Finite Group Databasebeta

← #25253202

Subgroups — #25253202

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583339C211yesmaximal, characteristic, complemented
2C2×#14583335C211yesmaximal, characteristic, complemented
3#19146338C211yesmaximal, characteristic, complemented
4#19136854C211yesmaximal, characteristic, complemented
5#19136701C211yesmaximal, characteristic, complemented
6#19136696C211yesmaximal, characteristic, complemented
7#19136654C211yesmaximal, characteristic, complemented
8#19136650C211yesmaximal, characteristic, complemented
9#19136533C211yesmaximal, characteristic, complemented
10#19136524C211yesmaximal, characteristic, complemented
11#19136518C211yesmaximal, characteristic, complemented
12#19136511C211yesmaximal, characteristic, complemented
13C4×#13063269C211yesmaximal, characteristic, complemented
14#19136427C211yesmaximal, characteristic, complemented
15C43×#3280C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×Dic172C2211yescharacteristic, complemented
18#14583558—21no—
19#14583339—24no—
20#14583335—24no—
21C2×#13063271C2211yescharacteristic, complemented
22C2×#13063271C2211yescharacteristic, complemented
23C2×#13063269C2211yescharacteristic
24C2×#13063269C2211yescharacteristic
25C2×#13063269C2211yescharacteristic
26C2×#13063269C2211yescharacteristic
27C2×#13063268C2211yescharacteristic, complemented
28C2×#13063266C2211yescharacteristic
29C2×#13063266C2211yescharacteristic
30C2×#13063265C2211yescharacteristic
31C2×#13063265C2211yescharacteristic, complemented
32#14583283C2211yescharacteristic, complemented
33#14583140C2211yescharacteristic
34#14583135C2211yescharacteristic, complemented
35#14583122—21no—
36#14583063—21no—
37#14583040—21no—
38C4×Dic172C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40C4⋊(C43⋊C16)C2211yescharacteristic, complemented
41#14582703C2211yescharacteristic, complemented
42#14582702C2211yescharacteristic, complemented
43#14582702C2211yescharacteristic, complemented
44#14582700C2211yescharacteristic
45#14582700C2211yescharacteristic
46#14582699C2211yescharacteristic, complemented
47C22⋊(C43⋊C16)C2211yescharacteristic
48C22⋊(C43⋊C16)C2211yescharacteristic, complemented
49C4×C43⋊C16C2211yescharacteristic, complemented
50C2×#135×C43C2211yescharacteristic
51C22×D8×C43C2211yescharacteristic
52C43×#546—21no—
53C43×#495C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#463—21no—
57C43×#450—21no—
58C43×#449—21no—
59C4×D8×C43C2211yescharacteristic
60C8×D4×C43C2211yescharacteristic
61C2×#10621898—21no—
62C22×Dic86—21no—
63#13063347—22no—
64#13063347—41no—
65C2×Dic172—22no—
66C2×Dic172—21no—
67C2×Dic172—41no—
68C2×Dic172C2311yescharacteristic
69C2×Dic172C2311yescharacteristic
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×D344C2311yescharacteristic
73#13063313—21no—
74#13063311—41no—
75#13063304—21no—
76#13063303—41no—
77#13063299—21no—
78#13063297—41no—
79C4×Dic86—21no—
80(C22⋊D43)⋊C4—41no—
81#13063271—22no—
82#13063271—22no—
83#13063269—22no—
84#13063269—22no—
85#13063269—41no—
86#13063269D414yescomplemented
87#13063268—41no—
88#13063266—22no—
89#13063266—22no—
90#13063265—22no—
91#13063265—22no—
92C2×C43⋊C16C2311yescharacteristic
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C2×C43⋊C16C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063247—21no—
100C2×#41×C43—21no—
101C22×D4×C43—21no—
102#135×C43—22no—
103#135×C43—41no—
104C2×Q16×C43C2311yescharacteristic
105C2×SD16×C43—21no—
106C2×SD16×C43—21no—
107C2×D8×C43—22no—
108C2×D8×C43—21no—
109C2×D8×C43—41no—
110C2×D8×C43C2311yescharacteristic
111C2×D8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#124×C43—21no—
115#123×C43—41no—
116C22⋊Q8×C43—21no—
117#121×C43—21no—
118#121×C43—41no—
119#120×C43—41no—
120C4×D4×C43—21no—
121C4×D4×C43D411yescharacteristic
122C2×C22⋊C4×C43—41no—
123#107×C43C2311yescharacteristic
124C4⋊C8×C43D411yescharacteristic
125#103×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
128C22⋊C8×C43D411yescharacteristic
129C22⋊C8×C43D411yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C24×C43—41no—
132#41×C43—42no—
133#41×C43—81no—
134C2×Q8×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—41no—
138C2×D4×C43—41no—
139C2×D4×C43—41no—
140C2×D4×C43—42no—
141C2×D4×C43—81no—
142C2×D4×C43D811yescharacteristic
143C22×C4×C43—41no—
144C22×C4×C43—41no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C2×C22⋊D43—41no—
