Finite Group Databasebeta

← #25253189

Subgroups — #25253189

Order 11008.

748 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583336C211yesmaximal, characteristic, complemented
2#19146349C211yesmaximal, characteristic, complemented
3D8×C22⋊D43C211yesmaximal, characteristic, complemented
4#19136843C211yesmaximal, characteristic, complemented
5#19136698C211yesmaximal, characteristic, complemented
6#19136695C211yesmaximal, characteristic, complemented
7#19136633C211yesmaximal, characteristic, complemented
8#19136628C211yesmaximal, characteristic, complemented
9#19136518C211yesmaximal, characteristic, complemented
10#19136517C211yesmaximal, characteristic, complemented
11#19136507C211yesmaximal, characteristic, complemented
12#19136505C211yesmaximal, characteristic, complemented
13SD32×Dic43C211yesmaximal, characteristic, complemented
14#19136425C211yesmaximal, characteristic, complemented
15C2×C43×#509C211yesmaximal, characteristic, complemented
16C2×#13063348C2211yescharacteristic, complemented
17C2×D8×D43C2211yescharacteristic
18#14583568—21no—
19D4×C22⋊D43—21no—
20#14583336—24no—
21C2×#13063268C2211yescharacteristic, complemented
22C2×D688C2211yescharacteristic, complemented
23C2×#13063266C2211yescharacteristic
24C2×#13063266C2211yescharacteristic, complemented
25C2×#13063266C2211yescharacteristic, complemented
26C2×#13063264C2211yescharacteristic, complemented
27#14583274C2211yescharacteristic
28#14583274C2211yescharacteristic, complemented
29#14583135C2211yescharacteristic
30#14583135C2211yescharacteristic, complemented
31#14583132C2211yescharacteristic
32#14583132C2211yescharacteristic, complemented
33#14583097—21no—
34#14583092—21no—
35#14583044—21no—
36#14583043—21no—
37#14583033—21no—
38#14583031—21no—
39Q16×Dic43C2211yescharacteristic, complemented
40D8×Dic43C2211yescharacteristic
41C8×C22⋊D43C2211yescharacteristic
42#14582727C2211yescharacteristic, complemented
43Dic43⋊C16C2211yescharacteristic, complemented
44#14582703C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic, complemented
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic, complemented
49#14582700C2211yescharacteristic, complemented
50C22⋊(C43⋊C16)C2211yescharacteristic, complemented
51(C2×D43)⋊C16C2211yescharacteristic, complemented
52C16×Dic43C2211yescharacteristic, complemented
53C2×#135×C43C2211yescharacteristic, complemented
54C22×D8×C43C2211yescharacteristic
55C43×#509—24no—
56C2×SD32×C43C2211yescharacteristic
57C2×SD32×C43C2211yescharacteristic, complemented
58C2×D16×C43C2211yescharacteristic
59C2×D16×C43C2211yescharacteristic, complemented
60C2×M32×C43C2211yescharacteristic, complemented
61C2×#10621902—21no—
62C22×C22⋊D43—41no—
63C2×D4×D43—21no—
64#13063348—22no—
65#13063348—41no—
66C2×#10621884—21no—
67C2×D344C2311yescharacteristic
68C2×D344C2311yescharacteristic
69C2×#10621882—21no—
70C2×#10621882—21no—
71C2×#10621882—21no—
72D8×D43—22no—
73D8×D43—41no—
74C2×C8×D43C2311yescharacteristic
75#13063321—21no—
76#13063321—21no—
77#13063321—41no—
78#13063299—21no—
79#13063299—21no—
80#13063299—41no—
81#13063297—41no—
82#13063296—21no—
83#13063296—21no—
84#13063296—41no—
85#13063294—41no—
86#13063293—41no—
87Q8×Dic43—21no—
88D4×Dic43—21no—
89C4×C22⋊D43—41no—
90C4×C22⋊D43D411yescharacteristic
91#13063268—22no—
92D688—22no—
93#13063266—22no—
94#13063266—41no—
