Finite Group Databasebeta

← #25253049

Subgroups — #25253049

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D16×D43C211yesmaximal, characteristic, complemented
2#19146274C211yesmaximal, characteristic, complemented
3D8×C22⋊D43C211yesmaximal, characteristic, complemented
4#19136860C211yesmaximal, characteristic, complemented
5#19136698C211yesmaximal, characteristic, complemented
6#19136688C211yesmaximal, characteristic, complemented
7#19136652C211yesmaximal, characteristic, complemented
8#19136628C211yesmaximal, characteristic, complemented
9#19136522C211yesmaximal, characteristic, complemented
10#19136518C211yesmaximal, characteristic, complemented
11#19136507C211yesmaximal, characteristic, complemented
12#19136505C211yesmaximal, characteristic, complemented
13#19136471C211yesmaximal, characteristic, complemented
14#19136418C211yesmaximal, characteristic, complemented
15C2×C43×#509C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic, complemented
18#14583537—21no—
19D4×C22⋊D43—21no—
20C2×#13063268C2211yescharacteristic, complemented
21C2×D688C2211yescharacteristic, complemented
22C2×#13063266C2211yescharacteristic
23C2×#13063266C2211yescharacteristic, complemented
24C2×#13063266C2211yescharacteristic, complemented
25D16×D43—24no—
26C2×C16×D43C2211yescharacteristic, complemented
27#14583284C2211yescharacteristic, complemented
28#14583274C2211yescharacteristic, complemented
29#14583137C2211yescharacteristic, complemented
30#14583135C2211yescharacteristic, complemented
31#14583135C2211yescharacteristic, complemented
32#14583132C2211yescharacteristic
33#14583116—21no—
34#14583092—21no—
35#14583048—21no—
36#14583044—21no—
37#14583033—21no—
38#14583031—21no—
39D8×Dic43C2211yescharacteristic, complemented
40D8×Dic43C2211yescharacteristic, complemented
41C8×C22⋊D43C2211yescharacteristic
42#14582727C2211yescharacteristic, complemented
43Dic43⋊C16C2211yescharacteristic, complemented
44#14582703C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic, complemented
47#14582700C2211yescharacteristic, complemented
48#14582700C2211yescharacteristic, complemented
49#14582700C2211yescharacteristic, complemented
50C22⋊(C43⋊C16)C2211yescharacteristic, complemented
51(C2×D43)⋊C16C2211yescharacteristic, complemented
52#14582674C2211yescharacteristic, complemented
53C2×#135×C43C2211yescharacteristic, complemented
54C22×D8×C43C2211yescharacteristic, complemented
55C43×#509—24no—
56C2×SD32×C43C2211yescharacteristic, complemented
57C2×SD32×C43C2211yescharacteristic, complemented
58C2×D16×C43C2211yescharacteristic
59C2×D16×C43C2211yescharacteristic, complemented
60C2×M32×C43C2211yescharacteristic, complemented
61C22×C22⋊D43—41no—
62C2×D4×D43—21no—
63C2×D4×D43—21no—
64C2×#10621884—21no—
65C2×D344C2311yescharacteristic
66C2×D344C2311yescharacteristic
67C2×#10621882—21no—
68C2×#10621882—21no—
69C2×#10621882—21no—
70D8×D43—22no—
71D8×D43—22no—
72D8×D43—41no—
73D8×D43—41no—
74C2×C8×D43C2311yescharacteristic
75#13063321—21no—
76#13063314—21no—
77#13063308—41no—
78#13063301—21no—
79#13063299—21no—
80#13063299—21no—
81#13063297—41no—
82#13063297—41no—
83#13063296—21no—
84#13063294—41no—
85#13063293—41no—
86#13063293—41no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89C4×C22⋊D43D411yescharacteristic
90C2×(C2×D43)⋊C4—41no—
91#13063268—41no—
92D688—22no—
93#13063266—22no—
94#13063266—22no—
95#13063266—41no—
96C2×C43⋊C16C2311yescharacteristic
97C2×C43⋊C16C2311yescharacteristic
98C16×D43—22no—
99#13063259C2311yescharacteristic
100#13063259C2311yescharacteristic
101Dic43⋊C8D411yescharacteristic
102#13063249—21no—
103#13063247—21no—
104#13063247—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108C22⋊(C43⋊C8)D411yescharacteristic
