Finite Group Databasebeta

← #25079339

Subgroups — #25079339

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145170C211yesmaximal, characteristic, complemented
2#19144655C211yesmaximal, characteristic, complemented
3#19143562C211yesmaximal, characteristic, complemented
4#19134137C211yesmaximal, characteristic, complemented
5#19134133C211yesmaximal, characteristic, complemented
6#19134130C211yesmaximal, characteristic, complemented
7#19134126C211yesmaximal, characteristic, complemented
8#19134121C211yesmaximal, characteristic, complemented
9#19134116C211yesmaximal, characteristic, complemented
10#19134077C211yesmaximal, characteristic, complemented
11#19134072C211yesmaximal, characteristic, complemented
12#19133341C211yesmaximal, characteristic, complemented
13#19133257C211yesmaximal, characteristic, complemented
14#19133255C211yesmaximal, characteristic, complemented
15C43×#3106C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583275C2211yescharacteristic
19#14583247C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583223—21no—
22#14583194C2211yescharacteristic
23#14583189C2211yescharacteristic
24#14583133—21no—
25#14583133—21no—
26#14583099C2211yescharacteristic
27#14583094C2211yescharacteristic
28#14583044—21no—
29#14583030C2211yescharacteristic
30#14583030C2211yescharacteristic
31C4×#10621884—21no—
32C4×#10621882—21no—
33C4×#10621882—21no—
34C4×#10621882—21no—
35#14582977C2211yescharacteristic
36#14582977C2211yescharacteristic
37#14582971—21no—
38#14582971—21no—
39#14582952—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42C4×#10621877—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582643C2211yescharacteristic
53#14582643C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#482—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C4×SD16×C43—21no—
65C4×D8×C43—21no—
66C43×#431C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621882—21no—
70C2×#10621882—21no—
71C2×#10621882—21no—
72C2×#10621877—21no—
73C2×#10621877—21no—
74C22×C43⋊C8D411yescharacteristic
75C22×C43⋊C8D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063313—21no—
79#13063299—21no—
80#13063299—21no—
81C4×D172—21no—
82C4×D172—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93#13063249—21no—
94#13063246—21no—
95#13063246—21no—
96#13063246—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106#13063236—21no—
107C4×C43⋊C8—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×#41×C43D411yescharacteristic
115C2×SD16×C43—21no—
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#124×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43D411yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144#41×C43—41no—
145#41×C43—41no—
146#41×C43—82no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C2×C22⋊D43—41no—
163#10621898—82no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×C4×D43—41no—
168C2×Dic86—21no—
169SD16×C43—42no—
170D8×C43—42no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43#4111yescharacteristic
190C42×C43C2411yescharacteristic
191#10621884—42no—
192#10621882—42no—
193#10621882—42no—
194#10621882—42no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—41no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199#10621877—42no—
200#10621877—42no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—41no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C23×C43—21no—
212C23×C43—41no—
213C23×C43#12111yescharacteristic
214C22×D43—41no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—81no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—42no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—81no—
226D4×C43—82no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—42no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—41no—
240C2×C4×C43—82no—
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C22⋊D43—82no—
248C2×Dic43—41no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—81no—
254C4×D43—82no—
255Dic86—81no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8#13512yes—
266#19160—431nomaximal, Sylow
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43C2×#12111yescharacteristic
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—81no—
287C4×C43#47212yes—
288C4×C43C2×#13511yescharacteristic
289C4×C43#57511yescharacteristic
290C4×C43#57511yescharacteristic
291C4×C43#57511yescharacteristic
292Dic43—81no—
293#3169—431no—
294#3106—431no—
295#3106D4311yescharacteristic, complemented
296#2965—431no—
297#1698—431no—
298#1698—431no—
299#1697—431no—
300#1697—431no—
301#1696—431no—
302#1695—431no—
303#1688—431no—
304#1687—431no—
305#1564—431no—
306#1543—431no—
307#1543—431no—
308C2×C43—41no—
309C2×C43—81no—
310C2×C43—161no—
311C2×C43#303511yescharacteristic
312C2×C43#305411yescharacteristic
313C2×C43C2×#47211yescharacteristic
314D43—161no—
315#532—431no—
316#532C2×D4311yescharacteristic
317C4×#41C2×D4311yescharacteristic
