Finite Group Databasebeta

← #25155494

Subgroups — #25155494

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145125C211yesmaximal, characteristic, complemented
2#19144461C211yesmaximal, characteristic
3#19144457C211yesmaximal, characteristic
4#19143188C211yesmaximal, characteristic
5#19136109C211yesmaximal, characteristic, complemented
6#19136108C211yesmaximal, characteristic, complemented
7#19135940C211yesmaximal, characteristic, complemented
8#19135939C211yesmaximal, characteristic, complemented
9#19135374C211yesmaximal, characteristic, complemented
10#19135342C211yesmaximal, characteristic, complemented
11#19134823C211yesmaximal, characteristic
12#19134751C211yesmaximal, characteristic, complemented
13#19134652C211yesmaximal, characteristic
14#19134433C211yesmaximal, characteristic
15C43×#1859C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583530C2211yescharacteristic
18#14583527C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583307—21no—
21#14583306—21no—
22#14583300—21no—
23#14583296—21no—
24#14583208—21no—
25#14583206—21no—
26#14583199—21no—
27#14583197—21no—
28#14583189—21no—
29#14583187—21no—
30#14583184—21no—
31#14583182—21no—
32C2×#13063260C2211yescharacteristic
33#14582942—21no—
34#14582942C2211yescharacteristic
35#14582941C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582939—21no—
38#14582939C2211yescharacteristic
39#14582939C2211yescharacteristic
40#14582935—21no—
41#14582935C2211yescharacteristic
42C2×#13063256—21no—
43C2×#13063256C2211yescharacteristic
44C2×#13063256C2211yescharacteristic
45C2×#13063256C2211yescharacteristic
46C2×#13063256C2211yescharacteristic
47#14582927C2211yescharacteristic
48#14582926C2211yescharacteristic
49#14582900C2211yescharacteristic
50#14582895C2211yescharacteristic
51#14582857C2211yescharacteristic
52C2×C4×C43⋊C8C2211yescharacteristic
53#14582769C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582663C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582659C2211yescharacteristic
60C43×#520C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C43×#384C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#339C2211yescharacteristic
67#13063332—22no—
68#13063332Q814yescomplemented
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C22×C43⋊C8—21no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063325—21no—
76#13063324—21no—
77#13063324—21no—
78#13063324—21no—
79#13063317—21no—
80#13063316—21no—
81#13063316—21no—
82#13063316—21no—
83#13063304—41no—
84#13063302—41no—
85Q8×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43—41no—
88#13063284—21no—
89#13063284C2311yescharacteristic
90#13063284C2311yescharacteristic
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95#13063260—22no—
96#13063259—21no—
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258D411yescharacteristic
102#13063258D411yescharacteristic
103#13063257—21no—
104#13063257—21no—
105#13063256—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256—21no—
110#13063256—21no—
111#13063256—21no—
112#13063256—21no—
113#13063256—21no—
114#13063256—21no—
115#13063256—21no—
116#13063256D411yescharacteristic
117#13063256D411yescharacteristic
118C4⋊(C43⋊C8)—21no—
119C4⋊(C43⋊C8)—21no—
120Dic43⋊C8—21no—
121Dic43⋊C8—21no—
122#13063249—21no—
123#13063249D411yescharacteristic
124#13063249D411yescharacteristic
125#13063246—21no—
126#13063246D411yescharacteristic
127#13063246D411yescharacteristic
128#13063235—21no—
129C4×C43⋊C8—22no—
130C8×Dic43—21no—
131C2×#41×C43C2311yescharacteristic
132C2×M16×C43C2311yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C4×Q8×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—41no—
137#117×C43—21no—
138#117×C43C2311yescharacteristic
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—41no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C42×C43C2311yescharacteristic
144#107×C43—21no—
145#106×C43—21no—
146#104×C43Q814yescomplemented
147#103×C43—21no—
148#102×C43—21no—
149#41×C43—21no—
