Finite Group Databasebeta

← #25082003

Subgroups — #25082003

Order 11008.

704 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
1#19145537C211yesmaximal, characteristic, complemented
2#19144386C211yesmaximal, characteristic, complemented
3#19144072C211yesmaximal, characteristic
4#19143705C211yesmaximal, characteristic, complemented
5#19134013C211yesmaximal, characteristic, complemented
6#19134007C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic, complemented
8#19133943C211yesmaximal, characteristic, complemented
9#19133941C211yesmaximal, characteristic, complemented
10#19133937C211yesmaximal, characteristic, complemented
11#19133935C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133282C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic, complemented
15C43×#1678C211yesmaximal, characteristic, complemented
16C2×#13063352—21no—
17#14583454C2211yescharacteristic
18#127×D43C2211yescharacteristic
19C4×#10621902C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583271C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583208—21no—
24#14583202—21no—
25#14583186C2211yescharacteristic, complemented
26#14583184C2211yescharacteristic, complemented
27#14583180C2211yescharacteristic, complemented
28#14583099C2211yescharacteristic
29#14583098—21no—
30#14583098—21no—
31#14583097—21no—
32#14583095C2211yescharacteristic
33#14583093—21no—
34#14583091C2211yescharacteristic
35#14583051—21no—
36#14583051—21no—
37Q8×C43⋊C8C2211yescharacteristic, complemented
38C8×D172—21no—
39C8×D172C2211yescharacteristic, complemented
40#14582964—21no—
41#14582964C2211yescharacteristic, complemented
42#14582950—21no—
43#14582950C2211yescharacteristic
44#14582936—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43—21no—
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582902—21no—
50#14582894—21no—
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#477C2211yescharacteristic, complemented
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic, complemented
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic
67C2×#10621902D411yescharacteristic
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71#13063352—44no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621883—21no—
75C2×#10621883—21no—
76C2×#10621884—21no—
77C2×D344—21no—
78C2×#10621882—21no—
79C2×#10621872—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83C2×C8×D43—21no—
84#13063325C2311yescharacteristic
85#13063322C2311yescharacteristic
86#13063321—21no—
87#13063321—21no—
88#13063321—21no—
89#13063316—21no—
90#13063305—21no—
91#13063301—21no—
92Q8×Dic43—21no—
93Q8×Dic43D411yescharacteristic
94#13063290—21no—
95C4×D172—21no—
96C4×D172C2311yescharacteristic
97#13063287—21no—
98#13063287D411yescharacteristic
99#13063283—21no—
100#13063283—21no—
101#13063283D411yescharacteristic
102C42×D43—21no—
103C42×D43C2311yescharacteristic
104#13063259—21no—
105#13063256—21no—
106#13063256—21no—
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8D411yescharacteristic
115Dic43⋊C8D411yescharacteristic
116#13063249—21no—
117#13063247—21no—
118#13063247—21no—
119#13063246—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123#13063245—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8D411yescharacteristic
127(C2×D43)⋊C8D411yescharacteristic
128C4×C43⋊C8—21no—
129C4×C43⋊C8C2311yescharacteristic
130C2×SD16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132#127×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#107×C43—21no—
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154#10621902—22no—
155#10621902SD1614yescomplemented
156D4×D43—42no—
157D4×D43—42no—
158D4×D43—81no—
159D4×D43—81no—
160D4×D43—82no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172C2×D411yescharacteristic
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43#4111yescharacteristic
172C2×Dic86—21no—
173SD16×C43—42no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43C2×D411yescharacteristic
183C42×C43—21no—
184C42×C43C2411yescharacteristic
185#10621884—42no—
186#10621883—81no—
187#10621883—81no—
188#10621882—42no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—41no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—41no—
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43#4111yescharacteristic
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210D344—42no—
211#10621873—81no—
212#10621873—81no—
213#10621872—42no—
214C8×D43—42no—
215C8×D43—81no—
216C8×D43—81no—
217C8×D43—81no—
218C23×C43—41no—
219C22×D43—21no—
220C22×D43—41no—
221C22×D43—82no—
222C22×D43—82no—
223C22×D43—82no—
224C22×D43#12111yescharacteristic
225Q8×C43—21no—
226Q8×C43—81no—
227Q8×C43C2×SD1612yes—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—81no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C22⋊D43—82no—
240C22⋊D43—82no—
241C22⋊D43—82no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43#12111yescharacteristic
245C2×Dic43#12111yescharacteristic
246C2×Dic43#12111yescharacteristic
247D172—24no—
248D172—21no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—81no—
254D172C2×SD1612yes—
255C4×D43—21no—
256C4×D43—21no—
257C4×D43—24no—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—81no—
262C4×D43C2×SD1612yes—
263C4×D43#13512yes—
264Dic86—41no—
265Dic86—41no—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—41no—
269C8×C43—41no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#19409—431nomaximal, Sylow
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C2×#12111yescharacteristic
281C2×D43—21no—
282C2×D43—21no—
