Finite Group Databasebeta

← #25081868

Subgroups — #25081868

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145532C211yesmaximal, characteristic
2#19144395C211yesmaximal, characteristic, complemented
3#460×D43C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic, complemented
5#19134012C211yesmaximal, characteristic, complemented
6#19134011C211yesmaximal, characteristic, complemented
7#19134010C211yesmaximal, characteristic, complemented
8#19134009C211yesmaximal, characteristic, complemented
9#19133946C211yesmaximal, characteristic, complemented
10#19133945C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133261C211yesmaximal, characteristic
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1666C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17#14583454C2211yescharacteristic
18#127×D43C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583273C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583209—21no—
24#14583208—21no—
25#14583195C2211yescharacteristic, complemented
26#14583194C2211yescharacteristic, complemented
27#14583181C2211yescharacteristic, complemented
28#14583100C2211yescharacteristic
29#14583099C2211yescharacteristic
30#14583098—21no—
31#14583097—21no—
32#14583097—21no—
33#14583097—21no—
34#14583096C2211yescharacteristic
35#14583048—21no—
36#14583048—21no—
37Q8×C43⋊C8C2211yescharacteristic, complemented
38C8×Dic86—21no—
39C8×Dic86C2211yescharacteristic, complemented
40#14583023—21no—
41#14583023C2211yescharacteristic, complemented
42#14582951—21no—
43#14582951C2211yescharacteristic
44#14582950—21no—
45#14582950C2211yescharacteristic
46#14582938—21no—
47#14582921C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582906—21no—
50#102×D43—21no—
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#475C2211yescharacteristic, complemented
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic, complemented
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic
67C2×Q8×D43D411yescharacteristic
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76SD16×D43—44no—
77C2×#10621872—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063321—21no—
82#13063321—21no—
83#13063321—21no—
84#13063316—21no—
85#13063305—21no—
86#13063301—21no—
87Q8×Dic43—21no—
88Q8×Dic43D411yescharacteristic
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91#13063290—21no—
92#13063290—21no—
93#13063290D411yescharacteristic
94#13063283—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43D411yescharacteristic
97C42×D43—21no—
98C42×D43C2311yescharacteristic
99#13063259—21no—
100#13063258—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8D411yescharacteristic
111Dic43⋊C8D411yescharacteristic
112#13063250—21no—
113#13063249—21no—
114#13063248—21no—
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063245—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—21no—
132C2×SD16×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×Q8×C43C2311yescharacteristic
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×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—
154Q8×D43—22no—
155Q8×D43SD1614yescomplemented
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×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43#4111yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86C2×D411yescharacteristic
172SD16×C43—42no—
173SD16×C43—81no—
174SD16×C43—81no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C2×D411yescharacteristic
184C42×C43—21no—
185C42×C43C2411yescharacteristic
186#10621884—42no—
187#10621884—81no—
188#10621884—81no—
189#10621883—42no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199Dic43⋊C4—41no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—41no—
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43C2×D411yescharacteristic
206C4×Dic43#4111yescharacteristic
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212#10621873—42no—
213#10621872—42no—
