Finite Group Databasebeta

← #25088203

Subgroups — #25088203

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147002C211yesmaximal, characteristic, complemented
2#19146839C211yesmaximal, characteristic
3D4×#10621884C211yesmaximal, characteristic, complemented
4#19134198C211yesmaximal, characteristic, complemented
5#19134139C211yesmaximal, characteristic, complemented
6#19134135C211yesmaximal, characteristic, complemented
7#19133968C211yesmaximal, characteristic, complemented
8#19133938C211yesmaximal, characteristic, complemented
9#19133822C211yesmaximal, characteristic, complemented
10#19133772C211yesmaximal, characteristic, complemented
11#19133760C211yesmaximal, characteristic, complemented
12#19133705C211yesmaximal, characteristic, complemented
13#19133485C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3367C211yesmaximal, characteristic, complemented
16C22×#10621884—21no—
17#14583614C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583295C2211yescharacteristic, complemented
20#14583273C2211yescharacteristic
21#14583251C2211yescharacteristic, complemented
22#14583247C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583237—21no—
25#14583226—21no—
26#14583223—21no—
27#14583194C2211yescharacteristic, complemented
28#14583189C2211yescharacteristic
29#14583176C2211yescharacteristic
30#14583151—21no—
31#14583130—21no—
32#14583130—21no—
33#14583101C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583049—21no—
37#14583038—21no—
38#14583031—21no—
39C4×#10621884C2211yescharacteristic
40#14582978C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43#14582935—21no—
44#14582902—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#556C2211yescharacteristic, complemented
57D4×Q8×C43C2211yescharacteristic
58C43×#489—21no—
59C43×#487C2211yescharacteristic, complemented
60C43×#477—21no—
61C43×#474C2211yescharacteristic, complemented
62C43×#463—21no—
63C43×#461C2211yescharacteristic
64C43×#446C2211yescharacteristic, complemented
65C43×#440—21no—
66C4×D8×C43C2211yescharacteristic
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621884—44no—
74C2×#10621884D411yescharacteristic
75C2×#10621882—21no—
76C2×#10621872—21no—
77C22×C43⋊C8—21no—
78C22×C43⋊C8—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063311—41no—
82#13063300—21no—
83#13063299—21no—
84#13063299—21no—
85#13063296—21no—
86#13063295—41no—
87C4×D172C2311yescharacteristic
88#13063284—21no—
89#13063283—21no—
90#13063258—21no—
91#13063258—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063249D411yescharacteristic
102#13063248—41no—
103#13063247—21no—
104#13063247—21no—
105#13063246—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—41no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×Q8×C43—21no—
117C2×SD16×C43—21no—
118C2×D8×C43D411yescharacteristic
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#126×C43—41no—
123#124×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143#97×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159D4×D43—42no—
160D4×D43—81no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—41no—
165C2×D172—42no—
166C2×D172—81no—
167C2×D172C2×D411yescharacteristic
168C2×C4×D43—21no—
169C2×Dic86—21no—
170SD16×C43—42no—
171D8×C43—22no—
172C2×C8×C43—21no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43C2×D411yescharacteristic
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C42×C43—21no—
191C42×C43—41no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—41no—
194#10621884—22no—
195#10621884—42no—
196#10621884—42no—
197#10621884—42no—
198#10621884—81no—
199#10621882—81no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206C4×Dic43—41no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—42no—
212C2×C43⋊C8—42no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215#10621872—81no—
216C23×C43—21no—
217C23×C43—21no—
218C22×D43—21no—
219C22×D43—41no—
220C22×D43—82no—
221C22×D43—82no—
222C22×D43—161no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—82no—
230D4×C43—21no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43#13512yes—
234C2×C4×C43—21no—
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—82no—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C22⋊D43—82no—
249C22⋊D43—161no—
250C2×Dic43—21no—
251C2×Dic43—41no—
252D172—21no—
253D172—21no—
254D172—41no—
255D172—41no—
256D172—41no—
257D172—41no—
258D172—81no—
259D172—82no—
260C4×D43—41no—
261C4×D43—41no—
262Dic86—81no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8AGL(1,ℤ/8)12yes—
272#19910—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43D4211yescharacteristic
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—164no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C2×#13511yescharacteristic
295C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C43#57711yescharacteristic
297C4×C43#57711yescharacteristic
298Dic43—41no—
299Dic43—81no—
300#3367D4311yescharacteristic, complemented
301#3340—431no—
302#3325—431no—
303D4×SD16—431no—
304#1708—431no—
305#1699—431no—
306#1698—431no—
307#1671—431no—
308#1665—431no—
309#1646—431no—
310#1639—431no—
311#1637—431no—
312#1628—431no—
313#1590—431no—
314C8×D8—431no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43#327211yescharacteristic
318C2×C43#328211yescharacteristic
319C2×C43#329011yescharacteristic
320D43—81no—
321D43—161no—
322C22×SD16—861no—
323#556C2×D4311yescharacteristic, complemented
324#555—431no—
325D4×Q8C2×D4311yescharacteristic
326D42—431no—
327#498—431no—
328#492—431no—
329#489—21no—
330#487—431no—
331#487C2×D4311yescharacteristic, complemented
332#486—431no—
333#486—431no—
334#485—861no—
335#482—861no—
336#482—861no—
337#477—21no—
338#477—431no—
339#476—431no—