318#500—431no—
319#493—431no—
320#486—431no—
321#486—431no—
322#482—21no—
323#482—861no—
324#477—431no—
325#477C2×D4311yescharacteristic
326#476—431no—
327#476C2×D4311yescharacteristic
328#466—861no—
329#466—861no—
330#460—431no—
331#460C2×D4311yescharacteristic
332#459—431no—
333#459C2×D4311yescharacteristic
334#449—21no—
335#449—861no—
336#446—431no—
337#446—431no—
338C4×SD16—21no—
339C4×SD16—861no—
340C4×D8—21no—
341C4×D8—861no—
342C4×D8—861no—
343C4×D8—861no—
344#436—431no—
345#436—431no—
346#435—861no—
347#435—861no—
348#431—431no—
349#431—431no—
350#431—861no—
351#431C2×D4311yescharacteristic
352C4×M16—861no—
353C2×C4×C8—431no—
354#335—431no—
355#335—431no—
356#334—431no—
357#334—431no—
358#333—431no—
359#333—431no—
360#333—431no—
361#333—431no—
362#331—431no—
363#331—431no—
364#331—431no—
365#331—431no—
366C43#1916011yescharacteristic, complemented, Sylow
367C2×#41—21no—
368C2×#41—861no—
369C2×#41C22⋊D4311yescharacteristic
370C2×SD16—21no—
371C2×SD16—861no—
372C2×D8—21no—
373C2×D8—861no—
374C2×D8—861no—
375C2×D8—861no—
376C2×M16—861no—
377C2×M16—861no—
378C22×C8—431no—
379C22×C8—431no—
380C4⋊Q8—431no—
381C4⋊Q8C22×D4311yescharacteristic
382#127—431no—
383#127C22×D4311yescharacteristic
384#124—21no—
385#124—861no—
386#121—21no—
387#121—21no—
388#121—861no—
389#121—861no—
390C4×Q8C22⋊D4311yescharacteristic
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—861no—
397C4×D4—861no—
398C4×D4C22⋊D4311yescharacteristic
399C4×D4C22×D4311yescharacteristic
400#117—21no—
401#117C22⋊D4311yescharacteristic
402C2×C42—21no—
403C2×C42C22×D4311yescharacteristic
404#107—21no—
405#107—861no—
406#107—861no—
407#107—861no—
408#106—21no—
409#106—861no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418#103—21no—
419#103—861no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430C22⋊C8—21no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435#97—861no—
436#97—861no—
437C4×C8—21no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—861no—
443C4×C8—861no—
444#41—41no—
445#41—41no—
446#41—82no—
447#41—3442no—
448C2×Q8—21no—
449C2×Q8—861no—
450C2×Q8C2×C22⋊D4311yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—1721no—
460C2×D4C2×C22⋊D4311yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—1721no—
466C22×C4D4×D4311yescharacteristic
467C22×C4#1062190011yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469SD16—42no—
470SD16—1722no—
471D8—42no—
472D8—1722no—
473D8—1722no—
474D8—1722no—
475M16—1722no—
476M16—1722no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—862no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—1721no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4C2×C22⋊D4311yescharacteristic
496C4⋊C4C2×C22⋊D4311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42D4×D4311yescharacteristic
508C42#1062190011yescharacteristic
509C42C2×C22⋊D4311yescharacteristic
510C42C23×D4311yescharacteristic
511C23—21no—
512C23—41no—
513C23—1721no—
514C23#1306329711yescharacteristic
515Q8—21no—
516Q8—21no—
517Q8—81no—
518Q8—3441no—
519D4—21no—
520D4—21no—
521D4—42no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—81no—
527D4—82no—
528D4—3441no—
529D4—3442no—
530D4—1721no—
531D4—1721no—
532D4—1721no—
533D4—1721no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—3442no—
549C2×C4—1721no—
550C2×C4#1306329711yescharacteristic
551C2×C4#1306329711yescharacteristic
552C2×C4#1306329711yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C22×C22⋊D4311yescharacteristic
555C2×C4C2×#1062190011yescharacteristic
556C8—41no—
557C8—41no—
558C8—432no—
559C8—861no—
560C8—861no—
561C8—861no—
562C8—1721no—
563C8—1721no—
564C8—1721no—
565C8—1721no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22C2×#1306329711yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—3441no—
587C4#1458316712yes—
588C4#135×D4311yescharacteristic
589C4#1458369611yescharacteristic
590C4#1458369711yescharacteristic
591C4#1458369711yescharacteristic
592C2—41no—
593C2—81no—
594C2—161no—
595C2—6881no—
596C2#1914404611yescharacteristic
597C2#1914420111yescharacteristic
598C2C2×#1458316711yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3106C2
socleC22×C43C2×#121
hypercenter#3106D43
hypocenterC43#19160
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #19145170C2semidirect
2. #19144655C2semidirect
3. #19143562C2semidirect
4. #19134137C2semidirect
5. #19134133C2semidirect
6. #19134130C2semidirect
7. #19134126C2semidirect
8. #19134121C2semidirect
9. #19134116C2semidirect
10. #19134077C2semidirect
11. #19134072C2semidirect
12. #19133341C2semidirect
13. #19133257C2semidirect
14. #19133255C2semidirect
15. C43×#3106C2semidirect
295. #3106D43semidirect
366. C43#19160semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191446552
#191435622
#191341372
#191341332
#191341302
#191341262
#191341212
#191341162
#191340772
#191340722
#191333412
#191332572
#191332552
C43×#31062
#1916043