Finite Group Databasebeta

← D43×#2180 #25250026

Subgroups — D43×#2180 #25250026

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#510×D43C211yesmaximal, characteristic
2#444×D43C211yesmaximal, characteristic
3#441×D43C211yesmaximal, characteristic, complemented
4#19136489C211yesmaximal, characteristic, complemented
5#19136488C211yesmaximal, characteristic, complemented
6#19136487C211yesmaximal, characteristic, complemented
7#19136486C211yesmaximal, characteristic, complemented
8#19136485C211yesmaximal, characteristic, complemented
9#19136484C211yesmaximal, characteristic, complemented
10#19136483C211yesmaximal, characteristic, complemented
11#365×D43C211yesmaximal, characteristic, complemented
12#362×D43C211yesmaximal, characteristic, complemented
13#360×D43C211yesmaximal, characteristic
14#347×D43C211yesmaximal, characteristic, complemented
15C43×#2180C211yesmaximal, characteristic, complemented
16#135×D43C2211yescharacteristic
17C2×Q16×D43C2211yescharacteristic
18#131×D43—21no—
19C4×Q8×D43—21no—
20#14583342C2211yescharacteristic
21#14583341C412yescomplemented
22#14583340C2211yescharacteristic
23#14583339C2211yescharacteristic
24#14583338C412yescomplemented
25Q32×D43C412yescomplemented
26SD32×D43C412yescomplemented
27M32×D43C2211yescharacteristic
28M32×D43C2211yescharacteristic
29#14583022C2211yescharacteristic
30#14583021C2211yescharacteristic
31#14583020C2211yescharacteristic
32#14583019—21no—
33#14583018—21no—
34#14583007C2211yescharacteristic, complemented
35#14583006C2211yescharacteristic, complemented
36#14583005C2211yescharacteristic, complemented
37#14583004—21no—
38#14583003—21no—
39#108×D43C2211yescharacteristic
40#106×D43C2211yescharacteristic
41#104×D43—21no—
42#103×D43—21no—
43#97×D43C2211yescharacteristic
44#14582723C2211yescharacteristic, complemented
45#14582722C2211yescharacteristic, complemented
46#14582721C2211yescharacteristic, complemented
47#14582716C2211yescharacteristic, complemented
48#14582715C2211yescharacteristic, complemented
49#14582714C2211yescharacteristic, complemented
50#14582710C2211yescharacteristic
51#14582709C2211yescharacteristic
52#14582708C2211yescharacteristic
53#14582677C2211yescharacteristic, complemented
54#14582676C2211yescharacteristic, complemented
55#14582676C2211yescharacteristic, complemented
56C43×#510C2211yescharacteristic
57C43×#444C2211yescharacteristic
58C43×#441C2211yescharacteristic, complemented
59C43×#365C2211yescharacteristic, complemented
60C43×#362C2211yescharacteristic, complemented
61C43×#360C2211yescharacteristic
62C43×#347C2211yescharacteristic, complemented
63#41×D43—21no—
64C2×Q8×D43—21no—
65#13063348C2×C411yescharacteristic
66#13063347C2311yescharacteristic
67#13063346—21no—
68#13063345—21no—
69#13063344C2×C411yescharacteristic
70C2×Dic172C2311yescharacteristic
71C2×#10621885—21no—
72Q16×D43—21no—
73Q16×D43—21no—
74Q16×D43C2×C412yes—
75Q16×D43C2×C411yescharacteristic
76Q16×D43C2×C412yes—
77SD16×D43—21no—
78D8×D43C2×C411yescharacteristic
79#13063333—21no—
80#13063333—41no—
81#13063332—21no—
82#13063331—21no—
83#13063331—41no—
84M16×D43—21no—
85M16×D43—41no—
86C2×C8×D43—41no—
87C2×C8×D43D411yescharacteristic
88C2×C8×D43C2311yescharacteristic
89Q8×Dic43—21no—
90C4×Dic86—21no—
91C4×Dic86—41no—
92#13063290—21no—
93#13063290—41no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—41no—
96C42×D43—41no—
97C42×D43D411yescharacteristic
98Dic344C2×C412yescomplemented
99#13063271C2×C412yescomplemented
100#13063271C2×C412yescomplemented
101#13063270C2×C412yescomplemented
102#13063269C2×C412yescomplemented
103#13063268C2×C412yescomplemented
104#13063265C2311yescharacteristic
105#13063265C2311yescharacteristic
106#13063264—21no—
107#13063264C2×C412yes—
108C16×D43—21no—
109C16×D43C2×C412yes—
110#13063261C2311yescharacteristic
111#13063260—21no—
112#13063257C2311yescharacteristic
113#13063256—21no—
114#13063253—21no—
115#13063252—21no—
116#13063251—21no—
117#13063250—21no—
118#13063249—21no—
119#13063248—21no—
120#13063236D411yescharacteristic
121#13063235D411yescharacteristic
122#13063235C2311yescharacteristic
123#135×C43C2311yescharacteristic
124C2×Q16×C43C2311yescharacteristic
125#131×C43—21no—
126C4×Q8×C43—21no—
127Q32×C43C2×C412yescomplemented
128SD32×C43C2×C412yescomplemented
