Finite Group Databasebeta

← #25086244

Subgroups — #25086244

Order 11008.

656 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147013C211yesmaximal, characteristic, complemented
2#19146839C211yesmaximal, characteristic, complemented
3#19146402C211yesmaximal, characteristic, complemented
4#19134249C211yesmaximal, characteristic, complemented
5#19134167C211yesmaximal, characteristic, complemented
6#19134034C211yesmaximal, characteristic, complemented
7#19134004C211yesmaximal, characteristic, complemented
8#19133992C211yesmaximal, characteristic, complemented
9#19133821C211yesmaximal, characteristic, complemented
10#19133746C211yesmaximal, characteristic, complemented
11#19133710C211yesmaximal, characteristic, complemented
12#19133678C211yesmaximal, characteristic, complemented
13#19133424C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3303C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583302C2211yescharacteristic, complemented
19#14583273C2211yescharacteristic
20#14583251C2211yescharacteristic, complemented
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583226—21no—
24#14583223—21no—
25#14583220—21no—
26#14583212—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583186C2211yescharacteristic
30#14583176C2211yescharacteristic
31#14583151—21no—
32#14583133—21no—
33#14583133—21no—
34#14583094C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583032—21no—
37#14583031—21no—
38C4×#10621882C2211yescharacteristic
39#14582978C2211yescharacteristic
40D4×C43⋊C8C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic, complemented
42#14582935—21no—
43#14582902—21no—
44C2×#13063245—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic, complemented
56C43×#555C2211yescharacteristic, complemented
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic, complemented
59C43×#485—21no—
60C43×#476C2211yescharacteristic
61C43×#465—21no—
62C43×#461C2211yescharacteristic, complemented
63C43×#449—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic, complemented
66C43×#416—21no—
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621884—41no—
70C2×#10621882—21no—
71C2×#10621882—21no—
72C2×#10621882D411yescharacteristic
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063311—41no—
79#13063300—21no—
80#13063299—21no—
81#13063299—21no—
82#13063296—21no—
83#13063295—41no—
84C4×D172C2311yescharacteristic
85#13063284—21no—
86#13063283—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063248—41no—
98#13063247—21no—
99#13063247—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246D411yescharacteristic
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×SD16×C43—21no—
117C2×D8×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#124×C43—41no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43—21no—
132C2×C4⋊C4×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43—41no—
150C2×D4×C43—41no—
151C2×D4×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160D4×D43—42no—
161D4×D43—81no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—41no—
166C2×D172—42no—
167C2×D172—81no—
168C2×D172C2×D411yescharacteristic
169C2×C4×D43—21no—
170C2×Dic86—21no—
171SD16×C43—81no—
172D8×C43—22no—
173C2×C8×C43—21no—
174C2×C8×C43—81no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
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—21no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43—41no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—41no—
194#10621884—82no—
195#10621882—41no—
196#10621882—81no—
197#10621882—81no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—41no—
200(C2×D43)⋊C4—41no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D411yescharacteristic
204C4×Dic43—41no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—42no—
210C2×C43⋊C8—81no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213#10621872—81no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C22×D43—21no—
218C22×D43—41no—
219C22×D43—82no—
220C22×D43—82no—
221C22×D43—161no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—81no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—82no—
231D4×C43—161no—
232D4×C43#13512yes—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
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—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19775—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43D4211yescharacteristic
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—164no—
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43C2×#13511yescharacteristic
297C4×C43#57511yescharacteristic
298C4×C43#57611yescharacteristic
299C4×C43#57711yescharacteristic
300Dic43—41no—
301Dic43—81no—
302#3341—431no—
303#3325—431no—
304#3303D4311yescharacteristic, complemented
305#3294—431no—
306#1719—431no—
307#1703—431no—
308#1681—431no—
309#1677—431no—
310#1675—431no—
311#1646—431no—
312#1635—431no—
313#1629—431no—
314#1624—431no—
315#1581—431no—
316#1580—431no—
317C2×C43—42no—
318C2×C43—81no—
319C2×C43—81no—
320C2×C43#326711yescharacteristic
321C2×C43#328011yescharacteristic
322C2×C43#328811yescharacteristic
323D43—81no—
324D43—161no—
325#555—431no—
326#555C2×D4311yescharacteristic, complemented
327#547C2×D4311yescharacteristic
328D42—431no—
329#500—431no—
330#492—431no—
331#487—431no—
332#487C2×D4311yescharacteristic, complemented
333#486—431no—
334#486—431no—
335#485—21no—
336#482—861no—
337#482—861no—
338#482—861no—
339#480—861no—
340#476—431no—
341#476—431no—
342#476—431no—
343#476C2×D4311yescharacteristic
344#474—431no—
345#469—861no—
346#466—861no—
347#466—861no—
348#465—21no—
349#461C2×D4311yescharacteristic, complemented
350#459—431no—
351#459—431no—
352#449—21no—
353#447—861no—
354#447—861no—
355C4×D8—431no—
356C4×D8C2×D4311yescharacteristic
357#436—431no—
358C8×D4—431no—
359C8×D4—431no—
360C8×D4C2×D4311yescharacteristic, complemented
361#427—861no—
362#418—861no—
363#416—21no—
364C2×#102—861no—
365#335—431no—
366#334—431no—
367#333—431no—
368#333—431no—
369#332—431no—
370#331—431no—
371D4⋊C8—431no—
372D4⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375#322—431no—
376C43#1977511yescharacteristic, complemented, Sylow
377C2×#41—21no—
378C22×D4—861no—
379C22×D4—861no—
380C2×SD16—21no—
381C2×SD16—1721no—
382C2×D8—431no—
383C2×D8—861no—
384C2×D8—861no—
385C2×D8C22⋊D4311yescharacteristic
386C2×M16—861no—
387C22×C8—21no—
388C22×C8—861no—
389C22×C8—861no—
390C4⋊Q8—431no—
391C4⋊Q8C22×D4311yescharacteristic
392C4⋊Q8C22×D4311yescharacteristic
393#127—431no—
394#124—41no—
395#124—1721no—
396#123—41no—
397C22⋊Q8—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—861no—
402#121—861no—
403#121—861no—
404#121—861no—
405#120—1721no—
406C4×D4—431no—
407C4×D4C22×D4311yescharacteristic
408C4×D4C22×D4311yescharacteristic
409C4×D4C22×D4311yescharacteristic
410#117—21no—
411#117—21no—
412#117—861no—
413#117—861no—
414C2×C4⋊C4—21no—
415#107—431no—
416#107—861no—
417#107—861no—
418#107—861no—
419#107C22⋊D4311yescharacteristic
420#106—21no—
421#106—861no—
422#106—861no—
423#106—861no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8C22×D4311yescharacteristic
428#103—21no—
429#103—21no—
430#103—21no—
431#103—1721no—
432#102—21no—
433#102—431no—
434#102—431no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102C22⋊D4311yescharacteristic
446#102C22⋊D4311yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8C22×D4311yescharacteristic
454C24—1721no—
455#41—42no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—861no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—431no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—3441no—
467C2×D4—3441no—
468C2×D4—1721no—
469C2×D4—1722no—
470C2×D4—1721no—
471C2×D4—1722no—
472C2×D4—1721no—
473C2×D4D4×D4311yescharacteristic
474C2×D4C2×C22⋊D4311yescharacteristic
475C2×D4C2×C22⋊D4311yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—861no—
481SD16—81no—
482SD16—3442no—
483D8—22no—
484D8—3441no—
485D8—3441no—
486D8—1721no—
487M16—3441no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—3441no—
497C2×C8—1722no—
498C2×C8C2×C22⋊D4311yescharacteristic
499C2×C8C2×C22⋊D4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—431no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4D4×D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C4⋊C4C2×C22⋊D4311yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—861no—
518C22⋊C4—1721no—
519C22⋊C4—1721no—
520C22⋊C4—1721no—
521C42—41no—
522C42—1721no—
523C42C23×D4311yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—861no—
528C23—3442no—
529C23—3442no—
530C23—1721no—
531C23—6881no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—3441no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—82no—
542D4—161no—
543D4—861no—
544D4—861no—
545D4—3441no—
546D4—3442no—
547D4—3442no—
548D4—1721no—
549D4—1721no—
550D4—1721no—
551D4—1721no—
552D4—6881no—
553D4#1306334512yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—861no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4C2×D4×D4311yescharacteristic
571C2×C4C22×C22⋊D4311yescharacteristic
572C2×C4#1306337011yescharacteristic
573C8—21no—
574C8—21no—
575C8—41no—
576C8—861no—
577C8—861no—
578C8—1721no—
579C8—1721no—
580C8—1721no—
581C8—1721no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—3441no—
592C22—3441no—
593C22—3441no—
594C22—1721no—
595C22—1721no—
596C22—1721no—
597C22—6884no—
598C22D4×C22⋊D4311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—3441no—
606C4—1721no—
607C4C2×#1306334511yescharacteristic
608C4#1458369611yescharacteristic
609C4#1458370211yescharacteristic
610C4#1458370611yescharacteristic
611C2—42no—
612C2—81no—
613C2—81no—
614C2—3441no—
615C2—6881no—
616C2#1914612011yescharacteristic
617C2#1914627611yescharacteristic
618C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3303C2
socleC22×C43D42
hypercenter#3303D43
hypocenterC43#19775
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3303

