Finite Group Databasebeta

← #25086658

Subgroups — #25086658

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D8×Dic86C211yesmaximal, characteristic, complemented
2#19146454C211yesmaximal, characteristic, complemented
3D4×#10621883C211yesmaximal, characteristic, complemented
4#19134214C211yesmaximal, characteristic, complemented
5#19134108C211yesmaximal, characteristic, complemented
6#19134020C211yesmaximal, characteristic, complemented
7#19133940C211yesmaximal, characteristic, complemented
8#19133934C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133856C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133697C211yesmaximal, characteristic, complemented
13#19133436C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3272C211yesmaximal, characteristic
16C22×#10621883—21no—
17D4×Dic86C2211yescharacteristic
18D4×Dic86C2211yescharacteristic, complemented
19#14583304C2211yescharacteristic, complemented
20#14583303—21no—
21#14583295C2211yescharacteristic, complemented
22#14583271C2211yescharacteristic
23#14583251C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583229—21no—
26#14583181C2211yescharacteristic, complemented
27#14583179C2211yescharacteristic
28#14583179C2211yescharacteristic, complemented
29#14583177—21no—
30#14583177—21no—
31#14583126—21no—
32#14583126—21no—
33#14583104C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583096C2211yescharacteristic
36#14583050—21no—
37#14583037—21no—
38#14583037—21no—
39C8×Dic86C2211yescharacteristic, complemented
40C4×#10621883C2211yescharacteristic
41D8×Dic43—21no—
42D4×C43⋊C8C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic, complemented
44C2×#13063248—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582645C2211yescharacteristic, complemented
48#14582644C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51#14582629C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#547C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#468—21no—
61C43×#461C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#450—21no—
64C43×#449—21no—
65C4×D8×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C22×Dic86—21no—
68C22×Dic86—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621883—44no—
75C2×#10621883D411yescharacteristic
76C22×C43⋊C8—21no—
77C22×C43⋊C8—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063324—21no—
81#13063324—21no—
82#13063304—21no—
83#13063304—21no—
84#13063302—41no—
85#13063302—41no—
86C4×Dic86C2311yescharacteristic
87D4×Dic43—21no—
88D4×Dic43—21no—
89#13063259—21no—
90#13063259—21no—
91#13063258—21no—
92#13063258—21no—
93#13063256—21no—
94#13063256—41no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248D411yescharacteristic
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—41no—
110#13063246D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C8×Dic43—21no—
116C2×#41×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119AGL(1,ℤ/8)×C43—44no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×D8×C43—21no—
124C2×D8×C43D411yescharacteristic
125C2×M16×C43—21no—
126C4⋊Q8×C43C2311yescharacteristic
127#127×C43C2311yescharacteristic
128#123×C43—41no—
129C22⋊Q8×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#120×C43—41no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137C2×C4⋊C4×C43—21no—
138#107×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147#41×C43—42no—
148#41×C43—81no—
149C2×Q8×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C22×Dic43—41no—
168C22×Dic43—41no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173C2×Dic86—41no—
174C2×Dic86—41no—
175C2×Dic86—81no—
176C2×Dic86—81no—
177C2×Dic86C2×D411yescharacteristic
178SD16×C43—42no—
179SD16×C43—42no—
180SD16×C43—81no—
181D8×C43—42no—
182D8×C43SD1614yescomplemented
183M16×C43—42no—
184C2×C8×C43—21no—
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C42×C43C2411yescharacteristic
199C22⋊Dic43—41no—
200C22⋊Dic43—41no—
201#10621883—22no—
202#10621883—42no—
203#10621883—42no—
204#10621883—42no—
205#10621883—81no—
206#10621883—81no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43C2×D411yescharacteristic
212Dic43⋊C4—21no—
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215C4×Dic43—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—42no—
221C2×C43⋊C8—81no—
222C2×C43⋊C8C2×D411yescharacteristic
223C2×C43⋊C8C2×D411yescharacteristic
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—41no—
228C23×C43—82no—
229C23×C43—82no—
230C23×C43—161no—
231Q8×C43—41no—
232Q8×C43—41no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—81no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43—82no—
245D4×C43C2×SD1612yes—
246D4×C43C2×SD1612yescomplemented
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
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—41no—
257C2×C4×C43—82no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—82no—
266C2×Dic43—82no—
267Dic86—21no—
268Dic86—41no—
269Dic86—41no—
270Dic86—41no—
271Dic86—41no—
272Dic86—82no—
273Dic86—82no—
274Dic86AGL(1,ℤ/8)12yescomplemented
275C8×C43—21no—
276C8×C43—41no—
277C8×C43C2×SD1612yescomplemented
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#19803—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
299C4×C43—21no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—81no—
304C4×C43C22×SD1611yescharacteristic
305C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C43#57611yescharacteristic
307C4×C43#57711yescharacteristic
