Finite Group Databasebeta

← #14743129

Subgroups — #14743129

Order 2816.

808 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081247C211yesmaximal, characteristic, complemented
2SD16×D44C211yesmaximal, characteristic, complemented
3D4×#4323C211yesmaximal, characteristic, complemented
4#13068283C211yesmaximal, characteristic, complemented
5#13068081C211yesmaximal, characteristic, complemented
6#13068051C211yesmaximal, characteristic, complemented
7#13067974C211yesmaximal, characteristic, complemented
8#13067968C211yesmaximal, characteristic, complemented
9#13067795C211yesmaximal, characteristic, complemented
10#13067717C211yesmaximal, characteristic, complemented
11#13067681C211yesmaximal, characteristic, complemented
12#13067669C211yesmaximal, characteristic, complemented
13#13067443C211yesmaximal, characteristic, complemented
14SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C11×#3274C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)—21no—
17C11×#550C2211yescharacteristic, complemented
18D42×C11C2211yescharacteristic
19C22×#4323—21no—
20C2×SD16×D11—21no—
21Q8×D44C2211yescharacteristic, complemented
22D4×D44C2211yescharacteristic
23C11×#493C2211yescharacteristic, complemented
24C11×#469—21no—
25C11×#460C2211yescharacteristic, complemented
26C11×#459C2211yescharacteristic
27C11×#449—21no—
28C11×#447—21no—
29C4×C11×SD16C2211yescharacteristic
30C11×#436C2211yescharacteristic, complemented
31#10622830—21no—
32#10622686C2211yescharacteristic
33#10622686C2211yescharacteristic, complemented
34#10622685—21no—
35#10622685C2211yescharacteristic
36#10622685C2211yescharacteristic, complemented
37#10622683—21no—
38#10622683C2211yescharacteristic, complemented
39#10622683C2211yescharacteristic, complemented
40#10622651—21no—
41#10622649—21no—
42#10622640C2211yescharacteristic, complemented
43Q8×C11⋊C8C2211yescharacteristic, complemented
44#10622632C2211yescharacteristic
45#10622628C2211yescharacteristic
46C4×#4323—21no—
47C4×#4323C2211yescharacteristic
48D4×C11⋊C8C2211yescharacteristic
49#10622620—21no—
50#10622620C2211yescharacteristic, complemented
51#10622477—21no—
52#10622419—21no—
53#10622389—21no—
54#10622306C2211yescharacteristic, complemented
55C8×D44C2211yescharacteristic, complemented
56#10622182C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622121C2211yescharacteristic, complemented
63#10622120C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622093C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×Q8×D11—21no—
71C2×D4×D11—21no—
72C22×D44—21no—
73C11×AGL(1,ℤ/8)—44no—
74C2×C11×SD16—21no—
75C2×C11×SD16D411yescharacteristic
76C2×C11×D8—21no—
77C2×C11×D8—21no—
78C2×C11×D8—21no—
79C2×C11×M16—21no—
80C11×#127—21no—
81C11×#127C2311yescharacteristic
82C11×#127C2311yescharacteristic
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—41no—
87C11×#120—41no—
88C4×Q8×C11C2311yescharacteristic
89C4×D4×C11—21no—
90C4×D4×C11C2311yescharacteristic
91C4×D4×C11C2311yescharacteristic
92C2×#4325—21no—
93C2×#4324—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4323—21no—
97C2×#4323—21no—
98C2×#4323—21no—
99C2×#4323—41no—
100C2×#4323—44no—
101C2×#4323D411yescharacteristic
102#66983—21no—
103C22×C11⋊C8—21no—
104SD16×D11—44no—
105C2×#4314—21no—
106C2×#4314—21no—
107C2×C8×D11—21no—
108#66950—21no—
109#66950—41no—
110#66948—21no—
111#66935—41no—
112#66927C2311yescharacteristic
113C4×D44—21no—
114C4×D44C2311yescharacteristic
115#66922—21no—
116#66922C2311yescharacteristic
117C11×#106D411yescharacteristic
118C11×C4⋊C8C2311yescharacteristic
119C11×#103D411yescharacteristic
120C11×#102—21no—
121C11×#102—21no—
122C11×#102D411yescharacteristic
123C11×C22⋊C8—21no—
124C4×C8×C11C2311yescharacteristic
125#66896—21no—
126#66896—21no—
127#66896—21no—
128#66896—21no—
129#66896—21no—
130#66896—41no—
131#66896D411yescharacteristic
132C22⋊(C11⋊C8)—21no—
133(C2×D11)⋊C8—21no—
134#66874—21no—
135#66873—21no—
136#66873—21no—
137#66873D411yescharacteristic
138#66871—21no—
139#66871D411yescharacteristic
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8—21no—
145C4×C11⋊C8C2311yescharacteristic
146C4×C11⋊C8C2311yescharacteristic
147#19756—111nomaximal, Sylow
148C24×C11—41no—
149C23×D11—41no—
150C11×#41—42no—
151C11×#41—81no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—81no—
166C2×D4×C11—81no—
167C2×D4×C11C2×D411yescharacteristic