129M32×C43C2311yescharacteristic
130M32×C43C2311yescharacteristic
131#108×C43C2311yescharacteristic
132#106×C43C2311yescharacteristic
133#104×C43—21no—
134#103×C43—21no—
135#97×C43C2311yescharacteristic
136#41×C43—21no—
137C2×Q8×C43—21no—
138#10621902—21no—
139Q8×D43—21no—
140Q8×D43—22no—
141Q8×D43—22no—
142Q8×D43—41no—
143Q8×D43—41no—
144#10621900—21no—
145#10621900—41no—
146D4×D43—21no—
147D4×D43—41no—
148#10621898—21no—
149#10621898—41no—
150C2×C4×D43—21no—
151C2×C4×D43—41no—
152C2×C4×D43—41no—
153C2×C4×D43—41no—
154C2×C4×D43C2×D411yescharacteristic
155C2×Dic86—21no—
156C2×Dic86—41no—
157Q16×C43—21no—
158Q16×C43C22×C412yes—
159Q16×C43C22×C411yescharacteristic
160SD16×C43—21no—
161D8×C43C22×C411yescharacteristic
162M16×C43—21no—
163M16×C43—41no—
164C2×C8×C43—41no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C42×C43—41no—
170C42×C43C2×D411yescharacteristic
171#10621885—22no—
172#10621885—22no—
173#10621885—21no—
174#10621884—21no—
175#10621883—21no—
176#10621882—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—41no—
179Dic43⋊C4—41no—
180Dic43⋊C4—41no—
181Dic43⋊C4—41no—
182C4×Dic43—21no—
183C4×Dic43—41no—
184C4×Dic43—41no—
185C4×Dic43—41no—
186C4×Dic43C2×D411yescharacteristic
187#10621877—21no—
188#10621877—41no—
189C2×C43⋊C8—41no—
190C2×C43⋊C8C2×D411yescharacteristic
191C2×C43⋊C8C2×D411yescharacteristic
192Dic172—21no—
193Dic172C22×C412yes—
194Dic172C22×C411yescharacteristic
195D344C22×C411yescharacteristic
196#10621873—21no—
197#10621872—41no—
198#10621872—41no—
199#10621872—41no—
200C8×D43—21no—
201C8×D43—21no—
202C8×D43—41no—
203C8×D43—41no—
204C8×D43—41no—
205C8×D43C22×C411yescharacteristic
206C8×D43C22×C411yescharacteristic
207C8×D43#4111yescharacteristic
208C8×D43#4111yescharacteristic
209C16×C43—21no—
210C16×C43C22×C412yes—
211C43⋊C16—21no—
212C43⋊C16C22×C412yes—
213C22×D43—41no—
214C22×D43AGL(1,ℤ/8)11yescharacteristic
215Q8×C43—21no—
216Q8×C43—22no—
217Q8×C43—41no—
218D4×C43—21no—
219D4×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C22×D411yescharacteristic
225C22⋊D43—41no—
226C22⋊D43—41no—
227C22⋊D43—41no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43AGL(1,ℤ/8)11yescharacteristic
233D172—21no—
234D172—41no—
235C4×D43—42no—
236C4×D43—41no—
237C4×D43—42no—
238C4×D43—42no—
239C4×D43—41no—
240C4×D43—41no—
241C4×D43—82no—
242C4×D43C4×D411yescharacteristic
243C4×D43C4×D411yescharacteristic
244C4×D43AGL(1,ℤ/8)11yescharacteristic
245C4×D43AGL(1,ℤ/8)11yescharacteristic
246Dic86—21no—
247Dic86—22no—
248Dic86—41no—
249Dic86—42no—
250Dic86—42no—
251Dic86—41no—
252C8×C43—21no—
253C8×C43—41no—
254C8×C43C23×C411yescharacteristic
255C8×C43C2×#4111yescharacteristic
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8C4×D411yescharacteristic
259C43⋊C8C4×D411yescharacteristic
260C2×#2180—431nomaximal, Sylow
261C22×C43—41no—
262C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
263C2×D43—22no—
264C2×D43—41no—
265C2×D43—82no—
266C2×D43#44211yescharacteristic
267C2×D43#44211yescharacteristic
268C4×C43—41no—
269C4×C43—42no—
270C4×C43—41no—
271C4×C43—81no—
272C4×C43C2×C4×D411yescharacteristic
273C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
274Dic43—41no—
275Dic43—42no—
276Dic43—41no—
277Dic43—81no—
278Dic43#44211yescharacteristic
279Dic43#44211yescharacteristic
280C2×#510—431no—
281C2×#444—431no—
282C2×#441—431no—
283#2180—431no—
284#2180—431no—
285#2180—431no—
286#2180—431no—
287#2180—431no—
288#2180—431no—
289#2180—431no—
290#2180D4311yescharacteristic, direct product factor
291C2×#365—431no—
292C2×#362—431no—
293C2×#360—431no—
294C2×#347—431no—
295C2×C43—21no—
296C2×C43—81no—
297C2×C43C2×#44211yescharacteristic
298D43—21no—
299D43—81no—
300D43#218012yesdirect product factor
301C2×#135—431no—
302C22×Q16—431no—
303C2×#131—861no—
304C2×C4×Q8—861no—
305#510—431no—
306#510—431no—
307#510—432no—
308#510—432no—
309#510—431no—
310#510C2×D4311yescharacteristic
311C2×Q32—432no—
312C2×SD32—432no—
313C2×M32—431no—
314C2×M32—431no—
315#444—431no—
316#444—431no—
317#444—431no—
318#444—861no—
319#444—861no—
320#444C2×D4311yescharacteristic
321#441—431no—
322#441—431no—
323#441—431no—
324#441—861no—
325#441—861no—
326#441C2×D4311yescharacteristic, complemented
327C2×#108—431no—
328C2×#106—431no—
329C2×#104—861no—
330C2×#103—861no—
331C2×#97—431no—