109(C2×D43)⋊C8D411yescharacteristic
110C8×Dic43C2311yescharacteristic
111C2×#41×C43—21no—
112C22×D4×C43—21no—
113#135×C43—22no—
114#135×C43—41no—
115C2×Q16×C43C2311yescharacteristic
116C2×SD16×C43—21no—
117C2×D8×C43—22no—
118C2×D8×C43—21no—
119C2×D8×C43—41no—
120C2×D8×C43C2311yescharacteristic
121C2×D8×C43C2311yescharacteristic
122C2×D8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124SD32×C43—22no—
125SD32×C43—22no—
126D16×C43—22no—
127D16×C43D414yescomplemented
128M32×C43—22no—
129C2×C16×C43C2311yescharacteristic
130C2×C16×C43C2311yescharacteristic
131C24×C43—41no—
132C23×D43—41no—
133C23×D43—41no—
134#41×C43—42no—
135#41×C43—81no—
136C2×Q8×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—41no—
141C2×D4×C43—41no—
142C2×D4×C43—42no—
143C2×D4×C43—81no—
144C22×C4×C43—41no—
145C22×C4×C43C2×D411yescharacteristic
146C2×C22⋊D43—41no—
147C2×C22⋊D43—41no—
148C2×C22⋊D43—41no—
149C2×C22⋊D43—41no—
150C2×C22⋊D43—41no—
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—84no—
154C2×C22⋊D43D811yescharacteristic
155C22×Dic43—41no—
156C22×Dic43—41no—
157D4×D43—42no—
158D4×D43—42no—
159D4×D43—81no—
160D4×D43—81no—
161C2×D172—21no—
162C2×D172—21no—
163C2×C4×D43C2×D411yescharacteristic
164Q16×C43—21no—
165Q16×C43—21no—
166SD16×C43—42no—
167D8×C43—21no—
168D8×C43—21no—
169D8×C43—21no—
170D8×C43—21no—
171D8×C43—42no—
172D8×C43C2×D412yes—
173D8×C43C2×D412yescomplemented
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2411yescharacteristic
178C22⋊Dic43—41no—
179C22⋊Dic43—41no—
180C22⋊Dic43—41no—
181C22⋊Dic43D811yescharacteristic
182#10621884—81no—
183#10621882—42no—
184#10621882—42no—
185#10621882—81no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4D811yescharacteristic
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4D811yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199D344—21no—
200D344—21no—
201D344—21no—
202D344—21no—
203C8×D43—21no—
204C8×D43—21no—
205C16×C43—21no—
206C16×C43C2×D412yescomplemented
207C43⋊C16—21no—
208C43⋊C16—21no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—82no—
213C23×C43—82no—
214C23×C43—161no—
215C23×C43C2×D811yescharacteristic
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—82no—
219C22×D43—82no—
220C22×D43—82no—
221C22×D43—82no—
222C22×D43—161no—
223C22×D43—161no—
224C22×D43C2×D811yescharacteristic
225Q8×C43—41no—
226Q8×C43—41no—
227D4×C43—22no—
228D4×C43—22no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—82no—
234D4×C43—82no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43C2×D811yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C22⋊D43—22no—
242C22⋊D43—82no—
243C22⋊D43—82no—
244C22⋊D43—82no—
245C22⋊D43—82no—
246C22⋊D43—82no—
247C22⋊D43—161no—
248C22⋊D43—161no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—82no—
252C2×Dic43—161no—
253C2×Dic43C2×D811yescharacteristic
254C2×Dic43C2×D811yescharacteristic
255C2×Dic43C2×D811yescharacteristic
256D172—41no—
257D172—41no—
258D172—41no—
259D172—41no—
260C4×D43—21no—
261C4×D43—21no—
262C8×C43—21no—
263C8×C43C22×D411yescharacteristic
264C8×C43H(5,𝔽2)11yescharacteristic
265C43⋊C8—21no—
266C43⋊C8—21no—
267#33830—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—164no—
281C22×C43C22×D811yescharacteristic
282C2×D43—21no—
283C2×D43—21no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—164no—
291C2×D43—164no—
292C2×D43#50912yescomplemented
293C4×C43—21no—
294C4×C43—81no—
295C4×C43D4211yescharacteristic
296C4×C43#57611yescharacteristic
297Dic43—21no—
298Dic43—21no—
299Dic43—21no—
300Dic43—81no—
301Dic43—81no—
302C2×#509D4311yescharacteristic, complemented
303C22×D16—431no—
304#3280—431no—
305D4×D8—431no—
306#2250—431no—
307#2218—431no—
308#2217—431no—
309#2210—431no—
310#2206—431no—
