Finite Group Databasebeta

← #25081802

Subgroups — #25081802

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145531C211yesmaximal, characteristic, complemented
2#19144688C211yesmaximal, characteristic, complemented
3#19144597C211yesmaximal, characteristic, complemented
4#19143616C211yesmaximal, characteristic, complemented
5#19134043C211yesmaximal, characteristic, complemented
6#19134007C211yesmaximal, characteristic, complemented
7#19134006C211yesmaximal, characteristic, complemented
8#19133951C211yesmaximal, characteristic, complemented
9#19133950C211yesmaximal, characteristic, complemented
10#19133939C211yesmaximal, characteristic, complemented
11#19133938C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic, complemented
13#19133299C211yesmaximal, characteristic, complemented
14#19133256C211yesmaximal, characteristic, complemented
15C43×#1683C211yesmaximal, characteristic, complemented
16#14583450C2211yescharacteristic
17#14583450C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583276C2211yescharacteristic, complemented
20#14583273C2211yescharacteristic, complemented
21#14583247C2211yescharacteristic, complemented
22#14583219—21no—
23#14583214—21no—
24#14583186C2211yescharacteristic
25#14583176C2211yescharacteristic
26#14583117—21no—
27#14583117—21no—
28#14583095C2211yescharacteristic
29#14583095C2211yescharacteristic
30#14583094C2211yescharacteristic
31#14583094C2211yescharacteristic
32#14583047—21no—
33#14583047—21no—
34#14583034—21no—
35#14583034—21no—
36#14583010—21no—
37#14583008—21no—
38#14582981—21no—
39#14582979—21no—
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582964C2211yescharacteristic
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582950C2211yescharacteristic
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582652C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582645C2211yescharacteristic, complemented
56#14582642C2211yescharacteristic, complemented
57#14582642C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#487C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×#10621902—21no—
68C2×#10621902—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×D344—21no—
74C2×D344—21no—
75C2×D344—21no—
76C2×D344—21no—
77C2×#10621882—21no—
78C2×#10621882—21no—
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82#13063322C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063314—21no—
85#13063314—21no—
86#13063300—21no—
87#13063300—21no—
88#13063300—21no—
89#13063300—21no—
90C4×D172C2311yescharacteristic
91D4×Dic43D411yescharacteristic
92#13063287—21no—
93#13063287—21no—
94#13063287—21no—
95#13063287—21no—
96#13063287D411yescharacteristic
97C4×C22⋊D43—21no—
98(C22⋊D43)⋊C4—21no—
99C4⋊C4×D43D411yescharacteristic
100C22⋊C4×D43—21no—
101C42×D43C2311yescharacteristic
102#13063258—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8D411yescharacteristic
108Dic43⋊C8D411yescharacteristic
109#13063247—21no—
110#13063247—21no—
111#13063245—21no—
112#13063245—21no—
113#13063245—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125#13063235—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C22×C8×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#107×C43—21no—
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43C2×D411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151#10621902—81no—
152#10621902—81no—
153#10621902—82no—
154D4×D43—22no—
155D4×D43—22no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—41no—
163C2×D172—41no—
164C2×D172C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—41no—
169C2×C4×D43—41no—
170C2×C4×D43—81no—
171C2×C4×D43—81no—
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43#4111yescharacteristic
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—81no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C42×C43C2411yescharacteristic
188C22⋊Dic43—21no—
189#10621884—81no—
190#10621884—81no—
191#10621882—42no—
192#10621882—42no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—41no—
197(C2×D43)⋊C4—41no—
198(C2×D43)⋊C4—41no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43#4111yescharacteristic
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210D344—42no—
211D344—42no—
212D344—81no—
213D344—81no—
214C8×D43—81no—
215C8×D43—81no—
216C23×C43—21no—
217C22×D43—21no—
218C22×D43—24no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—81no—
222C22×D43—81no—
223C22×D43#12111yescharacteristic
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—81no—
227D4×C43—21no—
228D4×C43#13512yes—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
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—
238C2×Dic43—21no—
239C2×Dic43—81no—
240C2×Dic43#12111yescharacteristic
241C2×Dic43#12111yescharacteristic
242C2×Dic43#12111yescharacteristic
243D172—21no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—41no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—81no—
253D172—81no—
254D172—82no—
255D172—82no—
256D172#13512yes—
257C4×D43—21no—
258C4×D43—21no—
259C4×D43—21no—
260C4×D43—21no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—81no—
265C4×D43—82no—
266C4×D43—82no—
267C4×D43—81no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C43⋊C8—21no—
274C43⋊C8—21no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#19389—431nomaximal, Sylow
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43C2×#12111yescharacteristic
283C2×D43—21no—
284C2×D43—21no—
285C2×D43—22no—
286C2×D43—21no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—84no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C2×D43—81no—
296C4×C43—21no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43C2×#13511yescharacteristic
