Finite Group Databasebeta

← #25078902

Subgroups — #25078902

Order 11008.

716 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144914C211yesmaximal, characteristic, complemented
2#19144605C211yesmaximal, characteristic, complemented
3#19144594C211yesmaximal, characteristic
4C8×D4×D43C211yesmaximal, characteristic, complemented
5#19134049C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic, complemented
7#19134031C211yesmaximal, characteristic, complemented
8#19134030C211yesmaximal, characteristic, complemented
9#19134019C211yesmaximal, characteristic, complemented
10#19134018C211yesmaximal, characteristic, complemented
11#19134001C211yesmaximal, characteristic, complemented
12#19133340C211yesmaximal, characteristic, complemented
13#19133249C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic, complemented
15C43×#1677C211yesmaximal, characteristic, complemented
16C22×C8×D43—21no—
17#14583454C2211yescharacteristic
18#14583447C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583252—21no—
21#14583252—21no—
22#14583251C2211yescharacteristic, complemented
23#14583250C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic, complemented
25#14583231—21no—
26#14583211—21no—
27#14583186C2211yescharacteristic
28#14583180C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583105C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583091C2211yescharacteristic
33#14583051—21no—
34#14583031—21no—
35#14582990—21no—
36#14582986—21no—
37D8×Dic43—21no—
38#14582979—21no—
39C8×D172C2211yescharacteristic
40D4×C43⋊C8C2211yescharacteristic
41#14582964C2211yescharacteristic
42C8×C22⋊D43—21no—
43(C22⋊D43)⋊C8—21no—
44#14582951C2211yescharacteristic
45#14582951C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582892—21no—
48#14582892—21no—
49C22⋊C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582650C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582646C2211yescharacteristic, complemented
57#14582644C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582643C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621873—21no—
71C2×#10621883—21no—
72C2×#10621882—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—44no—
78C2×C8×D43D411yescharacteristic
79C2×C8×D43D411yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063316—21no—
83#13063312—21no—
84#13063305—21no—
85#13063301—21no—
86#13063296—21no—
87#13063296—21no—
88Q8×Dic43—21no—
89#13063290—21no—
90C4×D172C2311yescharacteristic
91D4×Dic43—21no—
92D4×Dic43—21no—
93D4×Dic43D411yescharacteristic
94#13063287D411yescharacteristic
95C4×C22⋊D43—21no—
96(C22⋊D43)⋊C4—21no—
97#13063283—21no—
98C4⋊C4×D43D411yescharacteristic
99C22⋊C4×D43—21no—
100C42×D43C2311yescharacteristic
101#13063259—21no—
102#13063258—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063248—21no—
112#13063248—21no—
113#13063248—21no—
114#13063247—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063245—21no—
120C22⋊(C43⋊C8)—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×D8×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133#127×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—41no—
154C22×Dic43—21no—
155C22×Dic43—41no—
156#10621900—42no—
157#10621900—42no—
158D4×D43—22no—
159D4×D43—22no—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43#4111yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171D8×C43—42no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—42no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186#10621883—42no—
187#10621882—42no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199C4×Dic43—41no—
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43#4111yescharacteristic
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621873—42no—
210C8×D43—22no—
211C8×D43—22no—
212C8×D43—42no—
213C8×D43—42no—
214C8×D43—42no—
215C23×C43—21no—
216C23×C43—41no—
217C22×D43—24no—
218C22×D43—21no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43#12111yescharacteristic
222Q8×C43—81no—
223D4×C43—21no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43#13512yes—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—24no—
238C22⋊D43—82no—
239C2×Dic43—21no—
240C2×Dic43—42no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—82no—
244C2×Dic43#12111yescharacteristic
245C2×Dic43#12111yescharacteristic
246C2×Dic43#12111yescharacteristic
247D172—21no—
248D172#13512yes—
249C4×D43—21no—
250C4×D43—21no—
251C4×D43—41no—
252C4×D43—42no—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—42no—
256C4×D43#13512yes—
257C4×D43AGL(1,ℤ/8)12yes—
258Dic86—41no—
259Dic86—41no—
260Dic86—41no—
261Dic86—41no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C43⋊C8—21no—
268C43⋊C8—21no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19110—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43C2×#12111yescharacteristic
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—22no—
283C2×D43—48no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43#46312yes—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—81no—
290C4×C43C2×#13511yescharacteristic
291C4×C43C2×#13511yescharacteristic
292C4×C43C2×#13511yescharacteristic
293C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
294Dic43—21no—
295Dic43—21no—
296Dic43—41no—
297Dic43—81no—
298Dic43—81no—
299Dic43#46312yes—