311#2187—431no—
312#2186—431no—
313#2184—431no—
314#2184—431no—
315#2177—431no—
316#2168—431no—
317C2×C43—41no—
318C2×C43—82no—
319C2×C43—82no—
320C2×C43—161no—
321C2×C43D4×D811yescharacteristic
322C2×C43C2×#50911yescharacteristic
323C2×C43#341511yescharacteristic
324D43—22no—
325D43—161no—
326D43—161no—
327C2×#135C2×D4311yescharacteristic, complemented
328C22×D8—431no—
329C22×D8—431no—
330C22×D8C2×D4311yescharacteristic, complemented
331#546—861no—
332D42—861no—
333#509—24no—
334C2×SD32—431no—
335C2×SD32C2×D4311yescharacteristic, complemented
336C2×SD32C2×D4311yescharacteristic, complemented
337C2×D16—431no—
338C2×D16—431no—
339C2×D16—431no—
340C2×D16—431no—
341C2×D16—864no—
342C2×D16C2×D4311yescharacteristic
343C2×D16C2×D4311yescharacteristic, complemented
344C2×M32C2×D4311yescharacteristic, complemented
345C22×C16—431no—
346#495—431no—
347#493—431no—
348#467—431no—
349#466—431no—
350#466—431no—
351#466—431no—
352#463—861no—
353#459—861no—
354#450—861no—
355#449—861no—
356#447—861no—
357#447—861no—
358C4×D8—431no—
359C4×D8—431no—
360C8×D4—431no—
361#367—431no—
362C4⋊C16—431no—
363#358—431no—
364#357—431no—
365#357—431no—
366#357—431no—
367#357—431no—
368#357—431no—
369C22⋊C16—431no—
370C22⋊C16—431no—
371#346—431no—
372C43#3383011yescharacteristic, complemented, Sylow
373C2×#41—21no—
374C22×D4—21no—
375C22×D4—861no—
376C22×D4—861no—
377C22×D4—1721no—
378#135—22no—
379#135—41no—
380C2×Q16C22×D4311yescharacteristic
381C2×SD16—21no—
382C2×SD16—861no—
383C2×D8—22no—
384C2×D8—21no—
385C2×D8—41no—
386C2×D8—431no—
387C2×D8—431no—
388C2×D8—861no—
389C2×D8—861no—
390C2×D8—861no—
391C2×D8—862no—
392C2×D8—862no—
393C2×D8—1721no—
394C2×D8—1721no—
395C2×D8C22×D4311yescharacteristic
396C2×D8C22×D4311yescharacteristic
397C2×D8C22×D4311yescharacteristic
398C22×C8—431no—
399C22×C8C22×D4311yescharacteristic
400#127—861no—
401#124—861no—
402#123—1721no—
403C22⋊Q8—861no—
404#121—861no—
405#121—861no—
406#121—861no—
407#121—1721no—
408#121—1721no—
409#120—1721no—
410#120—1721no—
411#120—1721no—
412C4×D4—431no—
413C4×D4—861no—
414C4×D4—861no—
415C2×C22⋊C4—1721no—
416SD32—22no—
417SD32—22no—
418SD32—1721no—
419D16—22no—
420D16—862no—
421D16—862no—
422D16—862no—
423D16—1721no—
424D16C22⋊D4314yescomplemented
425M32—22no—
426C2×C16—431no—
427C2×C16—431no—
428C2×C16—862no—
429C2×C16C22×D4311yescharacteristic
430C2×C16C22×D4311yescharacteristic
431#107—431no—
432#107—431no—
433C4⋊C8—431no—
434#103—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440C22⋊C8—431no—
441C22⋊C8—431no—
442C4×C8—431no—
443C24—41no—
444C24—1721no—
445C24—1721no—
446#41—42no—
447#41—81no—
448C2×Q8—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—42no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—81no—
456C2×D4—431no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—3441no—
460C2×D4—3441no—
461C2×D4—3444no—
462C2×D4—1721no—
463C2×D4—1721no—
464C2×D4—1721no—
465C2×D4—1721no—
466C2×D4—1722no—
467C2×D4—1722no—
468C2×D4—1721no—
469C2×D4—1721no—
470C2×D4—1721no—
471C22×C4—41no—
472C22×C4—431no—
473C22×C4—1721no—
474C22×C4—1721no—
475C22×C4D4×D4311yescharacteristic
476Q16—21no—
477Q16—21no—
478SD16—42no—
479SD16—3441no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—42no—
485D8—861no—
486D8—861no—
487D8—861no—
488D8—861no—
489D8—3441no—
490D8—1722no—
491D8—1722no—
492D8C2×C22⋊D4312yes—
493D8C2×C22⋊D4312yescomplemented
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8D4×D4311yescharacteristic
501C2×C8C23×D4311yescharacteristic
502C4⋊C4—431no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—1721no—
506C22⋊C4—431no—
507C22⋊C4—431no—
508C22⋊C4—1721no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C22⋊C4—1721no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C22⋊C4—1721no—
