Finite Group Databasebeta

← #25080419

Subgroups — #25080419

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145180C211yesmaximal, characteristic, complemented
2#19144696C211yesmaximal, characteristic
3#19144693C211yesmaximal, characteristic
4C8×D4×D43C211yesmaximal, characteristic
5#19134019C211yesmaximal, characteristic, complemented
6#19134018C211yesmaximal, characteristic, complemented
7#19134015C211yesmaximal, characteristic, complemented
8#19133983C211yesmaximal, characteristic, complemented
9#19133982C211yesmaximal, characteristic, complemented
10#19133959C211yesmaximal, characteristic, complemented
11#19133958C211yesmaximal, characteristic, complemented
12#19133355C211yesmaximal, characteristic, complemented
13#19133294C211yesmaximal, characteristic, complemented
14#19133292C211yesmaximal, characteristic, complemented
15C43×#1679C211yesmaximal, characteristic, complemented
16C22×C8×D43—21no—
17#14583454C2211yescharacteristic
18#14583454C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583302C2211yescharacteristic, complemented
21#14583278C2211yescharacteristic, complemented
22#14583250C2211yescharacteristic, complemented
23#14583236—21no—
24#14583233—21no—
25#14583180C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583139—21no—
29#14583139—21no—
30#14583105C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583101C2211yescharacteristic
33#14583051—21no—
34#14583048—21no—
35#14583002—21no—
36#14583000—21no—
37#14582998—21no—
38#14582996—21no—
39#14582991—21no—
40#14582991—21no—
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582964C2211yescharacteristic
44C8×C22⋊D43—21no—
45(C22⋊D43)⋊C8—21no—
46#14582955C2211yescharacteristic
47#14582955C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49C22⋊C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582650C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582645C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#487C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×D4×D43D411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—44no—
79C2×C8×D43D411yescharacteristic
80C2×C8×D43D411yescharacteristic
81#13063325C2311yescharacteristic
82#13063325C2311yescharacteristic
83#13063316—21no—
84#13063316—21no—
85#13063305—21no—
86#13063305—21no—
87#13063301—21no—
88#13063301—21no—
89Q8×Dic43—21no—
90Q8×Dic43—21no—
91#13063290—21no—
92#13063290—21no—
93C4×D172C2311yescharacteristic
94D4×Dic43D411yescharacteristic
95#13063287D411yescharacteristic
96C4×C22⋊D43—21no—
97(C22⋊D43)⋊C4—21no—
98#13063283—21no—
99#13063283—21no—
100C4⋊C4×D43D411yescharacteristic
101C22⋊C4×D43—21no—
102C42×D43C2311yescharacteristic
103#13063259—21no—
104#13063258—21no—
105#13063258—21no—
106#13063258—21no—
107#13063258—21no—
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063248—21no—
117#13063247—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—
125#13063235—21no—
126#13063235—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152D4×D43—22no—
153D4×D43—22no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43#4111yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165SD16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—42no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180#10621885—42no—
181#10621885—42no—
182#10621884—42no—
183#10621883—42no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43—41no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—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—41no—
212C8×D43—42no—
213C8×D43—42no—
214C8×D43—42no—
215C23×C43—21no—
216C22×D43—24no—
217C22×D43—21no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43#12111yescharacteristic
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225D4×C43—21no—
226D4×C43#13512yes—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—24no—
236C2×Dic43—21no—
237C2×Dic43—42no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43#12111yescharacteristic
241C2×Dic43#12111yescharacteristic
242C2×Dic43#12111yescharacteristic
243D172—21no—
244D172#13512yes—
245C4×D43—22no—
246C4×D43—21no—
247C4×D43—21no—
248C4×D43—21no—
249C4×D43—21no—
250C4×D43—42no—
251C4×D43—42no—
252C4×D43—41no—
253C4×D43—41no—
254Dic86—41no—
255Dic86—41no—
256Dic86—41no—
257Dic86—41no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8AGL(1,ℤ/8)12yes—
268#19259—431nomaximal, Sylow
269C22×C43—22no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43C2×#12111yescharacteristic
273C2×D43—21no—
274C2×D43—21no—
275C2×D43—22no—
276C2×D43—48no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43#47312yes—
280C4×C43—21no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43C2×#13511yescharacteristic
285C4×C43C2×#13511yescharacteristic
286C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C43#57511yescharacteristic
288Dic43—21no—
289Dic43—21no—
290Dic43—21no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294#3170—431no—
295#3110—431no—
296#3110—431no—
297C2×C8×D4—431no—
298#1679—431no—
299#1679—431no—
300#1679—431no—
301#1679D4311yescharacteristic, complemented
302#1673—431no—
303#1673—431no—
304#1669—431no—
305#1669—431no—
306#1568—431no—
307#1552—431no—
308#1552—431no—
309C2×C43—42no—
310C2×C43#303611yescharacteristic
311C2×C43#305011yescharacteristic
312C2×C43C2×#47311yescharacteristic
313D43—22no—
314D43—42no—
315C23×C8—861no—
316#533—431no—
317#533—431no—
318C2×C4×D4—431no—
319#500—431no—
320#494—431no—
321#487—431no—
322#487C2×D4311yescharacteristic, complemented
323#484—861no—
324#484—861no—
325#474—431no—
326#474—431no—
327#474—431no—
328#474C2×D4311yescharacteristic
329#467—861no—
330#467—861no—
331#461—431no—
332#461—431no—
333#461—431no—
334#461C2×D4311yescharacteristic
335#450—861no—
336#450—861no—
337#440—861no—
338#440—861no—
339#440—861no—
340#440—861no—
341C4×Q16—861no—
342C4×Q16—861no—
343C8×D4—431no—
344C8×D4—431no—
345C8×D4—431no—
346C8×D4—861no—
347C8×D4—861no—
348C8×D4C2×D4311yescharacteristic
349#432—431no—
350#432—431no—
351C2×C4⋊C8—431no—
352C2×C22⋊C8—861no—
353C2×C4×C8—431no—
354#335—431no—
355#335—431no—
356#334—431no—
357#334C2×D4311yescharacteristic, complemented
358#332—431no—
359#332—431no—
360#332—431no—
361#332—431no—
362#332—431no—
363#332—431no—
364#332C2×D4311yescharacteristic, complemented
365#332C2×D4311yescharacteristic, complemented
366C43#1925911yescharacteristic, complemented, Sylow
367C22×D4—431no—
368C23×C4—861no—
369C2×Q16—861no—
370C2×Q16—861no—
371C2×SD16—21no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×SD16—861no—
375C22×C8—21no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—1724no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8C22×D4311yescharacteristic
386C4⋊Q8C22×D4311yescharacteristic
387#125—861no—
388#125—861no—
389C22⋊Q8—861no—
390C22⋊Q8—861no—
391C22⋊Q8—861no—
392C22⋊Q8—861no—
393C4×Q8—861no—
394C4×Q8—861no—
395C4×Q8—861no—
396C4×Q8—861no—
397C4×D4—431no—
398C4×D4—431no—
399C4×D4—431no—
400C4×D4—861no—
401C4×D4—861no—
402C4×D4C22×D4311yescharacteristic
403#117—861no—
404#117—861no—
405C2×C4⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C42—431no—
408#107—21no—
409#107—861no—
410#107—861no—
411#107—861no—
412#107—861no—
413#107—861no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—861no—
418C4⋊C8C22×D4311yescharacteristic
419C4⋊C8C22×D4311yescharacteristic
420C4⋊C8C22×D4311yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—861no—
425#103—861no—
426#103—861no—
427#103—861no—
428#103—861no—
429#102—21no—
430#102—861no—
431#102—861no—
432#102—861no—
433C22⋊C8—21no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—861no—
440#97—861no—
441C4×C8—431no—
442C4×C8—431no—
443C4×C8—431no—
444C4×C8C22×D4311yescharacteristic
445C24—861no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×D4—431no—
451C2×D4—861no—
452C2×D4—862no—
453C2×D4—862no—
454C2×D4D4×D4311yescharacteristic
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—1722no—
464C22×C4—1722no—
465Q16—1722no—
466Q16—1722no—
467SD16—42no—
468SD16—1722no—
469SD16—1722no—
470SD16—1722no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—862no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—1721no—
482C2×C8—1722no—
483C2×C8—1722no—
484C2×C8—1722no—
485C2×C8—1722no—
486C2×C8D4×D4311yescharacteristic
487C2×C8D4×D4311yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—431no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—1721no—
499C4⋊C4—1721no—
500C4⋊C4—1721no—
501C4⋊C4—1721no—
502C4⋊C4D4×D4311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—1721no—
508C22⋊C4—1721no—
509C42—431no—
510C42—431no—
511C42—431no—
512C42—1721no—
513C42—1721no—
514C42C23×D4311yescharacteristic
515C23—21no—
516C23—431no—
517C23—864no—
518C23—861no—
519C23—1722no—
520C23—1722no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—1721no—
526Q8—1721no—
527Q8—1721no—
528Q8—1721no—
529D4—21no—
530D4—432no—
531D4—864no—
532D4—861no—
533D4#1306334612yes—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—431no—
540C2×C4—431no—
541C2×C4—431no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4—1722no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—432no—
564C8—861no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—432no—
572C22—861no—
573C22—861no—
574C22—862no—
575C22—1728no—
576C22—1721no—
577C22—1721no—
578C22#121×D4311yescharacteristic
579C4—21no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—861no—
584C4—861no—
585C4—861no—
586C4—3441no—
587C4—3441no—
588C4—1721no—
589C4#135×D4311yescharacteristic
590C4C2×#1306334611yescharacteristic
591C4AGL(1,ℤ/8)×D4311yescharacteristic
592C4#1458369611yescharacteristic
593C2—42no—
594C2—862no—
595C2—1722no—
596C2#1914405711yescharacteristic
597C2#1914417111yescharacteristic
598C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1679C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1679D43
hypocenterC43#19259
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1679