301C4×C43C2×#13511yescharacteristic
302C4×C43#57611yescharacteristic
303C4×C43#57611yescharacteristic
304Dic43—21no—
305Dic43—21no—
306Dic43—21no—
307Dic43—41no—
308#3207—431no—
309#3109—431no—
310#3100—431no—
311#2972—431no—
312#1683—431no—
313#1683D4311yescharacteristic, complemented
314#1677—431no—
315#1677—431no—
316#1667—431no—
317#1667—431no—
318#1665—431no—
319#1665—431no—
320#1572—431no—
321#1553—431no—
322#1543—431no—
323C2×C43—42no—
324C2×C43#304111yescharacteristic
325C2×C43#305011yescharacteristic
326C2×C43#306811yescharacteristic
327D43—41no—
328D43—42no—
329D43—161no—
330D43—161no—
331#532—431no—
332#532—431no—
333C2×C4×D4—431no—
334#493—431no—
335#492—431no—
336#487C2×D4311yescharacteristic, complemented
337#486—431no—
338#481—861no—
339#480—861no—
340#476—431no—
341#476C2×D4311yescharacteristic
342#474—431no—
343#474C2×D4311yescharacteristic
344#463—861no—
345#463—861no—
346#459—431no—
347#459—431no—
348#459—431no—
349#459—431no—
350#449—861no—
351#449—861no—
352#447—861no—
353#447—861no—
354#442—861no—
355#442—861no—
356C4×D8—861no—
357C4×D8—861no—
358C8×D4—431no—
359C8×D4—431no—
360C8×D4—431no—
361C8×D4—861no—
362C8×D4—861no—
363C8×D4C2×D4311yescharacteristic
364#432—431no—
365#431—431no—
366#431—431no—
367#431—431no—
368C2×C22⋊C8—861no—
369C2×C22⋊C8—861no—
370#335—431no—
371#335C2×D4311yescharacteristic, complemented
372#334—431no—
373#334—431no—
374#333—431no—
375#333C2×D4311yescharacteristic, complemented
376#332—431no—
377#332C2×D4311yescharacteristic, complemented
378#331—431no—
379#331—431no—
380#331—431no—
381#331—431no—
382C43#1938911yescharacteristic, complemented, Sylow
383C2×#41—861no—
384C2×#41—861no—
385C22×D4—431no—
386C23×C4—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×D8—861no—
390C2×D8—861no—
391C2×D8—861no—
392C2×D8—861no—
393C2×D8—861no—
394C2×D8—861no—
395C22×C8—21no—
396C22×C8—861no—
397C22×C8—861no—
398C22×C8—861no—
399C4⋊Q8C22×D4311yescharacteristic
400C4⋊Q8C22×D4311yescharacteristic
401#127—431no—
402#127—431no—
403#124—861no—
404#124—861no—
405#121—861no—
406#121—861no—
407#121—861no—
408#121—861no—
409C4×D4—431no—
410C4×D4—431no—
411C4×D4—431no—
412C4×D4—861no—
413C4×D4—861no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4C22×D4311yescharacteristic
419C2×C4⋊C4—431no—
420C2×C22⋊C4—861no—
421C2×C42—431no—
422#107—21no—
423#107—861no—
424#106—21no—
425#106—861no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8C22×D4311yescharacteristic
432C4⋊C8C22×D4311yescharacteristic
433C4⋊C8C22×D4311yescharacteristic
434#103—21no—
435#103—21no—
436#102—21no—
437#102—21no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446C22⋊C8—21no—
447C22⋊C8—431no—
448C22⋊C8—431no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455#97—861no—
456C4×C8—431no—
457C4×C8—861no—
458C4×C8—861no—
459C4×C8C22×D4311yescharacteristic
460C24—861no—
461#41—3441no—
462#41—3441no—
463#41—3442no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—431no—
467C2×D4—861no—
468C2×D4—862no—
469C2×D4—862no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—1721no—
477C2×D4—1721no—
478C2×D4D4×D4311yescharacteristic
479C22×C4—21no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—3441no—
488C22×C4—3441no—
489C22×C4—1721no—
490C22×C4—1721no—
491SD16—3441no—
492SD16—3441no—
493D8—3441no—
494D8—3441no—
495D8—1722no—
496D8—1722no—
497D8—1722no—
498D8—1722no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—81no—
503C2×C8—431no—
504C2×C8—431no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—3441no—
509C2×C8—3441no—
510C2×C8—3441no—
511C2×C8D4×D4311yescharacteristic
512C2×C8D4×D4311yescharacteristic
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—431no—
518C4⋊C4—861no—
519C4⋊C4D4×D4311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—861no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C22⋊C4—1721no—
525C22⋊C4—1721no—
526C22⋊C4—1721no—
527C22⋊C4—1721no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42C23×D4311yescharacteristic
532C23—21no—
533C23—431no—
534C23—864no—
535C23—861no—
536C23—3441no—
537C23—3441no—
538C23—1721no—
539C23—1721no—
540Q8—41no—
541Q8—41no—
542Q8—81no—
543D4—21no—
544D4—432no—
545D4—864no—
546D4—861no—
547D4—3441no—
548D4—3441no—
549D4—3442no—
550D4—3442no—
551D4—1721no—
552D4—1721no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
559D4#1306334812yes—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—431no—
566C2×C4—431no—
567C2×C4—431no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—3441no—
574C2×C4—3441no—
575C2×C4—3442no—
576C2×C4—3442no—
577C2×C4—3441no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4C2×D4×D4311yescharacteristic
582C2×C4C2×D4×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—861no—
590C8—861no—
591C8—1721no—
592C8—1721no—
593C8—1721no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—861no—
598C22—861no—
599C22—861no—
600C22—862no—
601C22—3444no—
602C22—3441no—
603C22—3441no—
604C22—3441no—
605C22—3441no—
606C22—3441no—
607C22—3441no—
608C22—1721no—
609C22—1721no—
610C22#121×D4311yescharacteristic
611C4—21no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—861no—
616C4—861no—
617C4—861no—
618C4—1721no—
619C4#135×D4311yescharacteristic
620C4C2×#1306334811yescharacteristic
621C4#1458370111yescharacteristic
622C4#1458370311yescharacteristic
623C2—42no—
624C2—1721no—
625C2—1722no—
626C2—6881no—
627C2—6881no—
628C2#1914409611yescharacteristic
629C2#1914417811yescharacteristic
630C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1683C2
socleC22×C43C2×#121
hypercenter#1683D43
hypocenterC43#19389
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1683