515C22⋊C4—1721no—
516C42—431no—
517C16—21no—
518C16—861no—
519C16—861no—
520C16C2×C22⋊D4312yescomplemented
521C23—41no—
522C23—41no—
523C23—41no—
524C23—82no—
525C23—82no—
526C23—161no—
527C23—431no—
528C23—3442no—
529C23—3442no—
530C23—3442no—
531C23—3442no—
532C23—1721no—
533C23—1721no—
534C23—6881no—
535C23—6881no—
536C23D8×D4311yescharacteristic
537Q8—41no—
538Q8—41no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—82no—
546D4—82no—
547D4—862no—
548D4—3442no—
549D4—3442no—
550D4—3442no—
551D4—3442no—
552D4—3442no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557D4—6881no—
558D4—6881no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—82no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—3442no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—6881no—
572C2×C4D8×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C8—21no—
575C8—861no—
576C8—861no—
577C8C22×C22⋊D4311yescharacteristic
578C8#1306337011yescharacteristic
579C22—21no—
580C22—21no—
581C22—21no—
582C22—42no—
583C22—42no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—164no—
592C22—432no—
593C22—861no—
594C22—861no—
595C22—3441no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—3441no—
600C22—3441no—
601C22—6884no—
602C22—6884no—
603C22C2×D8×D4311yescharacteristic
604C4—21no—
605C4—81no—
606C4—861no—
607C4—861no—
608C4—861no—
609C4—3441no—
610C4—3441no—
611C4D4×C22⋊D4311yescharacteristic
612C4#1458370011yescharacteristic
613C2—41no—
614C2—82no—
615C2—82no—
616C2—161no—
617C2—862no—
618C2—6881no—
619C2—6881no—
620C2D8×C22⋊D4311yescharacteristic
621C2#509×D4311yescharacteristic
622C2#1914773511yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#509C2
socleC22×C43C22×D8
hypercenterC2×#509D43
hypocenterC43#33830
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×D16×D43C2semidirect
2. #19146274C2semidirect
3. D8×C22⋊D43C2semidirect
4. #19136860C2semidirect
5. #19136698C2semidirect
6. #19136688C2semidirect
7. #19136652C2semidirect
8. #19136628C2semidirect
9. #19136522C2semidirect
10. #19136518C2semidirect
11. #19136507C2semidirect
12. #19136505C2semidirect
13. #19136471C2semidirect
14. #19136418C2semidirect
15. C2×C43×#509C2semidirect
17. C2×D8×D43C22semidirect
20. C2×#13063268C22semidirect
21. C2×D688C22semidirect
23. C2×#13063266C22semidirect
24. C2×#13063266C22semidirect
26. C2×C16×D43C22semidirect
27. #14583284C22semidirect
28. #14583274C22semidirect
29. #14583137C22semidirect
30. #14583135C22semidirect
31. #14583135C22semidirect
39. D8×Dic43C22semidirect
40. D8×Dic43C22semidirect
42. #14582727C22semidirect
43. Dic43⋊C16C22semidirect
44. #14582703C22semidirect
45. #14582701C22semidirect
46. #14582701C22semidirect
47. #14582700C22semidirect
48. #14582700C22semidirect
49. #14582700C22semidirect
50. C22⋊(C43⋊C16)C22semidirect
51. (C2×D43)⋊C16C22semidirect
52. #14582674C22semidirect
53. C2×#135×C43C22semidirect
54. C22×D8×C43C22semidirect
56. C2×SD32×C43C22semidirect
57. C2×SD32×C43C22semidirect
59. C2×D16×C43C22semidirect
60. C2×M32×C43C22semidirect
127. D16×C43D4semidirect
173. D8×C43C2×D4semidirect
206. C16×C43C2×D4semidirect
292. C2×D43#509semidirect
302. C2×#509D43semidirect
327. C2×#135C2×D43semidirect
330. C22×D8C2×D43semidirect
335. C2×SD32C2×D43semidirect
336. C2×SD32C2×D43semidirect
343. C2×D16C2×D43semidirect
344. C2×M32C2×D43semidirect
372. C43#33830semidirect
424. D16C22⋊D43semidirect
493. D8C2×C22⋊D43semidirect
520. C16C2×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×D16×D432
#191462742
D8×C22⋊D432
#191368602
#191366982
#191366882
#191366522
#191366282
#191365222
#191365182
#191365072
#191365052
#191364712
#191364182
C2×C43×#5092
#3383043