Finite Group Databasebeta

← #25087950

Subgroups — #25087950

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146460C211yesmaximal, characteristic, complemented
2#19146413C211yesmaximal, characteristic, complemented
3#19146196C211yesmaximal, characteristic
4#19134197C211yesmaximal, characteristic, complemented
5#19134091C211yesmaximal, characteristic, complemented
6#19134067C211yesmaximal, characteristic, complemented
7#19134016C211yesmaximal, characteristic, complemented
8#19134006C211yesmaximal, characteristic, complemented
9#19133802C211yesmaximal, characteristic, complemented
10#19133773C211yesmaximal, characteristic, complemented
11#19133744C211yesmaximal, characteristic, complemented
12#19133698C211yesmaximal, characteristic, complemented
13#19133485C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3384C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17#14583553C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583272C2211yescharacteristic
20#14583249C2211yescharacteristic, complemented
21#14583249C2211yescharacteristic, complemented
22#14583247C2211yescharacteristic
23#14583247C2211yescharacteristic
24#14583227—21no—
25#14583217—21no—
26#14583186C2211yescharacteristic
27#14583184C2211yescharacteristic, complemented
28#14583146—21no—
29#14583130—21no—
30#14583130—21no—
31#14583104C2211yescharacteristic
32#14583101C2211yescharacteristic
33#14583099C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583051—21no—
36#14583049—21no—
37#14583045—21no—
38#14583038—21no—
39C4×#10621884C2211yescharacteristic
40#14582978C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43C2×#13063249—21no—
44C2×#13063245—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, 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×#554C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic, complemented
58C43×#501—21no—
59C43×#498C2211yescharacteristic, complemented
60C43×#478—21no—
61C43×#476—21no—
62C43×#476C2211yescharacteristic, complemented
63C43×#474C2211yescharacteristic
64C43×#446C2211yescharacteristic, complemented
65C43×#442—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621900—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70#13063349—44no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884D411yescharacteristic
77C2×#10621882—21no—
78C2×#10621872—21no—
79C22×C43⋊C8—21no—
80C22×C43⋊C8—21no—
81#13063325C2311yescharacteristic
82#13063322C2311yescharacteristic
83#13063309—41no—
84#13063305—21no—
85#13063300—21no—
86#13063299—21no—
87#13063299—21no—
88#13063295—41no—
89C4×D172C2311yescharacteristic
90C2×C4⋊Dic43—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—41no—
102#13063249D411yescharacteristic
103#13063248—21no—
104#13063245—21no—
105#13063245—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×D8×C43D411yescharacteristic
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C22⋊Q8×C43—41no—
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139#102×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—
157C22×C4×C43—41no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160C22×Dic43—41no—
161#10621900—42no—
162#10621900—81no—
163D4×D43—42no—
164D4×D43—81no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—41no—
169C2×D172—42no—
170C2×D172—81no—
171C2×D172C2×D411yescharacteristic
172C2×C4×D43—21no—
173C2×Dic86—21no—
174D8×C43SD1614yescomplemented
175C2×C8×C43—21no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
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
195#10621884—41no—
196#10621884—81no—
197#10621884—81no—
198#10621883—42no—
199#10621882—42no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—41no—
206C4⋊Dic43C2×D411yescharacteristic
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—81no—
212C2×C43⋊C8—81no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215#10621873—42no—
216#10621873—81no—
217#10621872—42no—
218C23×C43—21no—
219C23×C43—21no—
220C22×D43—21no—
221C22×D43—41no—
222C22×D43—82no—
223C22×D43—82no—
224C22×D43—161no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—81no—
230Q8×C43—82no—
231D4×C43—21no—
232D4×C43—21no—
233D4×C43C2×SD1612yes—
234D4×C43C2×SD1612yes—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—82no—
246C2×C4×C43—161no—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C22⋊D43—82no—
251C22⋊D43—82no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254C2×Dic43—82no—
255D172—21no—
256D172—21no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—81no—
262D172—82no—
263C4×D43—41no—
264C4×D43—41no—
265Dic86—41no—
266Dic86—41no—
267C8×C43—21no—
268C8×C43—41no—
269C8×C43C2×SD1612yes—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#19891—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43D4211yescharacteristic
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—164no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43C22×SD1611yescharacteristic
299C4×C43#57511yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57711yescharacteristic
302Dic43—41no—
303Dic43—81no—
304#3384D4311yescharacteristic, complemented
305#3298—431no—
306#3295—431no—
307#3272—431no—
308#1708—431no—
309#1691—431no—
310#1686—431no—
311#1679—431no—
312#1677—431no—
313#1643—431no—
314#1639—431no—
315#1635—431no—
316#1627—431no—
317#1590—431no—
318C8×D8—431no—
