Finite Group Databasebeta

← #25081779

Subgroups — #25081779

Order 11008.

654 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145539C211yesmaximal, characteristic, complemented
2#19144387C211yesmaximal, characteristic
3#474×D43C211yesmaximal, characteristic
4#19143616C211yesmaximal, characteristic
5#19134047C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19134045C211yesmaximal, characteristic, complemented
8#19134044C211yesmaximal, characteristic, complemented
9#19133959C211yesmaximal, characteristic, complemented
10#19133958C211yesmaximal, characteristic, complemented
11#19133957C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133278C211yesmaximal, characteristic, complemented
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1669C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583278C2211yescharacteristic, complemented
20#14583250C2211yescharacteristic, complemented
21#14583249C2211yescharacteristic, complemented
22#14583202—21no—
23#14583201—21no—
24#14583190C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583180C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583178—21no—
29#14583177—21no—
30#14583176C2211yescharacteristic
31#14583176C2211yescharacteristic
32#14583107—21no—
33#14583107—21no—
34#14583053—21no—
35#14583053—21no—
36C8×D172C2211yescharacteristic
37D4×C43⋊C8C2211yescharacteristic
38#14582964C2211yescharacteristic
39C8×C22⋊D43—21no—
40(C22⋊D43)⋊C8—21no—
41#14582951C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582940—21no—
44#107×D43—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582902—21no—
48#102×D43—21no—
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582646C2211yescharacteristic, complemented
57#14582645C2211yescharacteristic, complemented
58#14582645C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#494C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621872—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063324—21no—
81#13063323—21no—
82#13063316—21no—
83#13063305—21no—
84#13063301—21no—
85Q8×Dic43—21no—
86#13063290—21no—
87C4×D172C2311yescharacteristic
88D4×Dic43D411yescharacteristic
89#13063287D411yescharacteristic
90C4×C22⋊D43—21no—
91(C22⋊D43)⋊C4—21no—
92#13063283—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43D411yescharacteristic
96C22⋊C4×D43—21no—
97C42×D43C2311yescharacteristic
98#13063259—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063257—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8D411yescharacteristic
110Dic43⋊C8D411yescharacteristic
111#13063250—21no—
112#13063250—21no—
113#13063249—21no—
114#13063249—21no—
115#13063247—21no—
116#13063247—21no—
117#13063246—21no—
118#13063246—21no—
119#13063245—21no—
120#13063245—21no—
121C22⋊(C43⋊C8)—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8D411yescharacteristic
126(C2×D43)⋊C8D411yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C2×Q16×C43—21no—
130C2×Q16×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43—21no—
136#107×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
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—
151Q8×D43—81no—
152Q8×D43—81no—
153D4×D43—22no—
154D4×D43Q1614yescomplemented
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—41no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43#4111yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—41no—
168Q16×C43—81no—
169Q16×C43—81no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—81no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184#10621885—81no—
185#10621885—81no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—41no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—41no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—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—81no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621872—42no—
210C8×D43—42no—
211C8×D43—81no—
212C8×D43—81no—
213C23×C43—21no—
214C22×D43—21no—
215C22×D43—24no—
216C22×D43—81no—
217C22×D43—81no—
218C22×D43#12111yescharacteristic
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223D4×C43—21no—
224D4×C43C2×Q1612yes—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—24no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—81no—
238C2×Dic43#12111yescharacteristic
239C2×Dic43#12111yescharacteristic
240C2×Dic43#12111yescharacteristic
241D172—21no—
242D172C2×Q1612yes—
243C4×D43—21no—
244C4×D43—21no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—81no—
249C4×D43—81no—
250C4×D43—82no—
251C4×D43C2×Q1612yes—
252C4×D43#13512yes—
253Dic86—41no—
254Dic86—41no—
255Dic86—82no—
256Dic86—81no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#19387—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—21no—
273C2×D43—21no—
274C2×D43—22no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—84no—
278C2×D43#46712yes—
279C4×C43—21no—
280C4×C43—41no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43C22×Q1611yescharacteristic
284C4×C43C2×#13511yescharacteristic
285C4×C43#57611yescharacteristic
286C4×C43#57611yescharacteristic
287Dic43—21no—
288Dic43—21no—
289Dic43—41no—
290Dic43—81no—
291Dic43—81no—
292Dic43#46712yes—
293#3209—431no—
294#3077—431no—
295C2×#474—431no—
296#2972—431no—
297#1683—431no—
298#1683—431no—
299#1683—431no—
300#1683—431no—
301#1669—431no—
302#1669—431no—
303#1669—431no—
304#1669D4311yescharacteristic, complemented
305#1571—431no—
306#1549—431no—
307#1542—431no—
308C2×C43—42no—
309C2×C43#304111yescharacteristic
310C2×C43C2×#46711yescharacteristic
311C2×C43#306911yescharacteristic
312D43—22no—
313D43—42no—
314#533—431no—
315C2×C4⋊Q8—431no—
316C2×C4×D4—431no—
317#494—431no—
