Finite Group Databasebeta

← #25086245

Subgroups — #25086245

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#19146831C211yesmaximal, characteristic, complemented
2#19146517C211yesmaximal, characteristic, complemented
3#19146410C211yesmaximal, characteristic, complemented
4#19134251C211yesmaximal, characteristic, complemented
5#19134172C211yesmaximal, characteristic, complemented
6#19134032C211yesmaximal, characteristic, complemented
7#19134006C211yesmaximal, characteristic, complemented
8#19133991C211yesmaximal, characteristic, complemented
9#19133823C211yesmaximal, characteristic, complemented
10#19133745C211yesmaximal, characteristic, complemented
11#19133710C211yesmaximal, characteristic, complemented
12#19133678C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15C43×#3341C211yesmaximal, characteristic, complemented
16#14583554C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583273C2211yescharacteristic
19#14583251C2211yescharacteristic, complemented
20#14583249C2211yescharacteristic, complemented
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583240—21no—
24#14583223—21no—
25#14583214—21no—
26#14583186C2211yescharacteristic
27#14583186C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583150—21no—
30#14583134—21no—
31#14583126—21no—
32#14583104C2211yescharacteristic, complemented
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583042—21no—
36#14583032—21no—
37#14583031—21no—
38C4×#10621882C2211yescharacteristic
39#14582977C2211yescharacteristic
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic, complemented
42#14582903—21no—
43#14582893—21no—
44#102×D43—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582648C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C43×#555C2211yescharacteristic
57C43×#555C2211yescharacteristic, complemented
58C43×#500C2211yescharacteristic, complemented
59C43×#482—21no—
60C43×#482—21no—
61C43×#476C2211yescharacteristic
62C43×#476C2211yescharacteristic, complemented
63C43×#466—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic, complemented
66C43×#427—21no—
67C2×#10621898—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621883—21no—
71C2×#10621884—41no—
72C2×#10621882—21no—
73C2×#10621882—21no—
74C2×#10621882D411yescharacteristic
75C2×#10621877—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063307—41no—
81#13063304—21no—
82#13063300—21no—
83#13063299—21no—
84#13063296—21no—
85#13063295—41no—
86C4×D172C2311yescharacteristic
87C4⋊C4×D43—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063256—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—41no—
96#13063248—21no—
97#13063248—21no—
98#13063248—21no—
99#13063247—21no—
100#13063247—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×D8×C43D411yescharacteristic
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#124×C43—41no—
120#124×C43—41no—
121#121×C43—21no—
122#121×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125C4×D4×C43C2311yescharacteristic
126C4×D4×C43C2311yescharacteristic
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129#117×C43—21no—
130#117×C43—21no—
131#117×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43—41no—
148C2×D4×C43—41no—
149C2×D4×C43C2×D411yescharacteristic
150C2×D4×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157D4×D43—42no—
158D4×D43—81no—
159#10621898—42no—
160#10621898—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×C4×D43—41no—
170C2×Dic86—21no—
171D8×C43—41no—
172C2×C8×C43—21no—
173C2×C8×C43—42no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C42×C43—41no—
191C42×C43—41no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—41no—
194#10621884—82no—
195#10621883—81no—
196#10621882—22no—
197#10621882—81no—
198#10621882—81no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—41no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—41no—
205#10621877—81no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—81no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C8×D43—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—81no—
223Q8×C43—81no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—161no—
231D4×C43—161no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C22⋊D43—82no—
247C22⋊D43—82no—
248C2×Dic43—21no—
249C2×Dic43—41no—
250D172—21no—
251D172—41no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—81no—
256D172—82no—
257D172#13512yes—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—82no—
261Dic86—41no—
262Dic86—41no—
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—41no—
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—22no—
