Finite Group Databasebeta

← #25086195

Subgroups — #25086195

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146900C211yesmaximal, characteristic, complemented
2#19146408C211yesmaximal, characteristic, complemented
3#19146316C211yesmaximal, characteristic, complemented
4#19134254C211yesmaximal, characteristic, complemented
5#19134154C211yesmaximal, characteristic, complemented
6#19134029C211yesmaximal, characteristic, complemented
7#19134016C211yesmaximal, characteristic, complemented
8#19133960C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133878C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133682C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15C43×#3294C211yesmaximal, characteristic, complemented
16C2×#13063344—21no—
17#14583553C2211yescharacteristic
18#14583553C2211yescharacteristic, complemented
19#14583295C2211yescharacteristic, complemented
20#14583279C2211yescharacteristic, complemented
21#14583249C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583232—21no—
25#14583210—21no—
26#14583179C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583147—21no—
29#14583141—21no—
30#14583133—21no—
31#14583104C2211yescharacteristic
32#14583104C2211yescharacteristic, complemented
33#14583101C2211yescharacteristic, complemented
34#14583091C2211yescharacteristic
35#14583062—21no—
36#14583062—21no—
37#14583044—21no—
38#14583033—21no—
39C4×#10621882C2211yescharacteristic
40#14582977C2211yescharacteristic, complemented
41C8×D172C2211yescharacteristic, complemented
42D4×C43⋊C8C2211yescharacteristic
43#14582900—21no—
44C2×#13063246—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55#14582621C2211yescharacteristic, complemented
56C43×#547C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#480—21no—
60C43×#474C2211yescharacteristic
61C43×#466—21no—
62C43×#459C2211yescharacteristic
63C43×#447—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#102×C43—21no—
67C2×#10621900—21no—
68C2×#10621900—21no—
69#13063344—44no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621882—21no—
76C2×#10621882D411yescharacteristic
77C2×#10621877—21no—
78C22×C43⋊C8—21no—
79C2×C8×D43—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063309—41no—
83#13063309—41no—
84#13063305—21no—
85#13063305—21no—
86#13063299—21no—
87#13063299—21no—
88C4×D172C2311yescharacteristic
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258D411yescharacteristic
94#13063256—41no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—41no—
109#13063246D411yescharacteristic
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C2×D8×C43—21no—
120C2×D8×C43D411yescharacteristic
121C22×C8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123#127×C43C2311yescharacteristic
124#123×C43—41no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#120×C43—41no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134#107×C43—21no—
135#107×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—41no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—41no—
168C22×Dic43—41no—
169C22×Dic43—41no—
170#10621900—42no—
171#10621900—42no—
172#10621900—81no—
173#10621900—81no—
174C2×D172C2×D411yescharacteristic
175C2×C4×D43—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178D8×C43—22no—
179D8×C43—81no—
180C2×C8×C43—21no—
181C2×C8×C43—81no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—41no—
194C22⋊C4×C43—41no—
195C42×C43C2411yescharacteristic
196#10621884—81no—
197#10621883—42no—
198#10621883—42no—
199#10621882—22no—
200#10621882—81no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—41no—
203(C2×D43)⋊C4—41no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—41no—
209C4⋊Dic43—41no—
210C4⋊Dic43C2×D411yescharacteristic
211#10621877—81no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—81no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219Dic172—42no—
220Dic172—81no—
221C8×D43—42no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—41no—