Complements

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

NH ≅ G/Ntype
1. #19145531C2semidirect
2. #19144688C2semidirect
3. #19144597C2semidirect
4. #19143616C2semidirect
5. #19134043C2semidirect
6. #19134007C2semidirect
7. #19134006C2semidirect
8. #19133951C2semidirect
9. #19133950C2semidirect
10. #19133939C2semidirect
11. #19133938C2semidirect
12. #19133374C2semidirect
13. #19133299C2semidirect
14. #19133256C2semidirect
15. C43×#1683C2semidirect
19. #14583276C22semidirect
20. #14583273C22semidirect
21. #14583247C22semidirect
51. #14582652C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582645C22semidirect
56. #14582642C22semidirect
57. #14582642C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#487C22semidirect
64. C43×#335C22semidirect
65. C43×#333C22semidirect
66. C43×#332C22semidirect
313. #1683D43semidirect
336. #487C2×D43semidirect
371. #335C2×D43semidirect
375. #333C2×D43semidirect
377. #332C2×D43semidirect
382. C43#19389semidirect

Maximal subgroups

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

subgroupindex
#191455312
#191446882
#191445972
#191436162
#191340432
#191340072
#191340062
#191339512
#191339502
#191339392
#191339382
#191333742
#191332992
#191332562
C43×#16832
#1938943