Finite Group Databasebeta

← #25088073

Subgroups — #25088073

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146894C211yesmaximal, characteristic, complemented
2#19146831C211yesmaximal, characteristic, complemented
3#19146410C211yesmaximal, characteristic, complemented
4#19134208C211yesmaximal, characteristic, complemented
5#19134144C211yesmaximal, characteristic, complemented
6#19134130C211yesmaximal, characteristic, complemented
7#19134043C211yesmaximal, characteristic, complemented
8#19134032C211yesmaximal, characteristic, complemented
9#19133823C211yesmaximal, characteristic, complemented
10#19133772C211yesmaximal, characteristic, complemented
11#19133745C211yesmaximal, characteristic, complemented
12#19133684C211yesmaximal, characteristic, complemented
13#19133480C211yesmaximal, characteristic, complemented
14C8×#10621882C211yesmaximal, characteristic, complemented
15C43×#3303C211yesmaximal, characteristic, complemented
16#14583554C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583251C2211yescharacteristic, complemented
19#14583249C2211yescharacteristic, complemented
20#14583247C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583234—21no—
24#14583223—21no—
25#14583214—21no—
26#14583186C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583176C2211yescharacteristic
29#14583150—21no—
30#14583143—21no—
31#14583134—21no—
32#14583104C2211yescharacteristic, complemented
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583042—21no—
36#14583032—21no—
37#14583031—21no—
38C4×#10621882C2211yescharacteristic
39#14582977C2211yescharacteristic
40#14582977C2211yescharacteristic, complemented
41C8×D172C2211yescharacteristic
42#14582903—21no—
43#14582898—21no—
44#102×D43—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#555C2211yescharacteristic
57C43×#547C2211yescharacteristic, complemented
58C43×#487C2211yescharacteristic, complemented
59C43×#485—21no—
60C43×#476C2211yescharacteristic, complemented
61C43×#465—21no—
62C43×#461C2211yescharacteristic
63C43×#449—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic, complemented
66C43×#416—21no—
67C2×#10621898—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621883—21no—
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621882D411yescharacteristic
74C2×#10621877—21no—
75C2×#10621877—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063307—41no—
80#13063304—21no—
81#13063300—21no—
82#13063299—21no—
83#13063296—21no—
84#13063295—41no—
85C4×D172C2311yescharacteristic
86C4⋊C4×D43—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063256—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94#13063249—41no—
95#13063248—21no—
96#13063248—21no—
97#13063248—21no—
98#13063247—21no—
99#13063247—21no—
100#13063246—21no—
101#13063246D411yescharacteristic
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—41no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×SD16×C43—21no—
117C2×D8×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#124×C43—41no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43—21no—
132C2×C4⋊C4×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43—41no—
150C2×D4×C43—41no—
151C2×D4×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160D4×D43—42no—
161D4×D43—81no—
162#10621898—42no—
163#10621898—81no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—41no—
168C2×D172—42no—
169C2×D172—81no—
170C2×D172C2×D411yescharacteristic
171C2×C4×D43—21no—
172C2×C4×D43—41no—
173C2×Dic86—21no—
174SD16×C43—81no—
175D8×C43—41no—
176C2×C8×C43—21no—
177C2×C8×C43—81no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—41no—
192C22⋊C4×C43—41no—
193C22⋊C4×C43—41no—
194C42×C43—41no—
195C42×C43C2411yescharacteristic
196C22⋊Dic43—41no—
197#10621883—81no—
198#10621882—22no—
199#10621882—81no—
200#10621882—81no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—41no—
207#10621877—81no—
208#10621877—81no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C8×D43—81no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C22×D43—21no—
220C22×D43—41no—
221C22×D43—82no—
222C22×D43—82no—
223C22×D43—161no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—81no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—82no—
234D4×C43—161no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—82no—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C22⋊D43—82no—
251C22⋊D43—82no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254D172—21no—
255D172—41no—
256D172—41no—
257D172—41no—
258D172—41no—
259D172—81no—
260D172—82no—
261D172#13512yes—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—82no—
265Dic86—41no—
266Dic86—41no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#19899—431nomaximal, Sylow
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43D4211yescharacteristic
287C2×D43—22no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—164no—
294C4×C43—21no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43C2×#13511yescharacteristic
301C4×C43#57511yescharacteristic
302C4×C43#57611yescharacteristic
303C4×C43#57611yescharacteristic
304Dic43—41no—
305Dic43—81no—
306#3330—431no—
307#3325—431no—
308#3303D4311yescharacteristic, complemented
309#3294—431no—