168C2×D4×C11C2×D411yescharacteristic
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—41no—
172C2×C22⋊D11—41no—
173Q8×D11—42no—
174Q8×D11—81no—
175D4×D11—42no—
176D4×D11—81no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—41no—
181C2×D44—42no—
182C2×D44—81no—
183C2×D44C2×D411yescharacteristic
184C2×C4×D11—21no—
185C2×C4×D11—41no—
186C2×Dic22—21no—
187C2×Dic22—41no—
188C11×SD16—42no—
189C11×SD16D814yescomplemented
190C11×D8—42no—
191C11×D8—42no—
192C11×D8—81no—
193C11×M16—42no—
194C2×C8×C11—21no—
195C2×C8×C11C2×D411yescharacteristic
196C2×C8×C11C2×D411yescharacteristic
197C11×C4⋊C4—21no—
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C22⋊C4—21no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C42×C11—21no—
206C42×C11C2411yescharacteristic
207#4325—42no—
208#4324—42no—
209#4323—22no—
210#4323—42no—
211#4323—42no—
212#4323—42no—
213#4323—42no—
214#4323—81no—
215#4323—82no—
216(C2×D11)⋊C4—21no—
217(C2×D11)⋊C4—41no—
218(C2×D11)⋊C4—41no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—41no—
222C4⋊Dic11C2×D411yescharacteristic
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—42no—
228C2×C11⋊C8C2×D411yescharacteristic
229C2×C11⋊C8C2×D411yescharacteristic
230#4314—42no—
231#4314—81no—
232C8×D11—42no—
233#3358—111no—
234D4×SD16—111no—
235D4×D8—111no—
236#3274D1111yescharacteristic, complemented
237#1721—111no—
238#1685—111no—
239#1681—111no—
240#1668—111no—
241#1667—111no—
242#1639—111no—
243#1627—111no—
244#1621—111no—
245#1619—111no—
246#1581—111no—
247SD16⋊C8—111no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—82no—
253C23×C11—82no—
254C23×C11—161no—
255C22×D11—21no—
256C22×D11—41no—
257C22×D11—82no—
258C22×D11—82no—
259C22×D11—161no—
260Q8×C11—21no—
261Q8×C11C2×D812yescomplemented
262D4×C11—21no—
263D4×C11—21no—
264D4×C11—21no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—82no—
274D4×C11—81no—
275D4×C11—81no—
276D4×C11—82no—
277D4×C11—82no—
278D4×C11—161no—
279D4×C11C2×D812yes—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—82no—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C22⋊D11—82no—
293C2×Dic11—21no—
294C2×Dic11—41no—
295D44—21no—
296D44—41no—
297D44—41no—
298D44—41no—
299D44—41no—
300D44—81no—
301D44—82no—
302D44AGL(1,ℤ/8)12yescomplemented
303C4×D11—41no—
304C4×D11—41no—
305C4×D11—82no—
306Dic22—41no—
307Dic22—41no—
308Dic22—82no—
309C8×C11—21no—
310C8×C11—41no—
311C8×C11C2×D812yescomplemented
312C11⋊C8—21no—
313C11⋊C8—21no—
314C11⋊C8—41no—
315C11⋊C8—41no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C2×AGL(1,ℤ/8)—21no—
319C22×SD16—221no—
320C22×D8—221no—
321#550C2×D1111yescharacteristic, complemented
322D4×Q8—111no—
323D42—111no—
324D42C2×D1111yescharacteristic
325#493—111no—
326#493—111no—
327#493C2×D1111yescharacteristic, complemented
328#492—111no—
329#486—111no—
330#486—111no—
331#486—221no—
332#474—111no—
333#474—221no—
334#469—21no—
335#466—221no—
336#465—221no—
337#461—111no—
338#460—111no—
339#460C2×D1111yescharacteristic, complemented
340#459—111no—
341#459—111no—
342#459—111no—
343#459—221no—
344#459C2×D1111yescharacteristic
345#450—221no—
346#449—21no—
347#448—221no—
348#447—21no—
349#447—221no—
350#447—221no—
351C8×Q8—111no—
352C4×SD16C2×D1111yescharacteristic
353C4×D8—111no—
354C4×D8—221no—
355#436C2×D1111yescharacteristic, complemented
356C8×D4—111no—
357C8×D4—111no—
358#335—111no—
359#335—111no—
360#332—111no—
361#331—111no—
362#331—111no—
363#331—111no—
364Q8⋊C8—111no—
365D4⋊C8—111no—
366D4⋊C8—111no—
367D4⋊C8—111no—
368#322—111no—
369C22×C11—22no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—164no—
382C22×C11D4211yescharacteristic
383C2×D11—22no—
384C2×D11—41no—
385C2×D11—41no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11—81no—
389C2×D11—164no—
390C4×C11—22no—
391C4×C11—21no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11C22×D811yescharacteristic
396C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
397C4×C11#57611yescharacteristic
398C4×C11#57711yescharacteristic
399Dic11—41no—
400Dic11—81no—
401C2×#41—21no—
402C22×Q8—221no—
403C22×D4—21no—
404C22×D4—21no—
405C22×D4—221no—
406C22×D4—221no—
407AGL(1,ℤ/8)—44no—
408C2×SD16—21no—
409C2×SD16—221no—
410C2×SD16—221no—
411C2×SD16—221no—
412C2×SD16—221no—
413C2×SD16—444no—
414C2×SD16C22⋊D1111yescharacteristic
415C2×D8—21no—
416C2×D8—21no—
417C2×D8—21no—
418C2×D8—111no—
419C2×D8—221no—
420C2×D8—221no—
421C2×D8—221no—
