Finite Group Databasebeta

← #25086075

Subgroups — #25086075

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147516C211yesmaximal, characteristic, complemented
2#19147235C211yesmaximal, characteristic, complemented
3D4×#10621883C211yesmaximal, characteristic
4#19134215C211yesmaximal, characteristic, complemented
5#19134065C211yesmaximal, characteristic, complemented
6#19134018C211yesmaximal, characteristic, complemented
7#19133982C211yesmaximal, characteristic, complemented
8#19133940C211yesmaximal, characteristic, complemented
9#19133858C211yesmaximal, characteristic, complemented
10#19133856C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic
12#19133689C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic
16C22×#10621883—21no—
17#14583627C2211yescharacteristic, complemented
18D4×Dic86C2211yescharacteristic
19#14583305—21no—
20#14583302C2211yescharacteristic, complemented
21#14583295C2211yescharacteristic, complemented
22#14583271C2211yescharacteristic
23#14583250C2211yescharacteristic, complemented
24#14583248—21no—
25#14583245C2211yescharacteristic
26#14583199—21no—
27#14583191—21no—
28#14583184C2211yescharacteristic, complemented
29#14583183—21no—
30#14583181C2211yescharacteristic, complemented
31#14583179C2211yescharacteristic
32#14583126—21no—
33#14583104C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583102—21no—
36#14583096C2211yescharacteristic
37#14583050—21no—
38#14583037—21no—
39#14583030C2211yescharacteristic, complemented
40C8×Dic86C2211yescharacteristic, complemented
41#14582999—21no—
42#14582990—21no—
43C4×#10621883C2211yescharacteristic
44D4×C43⋊C8C2211yescharacteristic
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C22×SD16×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#465—21no—
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C43×#448—21no—
65C4×SD16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—44no—
74C2×#10621883D411yescharacteristic
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063324—21no—
79#13063323—21no—
80#13063317—21no—
81#13063315—41no—
82#13063304—21no—
83#13063302—41no—
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86#13063290—21no—
87D4×Dic43—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—41no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100#13063250—21no—
101#13063250—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246—41no—
110#13063246D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C8×Dic43—21no—
116C22×Q8×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43—44no—
124C2×SD16×C43D411yescharacteristic
125C22×C8×C43—21no—
126C4⋊Q8×C43—21no—
127C4⋊Q8×C43C2311yescharacteristic
128#127×C43C2311yescharacteristic
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—41no—
131#121×C43—21no—
132#121×C43—21no—
133#120×C43—41no—
134C4×Q8×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138#106×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#102×C43—21no—
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43—81no—
160C2×D4×C43—81no—
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—41no—
166C22×Dic43—41no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—42no—
170C2×Dic86—41no—
171C2×Dic86—81no—
172C2×Dic86C2×D411yescharacteristic
173SD16×C43—22no—
174SD16×C43—42no—
175SD16×C43—42no—
176SD16×C43—42no—
177SD16×C43—81no—
178C2×C8×C43—21no—
179C2×C8×C43—42no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C4⋊C4×C43—21no—
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—41no—
192C22⋊C4×C43—41no—
193C42×C43—21no—
194C42×C43C2411yescharacteristic
195C22⋊Dic43—41no—
196#10621883—42no—
197#10621883—42no—
198#10621883—42no—
199#10621883—42no—
200#10621883—81no—
201#10621883SD1614yescomplemented
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—21no—
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210Dic43⋊C4—41no—
211Dic43⋊C4—41no—
212C4×Dic43—21no—
213C4×Dic43—41no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—42no—
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—41no—
224C23×C43—82no—
225C23×C43—82no—
226C23×C43—161no—
227Q8×C43—21no—
228Q8×C43—21no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—82no—
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×C43C2×SD1612yes—
242D4×C43AGL(1,ℤ/8)12yes—
243C2×C4×C43—21no—
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—82no—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—82no—
261Dic86—21no—
262Dic86—41no—
263Dic86—41no—
264Dic86—41no—
265Dic86—41no—
266Dic86—82no—
267Dic86C2×SD1612yescomplemented
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8C2×SD1612yescomplemented
277#19764—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—164no—
288C22×C43D4211yescharacteristic
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43C22×SD1611yescharacteristic
296C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
297C4×C43#57711yescharacteristic
298C4×C43#57711yescharacteristic
299Dic43—22no—
300Dic43—41no—
301Dic43—81no—
302Dic43—81no—
303#3386—431no—
304#3359—431no—
305D4×SD16—431no—
306D4×SD16D4311yescharacteristic
307#1714—431no—
308#1686—431no—
309#1679—431no—
310#1673—431no—
311#1666—431no—
312#1651—431no—
313#1651—431no—
314#1639—431no—
315#1626—431no—
316#1582—431no—
317SD16⋊C8—431no—
318C2×C43—42no—
319C2×C43—42no—
320C2×C43—161no—
321C2×C43#326511yescharacteristic
322C2×C43D4×SD1611yescharacteristic
323C2×C43#328911yescharacteristic
324C22×SD16—21no—
325C22×SD16—861no—
326#557—431no—
327D4×Q8—431no—
328D4×Q8C2×D4311yescharacteristic
329D42C2×D4311yescharacteristic
330#501—861no—
331#500—431no—
332#498—431no—