308Dic43—22no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312Q8×D8—431no—
313#3298—431no—
314D4×SD16—431no—
315#3272D4311yescharacteristic
316#1714—431no—
317#1693—431no—
318#1679—431no—
319#1666—431no—
320#1665—431no—
321#1654—431no—
322#1651—431no—
323#1639—431no—
324#1627—431no—
325#1583—431no—
326#1580—431no—
327C2×C43—42no—
328C2×C43—42no—
329C2×C43—81no—
330C2×C43—161no—
331C2×C43#326411yescharacteristic
332C2×C43D4×SD1611yescharacteristic
333C2×C43#328911yescharacteristic
334C2×AGL(1,ℤ/8)—21no—
335C22×SD16—861no—
336D4×Q8—431no—
337D4×Q8—431no—
338#547C2×D4311yescharacteristic
339D42C2×D4311yescharacteristic
340#500—431no—
341#500—861no—
342#498—431no—
343#492—431no—
344#492C2×D4311yescharacteristic
345#487—431no—
346#486—431no—
347#483—861no—
348#475—431no—
349#474—431no—
350#474—431no—
351#474—861no—
352#474—861no—
353#468—21no—
354#465—861no—
355#465—861no—
356#461—431no—
357#461—431no—
358#461C2×D4311yescharacteristic
359#460—431no—
360#459C2×D4311yescharacteristic
361#450—21no—
362#450—861no—
363#449—21no—
364#448—861no—
365#448—861no—
366C8×Q8—431no—
367C4×SD16—431no—
368C4×D8—861no—
369C4×D8C2×D4311yescharacteristic
370#436C2×D4311yescharacteristic
371C8×D4—431no—
372C8×D4—431no—
373C2×#103—861no—
374#334—431no—
375#334—431no—
376#332—431no—
377#332—431no—
378#332—431no—
379#331—431no—
380Q8⋊C8—431no—
381D4⋊C8—431no—
382D4⋊C8—431no—
383D4⋊C8—431no—
384#322—431no—
385C43#1980311yescharacteristic, complemented, Sylow
386C2×#41—21no—
387C22×Q8—861no—
388C22×Q8—861no—
389C22×D4—21no—
390C22×D4—21no—
391AGL(1,ℤ/8)—44no—
392C2×SD16—21no—
393C2×SD16—21no—
394C2×SD16—21no—
395C2×SD16—431no—
396C2×SD16—861no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16—861no—
401C2×SD16—1724no—
402C2×D8—21no—
403C2×D8C22⋊D4311yescharacteristic
404C2×M16—21no—
405C22×C8—861no—
406C22×C8—861no—
407C4⋊Q8—431no—
408C4⋊Q8—431no—
409C4⋊Q8—861no—
410C4⋊Q8—861no—
411C4⋊Q8C22×D4311yescharacteristic
412#127C22×D4311yescharacteristic
413#123—41no—
414C22⋊Q8—21no—
415C22⋊Q8—861no—
416C22⋊Q8—861no—
417C22⋊Q8—1721no—
418C22⋊Q8—1721no—
419#121—21no—
420#121—21no—
421#121—21no—
422#120—41no—
423C4×Q8—431no—
424C4×D4—861no—
425C4×D4—861no—
426C4×D4C22×D4311yescharacteristic
427C4×D4C22×D4311yescharacteristic
428C4×D4C22×D4311yescharacteristic
429C2×C4⋊C4—21no—
430#107—861no—
431#107—861no—
432#107—861no—
433#107—861no—
434#107C22⋊D4311yescharacteristic
435#106—431no—
436#106—861no—
437#106—1721no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—861no—
442C4⋊C8C22×D4311yescharacteristic
443#103—21no—
444#103—431no—
445#103—861no—
446#103—861no—
447#103—861no—
448#103—861no—
449#103—861no—
450#102—21no—
451#102—431no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—1721no—
456#102C22⋊D4311yescharacteristic
457#102C22⋊D4311yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461C4×C8—431no—
462C4×C8—431no—
463C4×C8—861no—
464C4×C8C22×D4311yescharacteristic
465C24—41no—
466#41—42no—
467#41—81no—
468C2×Q8—21no—
469C2×Q8—431no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—3441no—
473C2×Q8—3441no—
474C2×Q8—1721no—
475C2×Q8—1721no—
476C2×Q8—1722no—
477C2×Q8—1722no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—41no—
486C2×D4—81no—
487C2×D4—81no—
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—
497SD16—42no—
498SD16—42no—
499SD16—81no—
500SD16—862no—
501SD16—3441no—
502SD16—3441no—
503SD16—1722no—
504SD16—1722no—
505SD16—1722no—
506D8—42no—
507D8#1062188314yescomplemented
508M16—42no—
509C2×C8—21no—
510C2×C8—431no—
511C2×C8—431no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—3441no—
517C2×C8—1722no—
518C2×C8C2×C22⋊D4311yescharacteristic
519C2×C8C2×C22⋊D4311yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—41no—
523C4⋊C4—431no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—1721no—
530C4⋊C4—1721no—
531C4⋊C4D4×D4311yescharacteristic
532C4⋊C4C2×C22⋊D4311yescharacteristic
533C4⋊C4C2×C22⋊D4311yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—1721no—
540C22⋊C4—1721no—
541C42—861no—
542C42C23×D4311yescharacteristic
543C23—21no—
544C23—21no—
545C23—21no—
546C23—41no—
547C23—82no—
548C23—82no—
549C23—161no—
550Q8—41no—
551Q8—41no—
552Q8—432no—
553Q8—861no—
554Q8—3442no—
555Q8—3442no—
556Q8—1721no—
557Q8—1721no—
558Q8—1721no—
559Q8—1721no—
560D4—21no—
561D4—21no—
562D4—21no—
563D4—21no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—81no—
569D4—82no—
570D4—82no—
571D4—82no—
572D4C2×#1062188312yes—
573D4C2×#1062188312yescomplemented
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—3442no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4C22×C22⋊D4311yescharacteristic
593C2×C4#1306337011yescharacteristic
594C8—21no—
595C8—41no—
596C8—861no—
597C8—861no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8C2×#1062188312yescomplemented
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—164no—
616C22D4×C22⋊D4311yescharacteristic
617C4—21no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—862no—
623C4—3441no—
624C4—3441no—
625C4—1721no—
626C4C22×#1062188311yescharacteristic
627C4AGL(1,ℤ/8)×D4311yescharacteristic
628C4#1458370311yescharacteristic
629C4#1458371011yescharacteristic
630C2—42no—
631C2—42no—
632C2—81no—
633C2—161no—
634C2#1914606911yescharacteristic
635C2D4×#1062188311yescharacteristic
636C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3272C2
socleC22×C43D42
hypercenter#3272D43
hypocenterC43#19803
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3272