422C2×D8—221no—
423C2×D8—221no—
424C2×D8—441no—
425C2×D8—444no—
426C2×M16—21no—
427C22×C8—221no—
428C22×C8—221no—
429C4⋊Q8—111no—
430C4⋊Q8—221no—
431#127—21no—
432#127—111no—
433#127C22×D1111yescharacteristic
434#127C22×D1111yescharacteristic
435C22⋊Q8—221no—
436C22⋊Q8—441no—
437#121—21no—
438#121—21no—
439#121—21no—
440#121—41no—
441#121—221no—
442#121—221no—
443#120—41no—
444#120—441no—
445C4×Q8C22×D1111yescharacteristic
446C4×D4—21no—
447C4×D4—111no—
448C4×D4—221no—
449C4×D4C22×D1111yescharacteristic
450C4×D4C22×D1111yescharacteristic
451#107—111no—
452#107—221no—
453#106C22⋊D1111yescharacteristic
454C4⋊C8—111no—
455C4⋊C8—111no—
456C4⋊C8—111no—
457C4⋊C8—221no—
458C4⋊C8C22×D1111yescharacteristic
459#103—221no—
460#103C22⋊D1111yescharacteristic
461#102—21no—
462#102—21no—
463#102—111no—
464#102—111no—
465#102—221no—
466#102—221no—
467#102—221no—
468#102—221no—
469#102—221no—
470#102—221no—
471#102—221no—
472#102—441no—
473#102C22⋊D1111yescharacteristic
474C22⋊C8—21no—
475C22⋊C8—221no—
476C22⋊C8—221no—
477C4×C8—111no—
478C4×C8—111no—
479C4×C8—221no—
480C4×C8C22×D1111yescharacteristic
481C2×C11—42no—
482C2×C11—81no—
483C2×C11—161no—
484C2×C11—161no—
485C2×C11#326511yescharacteristic
486C2×C11D4×D811yescharacteristic
487C2×C11#328811yescharacteristic
488D11—42no—
489D11—161no—
490C24—41no—
491C24—441no—
492#41—42no—
493#41—81no—
494C2×Q8—221no—
495C2×Q8—441no—
496C2×Q8—442no—
497C2×Q8—881no—
498C2×Q8C2×C22⋊D1111yescharacteristic
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—81no—
512C2×D4—81no—
513C2×D4—111no—
514C2×D4—221no—
515C2×D4—221no—
516C2×D4—221no—
517C2×D4—441no—
518C2×D4—442no—
519C2×D4—441no—
520C2×D4—442no—
521C2×D4—881no—
522C2×D4—881no—
523C2×D4D4×D1111yescharacteristic
524C2×D4C2×C22⋊D1111yescharacteristic
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—41no—
528C22×C4—221no—
529C22×C4—441no—
530SD16—42no—
531SD16—442no—
532SD16—442no—
533SD16—442no—
534SD16—881no—
535SD16#432314yescomplemented
536D8—42no—
537D8—42no—
538D8—81no—
539D8—222no—
540D8—442no—
541D8—442no—
542D8—442no—
543D8—442no—
544D8—881no—
545D8—882no—
546M16—42no—
547C2×C8—21no—
548C2×C8—111no—
549C2×C8—111no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—442no—
555C2×C8—442no—
556C2×C8C2×C22⋊D1111yescharacteristic
557C2×C8C2×C22⋊D1111yescharacteristic
558C4⋊C4—21no—
559C4⋊C4—111no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—441no—
563C4⋊C4D4×D1111yescharacteristic
564C4⋊C4C2×C22⋊D1111yescharacteristic
565C4⋊C4C2×C22⋊D1111yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—221no—
571C22⋊C4—441no—
572C22⋊C4—441no—
573C42—21no—
574C42C23×D1111yescharacteristic
575C11#1975611yescharacteristic, complemented, Sylow
576C23—21no—
577C23—21no—
578C23—41no—
579C23—41no—
580C23—82no—
581C23—82no—
582C23—161no—
583C23—221no—
584C23—441no—
585C23—882no—
586C23—882no—
587C23—1761no—
588Q8—21no—
589Q8—441no—
590Q8—441no—
591Q8—882no—
592Q8C2×#432312yescomplemented
593D4—21no—
594D4—21no—
595D4—21no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—82no—
605D4—81no—
606D4—81no—
607D4—82no—
608D4—82no—
609D4—112no—
610D4—161no—
611D4—221no—
612D4—441no—
613D4—441no—
614D4—441no—
615D4—441no—
616D4—881no—
617D4—882no—
618D4—882no—
619D4C2×#432312yes—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—82no—
629C2×C4—221no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—882no—
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4C22×C22⋊D1111yescharacteristic
637C8—21no—
638C8—41no—
639C8—221no—
640C8—221no—
641C8—441no—
642C8—441no—
643C8—441no—
644C8—441no—
645C8C2×#432312yescomplemented
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—164no—
659C22—222no—
660C22—441no—
661C22—441no—
662C22—881no—
663C22—881no—
664C22—881no—
665C22—1764no—
666C22D4×C22⋊D1111yescharacteristic
667C4—21no—
668C4—22no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—441no—
673C4—881no—
674C4D11×AGL(1,ℤ/8)11yescharacteristic
675C4#1062330611yescharacteristic
676C4C22×#432311yescharacteristic
677C4#1062336611yescharacteristic
678C2—42no—
679C2—81no—
680C2—161no—
681C2—161no—
682C2—442no—
683C2—1761no—
684C2#1308010511yescharacteristic
685C2D4×#432311yescharacteristic
686C2#1308038011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3274C2
socleC22×C11D42
hypercenter#3274D11
hypocenterC11#19756
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3274