283C2×D43—22no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—164no—
290C2×D43#46512yes—
291C4×C43—22no—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43C22×SD1611yescharacteristic
296C4×C43C2×#13511yescharacteristic
297C4×C43#57611yescharacteristic
298C4×C43#57711yescharacteristic
299Dic43—21no—
300Dic43—21no—
301Dic43—41no—
302Dic43—81no—
303Dic43#46512yes—
304#3208—431no—
305#3076—431no—
306#3038—431no—
307#2988—431no—
308#1678—431no—
309#1678D4311yescharacteristic, complemented
310#1677—431no—
311#1677—431no—
312#1666—431no—
313#1666—431no—
314#1665—431no—
315#1665—431no—
316#1570—431no—
317#1550—431no—
318C2×#331—431no—
319C2×C43—161no—
320C2×C43#304511yescharacteristic
321C2×C43C2×#46511yescharacteristic
322C2×C43#306811yescharacteristic
323D43—22no—
324D43—42no—
325D43—161no—
326C2×AGL(1,ℤ/8)—861no—
327#533—431no—
328C2×#127—431no—
329C4×#41—431no—
330#492—431no—
331#492—431no—
332#486—431no—
333#486C2×D4311yescharacteristic
334#479—861no—
335#478—861no—
336#477C2×D4311yescharacteristic, complemented
337#476—431no—
338#475—431no—
339#474—431no—
340#460—431no—
341#460—861no—
342#460—861no—
343#460—861no—
344#460C2×D4311yescharacteristic
345#459—431no—
346#459—431no—
347#459—861no—
348#450—861no—
349#450—861no—
350C8×Q8—431no—
351C8×Q8C2×D4311yescharacteristic, complemented
352C8×D4—431no—
353C8×D4—431no—
354C8×D4—861no—
355C8×D4—861no—
356#431—431no—
357#431—861no—
358#427—861no—
359#423—431no—
360C2×C4⋊C8—431no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—861no—
363#418—861no—
364#416—861no—
365#334—431no—
366#334—431no—
367#334—431no—
368#334C2×D4311yescharacteristic, complemented
369#333—431no—
370#333C2×D4311yescharacteristic, complemented
371#332—431no—
372#332—431no—
373#331—431no—
374#331—431no—
375#331—431no—
376#331C2×D4311yescharacteristic
377C43#1940911yescharacteristic, complemented, Sylow
378C2×#41—431no—
379C22×D4—861no—
380C22×D4—861no—
381C22×D4—861no—
382AGL(1,ℤ/8)—1724no—
383C2×SD16—21no—
384C2×SD16—861no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×D8—861no—
390C2×D8—861no—
391C2×M16—861no—
392C22×C8—861no—
393C22×C8—861no—
394C22×C8—861no—
395C22×C8—861no—
396C4⋊Q8—431no—
397C4⋊Q8C22×D4311yescharacteristic
398#127—431no—
399#127—861no—
400#127—861no—
401#127—861no—
402#127C22×D4311yescharacteristic
403#125—861no—
404C22⋊Q8—861no—
405C22⋊Q8—861no—
406C4×Q8—431no—
407C4×Q8—861no—
408C4×Q8—861no—
409C4×Q8C22×D4311yescharacteristic
410C4×D4—431no—
411C4×D4—431no—
412C4×D4—861no—
413C4×D4—861no—
414#117—431no—
415#117—861no—
416#117—861no—
417C2×C42—431no—
418C2×C42—861no—
419#107—21no—
420#107—861no—
421#106—861no—
422#106—861no—
423C4⋊C8—21no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8C22×D4311yescharacteristic
434C4⋊C8C22×D4311yescharacteristic
435C4⋊C8C22×D4311yescharacteristic
436#103—21no—
437#103—861no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448C22⋊C8—431no—
449C22⋊C8—431no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C4×C8—21no—
453C4×C8—431no—
454C4×C8—861no—
455C4×C8C22×D4311yescharacteristic
456C24—1721no—
457#41—434no—
458#41—862no—
459C2×Q8—21no—
460C2×Q8—861no—
461C2×Q8D4×D4311yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—431no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—3441no—
471C2×D4—3441no—
472C2×D4—3442no—
473C2×D4—1722no—
474C2×D4—1722no—
475C2×D4—1721no—
476C2×D4—1721no—
477C2×D4—1721no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484SD16—42no—
485SD16—3441no—
486SD16—3441no—
487SD16—3441no—
488SD16—3441no—
489SD16—1722no—
490D8—1722no—
491D8—1722no—
492M16—1722no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—3441no—
502C2×C8—3441no—
503C2×C8—3441no—
504C2×C8—1722no—
505C2×C8D4×D4311yescharacteristic
506C2×C8D4×D4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—431no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1721no—
515C4⋊C4—1721no—
516C4⋊C4D4×D4311yescharacteristic
517C22⋊C4—861no—
518C22⋊C4—861no—
519C22⋊C4—861no—
520C22⋊C4—1721no—
521C42—21no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—861no—
526C42—861no—
527C42—1721no—
528C42C23×D4311yescharacteristic
529C23—41no—
530C23—431no—
531C23—861no—
532C23—3442no—
533C23—3442no—
534C23—3442no—
535C23—1721no—
536Q8—21no—
537Q8—81no—
538Q8—1721no—
539Q8—1721no—
540Q8SD16×D4312yes—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—432no—
547D4—864no—
548D4—861no—
549D4—3441no—
550D4—3442no—
551D4—3442no—
552D4—3442no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—431no—
561C2×C4—432no—
562C2×C4—432no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—864no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—3441no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—861no—
583C8—861no—
584C8—1721no—
585C8—1721no—
586C8—1721no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—432no—
591C22—861no—
592C22—861no—
593C22—862no—
594C22—3441no—
595C22—3441no—
596C22—3441no—
597C22—1721no—
598C22—1721no—
599C22—6884no—
600C22#121×D4311yescharacteristic
601C4—21no—
602C4—22no—
603C4—41no—
604C4—81no—
605C4—432no—
606C4—861no—
607C4—861no—
608C4—3441no—
609C4—1721no—
610C4C2×SD16×D4311yescharacteristic
611C4#135×D4311yescharacteristic
612C4#1458370111yescharacteristic
613C4#1458370811yescharacteristic
614C2—161no—
615C2—862no—
616C2—1722no—
617C2—6881no—
618C2#1914413711yescharacteristic
619C2#465×D4311yescharacteristic
620C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1678C2
socleC22×C43C2×#121
prime radical#19144072C2
hypercenter#1678D43
hypocenterC43#19409
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1678

