Finite Group Databasebeta

← #25086230

Subgroups — #25086230

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146905C211yesmaximal, characteristic, complemented
2#19146413C211yesmaximal, characteristic, complemented
3#19146410C211yesmaximal, characteristic
4#19134251C211yesmaximal, characteristic, complemented
5#19134130C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic, complemented
7#19134039C211yesmaximal, characteristic, complemented
8#19133991C211yesmaximal, characteristic, complemented
9#19133809C211yesmaximal, characteristic, complemented
10#19133745C211yesmaximal, characteristic, complemented
11#19133710C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15C43×#3380C211yesmaximal, characteristic, complemented
16#14583554C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583273C2211yescharacteristic
19#14583251C2211yescharacteristic, complemented
20#14583249C2211yescharacteristic, complemented
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583229—21no—
24#14583217—21no—
25#14583214—21no—
26#14583186C2211yescharacteristic
27#14583186C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583155—21no—
30#14583134—21no—
31#14583130—21no—
32#14583109C2211yescharacteristic, complemented
33#14583099C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583059—21no—
36#14583049—21no—
37#14583031—21no—
38C4×#10621884C2211yescharacteristic
39#14582977C2211yescharacteristic, complemented
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582898—21no—
43C2×#13063245—21no—
44#102×D43—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582648C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C43×#554C2211yescharacteristic
57C43×#554C2211yescharacteristic, complemented
58C43×#500C2211yescharacteristic, complemented
59C43×#499—21no—
60C43×#478—21no—
61C43×#478—21no—
62C43×#476C2211yescharacteristic
63C43×#476C2211yescharacteristic, complemented
64C8×Q8×C43C2211yescharacteristic, complemented
65C4×D8×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621885—21no—
71C2×#10621884—21no—
72C2×#10621884—41no—
73C2×#10621884D411yescharacteristic
74C2×#10621882—21no—
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#13063256—21no—
90#13063256—21no—
91#13063256D411yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—41no—
96#13063249D411yescharacteristic
97#13063248—21no—
98#13063248—21no—
99#13063248—21no—
100#13063247—21no—
101#13063247—21no—
102#13063246—21no—
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
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#125×C43—21no—
119#125×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—41no—
123C22⋊Q8×C43—41no—
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131#107×C43—21no—
132#107×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—41no—
153C22×C4×C43—41no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156D4×D43—42no—
157D4×D43—81no—
158#10621898—42no—
159#10621898—81no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—41no—
164C2×D172—42no—
165C2×D172—81no—
166C2×D172C2×D411yescharacteristic
167C2×C4×D43—21no—
168C2×C4×D43—41no—
169C2×Dic86—21no—
170D8×C43—22no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C42×C43—21no—
191C42×C43C2411yescharacteristic
192C22⋊Dic43—41no—
193#10621885—81no—
194#10621884—22no—
195#10621884—81no—
196#10621884—82no—
197#10621882—81no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—41no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—41no—
204#10621877—81no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C8×D43—81no—
213C23×C43—21no—
214C23×C43—21no—
215C22×D43—21no—
216C22×D43—41no—
217C22×D43—82no—
218C22×D43—82no—
219C22×D43—161no—
220Q8×C43—21no—
221Q8×C43—21no—
222Q8×C43—81no—
223Q8×C43—81no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43#13712yes—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—161no—
239C2×C4×C43—161no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C22⋊D43—82no—
244C22⋊D43—82no—
245C2×Dic43—21no—
246C2×Dic43—41no—
247D172—21no—
248D172—41no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—81no—
253D172—82no—
254D172#13512yes—
255C4×D43—41no—
256C4×D43—41no—
257C4×D43—82no—
258Dic86—41no—
259Dic86—41no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19774—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43D4211yescharacteristic
277C2×D43—22no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—164no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43C2×#13511yescharacteristic
292C4×C43C2×#13711yescharacteristic
293C4×C43#57611yescharacteristic
294C4×C43#57711yescharacteristic
295Dic43—41no—
296Dic43—81no—
297#3380D4311yescharacteristic, complemented
298#3331—431no—
299#3295—431no—
300#3294—431no—
301#1719—431no—
302#1697—431no—
303#1683—431no—
304#1682—431no—
305#1675—431no—
306#1644—431no—
307#1635—431no—
308#1629—431no—
309#1622—431no—
310#1581—431no—
311SD16⋊C8—431no—
312C2×C43—42no—
313C2×C43—81no—
314C2×C43#326611yescharacteristic
315C2×C43#328011yescharacteristic
316C2×C43#328811yescharacteristic
317D43—42no—
318D43—161no—
319#554C2×D4311yescharacteristic
320#554C2×D4311yescharacteristic, complemented
321#547—431no—
322D42—431no—
323#500C2×D4311yescharacteristic, complemented
324#499—21no—
325#492—431no—
326#487—431no—
327#487—431no—
328#486—431no—
329#486—431no—
330#483—861no—
331#481—861no—
332#480—861no—
333#478—21no—
334#478—21no—
335#476—431no—
336#476—431no—
337#476C2×D4311yescharacteristic
338#476C2×D4311yescharacteristic, complemented
339#474—431no—
340#470—861no—
341#466—861no—
342#465—861no—
