect

Maximal subgroups

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

subgroupindex
#130820212
C2×#106226192
#130697942
#130683492
#130683482
C11×#17402
#2347411