Finite Group Databasebeta

← #25079382

Subgroups — #25079382

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145136C211yesmaximal, characteristic, complemented
2#19144605C211yesmaximal, characteristic
3#461×D43C211yesmaximal, characteristic
4#19143331C211yesmaximal, characteristic
5#19134108C211yesmaximal, characteristic, complemented
6#19134106C211yesmaximal, characteristic, complemented
7#19134096C211yesmaximal, characteristic, complemented
8#19133985C211yesmaximal, characteristic, complemented
9#19133983C211yesmaximal, characteristic, complemented
10#19133973C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#19133346C211yesmaximal, characteristic, complemented
13#19133282C211yesmaximal, characteristic, complemented
14#19133278C211yesmaximal, characteristic, complemented
15C43×#1691C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C2×M16×D43—21no—
18#14583454C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20C4×D4×D43C2211yescharacteristic
21#14583306—21no—
22#14583306—21no—
23#14583304C2211yescharacteristic, complemented
24#14583302C2211yescharacteristic, complemented
25#14583295C2211yescharacteristic, complemented
26#14583231—21no—
27#14583186C2211yescharacteristic
28#14583105C2211yescharacteristic
29#14583105C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583103—21no—
33#14583102—21no—
34#14583101C2211yescharacteristic
35#14583051—21no—
36#14582990—21no—
37#14582986—21no—
38#14582977C2211yescharacteristic
39#14582973—21no—
40#14582968—21no—
41C8×D172C2211yescharacteristic
42#14582964C2211yescharacteristic
43#14582951C2211yescharacteristic
44#14582938—21no—
45#14582938—21no—
46#14582921C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48#103×D43—21no—
49#14582861—21no—
50C4×#10621872C2211yescharacteristic
51#14582651C2211yescharacteristic, complemented
52#14582650C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582646C2211yescharacteristic, complemented
57#14582645C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#498C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75SD16×D43—44no—
76C2×#10621877—21no—
77C2×#10621872—21no—
78C2×#10621872D411yescharacteristic
79C2×#10621872D411yescharacteristic
80M16×D43—44no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83C2×C8×D43—21no—
84#13063325C2311yescharacteristic
85#13063325C2311yescharacteristic
86#13063324—21no—
87#13063324—21no—
88#13063323—21no—
89#13063316—21no—
90#13063305—21no—
91#13063301—21no—
92Q8×Dic43—21no—
93#13063290—21no—
94C4×D172C2311yescharacteristic
95D4×Dic43D411yescharacteristic
96#13063287D411yescharacteristic
97C4×C22⋊D43—21no—
98(C22⋊D43)⋊C4—21no—
99#13063283—21no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43—21no—
102C4⋊C4×D43D411yescharacteristic
103C22⋊C4×D43—21no—
104C42×D43C2311yescharacteristic
105#13063259—21no—
106#13063259—21no—
107#13063258—21no—
108#13063258—21no—
109#13063256—21no—
110#13063256—21no—
111#13063256—21no—
112C4⋊(C43⋊C8)C2311yescharacteristic
113C4⋊(C43⋊C8)C2311yescharacteristic
114C4⋊(C43⋊C8)C2311yescharacteristic
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117#13063250—21no—
118#13063250—21no—
119#13063249—21no—
120#13063248—21no—
121#13063248—21no—
122#13063245—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127#13063235D411yescharacteristic
128#13063235D411yescharacteristic
129C4×C43⋊C8C2311yescharacteristic
130C8×Dic43—21no—
131C2×SD16×C43—21no—
132C2×M16×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134C4⋊Q8×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#106×C43—21no—
137#106×C43—21no—
138#106×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142#103×C43—21no—
143#102×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C22×Dic43—21no—
153Q8×D43—42no—
154Q8×D43—42no—
155D4×D43—22no—
156D4×D43—41no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—41no—
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43#4111yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—41no—
170SD16×C43—42no—
171M16×C43—42no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185#10621884—42no—
186#10621883—42no—
187#10621883—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—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C4×Dic43—41no—
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43#4111yescharacteristic
205#10621877—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211#10621873—42no—
212#10621873—42no—
213#10621872—22no—
214#10621872—42no—
215#10621872SD1614yescomplemented
216C8×D43—42no—
217C8×D43—42no—
218C8×D43—42no—
219C23×C43—21no—
220C22×D43—21no—
221C22×D43—42no—
222C22×D43—42no—
223C22×D43—81no—
224C22×D43#12111yescharacteristic
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—81no—
228D4×C43—21no—
229D4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—42no—
239C2×Dic43—21no—
240C2×Dic43—42no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43#12111yescharacteristic
244C2×Dic43#12111yescharacteristic
245C2×Dic43#12111yescharacteristic
246D172—21no—
247D172AGL(1,ℤ/8)12yes—
248C4×D43—21no—
249C4×D43—21no—
250C4×D43—41no—
251C4×D43—42no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—42no—
255C4×D43—82no—
256C4×D43C2×SD1612yes—
257C4×D43#13712yes—
258Dic86—41no—
259Dic86—41no—
260Dic86—41no—
261Dic86—41no—
262Dic86—82no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43C2×SD1612yescomplemented
268C43⋊C8—21no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C43⋊C8C2×SD1612yescomplemented
273#19164—431nomaximal, Sylow
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43C2×#12111yescharacteristic
278C2×D43—21no—
279C2×D43—21no—
280C2×D43—22no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—84no—
284C2×D43#46112yes—