Complements

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

NH ≅ G/Ntype
1. #19147013C2semidirect
2. #19146839C2semidirect
3. #19146402C2semidirect
4. #19134249C2semidirect
5. #19134167C2semidirect
6. #19134034C2semidirect
7. #19134004C2semidirect
8. #19133992C2semidirect
9. #19133821C2semidirect
10. #19133746C2semidirect
11. #19133710C2semidirect
12. #19133678C2semidirect
13. #19133424C2semidirect
14. #19133419C2semidirect
15. C43×#3303C2semidirect
18. #14583302C22semidirect
20. #14583251C22semidirect
28. #14583189C22semidirect
41. D4×C43⋊C8C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582645C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
56. C43×#555C22semidirect
58. C43×#487C22semidirect
62. C43×#461C22semidirect
65. C8×D4×C43C22semidirect
304. #3303D43semidirect
326. #555C2×D43semidirect
332. #487C2×D43semidirect
349. #461C2×D43semidirect
360. C8×D4C2×D43semidirect
376. C43#19775semidirect

Maximal subgroups

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

subgroupindex
#191470132
#191468392
#191464022
#191342492
#191341672
#191340342
#191340042
#191339922
#191338212
#191337462
#191337102
#191336782
#191334242
#191334192
C43×#33032
#1977543