Complements

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

NH ≅ G/Ntype
1. #13081247C2semidirect
2. SD16×D44C2semidirect
3. D4×#4323C2semidirect
4. #13068283C2semidirect
5. #13068081C2semidirect
6. #13068051C2semidirect
7. #13067974C2semidirect
8. #13067968C2semidirect
9. #13067795C2semidirect
10. #13067717C2semidirect
11. #13067681C2semidirect
12. #13067669C2semidirect
13. #13067443C2semidirect
14. SD16⋊(C11⋊C8)C2semidirect
15. C11×#3274C2semidirect
17. C11×#550C22semidirect
21. Q8×D44C22semidirect
23. C11×#493C22semidirect
25. C11×#460C22semidirect
30. C11×#436C22semidirect
33. #10622686C22semidirect
36. #10622685C22semidirect
38. #10622683C22semidirect
39. #10622683C22semidirect
42. #10622640C22semidirect
43. Q8×C11⋊C8C22semidirect
50. #10622620C22semidirect
54. #10622306C22semidirect
55. C8×D44C22semidirect
56. #10622182C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622123C22semidirect
62. #10622121C22semidirect
63. #10622120C22semidirect
64. #10622117C22semidirect
65. #10622096C22semidirect
66. #10622093C22semidirect
189. C11×SD16D8semidirect
236. #3274D11semidirect
261. Q8×C11C2×D8semidirect
302. D44AGL(1,ℤ/8)semidirect
311. C8×C11C2×D8semidirect
321. #550C2×D11semidirect
327. #493C2×D11semidirect
339. #460C2×D11semidirect
355. #436C2×D11semidirect
535. SD16#4323semidirect
575. C11#19756semidirect
592. Q8C2×#4323semidirect
645. C8C2×#4323semidirect

Maximal subgroups

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

subgroupindex
#130812472
SD16×D442
D4×#43232
#130682832
#130680812
#130680512
#130679742
#130679682
#130677952
#130677172
#130676812
#130676692
#130674432
SD16⋊(C11⋊C8)2
C11×#32742
#1975611