Finite Group Databasebeta

← D43×#2217 #25251023

Subgroups — D43×#2217 #25251023

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D43C211yesmaximal, characteristic, complemented
2C22×C16×D43C211yesmaximal, characteristic, complemented
3#467×D43C211yesmaximal, characteristic, complemented
4#466×D43C211yesmaximal, characteristic
5#19136694C211yesmaximal, characteristic, complemented
6#19136693C211yesmaximal, characteristic, complemented
7#19136692C211yesmaximal, characteristic, complemented
8#19136691C211yesmaximal, characteristic, complemented
9#19136690C211yesmaximal, characteristic, complemented
10#19136689C211yesmaximal, characteristic, complemented
11#19136688C211yesmaximal, characteristic, complemented
12#367×D43C211yesmaximal, characteristic, complemented
13#358×D43C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2217C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C22⋊Q8×D43—21no—
20#121×D43—21no—
21C2×#13063270C2211yescharacteristic, complemented
22C2×#13063269C2211yescharacteristic, complemented
23C2×#13063268C2211yescharacteristic, complemented
24SD32×D43—24no—
25C22×C43⋊C16C2211yescharacteristic, complemented
26C2×C16×D43—24no—
27C2×C16×D43C2211yescharacteristic
28C2×C16×D43C2211yescharacteristic
29C2×C16×D43C2211yescharacteristic, complemented
30C2×C16×D43C2211yescharacteristic, complemented
31#14583141C2211yescharacteristic, complemented
32#14583140C2211yescharacteristic, complemented
33#14583139—21no—
34#14583138—21no—
35#14583137C2211yescharacteristic, complemented
36#14583136C2211yescharacteristic
37#14583135C2211yescharacteristic
38#14583134—21no—
39#14583133—21no—
40#14583132C2211yescharacteristic
41#107×D43C2211yescharacteristic
42#107×D43C2211yescharacteristic
43#103×D43—21no—
44#102×D43—21no—
45#14582727C2211yescharacteristic, complemented
46#14582726C2211yescharacteristic, complemented
47#14582726C2211yescharacteristic, complemented
48#14582704C2211yescharacteristic, complemented
49#14582703C2211yescharacteristic, complemented
50#14582702C2211yescharacteristic, complemented
51#14582701C2211yescharacteristic, complemented
52#14582700C2211yescharacteristic, complemented
53#14582699C2211yescharacteristic, complemented
54C2×SD32×C43C2211yescharacteristic, complemented
55C22×C16×C43C2211yescharacteristic, complemented
56C43×#467C2211yescharacteristic, complemented
57C43×#466C2211yescharacteristic
58C43×#367C2211yescharacteristic, complemented
59C43×#358C2211yescharacteristic, complemented
60C43×#357C2211yescharacteristic, complemented
61C2×Q8×D43—21no—
62C2×D4×D43—21no—
63C2×D4×D43—41no—
64C22×C4×D43D411yescharacteristic
65C2×Dic172C2311yescharacteristic
66C2×#10621885—21no—
67Q16×D43—22no—
68Q16×D43—22no—
69C2×D344C2311yescharacteristic
70C2×#10621882—21no—
71D8×D43—22no—
72D8×D43—22no—
73C22×C43⋊C8D411yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43D411yescharacteristic
77C2×C8×D43D411yescharacteristic
78C2×C8×D43C2311yescharacteristic
79C2×C8×D43C2311yescharacteristic
80#13063305—21no—
81#13063304—21no—
82#13063303—41no—
83#13063302—41no—
84#13063301—21no—
85#13063300—21no—
86#13063299—21no—
87#13063298—41no—
88#13063297—41no—
89#13063296—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—41no—
93C22⋊C4×D43—41no—
94C22⋊C4×D43—41no—
95#13063270—22no—
96#13063269—22no—
97#13063268—22no—
98C2×C43⋊C16—22no—
99C2×C43⋊C16C2311yescharacteristic
100C2×C43⋊C16C2311yescharacteristic
101C16×D43—22no—
102C16×D43—22no—
103C16×D43—22no—
104C16×D43D414yescomplemented
105#13063259C2311yescharacteristic
106#13063259C2311yescharacteristic