Complements

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

NH ≅ G/Ntype
1. D8×Dic86C2semidirect
2. #19146454C2semidirect
3. D4×#10621883C2semidirect
4. #19134214C2semidirect
5. #19134108C2semidirect
6. #19134020C2semidirect
7. #19133940C2semidirect
8. #19133934C2semidirect
9. #19133879C2semidirect
10. #19133856C2semidirect
11. #19133774C2semidirect
12. #19133697C2semidirect
13. #19133436C2semidirect
14. #19133419C2semidirect
18. D4×Dic86C22semidirect
19. #14583304C22semidirect
21. #14583295C22semidirect
23. #14583251C22semidirect
26. #14583181C22semidirect
28. #14583179C22semidirect
39. C8×Dic86C22semidirect
43. D4×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582645C22semidirect
48. #14582644C22semidirect
49. #14582644C22semidirect
51. #14582629C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
182. D8×C43SD16semidirect
246. D4×C43C2×SD16semidirect
274. Dic86AGL(1,ℤ/8)semidirect
277. C8×C43C2×SD16semidirect
385. C43#19803semidirect
507. D8#10621883semidirect
573. D4C2×#10621883semidirect
602. C8C2×#10621883semidirect

Maximal subgroups

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

subgroupindex
D8×Dic862
#191464542
D4×#106218832
#191342142
#191341082
#191340202
#191339402
#191339342
#191338792
#191338562
#191337742
#191336972
#191334362
#191334192
C43×#32722
#1980343