148C2×C22⋊D43—41no—
149C22×Dic43—41no—
150#10621898—42no—
151#10621898—81no—
152C2×D172—21no—
153C2×C4×D43—41no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—42no—
157C2×Dic86—41no—
158C2×Dic86—81no—
159Q16×C43—21no—
160Q16×C43—21no—
161SD16×C43—42no—
162SD16×C43—81no—
163D8×C43—21no—
164D8×C43—21no—
165D8×C43—21no—
166D8×C43—42no—
167D8×C43C2×D412yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43D811yescharacteristic
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43D811yescharacteristic
185C22⋊C4×C43D811yescharacteristic
186C42×C43C2×D411yescharacteristic
187C22⋊Dic43—41no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—41no—
195Dic172—21no—
196Dic172—21no—
197Dic172—21no—
198Dic172—42no—
199Dic172C2×D412yes—
200D344—21no—
201D344—21no—
202#10621873—42no—
203#10621873—81no—
204C43⋊C16—21no—
205C43⋊C16—21no—
206C43⋊C16—21no—
207C43⋊C16C2×D412yes—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—82no—
211C23×C43—82no—
212C23×C43—161no—
213C23×C43C2×D811yescharacteristic
214C23×C43C2×D811yescharacteristic
215C22×D43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218D4×C43—22no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—82no—
224D4×C43—82no—
225D4×C43—161no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—82no—
233C2×C4×C43—161no—
234C2×C4×C43C2×D811yescharacteristic
235C2×C4×C43C2×D811yescharacteristic
236C2×C4×C43C2×D811yescharacteristic
237C2×C4×C43C2×D811yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C22⋊D43—82no—
240C22⋊D43—82no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—82no—
245D172—41no—
246D172—41no—
247C4×D43—82no—
248Dic86—22no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—82no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43C22×D411yescharacteristic
257C8×C43H(5,𝔽2)11yescharacteristic
258#33841—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—42no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—164no—
272C22×C43C22×D811yescharacteristic
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43D4211yescharacteristic
283C4×C43#57611yescharacteristic
284Dic43—42no—
285Dic43—81no—
286Dic43—81no—
287C2×#510—431no—
288C2×#509—431no—
289#3285—431no—
290#3280D4311yescharacteristic, complemented
291#2249—431no—
292#2219—431no—
293#2218—431no—
294#2211—431no—
295#2210—431no—
296#2189—431no—
297#2187—431no—
298#2186—431no—
299#2185—431no—
300C4×SD32—431no—
301#2169—431no—
302C2×C43—41no—
303C2×C43—41no—
304C2×C43—82no—
305C2×C43—161no—
306C2×C43D4×D811yescharacteristic
307C2×C43#341411yescharacteristic
308C2×C43#341611yescharacteristic
309D43—161no—
310C2×#135—431no—
311C2×#135C2×D4311yescharacteristic
312C22×Q16—431no—
313C22×D8C2×D4311yescharacteristic
314#548—861no—
315#546—21no—
316#510—864no—
317#509—864no—
318C2×Q32—431no—
319C2×Q32—431no—
320C2×SD32—431no—
321C2×SD32—431no—
322C2×SD32—431no—
323C2×SD32—431no—
324C2×SD32—431no—
325C2×D16—431no—
326C2×D16—431no—
327C2×M32—431no—
328C2×M32—431no—
329#495—431no—
330#495C2×D4311yescharacteristic
331#467—431no—
332#467C2×D4311yescharacteristic
333#466—431no—
334#466C2×D4311yescharacteristic
335#464—861no—
336#463—21no—
337#452—861no—
338#450—21no—
339#449—21no—
340#448—861no—
341C4×Q16—431no—
342C4×D8C2×D4311yescharacteristic
343C8×D4C2×D4311yescharacteristic
344#367—431no—
345C4⋊C16—431no—
346#358—431no—
347#358—431no—
348#358—431no—
349#357—431no—
350#357—431no—
351#357—431no—
352C22⋊C16—431no—
353C22⋊C16—431no—
354C4×C16—431no—
355C43#3384111yescharacteristic, complemented, Sylow
356C2×#41—21no—
357C2×#41—861no—
358C22×Q8—861no—
359C22×D4—21no—
360#135—22no—
361#135—41no—
362#135—862no—
363#135—1721no—
364C2×Q16—431no—
365C2×Q16—431no—
366C2×Q16—862no—
367C2×Q16—861no—
368C2×Q16—1721no—
369C2×Q16C22×D4311yescharacteristic
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×D8—22no—
375C2×D8—21no—
376C2×D8—41no—
377C2×D8—431no—
378C2×D8C22×D4311yescharacteristic
379C2×D8C22×D4311yescharacteristic
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382#124—21no—
383#124—861no—
384#124—1721no—
385#123—41no—
386C22⋊Q8—21no—
387C22⋊Q8—861no—
388C22⋊Q8—1721no—
389#121—21no—
390#121—41no—
391#121—861no—
392#121—1721no—
393#120—41no—
394C4×Q8—861no—
395C4×D4—21no—
396C4×D4—1721no—
397C4×D4C22⋊D4311yescharacteristic
398C2×C22⋊C4—41no—
399Q32—862no—
400Q32—862no—
401SD32—434no—
402SD32—862no—
403SD32—862no—
404SD32—1721no—
405SD32—1721no—
