Finite Group Databasebeta

← #25086418

Subgroups — #25086418

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146506C211yesmaximal, characteristic, complemented
2#19146410C211yesmaximal, characteristic
3D4×#10621884C211yesmaximal, characteristic, complemented
4#19134249C211yesmaximal, characteristic, complemented
5#19134163C211yesmaximal, characteristic, complemented
6#19134020C211yesmaximal, characteristic, complemented
7#19134015C211yesmaximal, characteristic, complemented
8#19133938C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic, complemented
10#19133829C211yesmaximal, characteristic, complemented
11#19133772C211yesmaximal, characteristic, complemented
12#19133705C211yesmaximal, characteristic, complemented
13#19133429C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3367C211yesmaximal, characteristic, complemented
16C22×#10621884—21no—
17#14583554C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583302C2211yescharacteristic, complemented
20#14583273C2211yescharacteristic
21#14583251C2211yescharacteristic, complemented
22#14583247C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583240—21no—
25#14583214—21no—
26#14583179C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583138—21no—
29#14583134—21no—
30#14583130—21no—
31#14583109C2211yescharacteristic, complemented
32#14583101C2211yescharacteristic
33#14583099C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583059—21no—
36#14583049—21no—
37#14583038—21no—
38#14583031—21no—
39C4×#10621884C2211yescharacteristic
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43#14582893—21no—
44#102×D43—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582645C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic, 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
67C2×#10621898—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621885—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621884—44no—
76C2×#10621884D411yescharacteristic
77C2×#10621882—21no—
78C22×C43⋊C8—21no—
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81#13063325C2311yescharacteristic
82#13063322C2311yescharacteristic
83#13063307—41no—
84#13063304—21no—
85#13063300—21no—
86#13063299—21no—
87#13063296—21no—
88#13063295—41no—
89C4×D172C2311yescharacteristic
90C4⋊C4×D43—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—41no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98#13063249—21no—
99#13063249D411yescharacteristic
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
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—
161#10621898—42no—
162#10621898—81no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—41no—
167C2×D172—42no—
168C2×D172—81no—
169C2×D172C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×C4×D43—41no—
172C2×Dic86—21no—
173SD16×C43—42no—
174D8×C43—22no—
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×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C22⋊C4×C43—41no—
193C42×C43—21no—
194C42×C43—41no—
195C42×C43C2411yescharacteristic
196C22⋊Dic43—41no—
197#10621885—81no—
198#10621884—22no—
199#10621884—42no—
200#10621884—42no—
201#10621884—42no—
202#10621884—81no—
203#10621882—81no—
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—41no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43C2×D411yescharacteristic
209Dic43⋊C4—41no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—42no—
215C2×C43⋊C8—81no—
216C2×C43⋊C8C2×D411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218C8×D43—81no—
219C23×C43—21no—
220C23×C43—21no—
221C22×D43—21no—
222C22×D43—41no—
223C22×D43—82no—
224C22×D43—82no—
225C22×D43—161no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—82no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43#13512yes—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—82no—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C22⋊D43—82no—
252C22⋊D43—82no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255D172—21no—
256D172—41no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—81no—
261D172—82no—
262D172AGL(1,ℤ/8)12yes—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—82no—
266Dic86—41no—
267Dic86—41no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277#19787—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43D4211yescharacteristic
285C2×D43—22no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—164no—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43C2×#13511yescharacteristic
300C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C43#57611yescharacteristic
302C4×C43#57711yescharacteristic
303Dic43—41no—
304Dic43—81no—
305#3367D4311yescharacteristic, complemented
306#3302—431no—
307#3294—431no—
308D4×SD16—431no—
309#1719—431no—
310#1702—431no—
311#1679—431no—
312#1679—431no—
313#1665—431no—
314#1649—431no—
315#1647—431no—
316#1639—431no—
317#1628—431no—
318#1582—431no—
319#1580—431no—
320C2×C43—42no—
321C2×C43—81no—
322C2×C43#326411yescharacteristic
323C2×C43#328211yescharacteristic
324C2×C43#328911yescharacteristic
325D43—42no—
326D43—161no—
327C22×SD16—861no—
328#556C2×D4311yescharacteristic, complemented
329D4×Q8C2×D4311yescharacteristic
330#547—431no—
331D42—431no—
332#500—431no—
333#492—431no—
334#489—21no—
335#487—431no—
336#487C2×D4311yescharacteristic, complemented
337#486—431no—
338#486—431no—
339#485—861no—
340#480—861no—
341#477—21no—
342#474—431no—
343#474—431no—
344#474C2×D4311yescharacteristic, complemented
345#467—861no—
346#466—861no—