300#3131—431no—
301#3101—431no—
302#3100—431no—
303C2×C8×D4—431no—
304#1683—431no—
305#1683—431no—
306#1681—431no—
307#1681—431no—
308#1679—431no—
309#1679—431no—
310#1677—431no—
311#1677D4311yescharacteristic, complemented
312#1564—431no—
313#1542—431no—
314#1540—431no—
315C2×C43—42no—
316C2×C43—161no—
317C2×C43C2×#46311yescharacteristic
318C2×C43#305011yescharacteristic
319C2×C43#306711yescharacteristic
320D43—22no—
321D43—42no—
322C23×C8—861no—
323#533—431no—
324#532—431no—
325C2×C4×D4—431no—
326#488—861no—
327#488—861no—
328#487—431no—
329#487—431no—
330#486—431no—
331#486C2×D4311yescharacteristic, complemented
332#483—861no—
333#480—861no—
334#476—431no—
335#476C2×D4311yescharacteristic
336#474—431no—
337#474—431no—
338#461—431no—
339#461—431no—
340#459—431no—
341#459C2×D4311yescharacteristic
342#450—861no—
343#447—861no—
344C4×SD16—861no—
345C4×SD16—861no—
346C4×D8—861no—
347C4×D8—861no—
348C8×D4—431no—
349C8×D4—431no—
350C8×D4—431no—
351C8×D4—861no—
352C8×D4—861no—
353C8×D4C2×D4311yescharacteristic
354#431—431no—
355#431—431no—
356C2×C4⋊C8—431no—
357#416—861no—
358#416—861no—
359C2×C22⋊C8—861no—
360C2×C4×C8—431no—
361#335—431no—
362#335—431no—
363#334—431no—
364#334C2×D4311yescharacteristic, complemented
365#333—431no—
366#333C2×D4311yescharacteristic, complemented
367#332—431no—
368#332—431no—
369#332—431no—
370#332—431no—
371#331—431no—
372#331C2×D4311yescharacteristic, complemented
373C43#1911011yescharacteristic, complemented, Sylow
374C2×#41—861no—
375C22×D4—431no—
376C23×C4—861no—
377C2×SD16—861no—
378C2×SD16—861no—
379C2×D8—21no—
380C2×D8—861no—
381C22×C8—21no—
382C22×C8—431no—
383C22×C8—431no—
384C22×C8—861no—
385C22×C8—861no—
386C22×C8—861no—
387C22×C8—861no—
388C22×C8—1724no—
389C4⋊Q8—431no—
390C4⋊Q8—431no—
391C4⋊Q8C22×D4311yescharacteristic
392#127C22×D4311yescharacteristic
393#125—861no—
394#124—861no—
395C22⋊Q8—861no—
396C22⋊Q8—861no—
397#121—861no—
398#121—861no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×D4—431no—
402C4×D4—431no—
403C4×D4—431no—
404C4×D4—861no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4—861no—
408C4×D4C22×D4311yescharacteristic
409#117—861no—
410C2×C4⋊C4—431no—
411C2×C22⋊C4—861no—
412C2×C42—431no—
413#107—861no—
414#107—861no—
415#106—21no—
416#106—861no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—861no—
421C4⋊C8C22×D4311yescharacteristic
422C4⋊C8C22×D4311yescharacteristic
423C4⋊C8C22×D4311yescharacteristic
424#103—861no—
425#103—861no—
426#103—861no—
427#103—861no—
428#103—861no—
429#103—861no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440C22⋊C8—21no—
441C22⋊C8—861no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446C4×C8—431no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8—861no—
450C4×C8—861no—
451C4×C8C22×D4311yescharacteristic
452C24—861no—
453#41—1722no—
454#41—1722no—
455C2×Q8—21no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—431no—
462C2×D4—861no—
463C2×D4—862no—
464C2×D4—862no—
465C2×D4—1721no—
466C2×D4D4×D4311yescharacteristic
467C22×C4—21no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4—1721no—
478SD16—1722no—
479SD16—1722no—
480D8—42no—
481D8—1722no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—42no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—862no—
489C2×C8—862no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—1722no—
494C2×C8—1722no—
495C2×C8—1722no—
496C2×C8—1722no—
497C2×C8D4×D4311yescharacteristic
498C2×C8D4×D4311yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—431no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4D4×D4311yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—1721no—
515C22⋊C4—1721no—
516C22⋊C4—1721no—
517C42—431no—
518C42—431no—
519C42—431no—
520C42—1721no—
521C42C23×D4311yescharacteristic
522C23—21no—
523C23—41no—
524C23—431no—
525C23—864no—
526C23—861no—
527C23—1722no—
528C23—1722no—
529Q8—81no—
530Q8—1721no—
531Q8—1721no—
532Q8—1721no—
533Q8—1721no—
534D4—21no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—432no—
541D4—864no—
542D4—861no—
543D4—3442no—
544D4#1306334612yes—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—431no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—431no—
553C2×C4—431no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—3442no—
558C2×C4—1721no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4#41×D4311yescharacteristic
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—861no—
575C8—861no—
576C8—1721no—
577C8—1721no—
578C8—1721no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—432no—
586C22—861no—
587C22—861no—
588C22—862no—
589C22—1728no—
590C22—1721no—
591C22—1721no—
592C22#121×D4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—81no—
596C4—432no—
597C4—861no—
598C4—861no—
599C4—3441no—
600C4—3441no—
601C4—1721no—
602C4#135×D4311yescharacteristic
603C4#135×D4311yescharacteristic
604C4C2×#1306334611yescharacteristic
605C4AGL(1,ℤ/8)×D4311yescharacteristic
606C2—42no—
607C2—161no—
608C2—862no—
609C2—1722no—
610C2#463×D4311yescharacteristic
611C2#1914417111yescharacteristic
612C2#1914431311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1677C2
socleC22×C43C2×#121
prime radical#19144594C2
hypercenter#1677D43
hypocenterC43#19110
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1677

