Finite Group Databasebeta

← #25080370

Subgroups — #25080370

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145152C211yesmaximal, characteristic, complemented
2#19144387C211yesmaximal, characteristic, complemented
3#19144054C211yesmaximal, characteristic
4C8×D4×D43C211yesmaximal, characteristic, complemented
5#19134017C211yesmaximal, characteristic, complemented
6#19134016C211yesmaximal, characteristic, complemented
7#19134003C211yesmaximal, characteristic, complemented
8#19134002C211yesmaximal, characteristic, complemented
9#19133971C211yesmaximal, characteristic, complemented
10#19133970C211yesmaximal, characteristic, complemented
11#19133933C211yesmaximal, characteristic, complemented
12#19133349C211yesmaximal, characteristic, complemented
13#19133284C211yesmaximal, characteristic, complemented
14#19133269C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C22×C8×D43—21no—
18#14583454C2211yescharacteristic
19#14583447C2211yescharacteristic
20C4×D4×D43C2211yescharacteristic
21#14583297C2211yescharacteristic, complemented
22#14583249C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic, complemented
24#14583202—21no—
25#14583201—21no—
26#14583190C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583176C2211yescharacteristic
29#14583125—21no—
30#14583125—21no—
31#14583113—21no—
32#14583112—21no—
33#14583105C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583091C2211yescharacteristic
36SD16×Dic43—21no—
37SD16×Dic43—21no—
38C8×D172C2211yescharacteristic
39D4×C43⋊C8C2211yescharacteristic
40#14582964C2211yescharacteristic
41C8×C22⋊D43—21no—
42(C22⋊D43)⋊C8—21no—
43#14582940—21no—
44#14582921C2211yescharacteristic
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582902—21no—
48#14582897—21no—
49C22⋊C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582646C2211yescharacteristic, complemented
57#14582645C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582643C2211yescharacteristic, complemented
60C43×#492C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×D4×D43D411yescharacteristic
69C22×C4×D43—21no—
70#13063349—44no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621882—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C2×C8×D43—44no—
81C2×C8×D43D411yescharacteristic
82C2×C8×D43D411yescharacteristic
83#13063325C2311yescharacteristic
84#13063325C2311yescharacteristic
85#13063316—21no—
86#13063312—21no—
87#13063305—21no—
88#13063301—21no—
89#13063296—21no—
90#13063296—21no—
91Q8×Dic43—21no—
92#13063290—21no—
93C4×D172C2311yescharacteristic
94D4×Dic43—21no—
95D4×Dic43—21no—
96D4×Dic43D411yescharacteristic
97#13063287D411yescharacteristic
98C4×C22⋊D43—21no—
99(C22⋊D43)⋊C4—21no—
100#13063283—21no—
101C4⋊C4×D43D411yescharacteristic
102C22⋊C4×D43—21no—
103C42×D43C2311yescharacteristic
104#13063258—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108#13063256—21no—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115#13063250—21no—
116#13063249—21no—
117#13063249—21no—
118#13063248—21no—
119#13063247—21no—
120#13063246—21no—
121#13063246—21no—
122#13063246—21no—
123#13063246—21no—
124#13063245—21no—
125C22⋊(C43⋊C8)—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C2×SD16×C43—21no—
132C2×SD16×C43—21no—
133C2×D8×C43—21no—
134C22×C8×C43—21no—
135C4⋊Q8×C43C2311yescharacteristic
136#127×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138#107×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142#102×C43—21no—
143#102×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—41no—
155C22×Dic43—21no—
156C22×Dic43—41no—
157#10621900—42no—
158#10621900—42no—
159D4×D43—22no—
160D4×D43SD1614yescomplemented
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43#4111yescharacteristic
170C2×Dic86—21no—
171C2×Dic86—21no—
172SD16×C43—42no—
173SD16×C43—42no—
174D8×C43—42no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—42no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C2×D411yescharacteristic
184C22⋊C4×C43—21no—
185C42×C43C2411yescharacteristic
186C22⋊Dic43—21no—
187C22⋊Dic43—41no—
188C22⋊Dic43—41no—
189#10621883—42no—
190#10621882—42no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202C4×Dic43—41no—
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43#4111yescharacteristic
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—42no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212#10621873—42no—
213#10621872—42no—
214#10621872—42no—
215C8×D43—22no—
216C8×D43—41no—
217C8×D43—42no—
218C8×D43—42no—
219C8×D43—42no—
220C23×C43—21no—
221C23×C43—41no—
222C22×D43—21no—
223C22×D43—24no—
224C22×D43—42no—
225C22×D43—42no—
226C22×D43#12111yescharacteristic
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—21no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—81no—
235D4×C43C2×SD1612yes—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C22⋊D43—24no—
244C22⋊D43—82no—
245C2×Dic43—21no—
246C2×Dic43—42no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—82no—
250C2×Dic43#12111yescharacteristic
251C2×Dic43#12111yescharacteristic
252C2×Dic43#12111yescharacteristic
253D172—21no—
254D172C2×SD1612yes—
255C4×D43—21no—
256C4×D43—21no—
257C4×D43—41no—
258C4×D43—42no—
259C4×D43—42no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43C2×SD1612yes—
263C4×D43#13512yes—
264Dic86—41no—
265Dic86—41no—
266Dic86—81no—
267C8×C43—21no—
268C8×C43—41no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43AGL(1,ℤ/8)12yescomplemented
272C43⋊C8—21no—
273C43⋊C8—21no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277#19254—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43C2×#12111yescharacteristic
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—22no—