347#465—861no—
348#463—21no—
349#462—431no—
350#461—431no—
351#461C2×D4311yescharacteristic
352#460—431no—
353#459—431no—
354#452—861no—
355#450—861no—
356#448—861no—
357#447—861no—
358#446C2×D4311yescharacteristic, complemented
359#440—21no—
360C4×SD16—431no—
361C4×D8C2×D4311yescharacteristic
362C8×D4—431no—
363C8×D4—431no—
364C8×D4—431no—
365#416—861no—
366C2×#102—861no—
367#334—431no—
368#334—431no—
369#332—431no—
370#332—431no—
371#332—431no—
372#331—431no—
373Q8⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377#322—431no—
378C43#1978711yescharacteristic, complemented, Sylow
379C2×#41—861no—
380C22×Q8—21no—
381C22×D4—861no—
382C22×D4—861no—
383C2×Q16—861no—
384C2×SD16—21no—
385C2×SD16—431no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×SD16—861no—
390C2×SD16—1724no—
391C2×D8—861no—
392C2×D8C22⋊D4311yescharacteristic
393C22×C8—861no—
394C22×C8—861no—
395C22×C8—861no—
396C4⋊Q8—21no—
397C4⋊Q8—431no—
398C4⋊Q8C22×D4311yescharacteristic
399C4⋊Q8C22×D4311yescharacteristic
400#127—431no—
401#126—41no—
402#124—21no—
403#123—1721no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—41no—
407C22⋊Q8—861no—
408#121—861no—
409#121—861no—
410#121—861no—
411#120—1721no—
412C4×Q8—21no—
413C4×Q8C22×D4311yescharacteristic
414C4×D4—21no—
415C4×D4—431no—
416C4×D4C22×D4311yescharacteristic
417C4×D4C22×D4311yescharacteristic
418#117—21no—
419C2×C4⋊C4—861no—
420#107—21no—
421#107—861no—
422#107—861no—
423#107—1721no—
424#107C22⋊D4311yescharacteristic
425#106—431no—
426C4⋊C8—21no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8C22×D4311yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—431no—
435#103—861no—
436#103—861no—
437#103—861no—
438#103—861no—
439#102—21no—
440#102—431no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—1721no—
448#102C22⋊D4311yescharacteristic
449#102C22⋊D4311yescharacteristic
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453#97—21no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8C22×D4311yescharacteristic
457C24—1721no—
458#41—3441no—
459#41—1722no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—41no—
463C2×Q8—42no—
464C2×Q8—81no—
465C2×Q8—861no—
466C2×Q8D4×D4311yescharacteristic
467C2×D4—431no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—3441no—
472C2×D4—3441no—
473C2×D4—1721no—
474C2×D4—1722no—
475C2×D4—1721no—
476C2×D4—1721no—
477C2×D4—1722no—
478C2×D4C2×C22⋊D4311yescharacteristic
479C2×D4C2×C22⋊D4311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—861no—
484C22×C4—1721no—
485Q16—3441no—
486SD16—42no—
487SD16—862no—
488SD16—3441no—
489SD16—1722no—
490SD16—1722no—
491SD16—1722no—
492D8—22no—
493D8—3441no—
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×C8—1722no—
504C2×C8C2×C22⋊D4311yescharacteristic
505C2×C8C2×C22⋊D4311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
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—41no—
525C22⋊C4—861no—
526C22⋊C4—1721no—
527C22⋊C4—1721no—
528C42—21no—
529C42—41no—
530C42C23×D4311yescharacteristic
531C23—21no—
532C23—21no—
533C23—861no—
534C23—3442no—
535C23—3442no—
536C23—1721no—
537C23—6881no—
538Q8—21no—
539Q8—21no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
544Q8—82no—
545Q8—1721no—
546Q8—1721no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—432no—
551D4—861no—
552D4—3441no—
553D4—3442no—
554D4—3442no—
555D4—3442no—
556D4—1721no—
557D4—1721no—
558D4—1721no—
559D4—1721no—
560D4#1306334512yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—861no—
573C2×C4—3442no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C22×C22⋊D4311yescharacteristic
579C2×C4#1306337011yescharacteristic
580C8—21no—
581C8—21no—
582C8—41no—
583C8—861no—
584C8—861no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—862no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—1721no—
600C22—1721no—
601C22—6884no—
602C22D4×C22⋊D4311yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—3441no—
611C4—1721no—
612C4C2×#1306334511yescharacteristic
613C4AGL(1,ℤ/8)×D4311yescharacteristic
614C4#1458370311yescharacteristic
615C4#1458370711yescharacteristic
616C2—42no—
617C2—81no—
618C2—1722no—
619C2—6881no—
620C2#1914606911yescharacteristic
621C2#1914630311yescharacteristic
622C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3367C2
socleC22×C43D42
prime radical#19146410C2
hypercenter#3367D43
hypocenterC43#19787
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. #19146506C2semidirect
3. D4×#10621884C2semidirect
4. #19134249C2semidirect
5. #19134163C2semidirect
6. #19134020C2semidirect
7. #19134015C2semidirect
8. #19133938C2semidirect
9. #19133844C2semidirect
10. #19133829C2semidirect
11. #19133772C2semidirect
12. #19133705C2semidirect
13. #19133429C2semidirect
14. #19133419C2semidirect
15. C43×#3367C2semidirect
19. #14583302C22semidirect
21. #14583251C22semidirect
31. #14583109C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582645C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
56. C43×#556C22semidirect
59. C43×#487C22semidirect
61. C43×#474C22semidirect
64. C43×#446C22semidirect
305. #3367D43semidirect
328. #556C2×D43semidirect
336. #487C2×D43semidirect
344. #474C2×D43semidirect
358. #446C2×D43semidirect
378. C43#19787semidirect

Maximal subgroups

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

subgroupindex
#191465062
#191464102
D4×#106218842
#191342492
#191341632
#191340202
#191340152
#191339382
#191338442
#191338292
#191337722
#191337052
#191334292
#191334192
C43×#33672
#1978743