95#13063266—41no—
96#13063264—22no—
97C2×C43⋊C16C2311yescharacteristic
98C2×C43⋊C16C2311yescharacteristic
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×C43D414yescomplemented
126D16×C43—22no—
127D16×C43—22no—
128M32×C43—22no—
129C2×C16×C43C2311yescharacteristic
130C2×C16×C43C2311yescharacteristic
131C24×C43—41no—
132C23×D43—41no—
133#41×C43—42no—
134#41×C43—81no—
135C2×Q8×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—41no—
140C2×D4×C43—41no—
141C2×D4×C43—42no—
142C2×D4×C43—81no—
143C22×C4×C43—41no—
144C22×C4×C43C2×D411yescharacteristic
145C2×C22⋊D43—41no—
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—41no—
154C2×C22⋊D43—84no—
155C2×C22⋊D43D811yescharacteristic
156C22×Dic43—41no—
157#10621902—42no—
158#10621902—81no—
159D4×D43—42no—
160D4×D43—81no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—41no—
164C2×C4×D43—41no—
165C2×C4×D43C2×D411yescharacteristic
166Q16×C43—21no—
167Q16×C43C2×D412yescomplemented
168SD16×C43—42no—
169D8×C43—21no—
170D8×C43—21no—
171D8×C43—21no—
172D8×C43—21no—
173D8×C43—21no—
174D8×C43—42no—
175D8×C43C2×D412yes—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182C22⋊Dic43—41no—
183C22⋊Dic43D811yescharacteristic
184#10621884—42no—
185#10621882—42no—
186#10621882—81no—
187#10621882—81no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4D811yescharacteristic
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—41no—
194Dic43⋊C4D811yescharacteristic
195C4×Dic43—41no—
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—161no—
221C22×D43C2×D811yescharacteristic
222Q8×C43—22no—
223Q8×C43—41no—
224D4×C43—22no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—82no—
231D4×C43—82no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—82no—
236C2×C4×C43C2×D811yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C22⋊D43—22no—
239C22⋊D43—82no—
240C22⋊D43—82no—
241C22⋊D43—82no—
242C22⋊D43—82no—
243C22⋊D43—82no—
244C22⋊D43—161no—
245C22⋊D43—161no—
246C22⋊D43—161no—
247C22⋊D43—161no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—82no—
251C2×Dic43C2×D811yescharacteristic
252C2×Dic43C2×D811yescharacteristic
253C2×Dic43C2×D811yescharacteristic
254D172—41no—
255D172—41no—
256D172—41no—
257D172—41no—
258D172—82no—
259C4×D43—21no—
260C4×D43—21no—
261C4×D43—82no—
262C8×C43—21no—
263C8×C43C22×D411yescharacteristic
264C8×C43H(5,𝔽2)11yescharacteristic
265C43⋊C8—21no—
266C43⋊C8—21no—
267#33840—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—42no—
272C22×C43—81no—
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—21no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—164no—
292C4×C43—21no—
293C4×C43—42no—
294C4×C43D4211yescharacteristic
295C4×C43#57611yescharacteristic
296Dic43—21no—
297Dic43—21no—
298Dic43—81no—
299Dic43—81no—
300Dic43#50912yescomplemented
301C2×#509—431no—
302C2×#509D4311yescharacteristic, complemented
303#3287—431no—
304D4×D8—431no—
305#2246—431no—
306#2218—431no—
307#2218—431no—
308#2207—431no—
309#2206—431no—
310#2186—431no—
311#2186—431no—
312#2184—431no—
313#2184—431no—
314C4×SD32—431no—
315#2169—431no—
316C2×C43—41no—
317C2×C43—82no—
318C2×C43—161no—
319C2×C43—161no—
320C2×C43D4×D811yescharacteristic
321C2×C43C2×#50911yescharacteristic
322C2×C43#341511yescharacteristic
323D43—41no—
324D43—161no—
325D43—161no—
326C2×#135—431no—
327C2×#135C2×D4311yescharacteristic, complemented
