Finite Group Databasebeta

← #25086439

Subgroups — #25086439

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147300C211yesmaximal, characteristic, complemented
2#19146419C211yesmaximal, characteristic, complemented
3#19146321C211yesmaximal, characteristic, complemented
4#19134235C211yesmaximal, characteristic, complemented
5#19134160C211yesmaximal, characteristic, complemented
6#19134004C211yesmaximal, characteristic, complemented
7#19134002C211yesmaximal, characteristic, complemented
8#19133938C211yesmaximal, characteristic, complemented
9#19133808C211yesmaximal, characteristic, complemented
10#19133746C211yesmaximal, characteristic, complemented
11#19133659C211yesmaximal, characteristic, complemented
12#19133649C211yesmaximal, characteristic, complemented
13#19133431C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3294C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583606C2211yescharacteristic
18#14583570C2211yescharacteristic, complemented
19#14583275C2211yescharacteristic
20#14583273C2211yescharacteristic, complemented
21#14583262—21no—
22#14583251C2211yescharacteristic, complemented
23#14583246C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583215—21no—
26#14583202—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583130—21no—
30#14583126—21no—
31#14583106C2211yescharacteristic, complemented
32#14583096C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583092—21no—
36#14583059—21no—
37#14583050—21no—
38#14583044—21no—
39#14583029C2211yescharacteristic, complemented
40#14583008—21no—
41C4×#10621883C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic, complemented
44C2×#13063246—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582642C2211yescharacteristic, complemented
51#14582629C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, 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×#10621898—21no—
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621883D411yescharacteristic
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—41no—
77C22×C43⋊C8—21no—
78C22×C43⋊C8—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063321—21no—
82#13063316—21no—
83#13063304—21no—
84#13063302—41no—
85#13063299—21no—
86#13063298—41no—
87C4×Dic86C2311yescharacteristic
88D4×Dic43—21no—
89#13063287—21no—
90C2×C4⋊Dic43—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98#13063249—21no—
99#13063248—41no—
100#13063248D411yescharacteristic
101#13063247—21no—
102#13063247—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063235—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—
169#10621898—42no—
170#10621898—81no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×C4×D43—41no—
175C2×Dic86—21no—
176C2×Dic86C2×D411yescharacteristic
177D8×C43—22no—
178D8×C43—81no—
179C2×C8×C43—21no—
180C2×C8×C43—81no—
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—41no—
193C22⋊C4×C43—41no—
194C42×C43C2411yescharacteristic
195C22⋊Dic43—41no—
196#10621885—42no—
197#10621884—42no—
198#10621884—81no—
199#10621883—22no—
200#10621883—81no—
201#10621882—42no—
202#10621882—42no—
203#10621882—82no—
204(C2×D43)⋊C4—41no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—41no—
208C4⋊Dic43C2×D411yescharacteristic
209Dic43⋊C4—21no—
210Dic43⋊C4—41no—
211C4×Dic43—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—42no—
217C2×C43⋊C8—81no—
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—41no—
224C23×C43—82no—
225C23×C43—82no—
226C23×C43—161no—
227C22×D43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—81no—
239D4×C43—82no—
240D4×C43—82no—
241D4×C43—82no—
242D4×C43#13512yescomplemented