319C2×C43—42no—
320C2×C43—42no—
321C2×C43#327311yescharacteristic
322C2×C43D4×SD1611yescharacteristic
323C2×C43#329011yescharacteristic
324D43—81no—
325D43—161no—
326C2×AGL(1,ℤ/8)—861no—
327#554C2×D4311yescharacteristic
328D4×Q8C2×D4311yescharacteristic, complemented
329#547—431no—
330D42—431no—
331#501—21no—
332#498C2×D4311yescharacteristic, complemented
333#492—431no—
334#487—431no—
335#487—431no—
336#486—431no—
337#486—431no—
338#483—861no—
339#481—861no—
340#478—21no—
341#476—21no—
342#476—431no—
343#476C2×D4311yescharacteristic, complemented
344#475—431no—
345#474C2×D4311yescharacteristic
346#468—861no—
347#465—861no—
348#465—861no—
349#461—431no—
350#461—431no—
351#460—431no—
352#459—431no—
353#450—861no—
354#450—861no—
355#449—861no—
356#448—861no—
357#446C2×D4311yescharacteristic, complemented
358#442—21no—
359C4×SD16—431no—
360C4×D8C2×D4311yescharacteristic
361#436—431no—
362C8×D4—431no—
363C8×D4—431no—
364C2×#103—861no—
365C2×#102—861no—
366#335—431no—
367#334—431no—
368#333—431no—
369#332—431no—
370#332—431no—
371#331—431no—
372Q8⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376C82—431no—
377C43#1989111yescharacteristic, complemented, Sylow
378C2×#41—861no—
379C22×Q8—21no—
380C22×D4—861no—
381C22×D4—861no—
382AGL(1,ℤ/8)—1724no—
383C2×SD16—431no—
384C2×SD16—861no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×D8—861no—
390C2×D8C22⋊D4311yescharacteristic
391C2×M16—861no—
392C22×C8—861no—
393C22×C8—861no—
394C4⋊Q8—21no—
395C4⋊Q8—431no—
396C4⋊Q8C22×D4311yescharacteristic
397C4⋊Q8C22×D4311yescharacteristic
398#127—431no—
399#125—21no—
400#123—1721no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—41no—
405C22⋊Q8—861no—
406#121—861no—
407#121—861no—
408#121—861no—
409#120—1721no—
410C4×Q8C22×D4311yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—431no—
414C4×D4C22×D4311yescharacteristic
415C4×D4C22×D4311yescharacteristic
416C2×C4⋊C4—21no—
417C2×C4⋊C4—861no—
418#107—21no—
419#107C22⋊D4311yescharacteristic
420#106—21no—
421#106—21no—
422#106—21no—
423#106—431no—
424#106—861no—
425#106—861no—
426C4⋊C8—21no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8C22×D4311yescharacteristic
431#103—431no—
432#103—861no—
433#103—861no—
434#103—861no—
435#103—861no—
436#103—861no—
437#103—1721no—
438#102—21no—
439#102—21no—
440#102—431no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—1721no—
447#102C22⋊D4311yescharacteristic
448#102C22⋊D4311yescharacteristic
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452#97—21no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8C22×D4311yescharacteristic
456C24—1721no—
457#41—3441no—
458#41—1722no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—41no—
462C2×Q8—42no—
463C2×Q8—81no—
464C2×Q8—861no—
465C2×Q8D4×D4311yescharacteristic
466C2×D4—431no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—3441no—
471C2×D4—3441no—
472C2×D4—1721no—
473C2×D4—1722no—
474C2×D4—1721no—
475C2×D4—1721no—
476C2×D4—1722no—
477C2×D4C2×C22⋊D4311yescharacteristic
478C2×D4C2×C22⋊D4311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—861no—
484C22×C4—1721no—
485SD16—3441no—
486SD16—3441no—
487SD16—3441no—
488SD16—1721no—
489SD16—1722no—
490SD16—1722no—
491D8—1722no—
492D8#1062188414yescomplemented
493M16—1722no—
494C2×C8—21no—
495C2×C8—431no—
496C2×C8—431no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—3441no—
502C2×C8—3441no—
503C2×C8C2×C22⋊D4311yescharacteristic
504C2×C8C2×C22⋊D4311yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—431no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—1721no—
517C4⋊C4D4×D4311yescharacteristic
518C4⋊C4C2×C22⋊D4311yescharacteristic
519C4⋊C4C2×C22⋊D4311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—861no—
525C22⋊C4—1721no—
526C22⋊C4—1721no—
527C42—21no—
528C42C23×D4311yescharacteristic
529C23—21no—
530C23—21no—
531C23—861no—
532C23—3442no—
533C23—3442no—
534C23—1721no—
535C23—6881no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—81no—
541Q8—82no—
542Q8—1721no—
543Q8—1721no—
544D4—21no—
545D4—21no—
546D4—861no—
547D4—861no—
548D4—3441no—
549D4—3442no—
550D4—3442no—
551D4—3442no—
552D4—1721no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4C2×#1062188412yes—
557D4C2×#1062188412yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—161no—
570C2×C4—861no—
571C2×C4—3442no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4C22×C22⋊D4311yescharacteristic
577C2×C4#1306337011yescharacteristic
578C8—21no—
579C8—41no—
580C8—861no—
581C8—861no—
582C8—1721no—
583C8—1721no—
584C8—1721no—
585C8—1721no—
586C8C2×#1062188412yes—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—3441no—
594C22—3441no—
595C22—3441no—
596C22—1721no—
597C22—1721no—
598C22—1721no—
599C22—6884no—
600C22D4×C22⋊D4311yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4—3441no—
609C4—1721no—
610C4C22×#1062188411yescharacteristic
611C4#1458369511yescharacteristic
612C4#1458370311yescharacteristic
613C4#1458370711yescharacteristic
614C2—42no—
615C2—42no—
616C2—3441no—
617C2—6881no—
618C2#1914620011yescharacteristic
619C2D4×#1062188411yescharacteristic
620C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3384C2
socleC22×C43D42
prime radical#19146196C2
hypercenter#3384D43
hypocenterC43#19891
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3384