318#494C2×D4311yescharacteristic, complemented
319#487—431no—
320#487—431no—
321#478—861no—
322#478—861no—
323#476—431no—
324#476—431no—
325#474—431no—
326#474—431no—
327#474—431no—
328#474—431no—
329#474—861no—
330#474—861no—
331#474C2×D4311yescharacteristic
332#474C2×D4311yescharacteristic
333#462—861no—
334#462—861no—
335#451—861no—
336#451—861no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—431no—
340C8×D4—861no—
341C8×D4—861no—
342C8×D4C2×D4311yescharacteristic
343#431—431no—
344#431—431no—
345#428—861no—
346C2×#107—861no—
347#423—431no—
348C2×C4⋊C8—431no—
349#418—861no—
350C2×#102—861no—
351C2×C22⋊C8—861no—
352C2×C22⋊C8—861no—
353#335—431no—
354#335—431no—
355#335—431no—
356#335C2×D4311yescharacteristic, complemented
357#333—431no—
358#333—431no—
359#332—431no—
360#332—431no—
361#332—431no—
362#332—431no—
363#332C2×D4311yescharacteristic, complemented
364#332C2×D4311yescharacteristic, complemented
365C43#1938711yescharacteristic, complemented, Sylow
366C22×Q8—861no—
367C22×D4—431no—
368C23×C4—861no—
369C2×Q16—21no—
370C2×Q16—21no—
371C2×Q16—861no—
372C2×Q16—861no—
373C2×M16—861no—
374C22×C8—21no—
375C22×C8—861no—
376C22×C8—861no—
377C22×C8—861no—
378C22×C8—861no—
379C4⋊Q8—431no—
380C4⋊Q8—431no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383C4⋊Q8—861no—
384C4⋊Q8C22×D4311yescharacteristic
385C4⋊Q8C22×D4311yescharacteristic
386#125—861no—
387C22⋊Q8—861no—
388C22⋊Q8—861no—
389C4×Q8—861no—
390C4×Q8—861no—
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4C22×D4311yescharacteristic
397#117—861no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—431no—
403#107—21no—
404#107—21no—
405#107—861no—
406#107—861no—
407#107—861no—
408#107—861no—
409#106—861no—
410#106—861no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8C22×D4311yescharacteristic
419C4⋊C8C22×D4311yescharacteristic
420C4⋊C8C22×D4311yescharacteristic
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#102—21no—
426#102—21no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433C22⋊C8—21no—
434C22⋊C8—431no—
435C22⋊C8—431no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440C4×C8—431no—
441C4×C8—861no—
442C4×C8C22×D4311yescharacteristic
443C24—861no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—3441no—
449C2×Q8—3441no—
450C2×Q8—1721no—
451C2×D4—434no—
452C2×D4—431no—
453C2×D4—862no—
454C2×D4—861no—
455C2×D4D4×D4311yescharacteristic
456C22×C4—21no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—3441no—
465C22×C4—3441no—
466C22×C4—1721no—
467Q16—81no—
468Q16—81no—
469Q16—3441no—
470Q16—3441no—
471M16—1722no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—3441no—
482C2×C8—3441no—
483C2×C8—3441no—
484C2×C8—1722no—
485C2×C8D4×D4311yescharacteristic
486C2×C8D4×D4311yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—431no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1721no—
498C4⋊C4—1721no—
499C4⋊C4—1721no—
500C4⋊C4—1721no—
501C4⋊C4D4×D4311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—1721no—
507C42—431no—
508C42—431no—
509C42—431no—
510C42—1721no—
511C42C23×D4311yescharacteristic
512C23—21no—
513C23—431no—
514C23—864no—
515C23—861no—
516C23—3441no—
517C23—3441no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—3441no—
523Q8—3442no—
524Q8—1721no—
525Q8—1721no—
526D4—21no—
527D4—432no—
528D4—864no—
529D4—861no—
530D4Q16×D4312yes—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—431no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—431no—
540C2×C4—431no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—3441no—
545C2×C4—3441no—
546C2×C4—3442no—
547C2×C4—3441no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—861no—
562C8—861no—
563C8—1721no—
564C8—1721no—
565C8—1721no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—432no—
570C22—861no—
571C22—861no—
572C22—862no—
573C22—3444no—
574C22—1721no—
575C22—1721no—
576C22#121×D4311yescharacteristic
577C4—21no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—432no—
582C4—861no—
583C4—861no—
584C4—3441no—
585C4—3441no—
586C4—1721no—
587C4C2×Q16×D4311yescharacteristic
588C4#135×D4311yescharacteristic
589C4#1458370011yescharacteristic
590C4#1458370311yescharacteristic
591C2—42no—
592C2—862no—
593C2—1722no—
594C2#1914409311yescharacteristic
595C2#467×D4311yescharacteristic
596C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1669C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1669D43
hypocenterC43#19387
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1669

Complements

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

NH ≅ G/Ntype
1. #19145539C2semidirect
5. #19134047C2semidirect
6. #19134046C2semidirect
7. #19134045C2semidirect
8. #19134044C2semidirect
9. #19133959C2semidirect
10. #19133958C2semidirect
11. #19133957C2semidirect
12. #19133368C2semidirect
13. #19133278C2semidirect
14. #19133251C2semidirect
15. C43×#1669C2semidirect
19. #14583278C22semidirect
20. #14583250C22semidirect
21. #14583249C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582646C22semidirect
57. #14582645C22semidirect
58. #14582645C22semidirect
59. #14582644C22semidirect
60. C43×#494C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
66. C43×#332C22semidirect
154. D4×D43Q16semidirect
304. #1669D43semidirect
318. #494C2×D43semidirect
356. #335C2×D43semidirect
363. #332C2×D43semidirect
364. #332C2×D43semidirect
365. C43#19387semidirect

Maximal subgroups

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

subgroupindex
#191455392
#191443872
#474×D432
#191436162
#191340472
#191340462
#191340452
#191340442
#191339592
#191339582
#191339572
#191333682
#191332782
#191332512
C43×#16692
#1938743