243D4×C43AGL(1,ℤ/8)12yes—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—82no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C22⋊D43—82no—
259C22⋊D43—161no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—161no—
264D172—41no—
265D172—41no—
266D172—41no—
267D172—41no—
268D172—81no—
269C4×D43—82no—
270Dic86—21no—
271Dic86—21no—
272Dic86—81no—
273C8×C43—21no—
274C8×C43—21no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#19788—431nomaximal, Sylow
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—164no—
296C22×C43D4211yescharacteristic
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C4×C43—21no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43C2×#13511yescharacteristic
306C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C43#57611yescharacteristic
308C4×C43#57711yescharacteristic
309Dic43—41no—
310Dic43—41no—
311Dic43—81no—
312#3366—431no—
313#3295—431no—
314#3294D4311yescharacteristic, complemented
315#3284—431no—
316#1717—431no—
317#1702—431no—
318#1677—431no—
319#1677—431no—
320#1665—431no—
321#1644—431no—
322#1635—431no—
323#1621—431no—
324#1619—431no—
325#1582—431no—
326#1580—431no—
327C2×C43—42no—
328C2×C43—42no—
329C2×C43—81no—
330C2×C43—161no—
331C2×C43#326411yescharacteristic
332C2×C43#328211yescharacteristic
333C2×C43#328811yescharacteristic
334D43—161no—
335C2×#135—861no—
336#554—431no—
337#550—431no—
338#547C2×D4311yescharacteristic
339D42C2×D4311yescharacteristic
340#493—431no—
341#492—431no—
342#490—861no—
343#487—431no—
344#486—431no—
345#486—431no—
346#486C2×D4311yescharacteristic
347#481—861no—
348#480—21no—
349#478—861no—
350#476—431no—
351#476—431no—
352#474C2×D4311yescharacteristic
353#466—21no—
354#465—861no—
355#465—861no—
356#462—431no—
357#460—431no—
358#459—431no—
359#459—431no—
360#459—861no—
361#459C2×D4311yescharacteristic
362#452—861no—
363#450—861no—
364#449—861no—
365#447—21no—
366#446—431no—
367#442—861no—
368C4×SD16—431no—
369C4×D8C2×D4311yescharacteristic
370C8×D4—431no—
371C8×D4—431no—
372C8×D4C2×D4311yescharacteristic
373C2×#102—21no—
374C2×#102—861no—
375#334—431no—
376#334—431no—
377#333—431no—
378#332—431no—
379#331—431no—
380#331—431no—
381Q8⋊C8—431no—
382D4⋊C8—431no—
383D4⋊C8—431no—
384D4⋊C8—431no—
385#322—431no—
386C43#1978811yescharacteristic, complemented, Sylow
387C2×#41—21no—
388C2×#41—861no—
389C22×D4—21no—
390C22×D4—21no—
391#135—1724no—
392C2×Q16—861no—
393C2×SD16—431no—
394C2×SD16—861no—
395C2×SD16—861no—
396C2×SD16—861no—
397C2×D8—21no—
398C2×D8—861no—
399C2×D8—861no—
400C2×D8—1721no—
401C2×D8C22⋊D4311yescharacteristic
402C22×C8—21no—
403C22×C8—861no—
404C22×C8—861no—
405C4⋊Q8—431no—
406C4⋊Q8C22×D4311yescharacteristic
407#127—431no—
408#127—861no—
409#127C22×D4311yescharacteristic
410#125—861no—
411#123—41no—
412C22⋊Q8—21no—
413C22⋊Q8—861no—
414C22⋊Q8—1721no—
415#121—21no—
416#121—21no—
417#121—21no—
418#121—861no—
419#121—1721no—
420#120—41no—
421C4×Q8—431no—
422C4×D4—861no—
423C4×D4—861no—
424C4×D4C22×D4311yescharacteristic
425C4×D4C22×D4311yescharacteristic
426C4×D4C22×D4311yescharacteristic
427C2×C4⋊C4—21no—
428C2×C4⋊C4—861no—
429#107—21no—
430#107C22⋊D4311yescharacteristic
431#106—431no—
432#106—861no—
433#106—861no—
434C4⋊C8—431no—
435C4⋊C8—431no—
436C4⋊C8—431no—
437C4⋊C8—861no—
438C4⋊C8C22×D4311yescharacteristic
439#103—431no—
440#103—861no—
441#103—1721no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—431no—
447#102—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102C22⋊D4311yescharacteristic
457#102C22⋊D4311yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461#97—861no—
462C4×C8—431no—
463C4×C8—431no—
464C4×C8C22×D4311yescharacteristic
465C24—41no—
466#41—42no—
467#41—81no—
468#41—3441no—
469#41—1722no—
470C2×Q8—21no—
471C2×Q8—431no—