107#13063258—21no—
108#13063258—21no—
109#13063250—21no—
110#13063249—21no—
111#13063248—21no—
112#13063247—21no—
113#13063246—21no—
114#13063245—21no—
115C2×Q16×C43C2311yescharacteristic
116C2×D8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22⋊Q8×C43—21no—
119#121×C43—21no—
120SD32×C43—22no—
121C2×C16×C43—22no—
122C2×C16×C43C2311yescharacteristic
123C2×C16×C43C2311yescharacteristic
124#107×C43C2311yescharacteristic
125#107×C43C2311yescharacteristic
126#103×C43—21no—
127#102×C43—21no—
128C23×D43—41no—
129C23×D43D811yescharacteristic
130C2×Q8×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—41no—
133C22×C4×C43C2×D411yescharacteristic
134C2×C22⋊D43—41no—
135C2×C22⋊D43—41no—
136C2×C22⋊D43—41no—
137C22×Dic43D811yescharacteristic
138Q8×D43—42no—
139Q8×D43—42no—
140D4×D43—42no—
141D4×D43—42no—
142D4×D43—84no—
143C2×D172—21no—
144C2×D172—41no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43D811yescharacteristic
151C2×C4×D43D811yescharacteristic
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43C2×D411yescharacteristic
154C2×Dic86—21no—
155C2×Dic86—41no—
156Q16×C43—21no—
157Q16×C43—21no—
158D8×C43—21no—
159D8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C22⋊Dic43—41no—
170C22⋊Dic43—41no—
171#10621885—42no—
172#10621882—42no—
173(C2×D43)⋊C4—41no—
174(C2×D43)⋊C4—41no—
175(C2×D43)⋊C4—41no—
176(C2×D43)⋊C4—41no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—41no—
180Dic43⋊C4—41no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183Dic43⋊C4—41no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8C2×D411yescharacteristic
186C2×C43⋊C8C2×D411yescharacteristic
187Dic172—21no—
188Dic172—21no—
189D344—21no—
190D344—21no—
191C8×D43—22no—
192C8×D43—21no—
193C8×D43—21no—
194C8×D43—22no—
195C8×D43C2×D412yes—
196C8×D43#4112yes—
197C16×C43—21no—
198C16×C43C2×D412yescomplemented
199C43⋊C16—21no—
200C43⋊C16C2×D412yescomplemented
201C23×C43—41no—
202C23×C43C2×D811yescharacteristic
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—41no—
206C22×D43—82no—
207C22×D43—82no—
208C22×D43—82no—
209C22×D43SD3214yescomplemented
210C22×D43C2×D811yescharacteristic
211C22×D43C2×D811yescharacteristic
212Q8×C43—41no—
213Q8×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—82no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C2×D811yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C22⋊D43—82no—
225C22⋊D43—82no—
226C22⋊D43—82no—
227C2×Dic43—22no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43C2×D811yescharacteristic
232C2×Dic43C2×D811yescharacteristic
233D172—41no—
234D172—41no—
235D172—82no—
236C4×D43—22no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—22no—
240C4×D43—82no—
241C4×D43—82no—
242C4×D43—82no—
243C4×D43#12112yes—
244C4×D43#13512yes—
245Dic86—41no—
246Dic86—41no—
247Dic86—82no—
248C8×C43—21no—
249C8×C43C22×D411yescharacteristic
250C8×C43C2×#4111yescharacteristic
251C43⋊C8—21no—
252C43⋊C8#12112yes—
253C2×#2217—431nomaximal, Sylow
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43C2×SD3212yescomplemented
260C22×C43C22×D811yescharacteristic
261C2×D43—21no—
262C2×D43—21no—
263C2×D43—28no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—164no—
268C2×D43#46612yes—
269C2×D43C2×SD3212yes—
270C2×D43C2×SD3212yescomplemented
271C2×D43#50812yes—
272C4×C43—21no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43C2×#12111yescharacteristic
277C4×C43C2×#13511yescharacteristic
278Dic43—21no—
279Dic43—81no—
280Dic43—81no—
281Dic43—81no—
282Dic43#46612yes—
283C22×SD32—431no—
284C23×C16—431no—
285C2×#467—431no—
286C2×#466—431no—