310#1711—431no—
311#1699—431no—
312#1697—431no—
313#1683—431no—
314#1681—431no—
315#1646—431no—
316#1639—431no—
317#1635—431no—
318#1625—431no—
319#1589—431no—
320C8×D8—431no—
321C2×C43—81no—
322C2×C43—81no—
323C2×C43—81no—
324C2×C43#327311yescharacteristic
325C2×C43#328011yescharacteristic
326C2×C43#329011yescharacteristic
327D43—42no—
328D43—161no—
329#555C2×D4311yescharacteristic
330#547—431no—
331#547C2×D4311yescharacteristic, complemented
332D42—431no—
333#487—431no—
334#487—431no—
335#487C2×D4311yescharacteristic, complemented
336#486—431no—
337#486—431no—
338#486—431no—
339#485—21no—
340#484—861no—
341#482—861no—
342#480—861no—
343#476—431no—
344#476C2×D4311yescharacteristic, complemented
345#474—431no—
346#474—431no—
347#469—861no—
348#468—861no—
349#466—861no—
350#465—21no—
351#461—431no—
352#461C2×D4311yescharacteristic
353#459—431no—
354#459—431no—
355#449—21no—
356#449—861no—
357#447—861no—
358#447—861no—
359C4×D8—431no—
360C4×D8C2×D4311yescharacteristic
361#436—431no—
362#436—431no—
363C8×D4—431no—
364C8×D4C2×D4311yescharacteristic, complemented
365#418—861no—
366#417—861no—
367#416—21no—
368C2×#102—861no—
369#335—431no—
370#335—431no—
371#333—431no—
372#332—431no—
373#332—431no—
374#331—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379C82—431no—
380C43#1989911yescharacteristic, complemented, Sylow
381C2×#41—21no—
382C2×#41—861no—
383C22×D4—861no—
384C22×D4—861no—
385C2×SD16—21no—
386C2×SD16—861no—
387C2×D8—431no—
388C2×D8—861no—
389C2×D8—861no—
390C2×D8C22⋊D4311yescharacteristic
391C2×M16—861no—
392C2×M16—861no—
393C22×C8—21no—
394C22×C8—861no—
395C4⋊Q8—431no—
396C4⋊Q8C22×D4311yescharacteristic
397C4⋊Q8C22×D4311yescharacteristic
398#127—431no—
399#124—41no—
400#123—41no—
401#123—1721no—
402C22⋊Q8—21no—
403C22⋊Q8—861no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—861no—
408#121—861no—
409#121—861no—
410#120—1721no—
411C4×D4—431no—
412C4×D4C22×D4311yescharacteristic
413C4×D4C22×D4311yescharacteristic
414C4×D4C22×D4311yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—861no—
419#107—431no—
420#107—861no—
421#107—861no—
422#107C22⋊D4311yescharacteristic
423#106—21no—
424#106—861no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8C22×D4311yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—861no—
433#103—861no—
434#103—861no—
435#103—1721no—
436#102—21no—
437#102—431no—
438#102—431no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—1721no—
449#102C22⋊D4311yescharacteristic
450#102C22⋊D4311yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C4×C8—431no—
456C4×C8—431no—
457C4×C8C22×D4311yescharacteristic
458C24—1721no—
459#41—42no—
460#41—81no—
461#41—3441no—
462#41—1722no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—861no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—431no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—3441no—
473C2×D4—3441no—
474C2×D4—1721no—
475C2×D4—1722no—
476C2×D4—1721no—
477C2×D4—1722no—
478C2×D4—1721no—
479C2×D4D4×D4311yescharacteristic
480C2×D4C2×C22⋊D4311yescharacteristic
481C2×D4C2×C22⋊D4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—861no—
487C22×C4—1721no—
488SD16—81no—
489SD16—3441no—
490D8—41no—
491D8—862no—
492D8—3441no—
493D8—3441no—
494M16—3441no—
495M16—3441no—
496C2×C8—21no—
497C2×C8—81no—
498C2×C8—431no—
499C2×C8—431no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—3441no—
505C2×C8C2×C22⋊D4311yescharacteristic
506C2×C8C2×C22⋊D4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—431no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—1721no—
516C4⋊C4D4×D4311yescharacteristic
517C4⋊C4C2×C22⋊D4311yescharacteristic
518C4⋊C4C2×C22⋊D4311yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—861no—
526C22⋊C4—1721no—
527C22⋊C4—1721no—
528C42—41no—
529C42C23×D4311yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—861no—
534C23—3442no—
535C23—3442no—
536C23—1721no—
537C23—6881no—
538Q8—41no—
539Q8—41no—
540Q8—81no—
541Q8—1721no—
542Q8—1721no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—82no—
550D4—161no—
551D4—432no—
552D4—861no—
553D4—3441no—
554D4—3442no—
555D4—3442no—
556D4—3442no—
557D4—1721no—
558D4—1721no—
559D4—1721no—
560D4—1721no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4—861no—
574C2×C4—3442no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C22×C22⋊D4311yescharacteristic
580C2×C4#1306337011yescharacteristic
581C8—21no—
582C8—21no—
583C8—41no—
584C8—861no—
585C8—861no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C8—1721no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—862no—
600C22—3441no—
601C22—3441no—
602C22—3441no—
603C22—1721no—
604C22—1721no—
605C22—6884no—
606C22D4×C22⋊D4311yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—3441no—
614C4—1721no—
615C4#135×D4311yescharacteristic
616C4#1458369711yescharacteristic
617C4#1458370111yescharacteristic
618C4#1458370211yescharacteristic
619C2—81no—
620C2—81no—
621C2—81no—
622C2—1722no—
623C2—6881no—
624C2#1914620211yescharacteristic
625C2#1914627411yescharacteristic
626C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3303C2
socleC22×C43D42
hypercenter#3303D43
hypocenterC43#19899
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3303