328C22×D8—431no—
329C22×D8C2×D4311yescharacteristic
330#550—861no—
331D42—861no—
332#509—24no—
333#509—864no—
334C2×SD32—431no—
335C2×SD32C2×D4311yescharacteristic
336C2×SD32C2×D4311yescharacteristic, complemented
337C2×D16—431no—
338C2×D16—431no—
339C2×D16—431no—
340C2×D16—431no—
341C2×D16C2×D4311yescharacteristic
342C2×D16C2×D4311yescharacteristic, complemented
343C2×M32—431no—
344C2×M32C2×D4311yescharacteristic, complemented
345#493—431no—
346#493—431no—
347#466—431no—
348#466—431no—
349#466—431no—
350#466—431no—
351#460—861no—
352#459—861no—
353#449—861no—
354#449—861no—
355#447—861no—
356#447—861no—
357C4×Q16—431no—
358C4×D8—431no—
359C8×D4—431no—
360#367—431no—
361C4⋊C16—431no—
362#358—431no—
363#357—431no—
364#357—431no—
365#357—431no—
366#357—431no—
367#357—431no—
368C22⋊C16—431no—
369C22⋊C16—431no—
370C4×C16—431no—
371C43#3384011yescharacteristic, complemented, Sylow
372C2×#41—21no—
373C2×#41—861no—
374C22×D4—21no—
375C22×D4—861no—
376C22×D4—1721no—
377#135—22no—
378#135—41no—
379#135—862no—
380#135—1721no—
381C2×Q16C22×D4311yescharacteristic
382C2×SD16—21no—
383C2×SD16—861no—
384C2×D8—22no—
385C2×D8—21no—
386C2×D8—41no—
387C2×D8—431no—
388C2×D8—431no—
389C2×D8—861no—
390C2×D8—861no—
391C2×D8—861no—
392C2×D8—862no—
393C2×D8—1721no—
394C2×D8C22×D4311yescharacteristic
395C2×D8C22×D4311yescharacteristic
396C2×D8C22×D4311yescharacteristic
397C22×C8—431no—
398C22×C8C22×D4311yescharacteristic
399#127—861no—
400#127—861no—
401#127—1721no—
402#121—861no—
403#121—861no—
404#121—861no—
405#121—861no—
406#121—1721no—
407#121—1721no—
408#121—1721no—
409#120—1721no—
410#120—1721no—
411C4×Q8—861no—
412C4×D4—431no—
413C4×D4—861no—
414C4×D4—1721no—
415SD32—22no—
416SD32—862no—
417SD32C22⋊D4314yescomplemented
418D16—22no—
419D16—22no—
420D16—862no—
421D16—862no—
422D16—1721no—
423D16—1721no—
424M32—22no—
425M32—862no—
426C2×C16—431no—
427C2×C16—431no—
428C2×C16C22×D4311yescharacteristic
429C2×C16C22×D4311yescharacteristic
430#107—431no—
431#107—431no—
432C4⋊C8—431no—
433#103—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439C22⋊C8—431no—
440C22⋊C8—431no—
441C4×C8—431no—
442C24—41no—
443C24—1721no—
444#41—42no—
445#41—81no—
446#41—3441no—
447#41—1722no—
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—3444no—
461C2×D4—1721no—
462C2×D4—1721no—
463C2×D4—1721no—
464C2×D4—1721no—
465C2×D4—1721no—
466C2×D4—1721no—
467C2×D4—1722no—
468C2×D4—1721no—
469C2×D4—1721no—
470C2×D4—1721no—
471C2×D4—1721no—
472C22×C4—41no—
473C22×C4—431no—
474C22×C4—1721no—
475C22×C4—1721no—
476C22×C4D4×D4311yescharacteristic
477Q16—21no—
478Q16C2×C22⋊D4312yescomplemented
479SD16—42no—
480SD16—1722no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—21no—
485D8—21no—
486D8—42no—
487D8—861no—
488D8—861no—
489D8—861no—
490D8—861no—
491D8—3441no—
492D8—3441no—
493D8—1722no—
494D8C2×C22⋊D4312yes—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—431no—
498C2×C8—431no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8D4×D4311yescharacteristic
502C2×C8C23×D4311yescharacteristic
503C4⋊C4—431no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—1721no—
507C22⋊C4—431no—
508C22⋊C4—431no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C22⋊C4—1721no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C42—431no—
515C42—1721no—
516C16—21no—
517C16—861no—
518C16—861no—