150#41×C43—21no—
151#41×C43C2×Q812yes—
152#41×C43C2×Q812yes—
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—41no—
165C2×Dic86—41no—
166C2×Dic86—41no—
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43C2×Q812yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—82no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43C2×Q812yes—
187C22⋊Dic43—21no—
188C22⋊Dic43—21no—
189C22⋊Dic43—41no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43—41no—
196C4⋊Dic43—41no—
197C4⋊Dic43—82no—
198C4⋊Dic43C2×D411yescharacteristic
199C4⋊Dic43C2×D411yescharacteristic
200C4⋊Dic43C2×D411yescharacteristic
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—41no—
209#10621877—21no—
210#10621877—24no—
211#10621877—21no—
212#10621877—21no—
213#10621877C2×Q812yes—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—24no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222C2×C43⋊C8C2×D411yescharacteristic
223C2×C43⋊C8C2×Q812yes—
224C2×C43⋊C8#4112yes—
225C23×C43—21no—
226C23×C43H(5,𝔽2)11yescharacteristic
227Q8×C43—21no—
228Q8×C43C4⋊Q812yes—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—21no—
232D4×C43C4⋊Q812yes—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—81no—
244C2×C4×C43—81no—
245C2×C4×C43—161no—
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×Q811yescharacteristic
249C2×C4×C43C22×Q811yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—81no—
259C2×Dic43—81no—
260C2×Dic43—161no—
261Dic86—161no—
262Dic86—161no—
263C8×C43—22no—
264C8×C43—41no—
265C43⋊C8—22no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8C22⋊Q812yes—
270C43⋊C8C22⋊Q812yes—
271#26081—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43#54411yescharacteristic
278C22×C43D4211yescharacteristic
279C22×C43#55411yescharacteristic
280C4×C43—24no—
281C4×C43—22no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43C2×C22⋊Q811yescharacteristic
287C4×C43C2×C4⋊Q811yescharacteristic
288C4×C43#54711yescharacteristic
289C4×C43D4×Q811yescharacteristic
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296#3163—431no—
297#3084—431no—
298#3084—431no—
299#2912—431no—
300#2090—431no—
301#2090—431no—
302#2060—431no—
303#2060—431no—
304#1951—431no—
305#1945—431no—
306#1859—431no—
307#1859D4311yescharacteristic
308#1844—431no—
309#1815—431no—
310#1764—431no—
311C2×C43—21no—
312C2×C43—21no—
313C2×C43—42no—
314C2×C43#244011yescharacteristic
315C2×C43#329111yescharacteristic
316C2×C43#329111yescharacteristic
317C2×#131—431no—
318#544—431no—
319#544—431no—
320#520—431no—
321#520C2×D4311yescharacteristic
322#501—861no—
323#501—861no—
324#499—861no—
325#498—861no—
326#479—861no—
327#479—861no—
328#478—861no—
329#478—861no—
330#476—861no—
331#476—861no—
332#475—861no—
333#475—861no—
334C2×#108—431no—
335#428—431no—
336#428—431no—
337#428—431no—
338#428—431no—
339#428—431no—
340#428—861no—
341#428—861no—
342#428C2×D4311yescharacteristic
343#427—431no—
344#427—861no—
345C2×#106—431no—
346C2×#106—431no—
347C2×#106—431no—
348C2×#106—431no—
349C2×#106—861no—
350#424—431no—
351#424—431no—
352C2×#104C2×D4311yescharacteristic
353#417—431no—
354#417C2×D4311yescharacteristic
355#416—431no—
356#405—431no—
357C2×C4×C8—431no—
358#384—431no—
359#384C2×D4311yescharacteristic
360#343—431no—
361#343—431no—
362#343—431no—
363#343C2×D4311yescharacteristic
364#341—431no—
365#339—431no—
366#339—431no—
367#339C2×D4311yescharacteristic
368C43#2608111yescharacteristic, complemented, Sylow
369C2×#41C22×D4311yescharacteristic
370#131—434no—
371#131—862no—
372C2×M16—431no—
373C2×M16—431no—
374C2×M16—861no—
375C2×M16C22×D4311yescharacteristic
376C2×M16C22×D4311yescharacteristic
377C22×C8—431no—
378C22×C8—431no—
379C22×C8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383C4⋊Q8—861no—
384#125—861no—
385#125—861no—
386#125—861no—
387#125—861no—
388C22⋊Q8—1721no—
389C22⋊Q8—1721no—
390C4×Q8—21no—
391C4×Q8—861no—
392C4×D4—21no—
393C4×D4—41no—
394C4×D4—861no—
395C4×D4—1721no—
396#117—21no—
397#117—431no—
398#117—431no—
399#117—861no—