285C4×C43—21no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C22×SD1611yescharacteristic
290C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C43C2×#13711yescharacteristic
292C4×C43#57511yescharacteristic
293Dic43—21no—
294Dic43—21no—
295Dic43—41no—
296Dic43—81no—
297Dic43—81no—
298Dic43#46112yes—
299#3165—431no—
300#3101—431no—
301C2×#461—431no—
302D4×M16—431no—
303#1693—431no—
304#1693—431no—
305#1691—431no—
306#1691D4311yescharacteristic, complemented
307#1673—431no—
308#1673—431no—
309#1671—431no—
310#1671—431no—
311#1565—431no—
312#1550—431no—
313#1549—431no—
314C2×C43—81no—
315C2×C43C2×#46111yescharacteristic
316C2×C43#305511yescharacteristic
317C2×C43#306911yescharacteristic
318D43—22no—
319D43—42no—
320C22×SD16—861no—
321C22×M16—861no—
322#533—431no—
323C2×C4⋊Q8—431no—
324C2×C4×D4—431no—
325#501—861no—
326#501—861no—
327#500—431no—
328#500—431no—
329#498—431no—
330#498C2×D4311yescharacteristic, complemented
331#483—861no—
332#476—431no—
333#476C2×D4311yescharacteristic
334#461—431no—
335#461—431no—
336#461—431no—
337#461—431no—
338#461—431no—
339#461—861no—
340#461—861no—
341#461C2×D4311yescharacteristic
342#450—861no—
343C4×SD16—861no—
344C4×SD16—861no—
345#436—431no—
346#436C2×D4311yescharacteristic
347#435—861no—
348#435—861no—
349C8×D4—431no—
350C8×D4—431no—
351#431—431no—
352#428—861no—
353#428—861no—
354#423—431no—
355C2×C4⋊C8—431no—
356C2×#103—861no—
357#407—861no—
358C4×M16—431no—
359#335—431no—
360#335C2×D4311yescharacteristic, complemented
361#334—431no—
362#334—431no—
363#333—431no—
364#333C2×D4311yescharacteristic, complemented
365#332—431no—
366#332—431no—
367#332—431no—
368#332—431no—
369#332—431no—
370#332C2×D4311yescharacteristic, complemented
371C43#1916411yescharacteristic, complemented, Sylow
372C22×Q8—861no—
373C22×D4—431no—
374C23×C4—861no—
375C2×SD16—21no—
376C2×SD16—861no—
377C2×SD16—861no—
378C2×SD16—861no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×SD16—1724no—
382C2×M16—21no—
383C2×M16—431no—
384C2×M16—431no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16—1724no—
388C22×C8—861no—
389C22×C8—861no—
390C22×C8—861no—
391C4⋊Q8—431no—
392C4⋊Q8—431no—
393C4⋊Q8—861no—
394C4⋊Q8—861no—
395C4⋊Q8—861no—
396C4⋊Q8C22×D4311yescharacteristic
397C4⋊Q8C22×D4311yescharacteristic
398#125—861no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×D4—431no—
404C4×D4—431no—
405C4×D4—431no—
406C4×D4—861no—
407C4×D4—861no—
408C4×D4C22×D4311yescharacteristic
409#117—861no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—431no—
415#107—861no—
416#107—861no—
417#107—861no—
418#107—861no—
419#106—21no—
420#106—21no—
421#106—21no—
422#106—861no—
423#106—861no—
424#106—861no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—861no—
429C4⋊C8—861no—
430C4⋊C8C22×D4311yescharacteristic
431C4⋊C8C22×D4311yescharacteristic
432C4⋊C8C22×D4311yescharacteristic
433#103—21no—
434#103—861no—
435#103—861no—
436#103—861no—
437#103—861no—
438#103—861no—
439#102—21no—
440#102—861no—
441C22⋊C8—21no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446#97—431no—
447#97—431no—
448C4×C8—431no—
449C4×C8—861no—
450C4×C8C22×D4311yescharacteristic
451C24—861no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—1721no—
457C2×Q8—1722no—
458C2×Q8—1722no—
459C2×D4—431no—
460C2×D4—861no—
461C2×D4—862no—
462C2×D4—1721no—
463C2×D4D4×D4311yescharacteristic
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—1722no—
473C22×C4—1722no—
474C22×C4—1721no—
475SD16—42no—
476SD16—1722no—
477SD16—1722no—
478SD16—1722no—
479SD16—1722no—
480SD16—1722no—
481M16—42no—
482M16—434no—
483M16—862no—
484M16—1722no—
485M16—1722no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—431no—
490C2×C8—431no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—1722no—
495C2×C8—1722no—
496C2×C8—1722no—
497C2×C8D4×D4311yescharacteristic
498C2×C8D4×D4311yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—431no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4—1721no—
512C4⋊C4—1721no—
513C4⋊C4D4×D4311yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—861no—
516C22⋊C4—861no—
517C22⋊C4—861no—
518C22⋊C4—1721no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42—1721no—
523C42C23×D4311yescharacteristic
524C23—21no—
525C23—431no—
526C23—861no—
527C23—3441no—
528C23—1722no—
529C23—1722no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533Q8—3442no—
534Q8—1721no—
535Q8—1721no—
536Q8—1721no—
537Q8—1721no—
538D4—21no—
539D4—21no—
540D4—432no—
541D4—861no—
542D4—1722no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—431no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—431no—
552C2×C4—431no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—3442no—
557C2×C4—1721no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4C2×D4×D4311yescharacteristic
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C8—21no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—432no—
573C8—861no—
574C8—1721no—
575C8—1721no—
576C8—1721no—
577C8SD16×D4312yescomplemented
578C22—41no—
579C22—41no—
580C22—41no—
581C22—432no—
582C22—861no—
583C22—861no—
584C22—862no—
585C22—3444no—
586C22—1721no—
587C22—1721no—
588C22#121×D4311yescharacteristic
589C4—21no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—432no—
594C4—861no—
595C4—861no—
596C4—3441no—
597C4—3441no—
598C4—1721no—
599C4C2×SD16×D4311yescharacteristic
600C4AGL(1,ℤ/8)×D4311yescharacteristic
601C4#137×D4311yescharacteristic
602C4#1458369811yescharacteristic
603C2—81no—
604C2—862no—
605C2—1722no—
606C2#461×D4311yescharacteristic
607C2#1914420911yescharacteristic
608C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1691C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1691D43
hypocenterC43#19164
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1691