226C23×C43—82no—
227C23×C43—82no—
228C23×C43—161no—
229C22×D43—21no—
230Q8×C43—41no—
231Q8×C43—41no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—81no—
241D4×C43—82no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43#13512yescomplemented
245D4×C43AGL(1,ℤ/8)12yes—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—82no—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C22⋊D43—82no—
261C22⋊D43—82no—
262C2×Dic43—21no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—82no—
266C2×Dic43—82no—
267D172—21no—
268D172—21no—
269C4×D43—41no—
270C4×D43—41no—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274Dic86—41no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—41no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#19772—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—164no—
298C22×C43D4211yescharacteristic
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C4×C43—21no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43C2×#13511yescharacteristic
308C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
309C4×C43#57611yescharacteristic
310C4×C43#57611yescharacteristic
311Dic43—41no—
312Dic43—81no—
313Dic43—81no—
314#3330—431no—
315#3294—431no—
316#3294D4311yescharacteristic, complemented
317#3283—431no—
318#1720—431no—
319#1701—431no—
320#1681—431no—
321#1679—431no—
322#1669—431no—
323#1654—431no—
324#1654—431no—
325#1639—431no—
326#1625—431no—
327#1581—431no—
328#1580—431no—
329C2×C43—42no—
330C2×C43—42no—
331C2×C43—81no—
332C2×C43—161no—
333C2×C43#326411yescharacteristic
334C2×C43#328011yescharacteristic
335C2×C43#328911yescharacteristic
336D43—81no—
337C2×#135—861no—
338#547—431no—
339#547—431no—
340#547C2×D4311yescharacteristic
341D42C2×D4311yescharacteristic
342#498—431no—
343#494—431no—
344#487—431no—
345#486—431no—
346#486—431no—
347#486C2×D4311yescharacteristic
348#484—861no—
349#480—21no—
350#480—861no—
351#474—431no—
352#474—431no—
353#474C2×D4311yescharacteristic
354#468—861no—
355#467—861no—
356#466—21no—
357#466—861no—
358#461—431no—
359#461—431no—
360#461—431no—
361#459—431no—
362#459C2×D4311yescharacteristic
363#452—861no—
364#452—861no—
365#449—861no—
366#447—21no—
367#447—861no—
368C4×D8—431no—
369C4×D8C2×D4311yescharacteristic
370#436—431no—
371C8×D4—431no—
372C8×D4—431no—
373C8×D4C2×D4311yescharacteristic
374#417—861no—
375C2×#102—21no—
376C2×#102—861no—
377#335—431no—
378#334—431no—
379#332—431no—
380#332—431no—
381#332—431no—
382#331—431no—
383D4⋊C8—431no—
384D4⋊C8—431no—
385D4⋊C8—431no—
386D4⋊C8—431no—
387#322—431no—
388C43#1977211yescharacteristic, complemented, Sylow
389C2×#41—21no—
390C2×#41—861no—
391C2×#41—861no—
392C22×D4—21no—
393C22×D4—21no—
394#135—1724no—
395C2×Q16—861no—
396C2×Q16—861no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×D8—21no—
401C2×D8—431no—
402C2×D8—861no—
403C2×D8C22⋊D4311yescharacteristic
404C2×M16—861no—
405C22×C8—21no—
406C22×C8—861no—
407C22×C8—861no—
408C4⋊Q8—431no—
409C4⋊Q8—431no—
410C4⋊Q8C22×D4311yescharacteristic
411#127C22×D4311yescharacteristic
412#123—41no—
413#123—1721no—
414#123—1721no—
415C22⋊Q8—21no—
416C22⋊Q8—861no—
417C22⋊Q8—861no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121—861no—
422#121—861no—
423#120—41no—
424C4×D4—431no—
425C4×D4C22×D4311yescharacteristic
426C4×D4C22×D4311yescharacteristic
427C4×D4C22×D4311yescharacteristic
428C2×C4⋊C4—21no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431#107—21no—
432#107—431no—
433#107—861no—
434#107—861no—
435#107C22⋊D4311yescharacteristic
436#106—1721no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8C22×D4311yescharacteristic
441#103—861no—
442#103—861no—
443#103—861no—
444#103—861no—
445#103—861no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102—21no—
450#102—431no—
451#102—431no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102—1721no—
458#102C22⋊D4311yescharacteristic
459#102C22⋊D4311yescharacteristic