333#492—431no—
334#492C2×D4311yescharacteristic
335#487—431no—
336#487—861no—
337#486—431no—
338#478—861no—
339#477—861no—
340#475—431no—
341#475—431no—
342#475—861no—
343#474—431no—
344#465—21no—
345#465—861no—
346#461—431no—
347#461—431no—
348#461—861no—
349#461C2×D4311yescharacteristic
350#460—431no—
351#460C2×D4311yescharacteristic
352#450—21no—
353#450—861no—
354#448—21no—
355#448—861no—
356#446—431no—
357C8×Q8—431no—
358#440—861no—
359C4×SD16—431no—
360C4×SD16—861no—
361C4×SD16C2×D4311yescharacteristic
362C8×D4—431no—
363C8×D4C2×D4311yescharacteristic
364#335—431no—
365#334—431no—
366#332—431no—
367#332—431no—
368#332—431no—
369#331—431no—
370Q8⋊C8—431no—
371Q8⋊C8—431no—
372D4⋊C8—431no—
373D4⋊C8—431no—
374#322—431no—
375C43#1976411yescharacteristic, complemented, Sylow
376C22×Q8—21no—
377C22×Q8—861no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—44no—
385C2×SD16—431no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—861no—
391C2×SD16—1724no—
392C2×SD16C22⋊D4311yescharacteristic
393C22×C8—21no—
394C22×C8—861no—
395C4⋊Q8—21no—
396C4⋊Q8—431no—
397C4⋊Q8—431no—
398C4⋊Q8—861no—
399C4⋊Q8—861no—
400C4⋊Q8C22×D4311yescharacteristic
401#127C22×D4311yescharacteristic
402#125—861no—
403#125—1721no—
404C22⋊Q8—21no—
405C22⋊Q8—41no—
406C22⋊Q8—861no—
407C22⋊Q8—1721no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×Q8—431no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8C22×D4311yescharacteristic
415C4×D4—21no—
416C4×D4—861no—
417C4×D4C22×D4311yescharacteristic
418C4×D4C22×D4311yescharacteristic
419#107—861no—
420#107—861no—
421#107—861no—
422#106—431no—
423#106—861no—
424#106—861no—
425#106—1721no—
426#106C22⋊D4311yescharacteristic
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—861no—
431C4⋊C8—861no—
432C4⋊C8C22×D4311yescharacteristic
433#103—21no—
434#103—431no—
435#103—861no—
436#103—861no—
437#103—861no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103C22⋊D4311yescharacteristic
442#102—21no—
443#102—431no—
444#102—861no—
445#102—861no—
446#102—1721no—
447#102C22⋊D4311yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—861no—
450#97—861no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8—861no—
454C4×C8C22×D4311yescharacteristic
455C24—41no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—42no—
459C2×Q8—81no—
460C2×Q8—431no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—3441no—
464C2×Q8—1721no—
465C2×Q8—1722no—
466C2×Q8C2×C22⋊D4311yescharacteristic
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4D4×D4311yescharacteristic
477C2×D4C2×C22⋊D4311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—1721no—
482SD16—22no—
483SD16—42no—
484SD16—42no—
485SD16—42no—
486SD16—81no—
487SD16—434no—
488SD16—3441no—
489SD16—1722no—
490SD16—1722no—
491SD16—1722no—
492SD16—1722no—
493C2×C8—21no—
494C2×C8—42no—
495C2×C8—431no—
496C2×C8—431no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—1722no—
502C2×C8C2×C22⋊D4311yescharacteristic
503C2×C8C2×C22⋊D4311yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—431no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1721no—
515C4⋊C4—1721no—
516C4⋊C4—1721no—
517C4⋊C4—1721no—
518C4⋊C4D4×D4311yescharacteristic
519C4⋊C4C2×C22⋊D4311yescharacteristic
520C4⋊C4C2×C22⋊D4311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—1721no—
526C42—21no—
527C42—861no—
528C42—1721no—
529C42C23×D4311yescharacteristic
530C23—21no—
531C23—21no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23—161no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—82no—
541Q8—432no—
542Q8—861no—
543Q8—3442no—
544Q8—1721no—
545Q8—1721no—
546Q8—1721no—
547Q8—1721no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4SD16×D4312yes—
558D4#1306335112yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—3442no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C22×C22⋊D4311yescharacteristic
576C2×C4#1306337011yescharacteristic
577C8—21no—
578C8—21no—
579C8—41no—
580C8—432no—
581C8—861no—
582C8—1721no—
583C8—1721no—
584C8—1721no—
585C8—1721no—
586C22—22no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—164no—
596C22D4×C22⋊D4311yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—862no—
604C4—3441no—
605C4—3441no—
606C4—1721no—
607C4C2×SD16×D4311yescharacteristic
608C4C2×#1306335111yescharacteristic
609C4#1458370511yescharacteristic
610C4#1458371011yescharacteristic
611C2—42no—
612C2—42no—
613C2—161no—
614C2#1914608611yescharacteristic
615C2SD16×C22⋊D4311yescharacteristic
616C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radicalD42×C43C22
hypercenterD4×SD16D43
hypocenterC43#19764
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. #19147516C2semidirect
2. #19147235C2semidirect
4. #19134215C2semidirect
5. #19134065C2semidirect
6. #19134018C2semidirect
7. #19133982C2semidirect
8. #19133940C2semidirect
9. #19133858C2semidirect
10. #19133856C2semidirect
12. #19133689C2semidirect
13. #19133432C2semidirect
14. #19133407C2semidirect
17. #14583627C22semidirect
20. #14583302C22semidirect
21. #14583295C22semidirect
23. #14583250C22semidirect
28. #14583184C22semidirect
30. #14583181C22semidirect
39. #14583030C22semidirect
40. C8×Dic86C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. #14582621C22semidirect
201. #10621883SD16semidirect
267. Dic86C2×SD16semidirect
276. C43⋊C8C2×SD16semidirect
375. C43#19764semidirect

Maximal subgroups

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

subgroupindex
#191475162
#191472352
D4×#106218832
#191342152
#191340652
#191340182
#191339822
#191339402
#191338582
#191338562
#191337742
#191336892
#191334322
#191334072
D4×SD16×C432
#1976443