Finite Group Databasebeta

← #25085953

Subgroups — #25085953

Order 11008.

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#19147226C211yesmaximal, characteristic, complemented
2SD16×D172C211yesmaximal, characteristic, complemented
3D4×#10621882C211yesmaximal, characteristic, complemented
4#19134262C211yesmaximal, characteristic, complemented
5#19134060C211yesmaximal, characteristic, complemented
6#19134030C211yesmaximal, characteristic, complemented
7#19133953C211yesmaximal, characteristic, complemented
8#19133947C211yesmaximal, characteristic, complemented
9#19133774C211yesmaximal, characteristic, complemented
10#19133696C211yesmaximal, characteristic, complemented
11#19133660C211yesmaximal, characteristic, complemented
12#19133648C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3274C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C22×#10621882—21no—
18Q8×D172C2211yescharacteristic, complemented
19D4×D172C2211yescharacteristic
20#14583275C2211yescharacteristic
21#14583275C2211yescharacteristic, complemented
22#14583272C2211yescharacteristic, complemented
23#14583245—21no—
24#14583245C2211yescharacteristic, complemented
25#14583245C2211yescharacteristic, complemented
26#14583179—21no—
27#14583179C2211yescharacteristic, complemented
28#14583133—21no—
29#14583129—21no—
30#14583104C2211yescharacteristic
31#14583099C2211yescharacteristic, complemented
32#14583094C2211yescharacteristic
33#14583091—21no—
34#14583091C2211yescharacteristic
35#14583091C2211yescharacteristic, complemented
36#14583051—21no—
37#14583039—21no—
38#14583033—21no—
39#14583032—21no—
40Q8×C43⋊C8C2211yescharacteristic, complemented
41C4×#10621882—21no—
42C4×#10621882C2211yescharacteristic
43C8×D172C2211yescharacteristic, complemented
44D4×C43⋊C8C2211yescharacteristic
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582643C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#550C2211yescharacteristic, complemented
58D42×C43C2211yescharacteristic
59C43×#493C2211yescharacteristic, complemented
60C43×#469—21no—
61C43×#460C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C43×#447—21no—
65C4×SD16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74SD16×D43—44no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77C2×#10621882—21no—
78C2×#10621882—21no—
79C2×#10621882—21no—
80C2×#10621882—41no—
81C2×#10621882—44no—
82C2×#10621882D411yescharacteristic
83C22×C43⋊C8—21no—
84C2×C8×D43—21no—
85#13063325—21no—
86#13063325C2311yescharacteristic
87#13063322C2311yescharacteristic
88#13063305—21no—
89#13063305—41no—
90#13063300—21no—
91#13063299—21no—
92#13063295—41no—
93C4×D172—21no—
94C4×D172C2311yescharacteristic
95#13063258—21no—
96#13063258D411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063248—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245—21no—
111#13063245D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114C4×C43⋊C8—21no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C2×#41×C43—21no—
118C22×D4×C43—21no—
119C22×D4×C43—21no—
120AGL(1,ℤ/8)×C43—44no—
121C2×SD16×C43—21no—
122C2×SD16×C43D411yescharacteristic
123C2×D8×C43—21no—
124C2×D8×C43—21no—
125C2×D8×C43—21no—
126C2×M16×C43—21no—
127#127×C43—21no—
128#127×C43C2311yescharacteristic
129#127×C43C2311yescharacteristic
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#121×C43—41no—
134#120×C43—41no—
135C4×Q8×C43C2311yescharacteristic
136C4×D4×C43—21no—
137C4×D4×C43C2311yescharacteristic
138C4×D4×C43C2311yescharacteristic
139#106×C43D411yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43D411yescharacteristic
142#102×C43—21no—
143#102×C43—21no—
144#102×C43D411yescharacteristic
145C22⋊C8×C43—21no—
146C4×C8×C43C2311yescharacteristic
147C24×C43—41no—
148C23×D43—41no—
149#41×C43—42no—
150#41×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43C2×D411yescharacteristic
167C2×D4×C43C2×D411yescharacteristic
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—41no—
171C2×C22⋊D43—41no—
172Q8×D43—42no—
173Q8×D43—81no—
174D4×D43—42no—
175D4×D43—81no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—41no—
180C2×D172—42no—
181C2×D172—81no—
182C2×D172C2×D411yescharacteristic
183C2×C4×D43—21no—
184C2×C4×D43—41no—
185C2×Dic86—21no—
186C2×Dic86—41no—
187SD16×C43—42no—