519C16C2×C22⋊D4312yescomplemented
520C23—41no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—161no—
526C23—431no—
527C23—3442no—
528C23—3442no—
529C23—1721no—
530C23—1721no—
531C23—6881no—
532C23D8×D4311yescharacteristic
533Q8—22no—
534Q8—41no—
535D4—22no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—82no—
542D4—82no—
543D4—862no—
544D4—3442no—
545D4—3442no—
546D4—3442no—
547D4—3442no—
548D4—3442no—
549D4—3442no—
550D4—1721no—
551D4—1721no—
552D4—1721no—
553D4—1721no—
554D4—6881no—
555D4—6881no—
556D4—6881no—
557D4—6881no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—82no—
562C2×C4—431no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—3442no—
568C2×C4—3442no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4D8×D4311yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C8—21no—
574C8—861no—
575C8—861no—
576C8C22×C22⋊D4311yescharacteristic
577C8#1306337011yescharacteristic
578C22—21no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—164no—
591C22—861no—
592C22—861no—
593C22—861no—
594C22—3441no—
595C22—3441no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—3441no—
600C22—6884no—
601C22C2×D8×D4311yescharacteristic
602C4—21no—
603C4—42no—
604C4—432no—
605C4—861no—
606C4—861no—
607C4—3441no—
608C4—3441no—
609C4D4×C22⋊D4311yescharacteristic
610C4#1458370011yescharacteristic
611C2—41no—
612C2—82no—
613C2—161no—
614C2—161no—
615C2—1721no—
616C2—6881no—
617C2—6881no—
618C2D8×C22⋊D4311yescharacteristic
619C2#509×D4311yescharacteristic
620C2#1914773511yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#509C2
socleC22×C43C22×D8
hypercenterC2×#509D43
hypocenterC43#33840
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×#14583336C2semidirect
2. #19146349C2semidirect
3. D8×C22⋊D43C2semidirect
4. #19136843C2semidirect
5. #19136698C2semidirect
6. #19136695C2semidirect
7. #19136633C2semidirect
8. #19136628C2semidirect
9. #19136518C2semidirect
10. #19136517C2semidirect
11. #19136507C2semidirect
12. #19136505C2semidirect
13. SD32×Dic43C2semidirect
14. #19136425C2semidirect
15. C2×C43×#509C2semidirect
16. C2×#13063348C22semidirect
21. C2×#13063268C22semidirect
22. C2×D688C22semidirect
24. C2×#13063266C22semidirect
25. C2×#13063266C22semidirect
26. C2×#13063264C22semidirect
28. #14583274C22semidirect
30. #14583135C22semidirect
32. #14583132C22semidirect
39. Q16×Dic43C22semidirect
42. #14582727C22semidirect
43. Dic43⋊C16C22semidirect
44. #14582703C22semidirect
45. #14582701C22semidirect
46. #14582701C22semidirect
48. #14582700C22semidirect
49. #14582700C22semidirect
50. C22⋊(C43⋊C16)C22semidirect
51. (C2×D43)⋊C16C22semidirect
52. C16×Dic43C22semidirect
53. C2×#135×C43C22semidirect
57. C2×SD32×C43C22semidirect
59. C2×D16×C43C22semidirect
60. C2×M32×C43C22semidirect
125. SD32×C43D4semidirect
167. Q16×C43C2×D4semidirect
206. C16×C43C2×D4semidirect
300. Dic43#509semidirect
302. C2×#509D43semidirect
327. C2×#135C2×D43semidirect
336. C2×SD32C2×D43semidirect
342. C2×D16C2×D43semidirect
344. C2×M32C2×D43semidirect
371. C43#33840semidirect
417. SD32C22⋊D43semidirect
478. Q16C2×C22⋊D43semidirect
519. C16C2×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833362
#191463492
D8×C22⋊D432
#191368432
#191366982
#191366952
#191366332
#191366282
#191365182
#191365172
#191365072
#191365052
SD32×Dic432
#191364252
C2×C43×#5092
#3384043