288C2×D43—48no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43#46512yes—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43C22×SD1611yescharacteristic
296C4×C43C2×#13511yescharacteristic
297C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C43#57511yescharacteristic
299Dic43—21no—
300Dic43—21no—
301Dic43—41no—
302Dic43—81no—
303Dic43—81no—
304Dic43#46512yes—
305#3167—431no—
306#3077—431no—
307#3036—431no—
308C2×C8×D4—431no—
309#1679—431no—
310#1679—431no—
311#1677—431no—
312#1677—431no—
313#1671—431no—
314#1671—431no—
315#1665—431no—
316#1665D4311yescharacteristic, complemented
317#1566—431no—
318#1550—431no—
319#1547—431no—
320C2×C43—42no—
321C2×C43—161no—
322C2×C43#303611yescharacteristic
323C2×C43C2×#46511yescharacteristic
324C2×C43#306711yescharacteristic
325D43—22no—
326D43—42no—
327C2×AGL(1,ℤ/8)—861no—
328C23×C8—861no—
329#533—431no—
330#532—431no—
331C2×C4×D4—431no—
332#498—431no—
333#492C2×D4311yescharacteristic, complemented
334#487—431no—
335#486—431no—
336#478—861no—
337#478—861no—
338#476—431no—
339#476—431no—
340#474—431no—
341#474C2×D4311yescharacteristic
342#465—861no—
343#465—861no—
344#463—861no—
345#463—861no—
346#461—431no—
347#461—431no—
348#459—431no—
349#459C2×D4311yescharacteristic
350C4×SD16—861no—
351C4×SD16—861no—
352C8×D4—431no—
353C8×D4—431no—
354C8×D4—431no—
355C8×D4—861no—
356C8×D4—861no—
357C8×D4C2×D4311yescharacteristic
358#428—861no—
359#423—431no—
360#423—431no—
361C2×C4⋊C8—431no—
362#418—861no—
363#417—861no—
364C2×C22⋊C8—861no—
365C2×C4×C8—431no—
366#334—431no—
367#334—431no—
368#334—431no—
369#334C2×D4311yescharacteristic, complemented
370#333—431no—
371#333—431no—
372#332—431no—
373#332—431no—
374#332—431no—
375#332C2×D4311yescharacteristic, complemented
376#331—431no—
377#331C2×D4311yescharacteristic, complemented
378C43#1925411yescharacteristic, complemented, Sylow
379C2×#41—861no—
380C22×D4—431no—
381C23×C4—861no—
382AGL(1,ℤ/8)—1724no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×D8—21no—
388C2×D8—861no—
389C2×M16—861no—
390C2×M16—861no—
391C22×C8—21no—
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—861no—
395C22×C8—861no—
396C22×C8—861no—
397C22×C8—861no—
398C22×C8—1724no—
399C4⋊Q8—431no—
400C4⋊Q8—431no—
401C4⋊Q8C22×D4311yescharacteristic
402#127C22×D4311yescharacteristic
403#125—861no—
404#124—861no—
405C22⋊Q8—861no—
406C22⋊Q8—861no—
407#121—861no—
408#121—861no—
409C4×Q8—861no—
410C4×Q8—861no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4C22×D4311yescharacteristic
419#117—861no—
420C2×C4⋊C4—431no—
421C2×C22⋊C4—861no—
422C2×C42—431no—
423#107—21no—
424#107—861no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106—861no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8C22×D4311yescharacteristic
436C4⋊C8C22×D4311yescharacteristic
437C4⋊C8C22×D4311yescharacteristic
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#102—21no—
443#102—21no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—861no—
449#102—861no—
450C22⋊C8—21no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8—431no—
457C4×C8C22×D4311yescharacteristic
458C24—861no—
459#41—1722no—
460#41—1722no—
461C2×Q8—21no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—434no—
468C2×D4—431no—
469C2×D4—862no—
470C2×D4—861no—
471C2×D4—1721no—
472C2×D4D4×D4311yescharacteristic
473C22×C4—21no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4—1721no—
484SD16—42no—
485SD16—42no—
486SD16—1722no—
487SD16—1722no—
488D8—42no—
489D8—1722no—
490M16—1722no—
491M16—1722no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—42no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—862no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—1721no—
503C2×C8—1722no—
504C2×C8—1722no—
505C2×C8—1722no—
506C2×C8—1722no—
507C2×C8D4×D4311yescharacteristic
508C2×C8D4×D4311yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—431no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—1721no—
518C4⋊C4—1721no—
519C4⋊C4D4×D4311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—861no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C22⋊C4—1721no—
525C22⋊C4—1721no—
526C22⋊C4—1721no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—1721no—
531C42C23×D4311yescharacteristic
532C23—21no—
533C23—41no—
534C23—431no—
535C23—864no—
536C23—861no—
537C23—1722no—
538C23—1722no—
539Q8—41no—
540Q8—41no—
541Q8—3441no—
542Q8—1721no—
543Q8—1721no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—81no—
550D4—432no—
551D4—864no—
552D4—861no—
553D4—3442no—
554D4SD16×D4312yes—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—431no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—431no—
563C2×C4—431no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—3442no—
568C2×C4—1721no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C8—21no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—861no—
584C8—861no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C8#1306334912yescomplemented
589C22—22no—
590C22—41no—
591C22—41no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—432no—
596C22—861no—
597C22—861no—
598C22—862no—
599C22—1728no—
600C22—1721no—
601C22—1721no—
602C22#121×D4311yescharacteristic
603C4—21no—
604C4—41no—
605C4—81no—
606C4—432no—
607C4—861no—
608C4—861no—
609C4—3441no—
610C4—3441no—
611C4—1721no—
612C4C2×SD16×D4311yescharacteristic
613C4#135×D4311yescharacteristic
614C4C2×#1306334911yescharacteristic
615C4#1458369511yescharacteristic
616C2—42no—
617C2—161no—
618C2—862no—
619C2—1722no—
620C2#1914405411yescharacteristic
621C2#465×D4311yescharacteristic
622C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#19144054C2
hypercenter#1665D43
hypocenterC43#19254
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1665