214C8×D43—42no—
215C23×C43—41no—
216C22×D43—41no—
217C22×D43—82no—
218C22×D43—82no—
219C22×D43—82no—
220C22×D43#12111yescharacteristic
221Q8×C43—21no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43C2×SD1612yes—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—81no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—82no—
237C22⋊D43—82no—
238C22⋊D43—82no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43#12111yescharacteristic
243C2×Dic43#12111yescharacteristic
244C2×Dic43#12111yescharacteristic
245D172—41no—
246D172—41no—
247D172—41no—
248D172—41no—
249D172—81no—
250C4×D43—24no—
251C4×D43—21no—
252C4×D43—21no—
253C4×D43—41no—
254C4×D43—81no—
255C4×D43C2×SD1612yes—
256C4×D43#13512yes—
257Dic86—21no—
258Dic86—24no—
259Dic86—81no—
260Dic86C2×SD1612yes—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#19396—431nomaximal, Sylow
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43C2×#12111yescharacteristic
276C2×D43—21no—
277C2×D43—21no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—164no—
282C2×D43#46512yes—
283C4×C43—22no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—81no—
287C4×C43C22×SD1611yescharacteristic
288C4×C43C2×#13511yescharacteristic
289C4×C43#57711yescharacteristic
290C4×C43#57711yescharacteristic
291Dic43—21no—
292Dic43—22no—
293Dic43—21no—
294Dic43—41no—
295Dic43—81no—
296Dic43#46512yes—
297#3208—431no—
298#3078—431no—
299C2×#460—431no—
300#2982—431no—
301#1678—431no—
302#1678—431no—
303#1678—431no—
304#1678—431no—
305#1666—431no—
306#1666—431no—
307#1666—431no—
308#1666D4311yescharacteristic, complemented
309#1570—431no—
310#1545—431no—
311#1542—431no—
312C2×C43—161no—
313C2×C43#304311yescharacteristic
314C2×C43C2×#46511yescharacteristic
315C2×C43#306811yescharacteristic
316D43—22no—
317D43—161no—
318C22×SD16—861no—
319#533—431no—
320C2×#127—431no—
321C2×C4×Q8—431no—
322#492—431no—
323#492C2×D4311yescharacteristic
324#486—431no—
325#486—431no—
326#479—861no—
327#479—861no—
328#477—431no—
329#477—431no—
330#475—431no—
331#475C2×D4311yescharacteristic, complemented
332#460—431no—
333#460—431no—
334#460—431no—
335#460—861no—
336#460—861no—
337#460—861no—
338#460—861no—
339#460C2×D4311yescharacteristic
340#450—861no—
341#450—861no—
342C8×Q8—431no—
343C8×Q8—431no—
344C8×Q8—431no—
345C8×Q8—861no—
346C8×Q8—861no—
347C8×Q8C2×D4311yescharacteristic, complemented
348#431—431no—
349#431—431no—
350#431—861no—
351#431—861no—
352#428—861no—
353#423—431no—
354C2×C4⋊C8—431no—
355#419—861no—
356C2×#102—861no—
357#334—431no—
358#334—431no—
359#334—431no—
360#334C2×D4311yescharacteristic, complemented
361#333—431no—
362#333—431no—
363#332—431no—
364#332C2×D4311yescharacteristic, complemented
365#331—431no—
366#331—431no—
367#331—431no—
368#331C2×D4311yescharacteristic
369C43#1939611yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C22×D4—861no—
372C22×D4—861no—
373C22×D4—861no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—861no—
378C2×SD16—861no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×SD16—861no—
382C2×SD16—1724no—
383C2×M16—861no—
384C22×C8—861no—
385C4⋊Q8—431no—
386C4⋊Q8C22×D4311yescharacteristic
387#127—431no—
388#127—861no—
389#127—861no—
390#127—861no—
391#127C22×D4311yescharacteristic
392#125—861no—
393C22⋊Q8—861no—
394C22⋊Q8—861no—
395C4×Q8—431no—
396C4×Q8—431no—
397C4×Q8—431no—
398C4×Q8—861no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8C22×D4311yescharacteristic
403#117—861no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—861no—
406C2×C42—431no—
407C2×C42—861no—
408#107—861no—
409#107—861no—
410#106—21no—
411#106—861no—
412C4⋊C8—21no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8—861no—
421C4⋊C8—861no—
422C4⋊C8—861no—
423C4⋊C8C22×D4311yescharacteristic
424C4⋊C8C22×D4311yescharacteristic
425C4⋊C8C22×D4311yescharacteristic
426#103—21no—
427#103—861no—
428#103—861no—
429#103—861no—
430#102—21no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438C22⋊C8—431no—