287#2217—431no—
288#2217—431no—
289#2217—431no—
290#2217—431no—
291#2217—431no—
292#2217—431no—
293#2217—431no—
294#2217D4311yescharacteristic, direct product factor
295C2×#367—431no—
296C2×#358—431no—
297C2×#357—431no—
298C2×C43—22no—
299C2×C43—161no—
300C2×C43C2×#46611yescharacteristic
301C2×C43C22×SD3211yescharacteristic
302C2×C43C2×#50811yescharacteristic
303D43—22no—
304D43—161no—
305D43#221714yesdirect product factor
306C22×Q16—431no—
307C22×D8—431no—
308C23×C8—431no—
309C2×C22⋊Q8—861no—
310C2×#121—861no—
311C2×SD32—431no—
312C2×SD32—431no—
313C2×SD32—431no—
314C2×SD32—864no—
315C2×SD32C2×D4311yescharacteristic, complemented
316C22×C16—431no—
317C22×C16—431no—
318C22×C16—431no—
319C22×C16—431no—
320C22×C16—431no—
321C22×C16—864no—
322C22×C16C2×D4311yescharacteristic, complemented
323#467—431no—
324#467—431no—
325#467—431no—
326#467—861no—
327#467—861no—
328#467C2×D4311yescharacteristic, complemented
329#466—431no—
330#466—431no—
331#466—431no—
332#466—861no—
333#466—861no—
334#466C2×D4311yescharacteristic
335C2×#107—431no—
336C2×#107—431no—
337C2×#103—861no—
338C2×#102—861no—
339#367—431no—
340#367—431no—
341#367—431no—
342#367C2×D4311yescharacteristic, complemented
343#358—431no—
344#358—431no—
345#358—431no—
346#358C2×D4311yescharacteristic, complemented
347#357—431no—
348#357—431no—
349#357—431no—
350#357C2×D4311yescharacteristic, complemented
351C43C2×#221711yescharacteristic, complemented, Sylow
352C22×Q8—861no—
353C22×D4—861no—
354C22×D4—1721no—
355C23×C4—431no—
356C2×Q16—431no—
357C2×Q16—862no—
358C2×Q16—862no—
359C2×Q16—861no—
360C2×Q16C22×D4311yescharacteristic
361C2×D8—431no—
362C2×D8—862no—
363C2×D8—862no—
364C2×D8—861no—
365C2×D8C22×D4311yescharacteristic
366C22×C8—431no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8—431no—
370C22×C8—431no—
371C22×C8—862no—
372C22×C8—862no—
373C22×C8C22×D4311yescharacteristic
374C22⋊Q8—21no—
375C22⋊Q8—861no—
376C22⋊Q8—861no—
377C22⋊Q8—861no—
378C22⋊Q8—1721no—
379C22⋊Q8—1721no—
380#121—21no—
381#121—861no—
382#121—861no—
383#121—861no—
384#121—1721no—
385#121—1721no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—1721no—
389C2×C22⋊C4—1721no—
390C2×C22⋊C4—1721no—
391SD32—22no—
392SD32—862no—
393SD32—862no—
394SD32—862no—
395C2×C16—22no—
396C2×C16—431no—
397C2×C16—434no—
398C2×C16—431no—
399C2×C16—862no—
400C2×C16—862no—
401C2×C16—862no—
402C2×C16—862no—
403C2×C16C22×D4311yescharacteristic
404C2×C16C22×D4311yescharacteristic
405#107—431no—
406#107—431no—
407#107—861no—
408#107—861no—
409#107C22×D4311yescharacteristic
410#107C22×D4311yescharacteristic
411#103—21no—
412#103—861no—
413#103—861no—
414#103—861no—
415#102—21no—
416#102—861no—
417#102—861no—
418#102—861no—
419C24—431no—
420C24—1721no—
421C2×Q8—21no—
422C2×Q8—861no—
423C2×Q8—1721no—
424C2×Q8—1722no—
425C2×Q8—1722no—
426C2×D4—21no—
427C2×D4—41no—
428C2×D4—861no—
429C2×D4—3444no—
430C2×D4—1721no—
431C2×D4—1722no—
432C2×D4—1722no—
433C2×D4—1721no—
434C2×D4—1721no—
435C2×D4—1721no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4D4×D4311yescharacteristic
447Q16—21no—
448Q16—21no—
449Q16—861no—
450Q16—861no—
451Q16—1722no—
452D8—21no—
453D8—21no—
454D8—861no—
455D8—861no—
456D8—1722no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—431no—
460C2×C8—432no—
461C2×C8—432no—
462C2×C8—431no—
463C2×C8—862no—
464C2×C8—862no—
465C2×C8—862no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8D4×D4311yescharacteristic
469C2×C8C23×D4311yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—41no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—1721no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—1721no—