406D16—862no—
407D16—862no—
408M32—862no—
409M32—862no—
410C2×C16—431no—
411C2×C16—431no—
412C2×C16—431no—
413C2×C16—431no—
414#107—431no—
415#107C22×D4311yescharacteristic
416C4⋊C8C22⋊D4311yescharacteristic
417#103—21no—
418#103—861no—
419#103—861no—
420#102—21no—
421#102—21no—
422#102—861no—
423C22⋊C8C22⋊D4311yescharacteristic
424C22⋊C8C22⋊D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426C24—41no—
427#41—42no—
428#41—81no—
429#41—3441no—
430#41—1722no—
431C2×Q8—21no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—3441no—
435C2×Q8—1722no—
436C2×Q8—1721no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—42no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—81no—
444C2×D4—861no—
445C2×D4—1721no—
446C2×D4—1721no—
447C2×D4#1062188211yescharacteristic
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454Q16—21no—
455Q16—21no—
456Q16—432no—
457Q16—861no—
458Q16—861no—
459Q16—861no—
460Q16—1722no—
461SD16—42no—
462SD16—81no—
463SD16—3441no—
464SD16—1722no—
465D8—21no—
466D8—21no—
467D8—21no—
468D8—42no—
469D8—861no—
470D8—861no—
471D8D4×D4312yes—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8C2×C22⋊D4311yescharacteristic
477C2×C8C2×C22⋊D4311yescharacteristic
478C2×C8C2×C22⋊D4311yescharacteristic
479C2×C8C23×D4311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—861no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C4⋊C4#1062188211yescharacteristic
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C22⋊C4—1721no—
495C22⋊C4#1062188211yescharacteristic
496C22⋊C4#1062188211yescharacteristic
497C42—1721no—
498C42C2×C22⋊D4311yescharacteristic
499C16—432no—
500C16—861no—
501C16—861no—
502C16—861no—
503C23—41no—
504C23—41no—
505C23—82no—
506C23—82no—
507C23—161no—
508C23—1721no—
509C23C2×#1062188211yescharacteristic
510C23C2×#1062188211yescharacteristic
511Q8—41no—
512Q8—41no—
513Q8—862no—
514Q8—3442no—
515Q8—1721no—
516Q8—1721no—
517Q8—1721no—
518D4—22no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—82no—
524D4—82no—
525D4—161no—
526D4—3442no—
527D4—3442no—
528D4—1721no—
529D4—1721no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—161no—
538C2×C4—3442no—
539C2×C4—3442no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4C2×#1062188211yescharacteristic
544C2×C4C2×#1062188211yescharacteristic
545C2×C4C2×#1062188211yescharacteristic
546C2×C4C2×#1062188211yescharacteristic
547C2×C4C22×C22⋊D4311yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8C2×D4×D4311yescharacteristic
552C8#1306337011yescharacteristic
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—42no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22—3441no—
567C22—3441no—
568C22—3441no—
569C22C22×#1062188211yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—81no—
575C4—81no—
576C4—3441no—
577C4—3441no—
578C4—1722no—
579C4D4×C22⋊D4311yescharacteristic
580C4#1458370211yescharacteristic
581C2—41no—
582C2—41no—
583C2—82no—
584C2—161no—
585C2—6881no—
586C2D4×#1062188211yescharacteristic
587C2#1914772911yescharacteristic
588C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3280C2
socleC22×C43C22×D8
hypercenter#3280D43
hypocenterC43#33841
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. C2×#14583339C2semidirect
2. C2×#14583335C2semidirect
3. #19146338C2semidirect
4. #19136854C2semidirect
5. #19136701C2semidirect
6. #19136696C2semidirect
7. #19136654C2semidirect
8. #19136650C2semidirect
9. #19136533C2semidirect
10. #19136524C2semidirect
11. #19136518C2semidirect
12. #19136511C2semidirect
13. C4×#13063269C2semidirect
14. #19136427C2semidirect
15. C43×#3280C2semidirect
17. C22×Dic172C22semidirect
21. C2×#13063271C22semidirect
22. C2×#13063271C22semidirect
27. C2×#13063268C22semidirect
31. C2×#13063265C22semidirect
32. #14583283C22semidirect
34. #14583135C22semidirect
38. C4×Dic172C22semidirect
39. #14582726C22semidirect
40. C4⋊(C43⋊C16)C22semidirect
41. #14582703C22semidirect
42. #14582702C22semidirect
43. #14582702C22semidirect
46. #14582699C22semidirect
48. C22⋊(C43⋊C16)C22semidirect
49. C4×C43⋊C16C22semidirect
86. #13063269D4semidirect
290. #3280D43semidirect
355. C43#33841semidirect

Maximal subgroups

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

subgroupindex
C2×#145833392
C2×#145833352
#191463382
#191368542
#191367012
#191366962
#191366542
#191366502
#191365332
#191365242
#191365182
#191365112
C4×#130632692
#191364272
C43×#32802
#3384143