Complements

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

NH ≅ G/Ntype
1. #19146460C2semidirect
2. #19146413C2semidirect
4. #19134197C2semidirect
5. #19134091C2semidirect
6. #19134067C2semidirect
7. #19134016C2semidirect
8. #19134006C2semidirect
9. #19133802C2semidirect
10. #19133773C2semidirect
11. #19133744C2semidirect
12. #19133698C2semidirect
13. #19133485C2semidirect
14. D8×C43⋊C8C2semidirect
15. C43×#3384C2semidirect
20. #14583249C22semidirect
21. #14583249C22semidirect
27. #14583184C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582646C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
57. D4×Q8×C43C22semidirect
59. C43×#498C22semidirect
62. C43×#476C22semidirect
64. C43×#446C22semidirect
174. D8×C43SD16semidirect
304. #3384D43semidirect
328. D4×Q8C2×D43semidirect
332. #498C2×D43semidirect
343. #476C2×D43semidirect
357. #446C2×D43semidirect
377. C43#19891semidirect
492. D8#10621884semidirect

Maximal subgroups

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

subgroupindex
#191464602
#191464132
#191461962
#191341972
#191340912
#191340672
#191340162
#191340062
#191338022
#191337732
#191337442
#191336982
#191334852
D8×C43⋊C82
C43×#33842
#1989143