Complements

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

NH ≅ G/Ntype
1. #19145152C2semidirect
2. #19144387C2semidirect
4. C8×D4×D43C2semidirect
5. #19134017C2semidirect
6. #19134016C2semidirect
7. #19134003C2semidirect
8. #19134002C2semidirect
9. #19133971C2semidirect
10. #19133970C2semidirect
11. #19133933C2semidirect
12. #19133349C2semidirect
13. #19133284C2semidirect
14. #19133269C2semidirect
15. C43×#1665C2semidirect
21. #14583297C22semidirect
22. #14583249C22semidirect
23. #14583245C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582646C22semidirect
57. #14582645C22semidirect
58. #14582644C22semidirect
59. #14582643C22semidirect
60. C43×#492C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
66. C43×#331C22semidirect
160. D4×D43SD16semidirect
271. C8×C43AGL(1,ℤ/8)semidirect
316. #1665D43semidirect
333. #492C2×D43semidirect
369. #334C2×D43semidirect
375. #332C2×D43semidirect
377. #331C2×D43semidirect
378. C43#19254semidirect
588. C8#13063349semidirect

Maximal subgroups

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

subgroupindex
#191451522
#191443872
#191440542
C8×D4×D432
#191340172
#191340162
#191340032
#191340022
#191339712
#191339702
#191339332
#191333492
#191332842
#191332692
C43×#16652
#1925443