343#462—431no—
344#460—431no—
345#459—431no—
346#452—861no—
347#450—861no—
348#447—861no—
349C8×Q8C2×D4311yescharacteristic, complemented
350C4×SD16—431no—
351C4×D8—21no—
352C4×D8C2×D4311yescharacteristic
353#436—431no—
354C8×D4—431no—
355C8×D4—431no—
356#417—861no—
357C2×#102—861no—
358C2×#102—861no—
359#335—431no—
360#335—431no—
361#333—431no—
362#333—431no—
363#332—431no—
364#331—431no—
365Q8⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8—431no—
368D4⋊C8—431no—
369#322—431no—
370C43#1977411yescharacteristic, complemented, Sylow
371C2×#41—861no—
372C22×D4—861no—
373C22×D4—861no—
374C2×Q16—861no—
375C2×SD16—431no—
376C2×SD16—861no—
377C2×SD16—1721no—
378C2×D8—861no—
379C2×D8C22⋊D4311yescharacteristic
380C2×M16—861no—
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8—431no—
384C4⋊Q8C22×D4311yescharacteristic
385C4⋊Q8C22×D4311yescharacteristic
386#127—431no—
387#125—21no—
388#125—21no—
389#123—1721no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—41no—
393C22⋊Q8—41no—
394C22⋊Q8—861no—
395#121—861no—
396#121—861no—
397#121—861no—
398#120—1721no—
399C4×Q8C22×D4311yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—431no—
403C4×D4C22×D4311yescharacteristic
404C4×D4C22×D4311yescharacteristic
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—861no—
408#107—21no—
409#107—21no—
410#107—861no—
411#107C22⋊D4311yescharacteristic
412#106—21no—
413#106—21no—
414#106—431no—
415#106—861no—
416#106—861no—
417C4⋊C8—21no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8C22×D4311yescharacteristic
422#103—431no—
423#103—861no—
424#103—861no—
425#103—861no—
426#103—1721no—
427#102—21no—
428#102—21no—
429#102—431no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102C22⋊D4311yescharacteristic
440#102C22⋊D4311yescharacteristic
441C22⋊C8—861no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C4×C8—21no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8C22×D4311yescharacteristic
448C24—1721no—
449#41—3441no—
450#41—1722no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—861no—
454C2×Q8D4×D4311yescharacteristic
455C2×D4—431no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—3441no—
460C2×D4—3441no—
461C2×D4—1721no—
462C2×D4—1722no—
463C2×D4—1721no—
464C2×D4—1721no—
465C2×D4—1722no—
466C2×D4C2×C22⋊D4311yescharacteristic
467C2×D4C2×C22⋊D4311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—861no—
473C22×C4—1721no—
474Q16—3441no—
475SD16—862no—
476SD16—3442no—
477SD16—3441no—
478D8—22no—
479D8—3441no—
480M16—3441no—
481C2×C8—21no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—3441no—
489C2×C8—3441no—
490C2×C8C2×C22⋊D4311yescharacteristic
491C2×C8C2×C22⋊D4311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—431no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—1721no—
505C4⋊C4D4×D4311yescharacteristic
506C4⋊C4C2×C22⋊D4311yescharacteristic
507C4⋊C4C2×C22⋊D4311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—861no—
513C22⋊C4—1721no—
514C22⋊C4—1721no—
515C42—21no—
516C42C23×D4311yescharacteristic
517C23—21no—
518C23—21no—
519C23—861no—
520C23—3442no—
521C23—3442no—
522C23—1721no—
523C23—6881no—
524Q8—21no—
525Q8—21no—
526Q8—81no—
527Q8—81no—
528Q8—1721no—
529Q8—1721no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—432no—
534D4—861no—
535D4—3441no—
536D4—3442no—
537D4—3442no—
538D4—3442no—
539D4—1721no—
540D4—1721no—
541D4—1721no—
542D4—1721no—
543D4#1306335612yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—161no—
555C2×C4—161no—
556C2×C4—861no—
557C2×C4—3442no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C22×C22⋊D4311yescharacteristic
563C2×C4#1306337011yescharacteristic
564C8—21no—
565C8—21no—
566C8—41no—
567C8—861no—
568C8—861no—
569C8—1721no—
570C8—1721no—
571C8—1721no—
572C8—1721no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—862no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—1721no—
584C22—1721no—
585C22—6884no—
586C22D4×C22⋊D4311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4—3441no—
595C4—1721no—
596C4#135×D4311yescharacteristic
597C4C2×#1306335611yescharacteristic
598C4#1458370111yescharacteristic
599C4#1458370711yescharacteristic
600C2—42no—
601C2—81no—
602C2—1722no—
603C2—6881no—
604C2#1914610611yescharacteristic
605C2#1914627411yescharacteristic
606C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3380C2
socleC22×C43D42
prime radical#19146410C2
hypercenter#3380D43
hypocenterC43#19774
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #19146905C2semidirect
2. #19146413C2semidirect
4. #19134251C2semidirect
5. #19134130C2semidirect
6. #19134048C2semidirect
7. #19134039C2semidirect
8. #19133991C2semidirect
9. #19133809C2semidirect
10. #19133745C2semidirect
11. #19133710C2semidirect
12. #19133667C2semidirect
13. #19133425C2semidirect
14. #19133405C2semidirect
15. C43×#3380C2semidirect
19. #14583251C22semidirect
20. #14583249C22semidirect
32. #14583109C22semidirect
39. #14582977C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582648C22semidirect
48. #14582648C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
57. C43×#554C22semidirect
58. C43×#500C22semidirect
63. C43×#476C22semidirect
64. C8×Q8×C43C22semidirect
297. #3380D43semidirect
320. #554C2×D43semidirect
323. #500C2×D43semidirect
338. #476C2×D43semidirect
349. C8×Q8C2×D43semidirect
370. C43#19774semidirect

Maximal subgroups

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

subgroupindex
#191469052
#191464132
#191464102
#191342512
#191341302
#191340482
#191340392
#191339912
#191338092
#191337452
#191337102
#191336672
#191334252
#191334052
C43×#33802
#1977443