Complements

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

NH ≅ G/Ntype
1. #19144914C2semidirect
2. #19144605C2semidirect
4. C8×D4×D43C2semidirect
5. #19134049C2semidirect
6. #19134048C2semidirect
7. #19134031C2semidirect
8. #19134030C2semidirect
9. #19134019C2semidirect
10. #19134018C2semidirect
11. #19134001C2semidirect
12. #19133340C2semidirect
13. #19133249C2semidirect
14. #19133241C2semidirect
15. C43×#1677C2semidirect
22. #14583251C22semidirect
23. #14583250C22semidirect
24. #14583245C22semidirect
51. #14582651C22semidirect
52. #14582651C22semidirect
53. #14582650C22semidirect
54. #14582648C22semidirect
55. #14582646C22semidirect
56. #14582646C22semidirect
57. #14582644C22semidirect
58. #14582644C22semidirect
59. #14582643C22semidirect
60. C43×#486C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
66. C43×#331C22semidirect
311. #1677D43semidirect
331. #486C2×D43semidirect
364. #334C2×D43semidirect
366. #333C2×D43semidirect
372. #331C2×D43semidirect
373. C43#19110semidirect

Maximal subgroups

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

subgroupindex
#191449142
#191446052
#191445942
C8×D4×D432
#191340492
#191340482
#191340312
#191340302
#191340192
#191340182
#191340012
#191333402
#191332492
#191332412
C43×#16772
#1911043