188SD16×C43D814yescomplemented
189D8×C43—42no—
190D8×C43—42no—
191D8×C43—81no—
192M16×C43—42no—
193C2×C8×C43—21no—
194C2×C8×C43C2×D411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C4⋊C4×C43—21no—
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C42×C43—21no—
205C42×C43C2411yescharacteristic
206#10621884—42no—
207#10621883—42no—
208#10621882—22no—
209#10621882—42no—
210#10621882—42no—
211#10621882—42no—
212#10621882—42no—
213#10621882—81no—
214#10621882—82no—
215(C2×D43)⋊C4—21no—
216(C2×D43)⋊C4—41no—
217(C2×D43)⋊C4—41no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—41no—
221C4⋊Dic43C2×D411yescharacteristic
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—42no—
227C2×C43⋊C8C2×D411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229#10621873—42no—
230#10621873—81no—
231C8×D43—42no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—82no—
237C23×C43—82no—
238C23×C43—161no—
239C22×D43—21no—
240C22×D43—41no—
241C22×D43—82no—
242C22×D43—82no—
243C22×D43—161no—
244Q8×C43—21no—
245Q8×C43C2×D812yescomplemented
246D4×C43—21no—
247D4×C43—21no—
248D4×C43—21no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—41no—
252D4×C43—41no—
253D4×C43—41no—
254D4×C43—41no—
255D4×C43—41no—
256D4×C43—41no—
257D4×C43—82no—
258D4×C43—81no—
259D4×C43—81no—
260D4×C43—82no—
261D4×C43—82no—
262D4×C43—161no—
263D4×C43C2×D812yes—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—82no—
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43H(5,𝔽2)11yescharacteristic
276C22⋊D43—82no—
277C2×Dic43—21no—
278C2×Dic43—41no—
279D172—21no—
280D172—41no—
281D172—41no—
282D172—41no—
283D172—41no—
284D172—81no—
285D172—82no—
286D172AGL(1,ℤ/8)12yescomplemented
287C4×D43—41no—
288C4×D43—41no—
289C4×D43—82no—
290Dic86—41no—
291Dic86—41no—
292Dic86—82no—
293C8×C43—21no—
294C8×C43—41no—
295C8×C43C2×D812yescomplemented
296C43⋊C8—21no—
297C43⋊C8—21no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300C43⋊C8—41no—
301C43⋊C8—41no—
302#19756—431nomaximal, Sylow
303C22×C43—22no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43—164no—
316C22×C43D4211yescharacteristic
317C2×D43—22no—
318C2×D43—41no—
319C2×D43—41no—
320C2×D43—81no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—164no—
324C4×C43—22no—
325C4×C43—21no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43C22×D811yescharacteristic
330C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
331C4×C43#57611yescharacteristic
332C4×C43#57711yescharacteristic
333Dic43—41no—
334Dic43—81no—
335#3358—431no—
336D4×SD16—431no—
337D4×D8—431no—
338#3274D4311yescharacteristic, complemented
339#1721—431no—
340#1685—431no—
341#1681—431no—
342#1668—431no—
343#1667—431no—
344#1639—431no—
345#1627—431no—
346#1621—431no—
347#1619—431no—
348#1581—431no—
349SD16⋊C8—431no—
350C2×C43—42no—
351C2×C43—81no—
352C2×C43—161no—
353C2×C43—161no—
354C2×C43#326511yescharacteristic
355C2×C43D4×D811yescharacteristic
356C2×C43#328811yescharacteristic
357D43—42no—
358D43—161no—
359C2×AGL(1,ℤ/8)—21no—
360C22×SD16—861no—
361C22×D8—861no—
362#550C2×D4311yescharacteristic, complemented
363D4×Q8—431no—
364D42—431no—
365D42C2×D4311yescharacteristic
366#493—431no—
367#493—431no—
368#493C2×D4311yescharacteristic, complemented
369#492—431no—
370#486—431no—
371#486—431no—
372#486—861no—
373#474—431no—
374#474—861no—
375#469—21no—
376#466—861no—
377#465—861no—
378#461—431no—
379#460—431no—
380#460C2×D4311yescharacteristic, complemented
381#459—431no—
382#459—431no—
383#459—431no—
384#459—861no—
385#459C2×D4311yescharacteristic
386#450—861no—
387#449—21no—
388#448—861no—
389#447—21no—
390#447—861no—
391#447—861no—
392C8×Q8—431no—
393C4×SD16C2×D4311yescharacteristic
394C4×D8—431no—
395C4×D8—861no—
396#436C2×D4311yescharacteristic, complemented
397C8×D4—431no—
398C8×D4—431no—
399#335—431no—
400#335—431no—
401#332—431no—
402#331—431no—
403#331—431no—
404#331—431no—
405Q8⋊C8—431no—
406D4⋊C8—431no—
407D4⋊C8—431no—
408D4⋊C8—431no—
409#322—431no—
410C43#1975611yescharacteristic, complemented, Sylow
411C2×#41—21no—
412C22×Q8—861no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—861no—
416C22×D4—861no—
417AGL(1,ℤ/8)—44no—
418C2×SD16—21no—
419C2×SD16—861no—
420C2×SD16—861no—
421C2×SD16—861no—
422C2×SD16—861no—