460C22⋊C8—21no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463C22⋊C8—861no—
464C4×C8—431no—
465C4×C8—431no—
466C4×C8C22×D4311yescharacteristic
467C24—41no—
468#41—42no—
469#41—81no—
470#41—3441no—
471#41—3441no—
472#41—1722no—
473#41—1722no—
474C2×Q8—21no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—41no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4—431no—
488C2×D4—1721no—
489C2×D4—1721no—
490C2×D4D4×D4311yescharacteristic
491C2×D4C2×C22⋊D4311yescharacteristic
492C2×D4C2×C22⋊D4311yescharacteristic
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—41no—
497C22×C4—861no—
498C22×C4—1721no—
499C22×C4—1721no—
500Q16—3441no—
501Q16—1722no—
502SD16—3441no—
503SD16—1722no—
504SD16—1722no—
505D8—22no—
506D8—81no—
507D8—862no—
508D8—3441no—
509M16—3441no—
510C2×C8—21no—
511C2×C8—81no—
512C2×C8—431no—
513C2×C8—431no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—3441no—
519C2×C8—1722no—
520C2×C8C2×C22⋊D4311yescharacteristic
521C2×C8C2×C22⋊D4311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—431no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—1721no—
531C4⋊C4—1721no—
532C4⋊C4D4×D4311yescharacteristic
533C4⋊C4C2×C22⋊D4311yescharacteristic
534C4⋊C4C2×C22⋊D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—861no—
541C22⋊C4—1721no—
542C22⋊C4—1721no—
543C42C23×D4311yescharacteristic
544C23—21no—
545C23—21no—
546C23—21no—
547C23—41no—
548C23—82no—
549C23—82no—
550C23—161no—
551C23—861no—
552Q8—41no—
553Q8—41no—
554Q8—1721no—
555Q8—1721no—
556Q8—1721no—
557Q8—1721no—
558D4—21no—
559D4—21no—
560D4—21no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—82no—
570D4—861no—
571D4—861no—
572D4—3442no—
573D4—3442no—
574D4#1306334412yescomplemented
575D4#1306335012yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—82no—
587C2×C4—861no—
588C2×C4—3442no—
589C2×C4—3442no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4C22×C22⋊D4311yescharacteristic
596C2×C4#1306337011yescharacteristic
597C8—21no—
598C8—21no—
599C8—41no—
600C8—861no—
601C8—861no—
602C8—1721no—
603C8—1721no—
604C8—1721no—
605C8—1721no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—164no—
619C22—1721no—
620C22—1721no—
621C22—1721no—
622C22D4×C22⋊D4311yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—3441no—
629C4—3441no—
630C4—1721no—
631C4C2×#1306334411yescharacteristic
632C4C2×#1306335011yescharacteristic
633C4#1458370011yescharacteristic
634C4#1458370211yescharacteristic
635C2—42no—
636C2—42no—
637C2—81no—
638C2—161no—
639C2—3441no—
640C2#1914607611yescharacteristic
641C2#1914628011yescharacteristic
642C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3294C2
socleC22×C43D42
hypercenter#3294D43
hypocenterC43#19772
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. #19146900C2semidirect
2. #19146408C2semidirect
3. #19146316C2semidirect
4. #19134254C2semidirect
5. #19134154C2semidirect
6. #19134029C2semidirect
7. #19134016C2semidirect
8. #19133960C2semidirect
9. #19133879C2semidirect
10. #19133878C2semidirect
11. #19133774C2semidirect
12. #19133682C2semidirect
13. #19133425C2semidirect
14. #19133417C2semidirect
15. C43×#3294C2semidirect
18. #14583553C22semidirect
19. #14583295C22semidirect
20. #14583279C22semidirect
21. #14583249C22semidirect
32. #14583104C22semidirect
33. #14583101C22semidirect
40. #14582977C22semidirect
41. C8×D172C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582646C22semidirect
48. #14582646C22semidirect
49. #14582645C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582621C22semidirect
244. D4×C43#135semidirect
316. #3294D43semidirect
388. C43#19772semidirect
574. D4#13063344semidirect

Maximal subgroups

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

subgroupindex
#191469002
#191464082
#191463162
#191342542
#191341542
#191340292
#191340162
#191339602
#191338792
#191338782
#191337742
#191336822
#191334252
#191334172
C43×#32942
#1977243