439C22⋊C8—431no—
440C22⋊C8—861no—
441C4×C8—21no—
442C4×C8—431no—
443C4×C8—861no—
444C4×C8—861no—
445C4×C8—861no—
446C4×C8—861no—
447C4×C8C22×D4311yescharacteristic
448C24—1721no—
449C2×Q8—21no—
450C2×Q8—434no—
451C2×Q8—431no—
452C2×Q8—861no—
453C2×Q8—862no—
454C2×Q8—861no—
455C2×Q8D4×D4311yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—3441no—
463C2×D4—3441no—
464C2×D4—3442no—
465C2×D4—1722no—
466C2×D4—1722no—
467C2×D4—1721no—
468C2×D4—1721no—
469C2×D4—1721no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—861no—
474C22×C4—861no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—3441no—
479SD16—3441no—
480SD16—1722no—
481SD16—1722no—
482SD16—1722no—
483M16—1722no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—1722no—
493C2×C8D4×D4311yescharacteristic
494C2×C8D4×D4311yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—431no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—1721no—
506C4⋊C4—1721no—
507C4⋊C4D4×D4311yescharacteristic
508C22⋊C4—1721no—
509C42—21no—
510C42—431no—
511C42—431no—
512C42—431no—
513C42—861no—
514C42—861no—
515C42—861no—
516C42—1721no—
517C42C23×D4311yescharacteristic
518C23—41no—
519C23—431no—
520C23—3442no—
521C23—3442no—
522C23—3442no—
523C23—1721no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—432no—
528Q8—864no—
529Q8—861no—
530Q8—3441no—
531Q8SD16×D4312yes—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—3441no—
538D4—3442no—
539D4—3442no—
540D4—3442no—
541D4—1721no—
542D4—1721no—
543D4—1721no—
544D4—1721no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—431no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—431no—
552C2×C4—431no—
553C2×C4—864no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—3441no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C2×D4×D4311yescharacteristic
563C2×C4#41×D4311yescharacteristic
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—861no—
570C8—861no—
571C8—1721no—
572C8—1721no—
573C8—1721no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—432no—
578C22—861no—
579C22—861no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—6884no—
584C22#121×D4311yescharacteristic
585C4—21no—
586C4—22no—
587C4—41no—
588C4—81no—
589C4—432no—
590C4—861no—
591C4—861no—
592C4—862no—
593C4—3441no—
594C4—1721no—
595C4C2×SD16×D4311yescharacteristic
596C4#135×D4311yescharacteristic
597C4#1458370511yescharacteristic
598C4#1458370911yescharacteristic
599C2—161no—
600C2—862no—
601C2—6881no—
602C2#1914411111yescharacteristic
603C2#465×D4311yescharacteristic
604C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1666C2
socleC22×C43C2×#121
prime radical#127×D43C22
hypercenter#1666D43
hypocenterC43#19396
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1666

Complements

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

NH ≅ G/Ntype
2. #19144395C2semidirect
4. #19143674C2semidirect
5. #19134012C2semidirect
6. #19134011C2semidirect
7. #19134010C2semidirect
8. #19134009C2semidirect
9. #19133946C2semidirect
10. #19133945C2semidirect
11. #19133940C2semidirect
12. #19133364C2semidirect
14. #19133251C2semidirect
15. C43×#1666C2semidirect
25. #14583195C22semidirect
26. #14583194C22semidirect
27. #14583181C22semidirect
37. Q8×C43⋊C8C22semidirect
39. C8×Dic86C22semidirect
41. #14583023C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582645C22semidirect
61. C43×#475C22semidirect
63. C8×Q8×C43C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
155. Q8×D43SD16semidirect
308. #1666D43semidirect
331. #475C2×D43semidirect
347. C8×Q8C2×D43semidirect
360. #334C2×D43semidirect
364. #332C2×D43semidirect
369. C43#19396semidirect

Maximal subgroups

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

subgroupindex
#191455322
#191443952
#460×D432
#191436742
#191340122
#191340112
#191340102
#191340092
#191339462
#191339452
#191339402
#191333642
#191332612
#191332512
C43×#16662
#1939643