Complements

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

NH ≅ G/Ntype
1. #19145180C2semidirect
5. #19134019C2semidirect
6. #19134018C2semidirect
7. #19134015C2semidirect
8. #19133983C2semidirect
9. #19133982C2semidirect
10. #19133959C2semidirect
11. #19133958C2semidirect
12. #19133355C2semidirect
13. #19133294C2semidirect
14. #19133292C2semidirect
15. C43×#1679C2semidirect
20. #14583302C22semidirect
21. #14583278C22semidirect
22. #14583250C22semidirect
51. #14582651C22semidirect
52. #14582651C22semidirect
53. #14582650C22semidirect
54. #14582646C22semidirect
55. #14582646C22semidirect
56. #14582645C22semidirect
57. #14582645C22semidirect
58. #14582644C22semidirect
59. #14582644C22semidirect
60. C43×#487C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
66. C43×#332C22semidirect
301. #1679D43semidirect
322. #487C2×D43semidirect
357. #334C2×D43semidirect
364. #332C2×D43semidirect
365. #332C2×D43semidirect
366. C43#19259semidirect

Maximal subgroups

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

subgroupindex
#191451802
#191446962
#191446932
C8×D4×D432
#191340192
#191340182
#191340152
#191339832
#191339822
#191339592
#191339582
#191333552
#191332942
#191332922
C43×#16792
#1925943