423C2×SD16—1724no—
424C2×SD16C22⋊D4311yescharacteristic
425C2×D8—21no—
426C2×D8—21no—
427C2×D8—21no—
428C2×D8—431no—
429C2×D8—861no—
430C2×D8—861no—
431C2×D8—861no—
432C2×D8—861no—
433C2×D8—861no—
434C2×D8—1721no—
435C2×D8—1724no—
436C2×M16—21no—
437C22×C8—861no—
438C22×C8—861no—
439C4⋊Q8—431no—
440C4⋊Q8—861no—
441#127—21no—
442#127—431no—
443#127C22×D4311yescharacteristic
444#127C22×D4311yescharacteristic
445C22⋊Q8—861no—
446C22⋊Q8—1721no—
447#121—21no—
448#121—21no—
449#121—21no—
450#121—41no—
451#121—861no—
452#121—861no—
453#120—41no—
454#120—1721no—
455C4×Q8C22×D4311yescharacteristic
456C4×D4—21no—
457C4×D4—431no—
458C4×D4—861no—
459C4×D4C22×D4311yescharacteristic
460C4×D4C22×D4311yescharacteristic
461#107—431no—
462#107—861no—
463#106C22⋊D4311yescharacteristic
464C4⋊C8—431no—
465C4⋊C8—431no—
466C4⋊C8—431no—
467C4⋊C8—861no—
468C4⋊C8C22×D4311yescharacteristic
469#103—861no—
470#103C22⋊D4311yescharacteristic
471#102—21no—
472#102—21no—
473#102—431no—
474#102—431no—
475#102—861no—
476#102—861no—
477#102—861no—
478#102—861no—
479#102—861no—
480#102—861no—
481#102—861no—
482#102—1721no—
483#102C22⋊D4311yescharacteristic
484C22⋊C8—21no—
485C22⋊C8—861no—
486C22⋊C8—861no—
487C4×C8—431no—
488C4×C8—431no—
489C4×C8—861no—
490C4×C8C22×D4311yescharacteristic
491C24—41no—
492C24—1721no—
493#41—42no—
494#41—81no—
495C2×Q8—861no—
496C2×Q8—3441no—
497C2×Q8—1721no—
498C2×Q8—1722no—
499C2×Q8C2×C22⋊D4311yescharacteristic
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—431no—
515C2×D4—861no—
516C2×D4—861no—
517C2×D4—861no—
518C2×D4—3441no—
519C2×D4—3441no—
520C2×D4—1721no—
521C2×D4—1722no—
522C2×D4—1721no—
523C2×D4—1722no—
524C2×D4D4×D4311yescharacteristic
525C2×D4C2×C22⋊D4311yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—41no—
529C22×C4—861no—
530C22×C4—1721no—
531SD16—42no—
532SD16—3441no—
533SD16—1722no—
534SD16—1722no—
535SD16—1722no—
536SD16#1062188214yescomplemented
537D8—42no—
538D8—42no—
539D8—81no—
540D8—862no—
541D8—3441no—
542D8—3442no—
543D8—1722no—
544D8—1722no—
545D8—1722no—
546D8—1722no—
547M16—42no—
548C2×C8—21no—
549C2×C8—431no—
550C2×C8—431no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—1722no—
556C2×C8—1722no—
557C2×C8C2×C22⋊D4311yescharacteristic
558C2×C8C2×C22⋊D4311yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—431no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—1721no—
564C4⋊C4D4×D4311yescharacteristic
565C4⋊C4C2×C22⋊D4311yescharacteristic
566C4⋊C4C2×C22⋊D4311yescharacteristic
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—861no—
572C22⋊C4—1721no—
573C22⋊C4—1721no—
574C42—21no—
575C42C23×D4311yescharacteristic
576C23—21no—
577C23—21no—
578C23—41no—
579C23—41no—
580C23—82no—
581C23—82no—
582C23—161no—
583C23—861no—
584C23—3442no—
585C23—3442no—
586C23—1721no—
587C23—6881no—
588Q8—21no—
589Q8—3442no—
590Q8—1721no—
591Q8—1721no—
592Q8C2×#1062188212yescomplemented
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—161no—
610D4—432no—
611D4—861no—
612D4—3441no—
613D4—3442no—
614D4—3442no—
615D4—1721no—
616D4—1721no—
617D4—1721no—
618D4—1721no—
619D4C2×#1062188212yes—
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—861no—
630C2×C4—3442no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4C2×D4×D4311yescharacteristic
635C2×C4C22×C22⋊D4311yescharacteristic
636C2×C4#1306337011yescharacteristic
637C8—21no—
638C8—41no—
639C8—861no—
640C8—861no—
641C8—1721no—
642C8—1721no—
643C8—1721no—
644C8—1721no—
645C8C2×#1062188212yescomplemented
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—862no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—1721no—
664C22—1721no—
665C22—6884no—
666C22D4×C22⋊D4311yescharacteristic
667C4—22no—
668C4—21no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—3441no—
673C4—1721no—
674C4C22×#1062188211yescharacteristic
675C4AGL(1,ℤ/8)×D4311yescharacteristic
676C4#1458370211yescharacteristic
677C4#1458370911yescharacteristic
678C2—42no—
679C2—81no—
680C2—161no—
681C2—161no—
682C2—1722no—
683C2—6881no—
684C2#1914608411yescharacteristic
685C2D4×#1062188211yescharacteristic
686C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3274C2
socleC22×C43D42
hypercenter#3274D43
hypocenterC43#19756
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3274

