Finite Group Databasebeta

← #25086223

Subgroups — #25086223

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#19147458C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic, complemented
3#19146402C211yesmaximal, characteristic
4#19134249C211yesmaximal, characteristic, complemented
5#19134128C211yesmaximal, characteristic, complemented
6#19134043C211yesmaximal, characteristic, complemented
7#19134041C211yesmaximal, characteristic, complemented
8#19133992C211yesmaximal, characteristic, complemented
9#19133807C211yesmaximal, characteristic, complemented
10#19133746C211yesmaximal, characteristic, complemented
11#19133710C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3331C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583302C2211yescharacteristic, complemented
19#14583298—21no—
20#14583273C2211yescharacteristic
21#14583251C2211yescharacteristic, complemented
22#14583247C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583219—21no—
25#14583212—21no—
26#14583199—21no—
27#14583196—21no—
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic, complemented
30#14583186C2211yescharacteristic
31#14583176C2211yescharacteristic
32#14583133—21no—
33#14583131—21no—
34#14583099C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583048—21no—
37#14583032—21no—
38Q8×C43⋊C8C2211yescharacteristic, complemented
39C4×#10621882—21no—
40C4×#10621882C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43C2×#13063245—21no—
44#102×D43—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic, complemented
56C43×#554C2211yescharacteristic, complemented
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic, complemented
59C43×#483—21no—
60C43×#476C2211yescharacteristic
61C43×#470—21no—
62C43×#462C2211yescharacteristic, complemented
63C43×#452—21no—
64C4×SD16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic, complemented
66C43×#417—21no—
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621884—21no—
70C2×#10621884—41no—
71C2×#10621882—21no—
72C2×#10621882D411yescharacteristic
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063322C2311yescharacteristic
77#13063317—21no—
78#13063303—41no—
79#13063301—21no—
80#13063300—21no—
81#13063299—21no—
82#13063295—41no—
83C4×D172—21no—
84C4×D172C2311yescharacteristic
85C4⋊C4×D43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93C4⋊(C43⋊C8)—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—
111(C2×D43)⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×Q16×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C2×M16×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126#121×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133#106×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
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×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—41no—
151C2×D4×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—41no—
156C22×C4×C43—41no—
157C2×C22⋊D43—41no—
158D4×D43—42no—
159D4×D43—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—
170Q16×C43—81no—
171SD16×C43—22no—
172M16×C43—81no—
173C2×C8×C43—21no—
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×C43—21no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43—21no—
192C42×C43C2411yescharacteristic
193#10621884—81no—
194#10621884—82no—
195#10621882—22no—
196#10621882—81no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
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—41no—
223Q8×C43—41no—
224Q8×C43—81no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—82no—
229D4×C43#13512yes—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—82no—
241C2×C4×C43—161no—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C22⋊D43—82no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248D172—21no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—81no—
254D172—82no—
255D172#13712yes—
256C4×D43—41no—
257C4×D43—41no—
258C4×D43—161no—
259Dic86—81no—
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#3380—431no—
298#3331D4311yescharacteristic, complemented
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#554—431no—
320#554C2×D4311yescharacteristic, complemented
321#547C2×D4311yescharacteristic
322D42—431no—
323#500—431no—
324#499—861no—
325#492—431no—
326#487—431no—
327#487C2×D4311yescharacteristic, complemented
328#486—431no—
329#486—431no—
330#483—21no—
331#481—861no—
332#480—861no—
333#478—861no—
334#478—861no—
335#476—431no—
336#476—431no—
337#476—431no—
338#476C2×D4311yescharacteristic