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C22⋊C4—1721no—
488C16—21no—
489C16—432no—
490C16—861no—
491C16D4×D4312yescomplemented
492C23—41no—
493C23—431no—
494C23—434no—
495C23—431no—
496C23—862no—
497C23—862no—
498C23—3442no—
499C23—3442no—
500C23—3442no—
501C23—1721no—
502C23D8×D4311yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—3442no—
506Q8—1721no—
507Q8—1721no—
508D4—41no—
509D4—41no—
510D4—82no—
511D4—3442no—
512D4—3442no—
513D4—3442no—
514D4—3442no—
515D4—1721no—
516D4—1721no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—431no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—431no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—3442no—
532C2×C4—3442no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4D8×D4311yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C8—21no—
540C8—432no—
541C8—861no—
542C8C2×D4×D4311yescharacteristic
543C8#41×D4311yescharacteristic
544C22—21no—
545C22—21no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—432no—
550C22—432no—
551C22—432no—
552C22—432no—
553C22—868no—
554C22—861no—
555C22—861no—
556C22—3441no—
557C22—3441no—
558C22—3441no—
559C22—6884no—
560C22SD32×D4312yescomplemented
561C22C2×D8×D4311yescharacteristic
562C4—21no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—432no—
567C4—861no—
568C4—3441no—
569C4—3441no—
570C4—3441no—
571C4#121×D4311yescharacteristic
572C4#135×D4311yescharacteristic
573C2—22no—
574C2—161no—
575C2—434no—
576C2—862no—
577C2—6881no—
578C2#466×D4311yescharacteristic
579C2C2×SD32×D4311yescharacteristic
580C2#508×D4311yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2217C2
socleC22×C43C22×D8
prime radical#466×D43C2
hypercenter#2217D43
hypocenterC43C2×#2217
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. C2×SD32×D43C2semidirect
2. C22×C16×D43C2semidirect
3. #467×D43C2semidirect
5. #19136694C2semidirect
6. #19136693C2semidirect
7. #19136692C2semidirect
8. #19136691C2semidirect
9. #19136690C2semidirect
10. #19136689C2semidirect
11. #19136688C2semidirect
12. #367×D43C2semidirect
13. #358×D43C2semidirect
14. #357×D43C2semidirect
15. C43×#2217C2semidirect
21. C2×#13063270C22semidirect
22. C2×#13063269C22semidirect
23. C2×#13063268C22semidirect
25. C22×C43⋊C16C22semidirect
29. C2×C16×D43C22semidirect
30. C2×C16×D43C22semidirect
31. #14583141C22semidirect
32. #14583140C22semidirect
35. #14583137C22semidirect
45. #14582727C22semidirect
46. #14582726C22semidirect
47. #14582726C22semidirect
48. #14582704C22semidirect
49. #14582703C22semidirect
50. #14582702C22semidirect
51. #14582701C22semidirect
52. #14582700C22semidirect
53. #14582699C22semidirect
54. C2×SD32×C43C22semidirect
55. C22×C16×C43C22semidirect
56. C43×#467C22semidirect
58. C43×#367C22semidirect
59. C43×#358C22semidirect
60. C43×#357C22semidirect
104. C16×D43D4semidirect
198. C16×C43C2×D4semidirect
200. C43⋊C16C2×D4semidirect
209. C22×D43SD32semidirect
259. C22×C43C2×SD32semidirect
270. C2×D43C2×SD32semidirect
294. #2217D43direct (N × H)
305. D43#2217direct (N × H)
315. C2×SD32C2×D43semidirect
322. C22×C16C2×D43semidirect
328. #467C2×D43semidirect
342. #367C2×D43semidirect
346. #358C2×D43semidirect
350. #357C2×D43semidirect
351. C43C2×#2217semidirect
491. C16D4×D43semidirect
560. C22SD32×D43semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D432
C22×C16×D432
#467×D432
#466×D432
#191366942
#191366932
#191366922
#191366912
#191366902
#191366892
#191366882
#367×D432
#358×D432
#357×D432
C43×#22172
C2×#221743