Complements

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

NH ≅ G/Ntype
1. #19146894C2semidirect
2. #19146831C2semidirect
3. #19146410C2semidirect
4. #19134208C2semidirect
5. #19134144C2semidirect
6. #19134130C2semidirect
7. #19134043C2semidirect
8. #19134032C2semidirect
9. #19133823C2semidirect
10. #19133772C2semidirect
11. #19133745C2semidirect
12. #19133684C2semidirect
13. #19133480C2semidirect
14. C8×#10621882C2semidirect
15. C43×#3303C2semidirect
18. #14583251C22semidirect
19. #14583249C22semidirect
32. #14583104C22semidirect
40. #14582977C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582648C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
57. C43×#547C22semidirect
58. C43×#487C22semidirect
60. C43×#476C22semidirect
65. C8×D4×C43C22semidirect
308. #3303D43semidirect
331. #547C2×D43semidirect
335. #487C2×D43semidirect
344. #476C2×D43semidirect
364. C8×D4C2×D43semidirect
380. C43#19899semidirect

Maximal subgroups

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

subgroupindex
#191468942
#191468312
#191464102
#191342082
#191341442
#191341302
#191340432
#191340322
#191338232
#191337722
#191337452
#191336842
#191334802
C8×#106218822
C43×#33032
#1989943