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#3341D4311yescharacteristic, complemented
303#3325—431no—
304#3303—431no—
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—81no—
318C2×C43—81no—
319C2×C43—81no—
320C2×C43#326711yescharacteristic
321C2×C43#328011yescharacteristic
322C2×C43#328811yescharacteristic
323D43—42no—
324D43—161no—
325#555C2×D4311yescharacteristic
326#555C2×D4311yescharacteristic, complemented
327#547—431no—
328D42—431no—
329#500C2×D4311yescharacteristic, complemented
330#492—431no—
331#487—431no—
332#487—431no—
333#486—431no—
334#486—431no—
335#485—861no—
336#482—21no—
337#482—21no—
338#482—861no—
339#480—861no—
340#476—431no—
341#476—431no—
342#476C2×D4311yescharacteristic
343#476C2×D4311yescharacteristic, complemented
344#474—431no—
345#469—861no—
346#466—21no—
347#466—861no—
348#465—861no—
349#461—431no—
350#459—431no—
351#459—431no—
352#449—861no—
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—21no—
362#418—861no—
363#416—861no—
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—861no—
378C22×D4—861no—
379C22×D4—861no—
380C2×SD16—861no—
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—41no—
396#123—1721no—
397C22⋊Q8—861no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
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—21no—
413#117—21no—
414C2×C4⋊C4—861no—
415#107—21no—
416#107—21no—
417#107—431no—
418#107—861no—
419#107C22⋊D4311yescharacteristic
420#106—21no—
421#106—21no—
422#106—861no—
423#106—861no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8C22×D4311yescharacteristic
428#103—861no—
429#103—861no—
430#103—861no—
431#103—1721no—
432#102—21no—
433#102—21no—
434#102—431no—
435#102—431no—
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—3441no—
456#41—1722no—
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—861no—
480C22×C4—1721no—
481SD16—3441no—
482SD16—3442no—
483D8—41no—
484D8—862no—
485D8—3441no—
486D8—3441no—
487M16—3441no—
488C2×C8—21no—
489C2×C8—42no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—3441no—
497C2×C8—3441no—
498C2×C8C2×C22⋊D4311yescharacteristic
499C2×C8C2×C22⋊D4311yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—431no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—1721no—
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—41no—
518C22⋊C4—861no—
519C22⋊C4—1721no—
520C22⋊C4—1721no—
521C42—41no—
522C42—41no—
523C42C23×D4311yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—861no—
528C23—3442no—
529C23—3442no—
530C23—1721no—
531C23—6881no—
532Q8—81no—
533Q8—81no—
534Q8—1721no—
535Q8—1721no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—161no—
543D4—161no—
544D4—432no—
545D4—861no—
546D4—3441no—
547D4—3442no—
548D4—3442no—
549D4—3442no—
550D4—1721no—
551D4—1721no—
552D4—1721no—
553D4—1721no—
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—861no—
566C2×C4—3442no—
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—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—862no—
592C22—3441no—
593C22—3441no—
594C22—3441no—
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—
607C4#135×D4311yescharacteristic
608C4#1458369711yescharacteristic
609C4#1458370111yescharacteristic
610C4#1458370711yescharacteristic
611C2—81no—
612C2—81no—
613C2—81no—
614C2—1722no—
615C2—6881no—
616C2#1914612111yescharacteristic
617C2#1914627411yescharacteristic
618C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3341C2
socleC22×C43D42
hypercenter#3341D43
hypocenterC43#19775
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #19146831C2semidirect
2. #19146517C2semidirect
3. #19146410C2semidirect
4. #19134251C2semidirect
5. #19134172C2semidirect
6. #19134032C2semidirect
7. #19134006C2semidirect
8. #19133991C2semidirect
9. #19133823C2semidirect
10. #19133745C2semidirect
11. #19133710C2semidirect
12. #19133678C2semidirect
13. #19133425C2semidirect
14. #19133417C2semidirect
15. C43×#3341C2semidirect
19. #14583251C22semidirect
20. #14583249C22semidirect
32. #14583104C22semidirect
41. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582648C22semidirect
49. #14582644C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
57. C43×#555C22semidirect
58. C43×#500C22semidirect
62. C43×#476C22semidirect
65. C8×D4×C43C22semidirect
302. #3341D43semidirect
326. #555C2×D43semidirect
329. #500C2×D43semidirect
343. #476C2×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
#191468312
#191465172
#191464102
#191342512
#191341722
#191340322
#191340062
#191339912
#191338232
#191337452
#191337102
#191336782
#191334252
#191334172
C43×#33412
#1977543