472C2×Q8—861no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—41no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—1721no—
487C2×D4—1721no—
488C2×D4D4×D4311yescharacteristic
489C2×D4C2×C22⋊D4311yescharacteristic
490C2×D4C2×C22⋊D4311yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—1721no—
496C22×C4—1721no—
497Q16—1722no—
498SD16—862no—
499SD16—3441no—
500SD16—3441no—
501SD16—1722no—
502D8—22no—
503D8—81no—
504D8—3442no—
505D8—1722no—
506D8—1722no—
507C2×C8—21no—
508C2×C8—81no—
509C2×C8—431no—
510C2×C8—431no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—3441no—
516C2×C8—1722no—
517C2×C8C2×C22⋊D4311yescharacteristic
518C2×C8C2×C22⋊D4311yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—41no—
522C4⋊C4—431no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—1721no—
527C4⋊C4—1721no—
528C4⋊C4D4×D4311yescharacteristic
529C4⋊C4C2×C22⋊D4311yescharacteristic
530C4⋊C4C2×C22⋊D4311yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—1721no—
537C22⋊C4—1721no—
538C42—861no—
539C42C23×D4311yescharacteristic
540C23—21no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—82no—
545C23—82no—
546C23—161no—
547C23—1721no—
548Q8—41no—
549Q8—41no—
550Q8—861no—
551Q8—861no—
552Q8—3441no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—81no—
562D4—82no—
563D4—82no—
564D4—82no—
565D4—3441no—
566D4—3442no—
567D4—1721no—
568D4—1721no—
569D4—1721no—
570D4—1721no—
571D4—6881no—
572D4#1306334512yescomplemented
573D4#1306334912yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—82no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—3442no—
588C2×C4—1721no—
589C2×C4—6881no—
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4C22×C22⋊D4311yescharacteristic
592C2×C4#1306337011yescharacteristic
593C8—21no—
594C8—21no—
595C8—41no—
596C8—861no—
597C8—861no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C22—22no—
603C22—22no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—164no—
615C22—3441no—
616C22—3441no—
617C22—3441no—
618C22D4×C22⋊D4311yescharacteristic
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—3441no—
625C4—1721no—
626C4—1721no—
627C4C2×#1306334511yescharacteristic
628C4C2×#1306334911yescharacteristic
629C4#1458370011yescharacteristic
630C4#1458371011yescharacteristic
631C2—42no—
632C2—42no—
633C2—81no—
634C2—161no—
635C2—6881no—
636C2#1914607511yescharacteristic
637C2#1914629811yescharacteristic
638C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3294C2
socleC22×C43D42
hypercenter#3294D43
hypocenterC43#19788
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. #19147300C2semidirect
2. #19146419C2semidirect
3. #19146321C2semidirect
4. #19134235C2semidirect
5. #19134160C2semidirect
6. #19134004C2semidirect
7. #19134002C2semidirect
8. #19133938C2semidirect
9. #19133808C2semidirect
10. #19133746C2semidirect
11. #19133659C2semidirect
12. #19133649C2semidirect
13. #19133431C2semidirect
14. #19133419C2semidirect
15. C43×#3294C2semidirect
18. #14583570C22semidirect
20. #14583273C22semidirect
22. #14583251C22semidirect
23. #14583246C22semidirect
28. #14583189C22semidirect
31. #14583106C22semidirect
39. #14583029C22semidirect
43. D4×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
50. #14582642C22semidirect
51. #14582629C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
242. D4×C43#135semidirect
314. #3294D43semidirect
386. C43#19788semidirect
572. D4#13063345semidirect

Maximal subgroups

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

subgroupindex
#191473002
#191464192
#191463212
#191342352
#191341602
#191340042
#191340022
#191339382
#191338082
#191337462
#191336592
#191336492
#191334312
#191334192
C43×#32942
#1978843