332#365—431no—
333#365—431no—
334#365—431no—
335#365C2×D4311yescharacteristic, complemented
336#362—431no—
337#362—431no—
338#362—431no—
339#362C2×D4311yescharacteristic, complemented
340#360—431no—
341#360—431no—
342#360—431no—
343#360C2×D4311yescharacteristic
344#347—431no—
345#347—431no—
346#347—431no—
347#347C2×D4311yescharacteristic, complemented
348C43C2×#218011yescharacteristic, complemented, Sylow
349C2×#41—861no—
350C22×Q8—861no—
351#135—431no—
352#135—431no—
353#135—431no—
354#135—861no—
355#135—861no—
356#135C22×D4311yescharacteristic
357C2×Q16—432no—
358C2×Q16—432no—
359C2×Q16—431no—
360C2×Q16—431no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×Q16—861no—
364C2×Q16C22×D4311yescharacteristic
365C2×SD16—861no—
366C2×D8—431no—
367#131—21no—
368#131—861no—
369#131—861no—
370#131—861no—
371#131—1721no—
372#131—1721no—
373C2×M16—861no—
374C2×M16—1721no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8—1721no—
378C4×Q8—21no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×Q8—1721no—
383C4×Q8—1721no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—1721no—
386C2×C42—431no—
387C2×C42—1721no—
388Q32—432no—
389Q32—432no—
390Q32—432no—
391Q32C4×D4312yescomplemented
392SD32—432no—
393SD32—432no—
394SD32—432no—
395SD32C4×D4312yescomplemented
396M32—431no—
397M32—432no—
398M32—431no—
399M32—861no—
400M32C22×D4311yescharacteristic
401M32C22×D4311yescharacteristic
402C2×C16—432no—
403C2×C16—861no—
404#108—431no—
405#108—861no—
406#108C22×D4311yescharacteristic
407#106—431no—
408#106—861no—
409#106C22×D4311yescharacteristic
410#104—21no—
411#104—861no—
412#104—861no—
413#104—861no—
414#103—21no—
415#103—861no—
416#103—861no—
417#103—861no—
418#97—431no—
419#97—431no—
420#97—431no—
421#97C22×D4311yescharacteristic
422#41—21no—
423#41—861no—
424#41—861no—
425#41—861no—
426#41—1721no—
427#41—1721no—
428C2×Q8—21no—
429C2×Q8—861no—
430C2×Q8—862no—
431C2×Q8—862no—
432C2×Q8—861no—
433C2×Q8—1721no—
434C2×Q8—1721no—
435C2×Q8—1721no—
436C2×D4—861no—
437C2×D4—1721no—
438C22×C4—431no—
439C22×C4—861no—
440C22×C4—1721no—
441C22×C4—1721no—
442C22×C4—1721no—
443Q16—21no—
444Q16—432no—
445Q16—431no—
446Q16—862no—
447Q16—862no—
448Q16—861no—
449Q16—861no—
450Q16C2×C4×D4312yes—
451Q16C2×C4×D4311yescharacteristic
452SD16—21no—
453SD16—861no—
454SD16—861no—
455SD16—861no—
456D8—431no—
457D8—861no—
458D8C2×C4×D4311yescharacteristic
459M16—21no—
460M16—41no—
461M16—861no—
462M16—1721no—
463M16—1721no—
464M16—1721no—
465M16—1721no—
466C2×C8—41no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—1721no—
476C2×C8—1721no—
477C2×C8—1721no—
478C2×C8—1721no—
479C2×C8D4×D4311yescharacteristic
480C2×C8C23×D4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—861no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C42—41no—
489C42—431no—
490C42—861no—
491C42—1721no—
492C42—1721no—
493C42—1721no—
494C42D4×D4311yescharacteristic
495C16—21no—
496C16—432no—
497C16—861no—
498C16C2×C4×D4312yes—
499C23—431no—
500C23—1721no—
501Q8—21no—
502Q8—22no—
503Q8—41no—
504Q8—861no—
505Q8—862no—
506Q8—1722no—
507Q8—1722no—
508Q8—1721no—
509Q8—1721no—
510D4—21no—
511D4—41no—
512D4—861no—
513D4—1721no—
514D4—1721no—
515D4—1721no—
516D4—1721no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—431no—
522C2×C4—431no—
523C2×C4—431no—
524C2×C4—431no—
525C2×C4—431no—
526C2×C4—861no—
527C2×C4—3442no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4C2×D4×D4311yescharacteristic
538C8—21no—
539C8—41no—
540C8—431no—
541C8—431no—
542C8—861no—
543C8—1721no—
544C8C22×C4×D4311yescharacteristic
545C8#41×D4311yescharacteristic
546C22—41no—
547C22—431no—
548C22—431no—
549C22—862no—
550C22—3442no—
551C22—1721no—
552C22AGL(1,ℤ/8)×D4311yescharacteristic
553C4—41no—
554C4—41no—
555C4—42no—
556C4—81no—
557C4—431no—
558C4—431no—
559C4—3441no—
560C4—1721no—
561C4—1721no—
562C4—1722no—
563C4C4×D4×D4311yescharacteristic
564C4AGL(1,ℤ/8)×D4311yescharacteristic
565C2—21no—
566C2—81no—
567C2—432no—
568C2—861no—
569C2—3441no—
570C2#442×D4311yescharacteristic
subgroupG/H
centerC2#442×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2180C2
socleC2×C43C2×#442
prime radical#135×D43C22
cosocleC2×C8×C43C24
hypercenter#2180D43
hypocenterC43C2×#2180
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #2180