339#474—431no—
340#470—21no—
341#466—861no—
342#465—861no—
343#462C2×D4311yescharacteristic, complemented
344#460—431no—
345#459—431no—
346#452—21no—
347#450—861no—
348#447—861no—
349C8×Q8—431no—
350C4×SD16C2×D4311yescharacteristic
351C4×D8—431no—
352C4×D8—861no—
353#436C2×D4311yescharacteristic, complemented
354C8×D4—431no—
355C8×D4—431no—
356#417—21no—
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—21no—
372C22×D4—861no—
373C22×D4—861no—
374C2×Q16—21no—
375C2×SD16—861no—
376C2×SD16—1721no—
377C2×SD16C22⋊D4311yescharacteristic
378C2×D8—431no—
379C2×D8—861no—
380C2×M16—21no—
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8—431no—
384C4⋊Q8C22×D4311yescharacteristic
385C4⋊Q8C22×D4311yescharacteristic
386#127—431no—
387#125—21no—
388#125—861no—
389#123—41no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—41no—
393C22⋊Q8—861no—
394C22⋊Q8—1721no—
395#121—21no—
396#121—861no—
397#121—861no—
398#120—1721no—
399C4×Q8C22×D4311yescharacteristic
400C4×D4—21no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4C22×D4311yescharacteristic
404C4×D4C22×D4311yescharacteristic
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—861no—
408#107—431no—
409#107—861no—
410#107—861no—
411#107—861no—
412#106—21no—
413#106—861no—
414#106—861no—
415#106—861no—
416#106C22⋊D4311yescharacteristic
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—861no—
421C4⋊C8C22×D4311yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—1721no—
426#103C22⋊D4311yescharacteristic
427#102—21no—
428#102—431no—
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#102—861no—
440#102C22⋊D4311yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—861no—
447C4×C8C22×D4311yescharacteristic
448C24—1721no—
449#41—42no—
450#41—81no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—861no—
454C2×Q8C2×C22⋊D4311yescharacteristic
455C2×D4—41no—
456C2×D4—431no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—3441no—
461C2×D4—3441no—
462C2×D4—1721no—
463C2×D4—1722no—
464C2×D4—1721no—
465C2×D4—1722no—
466C2×D4D4×D4311yescharacteristic
467C2×D4C2×C22⋊D4311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—861no—
473C22×C4—1721no—
474Q16—81no—
475SD16—22no—
476SD16—3442no—
477SD16—3441no—
478D8—862no—
479D8—3441no—
480M16—81no—
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—431no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—1721no—
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—41no—
527Q8—41no—
528Q8—81no—
529Q8—3441no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—82no—
534D4—432no—
535D4—861no—
536D4—3441no—
537D4—3442no—
538D4—3442no—
539D4—1721no—
540D4—1721no—
541D4—1721no—
542D4—1721no—
543D4#1306334512yes—
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—82no—
555C2×C4—161no—
556C2×C4—861no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—6881no—
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—
596C4C2×#1306334511yescharacteristic
597C4#137×D4311yescharacteristic
598C4#1458370211yescharacteristic
599C4#1458370811yescharacteristic
600C2—42no—
601C2—81no—
602C2—1722no—
603C2—6881no—
604C2#1914609911yescharacteristic
605C2#1914627611yescharacteristic
606C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3331C2
socleC22×C43D42
prime radical#19146402C2
hypercenter#3331D43
hypocenterC43#19774
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3331

Complements

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

NH ≅ G/Ntype
1. #19147458C2semidirect
2. #19146421C2semidirect
4. #19134249C2semidirect
5. #19134128C2semidirect
6. #19134043C2semidirect
7. #19134041C2semidirect
8. #19133992C2semidirect
9. #19133807C2semidirect
10. #19133746C2semidirect
11. #19133710C2semidirect
12. #19133667C2semidirect
13. #19133422C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3331C2semidirect
18. #14583302C22semidirect
21. #14583251C22semidirect
29. #14583189C22semidirect
38. Q8×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
56. C43×#554C22semidirect
58. C43×#487C22semidirect
62. C43×#462C22semidirect
65. C43×#436C22semidirect
298. #3331D43semidirect
320. #554C2×D43semidirect
327. #487C2×D43semidirect
343. #462C2×D43semidirect
353. #436C2×D43semidirect
370. C43#19774semidirect

Maximal subgroups

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

subgroupindex
#191474582
#191464212
#191464022
#191342492
#191341282
#191340432
#191340412
#191339922
#191338072
#191337462
#191337102
#191336672
#191334222
SD16⋊(C43⋊C8)2
C43×#33312
#1977443