400#117C22×D4311yescharacteristic
401C2×C4⋊C4—21no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—1721no—
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C42C22×D4311yescharacteristic
410#108—862no—
411#107—21no—
412#107—431no—
413#107—431no—
414#107—861no—
415#107—861no—
416#107—861no—
417#107—861no—
418#107—861no—
419#106—21no—
420#106—431no—
421#106—431no—
422#106—861no—
423#106—861no—
424#106—861no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106—861no—
429#106—861no—
430#106—861no—
431#106—861no—
432#106—861no—
433#106—861no—
434#106—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439#104Dic8614yescomplemented
440#103—21no—
441#103—431no—
442#103—431no—
443#103—861no—
444#102—21no—
445#102—431no—
446#102—431no—
447#102—861no—
448#97—861no—
449C4×C8—862no—
450C4×C8—861no—
451#41—21no—
452#41—21no—
453#41C2×Dic8612yes—
454#41Q8×D4312yes—
455C2×Q8—1721no—
456C2×Q8—1721no—
457C2×Q8D4×D4311yescharacteristic
458C2×D4—21no—
459C2×D4D4×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—1721no—
468C22×C4C23×D4311yescharacteristic
469M16—21no—
470M16—21no—
471M16—21no—
472M16—432no—
473M16—864no—
474M16—861no—
475M16—861no—
476M16—861no—
477M16C2×Dic8612yes—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—432no—
483C2×C8—432no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—864no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—82no—
497C4⋊C4—431no—
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—431no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—3442no—
506C4⋊C4—1721no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4—1721no—
512C4⋊C4—1721no—
513C4⋊C4D4×D4311yescharacteristic
514C4⋊C4D4×D4311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—41no—
517C22⋊C4—861no—
518C22⋊C4—861no—
519C22⋊C4—1721no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42—861no—
524C42—861no—
525C42—1721no—
526C42C2×Dic8612yes—
527C23—21no—
528C23#1306337011yescharacteristic
529Q8—21no—
530Q8—6881no—
531Q8—6881no—
532Q8#1306332412yes—
533D4—22no—
534D4—22no—
535D4—21no—
536D4#1306332412yes—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—161no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—3441no—
555C2×C4—3441no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—6881no—
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4C2×D4×D4311yescharacteristic
561C2×C4C2×Q8×D4311yescharacteristic
562C2×C4C22×Dic8611yescharacteristic
563C2×C4#41×D4311yescharacteristic
564C2×C4#1306337211yescharacteristic
565C8—22no—
566C8—41no—
567C8—432no—
568C8—432no—
569C8—862no—
570C8—861no—
571C8—861no—
572C8—1721no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22#1458352811yescharacteristic
579C22#1458353111yescharacteristic
580C22#1458360811yescharacteristic
581C4—24no—
582C4—22no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—3441no—
588C4—3441no—
589C4—1721no—
590C4—1721no—
591C4—1721no—
592C4—1721no—
593C4C22⋊Q8×D4311yescharacteristic
594C4C2×#1306332411yescharacteristic
595C4#1458354711yescharacteristic
596C4D4×Dic8611yescharacteristic
597C2—21no—
598C2—21no—
599C2—42no—
600C2#1913829611yescharacteristic
601C2#1914638511yescharacteristic
602C2#1914639011yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1859C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#1859D43
hypocenterC43#26081
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1859

Complements

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

NH ≅ G/Ntype
1. #19145125C2semidirect
5. #19136109C2semidirect
6. #19136108C2semidirect
7. #19135940C2semidirect
8. #19135939C2semidirect
9. #19135374C2semidirect
10. #19135342C2semidirect
12. #19134751C2semidirect
68. #13063332Q8semidirect
146. #104×C43Q8semidirect
368. C43#26081semidirect
439. #104Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451252
#191444612
#191444572
#191431882
#191361092
#191361082
#191359402
#191359392
#191353742
#191353422
#191348232
#191347512
#191346522
#191344332
C43×#18592
#2608143