Complements

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

NH ≅ G/Ntype
1. #19145136C2semidirect
5. #19134108C2semidirect
6. #19134106C2semidirect
7. #19134096C2semidirect
8. #19133985C2semidirect
9. #19133983C2semidirect
10. #19133973C2semidirect
11. #19133967C2semidirect
12. #19133346C2semidirect
13. #19133282C2semidirect
14. #19133278C2semidirect
15. C43×#1691C2semidirect
23. #14583304C22semidirect
24. #14583302C22semidirect
25. #14583295C22semidirect
51. #14582651C22semidirect
52. #14582650C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582646C22semidirect
56. #14582646C22semidirect
57. #14582645C22semidirect
58. #14582644C22semidirect
59. #14582644C22semidirect
60. C43×#498C22semidirect
64. C43×#335C22semidirect
65. C43×#333C22semidirect
66. C43×#332C22semidirect
215. #10621872SD16semidirect
267. C8×C43C2×SD16semidirect
272. C43⋊C8C2×SD16semidirect
306. #1691D43semidirect
330. #498C2×D43semidirect
360. #335C2×D43semidirect
364. #333C2×D43semidirect
370. #332C2×D43semidirect
371. C43#19164semidirect
577. C8SD16×D43semidirect

Maximal subgroups

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

subgroupindex
#191451362
#191446052
#461×D432
#191433312
#191341082
#191341062
#191340962
#191339852
#191339832
#191339732
#191339672
#191333462
#191332822
#191332782
C43×#16912
#1916443