340#474—431no—
341#474C2×D4311yescharacteristic, complemented
342#469—861no—
343#465—861no—
344#465—861no—
345#463—21no—
346#461—431no—
347#461C2×D4311yescharacteristic
348#460—431no—
349#459—431no—
350#450—861no—
351#448—861no—
352#447—861no—
353#446C2×D4311yescharacteristic, complemented
354#440—21no—
355C4×SD16—431no—
356C4×D8C2×D4311yescharacteristic
357#436—431no—
358C8×D4—431no—
359C8×D4—431no—
360#427—861no—
361#418—861no—
362#335—431no—
363#334—431no—
364#333—431no—
365#332—431no—
366#332—431no—
367#331—431no—
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372C82—431no—
373C43#1991011yescharacteristic, complemented, Sylow
374C22×Q8—21no—
375C22×D4—861no—
376C22×D4—861no—
377C2×SD16—21no—
378C2×SD16—431no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×SD16—861no—
382C2×SD16—861no—
383C2×SD16—1724no—
384C2×D8—861no—
385C2×D8C22⋊D4311yescharacteristic
386C2×M16—861no—
387C22×C8—861no—
388C22×C8—861no—
389C4⋊Q8—21no—
390C4⋊Q8—431no—
391C4⋊Q8C22×D4311yescharacteristic
392C4⋊Q8C22×D4311yescharacteristic
393#127—431no—
394#126—41no—
395#124—21no—
396#124—1721no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—41no—
400#121—861no—
401#121—861no—
402#121—861no—
403#121—861no—
404#120—1721no—
405C4×Q8—21no—
406C4×Q8C22×D4311yescharacteristic
407C4×D4—21no—
408C4×D4—431no—
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411#117—21no—
412#117—861no—
413#117—861no—
414#107—21no—
415#107—861no—
416#107—861no—
417#107C22⋊D4311yescharacteristic
418#106—431no—
419#106—861no—
420#106—861no—
421#106—861no—
422C4⋊C8—21no—
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8C22×D4311yescharacteristic
427#103—21no—
428#103—21no—
429#103—21no—
430#103—431no—
431#103—861no—
432#103—861no—
433#103—1721no—
434#102—21no—
435#102—431no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—1721no—
443#102C22⋊D4311yescharacteristic
444#102C22⋊D4311yescharacteristic
445C22⋊C8—861no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448#97—21no—
449C4×C8—431no—
450C4×C8—431no—
451C4×C8C22×D4311yescharacteristic
452C24—1721no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—41no—
456C2×Q8—42no—
457C2×Q8—81no—
458C2×Q8—861no—
459C2×Q8D4×D4311yescharacteristic
460C2×D4—431no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—3441no—
465C2×D4—3441no—
466C2×D4—1721no—
467C2×D4—1722no—
468C2×D4—1721no—
469C2×D4—1722no—
470C2×D4—1721no—
471C2×D4C2×C22⋊D4311yescharacteristic
472C2×D4C2×C22⋊D4311yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—861no—
477SD16—42no—
478SD16—862no—
479SD16—3441no—
480SD16—1722no—
481SD16—1722no—
482SD16—1722no—
483D8—22no—
484D8—3441no—
485M16—3441no—
486C2×C8—21no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—1722no—
494C2×C8—1722no—
495C2×C8C2×C22⋊D4311yescharacteristic
496C2×C8C2×C22⋊D4311yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—431no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4D4×D4311yescharacteristic
508C4⋊C4C2×C22⋊D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—861no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C22⋊C4—1721no—
519C42—21no—
520C42—41no—
521C42—1721no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—21no—
525C23—861no—
526C23—3442no—
527C23—3442no—
528C23—1721no—
529C23—6881no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—82no—
537Q8—3441no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—861no—
542D4—861no—
543D4—3441no—
544D4—3442no—
545D4—3442no—
546D4—1721no—
547D4—1721no—
548D4—1721no—
549D4—1721no—
550D4—6881no—
551D4#1306334512yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—82no—
563C2×C4—861no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C22×C22⋊D4311yescharacteristic
569C2×C4#1306337011yescharacteristic
570C8—21no—
571C8—21no—
572C8—41no—
573C8—432no—
574C8—861no—
575C8—1721no—
576C8—1721no—
577C8—1721no—
578C8—1721no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—3441no—
586C22—3441no—
587C22—3441no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—6884no—
592C22D4×C22⋊D4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—3441no—
601C4—1721no—
602C4C2×#1306334511yescharacteristic
603C4AGL(1,ℤ/8)×D4311yescharacteristic
604C4#1458370711yescharacteristic
605C4#1458370911yescharacteristic
606C2—42no—
607C2—81no—
608C2—3441no—
609C2—6881no—
610C2#1914618911yescharacteristic
611C2#1914630311yescharacteristic
612C2#1914638111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3367C2
socleC22×C43D42
prime radical#19146839C2
hypercenter#3367D43
hypocenterC43#19910
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3367

Complements

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

NH ≅ G/Ntype
1. #19147002C2semidirect
3. D4×#10621884C2semidirect
4. #19134198C2semidirect
5. #19134139C2semidirect
6. #19134135C2semidirect
7. #19133968C2semidirect
8. #19133938C2semidirect
9. #19133822C2semidirect
10. #19133772C2semidirect
11. #19133760C2semidirect
12. #19133705C2semidirect
13. #19133485C2semidirect
14. D8×C43⋊C8C2semidirect
15. C43×#3367C2semidirect
19. #14583295C22semidirect
21. #14583251C22semidirect
27. #14583194C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
56. C43×#556C22semidirect
59. C43×#487C22semidirect
61. C43×#474C22semidirect
64. C43×#446C22semidirect
300. #3367D43semidirect
323. #556C2×D43semidirect
331. #487C2×D43semidirect
341. #474C2×D43semidirect
353. #446C2×D43semidirect
373. C43#19910semidirect

Maximal subgroups

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

subgroupindex
#191470022
#191468392
D4×#106218842
#191341982
#191341392
#191341352
#191339682
#191339382
#191338222
#191337722
#191337602
#191337052
#191334852
D8×C43⋊C82
C43×#33672
#1991043