Complements

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

NH ≅ G/Ntype
1. #19147226C2semidirect
2. SD16×D172C2semidirect
3. D4×#10621882C2semidirect
4. #19134262C2semidirect
5. #19134060C2semidirect
6. #19134030C2semidirect
7. #19133953C2semidirect
8. #19133947C2semidirect
9. #19133774C2semidirect
10. #19133696C2semidirect
11. #19133660C2semidirect
12. #19133648C2semidirect
13. #19133422C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3274C2semidirect
18. Q8×D172C22semidirect
21. #14583275C22semidirect
22. #14583272C22semidirect
24. #14583245C22semidirect
25. #14583245C22semidirect
27. #14583179C22semidirect
31. #14583099C22semidirect
35. #14583091C22semidirect
40. Q8×C43⋊C8C22semidirect
43. C8×D172C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582646C22semidirect
48. #14582643C22semidirect
49. #14582643C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582620C22semidirect
57. C43×#550C22semidirect
59. C43×#493C22semidirect
61. C43×#460C22semidirect
66. C43×#436C22semidirect
188. SD16×C43D8semidirect
245. Q8×C43C2×D8semidirect
286. D172AGL(1,ℤ/8)semidirect
295. C8×C43C2×D8semidirect
338. #3274D43semidirect
362. #550C2×D43semidirect
368. #493C2×D43semidirect
380. #460C2×D43semidirect
396. #436C2×D43semidirect
410. C43#19756semidirect
536. SD16#10621882semidirect
592. Q8C2×#10621882semidirect
645. C8C2×#10621882semidirect

Maximal subgroups

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

subgroupindex
#191472262
SD16×D1722
D4×#106218822
#191342622
#191340602
#191340302
#191339532
#191339472
#191337742
#191336962
#191336602
#191336482
#191334222
SD16⋊(C43⋊C8)2
C43×#32742
#1975643