Complements

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

NH ≅ G/Ntype
1. #19145537C2semidirect
2. #19144386C2semidirect
4. #19143705C2semidirect
5. #19134013C2semidirect
6. #19134007C2semidirect
7. #19134001C2semidirect
8. #19133943C2semidirect
9. #19133941C2semidirect
10. #19133937C2semidirect
11. #19133935C2semidirect
12. #19133364C2semidirect
13. #19133282C2semidirect
14. #331×D43C2semidirect
15. C43×#1678C2semidirect
25. #14583186C22semidirect
26. #14583184C22semidirect
27. #14583180C22semidirect
37. Q8×C43⋊C8C22semidirect
39. C8×D172C22semidirect
41. #14582964C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582646C22semidirect
56. #14582644C22semidirect
61. C43×#477C22semidirect
63. C8×Q8×C43C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
155. #10621902SD16semidirect
309. #1678D43semidirect
336. #477C2×D43semidirect
351. C8×Q8C2×D43semidirect
368. #334C2×D43semidirect
370. #333C2×D43semidirect
377. C43#19409semidirect

Maximal subgroups

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

subgroupindex
#191455372
#191443862
#191440722
#191437052
#191340132
#191340072
#191340012
#191339432
#191339412
#191339372
#191339352
#191333642
#191332822
#331×D432
C43×#16782
#1940943