Complements

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

NH ≅ G/Ntype
3. #441×D43C2semidirect
4. #19136489C2semidirect
5. #19136488C2semidirect
6. #19136487C2semidirect
7. #19136486C2semidirect
8. #19136485C2semidirect
9. #19136484C2semidirect
10. #19136483C2semidirect
11. #365×D43C2semidirect
12. #362×D43C2semidirect
14. #347×D43C2semidirect
15. C43×#2180C2semidirect
21. #14583341C4semidirect
24. #14583338C4semidirect
25. Q32×D43C4semidirect
26. SD32×D43C4semidirect
34. #14583007C22semidirect
35. #14583006C22semidirect
36. #14583005C22semidirect
44. #14582723C22semidirect
45. #14582722C22semidirect
46. #14582721C22semidirect
47. #14582716C22semidirect
48. #14582715C22semidirect
49. #14582714C22semidirect
53. #14582677C22semidirect
54. #14582676C22semidirect
55. #14582676C22semidirect
58. C43×#441C22semidirect
59. C43×#365C22semidirect
60. C43×#362C22semidirect
62. C43×#347C22semidirect
98. Dic344C2×C4semidirect
99. #13063271C2×C4semidirect
100. #13063271C2×C4semidirect
101. #13063270C2×C4semidirect
102. #13063269C2×C4semidirect
103. #13063268C2×C4semidirect
127. Q32×C43C2×C4semidirect
128. SD32×C43C2×C4semidirect
290. #2180D43direct (N × H)
300. D43#2180direct (N × H)
326. #441C2×D43semidirect
335. #365C2×D43semidirect
339. #362C2×D43semidirect
347. #347C2×D43semidirect
348. C43C2×#2180semidirect
391. Q32C4×D43semidirect
395. SD32C4×D43semidirect

Maximal subgroups

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

subgroupindex
#510×D432
#444×D432
#441×D432
#191364892
#191364882
#191364872
#191364862
#191364852
#191364842
#191364832
#365×D432
#362×D432
#360×D432
#347×D432
C43×#21802
C2×#218043