Finite Group Databasebeta

← D43×#1720 #25084357

Subgroups — D43×#1720 #25084357

Order 11008.

850 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#498×D43C211yesmaximal, characteristic, complemented
2#494×D43C211yesmaximal, characteristic, complemented
3#487×D43C211yesmaximal, characteristic, complemented
4#486×D43C211yesmaximal, characteristic
5#486×D43C211yesmaximal, characteristic
6#486×D43C211yesmaximal, characteristic
7#19134258C211yesmaximal, characteristic, complemented
8#19134257C211yesmaximal, characteristic, complemented
9#19134256C211yesmaximal, characteristic, complemented
10#19134255C211yesmaximal, characteristic, complemented
11#19134254C211yesmaximal, characteristic, complemented
12#19134253C211yesmaximal, characteristic, complemented
13#19134252C211yesmaximal, characteristic, complemented
14#322×D43C211yesmaximal, characteristic, complemented
15C43×#1720C211yesmaximal, characteristic, complemented
16C2×Q16×D43—22no—
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#127×D43C2211yescharacteristic
21#14583297C2211yescharacteristic, complemented
22#14583296—22no—
23#14583295C2211yescharacteristic, complemented
24#14583295C2211yescharacteristic, complemented
25#14583279C2211yescharacteristic, complemented
26#14583278C2211yescharacteristic, complemented
27#14583278C2211yescharacteristic, complemented
28#14583277—22no—
29#14583251C2211yescharacteristic, complemented
30#14583250C2211yescharacteristic, complemented
31#14583249C2211yescharacteristic, complemented
32#14583248—22no—
33#14583247C2211yescharacteristic
34#14583247C2211yescharacteristic
35#14583247C2211yescharacteristic
36#14583246C2211yescharacteristic
37#14583246C2211yescharacteristic
38#14583246C2211yescharacteristic
39#14583245C2211yescharacteristic
40#14583245C2211yescharacteristic
41#14583245C2211yescharacteristic
42#14583244—22no—
43#14583244—22no—
44#14583244—22no—
45#106×D43—22no—
46#103×D43—22no—
47#102×D43—22no—
48#102×D43—22no—
49#102×D43—22no—
50C4×C8×D43C2211yescharacteristic
51C4×C8×D43C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic, complemented
54#14582621C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C43×#498C2211yescharacteristic, complemented
57C43×#494C2211yescharacteristic, complemented
58C43×#487C2211yescharacteristic, complemented
59C43×#486C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#322C2211yescharacteristic, complemented
63C2×Q8×D43—21no—
64C2×Q8×D43—21no—
65C2×Q8×D43—21no—
66C2×D4×D43—21no—
67C2×D4×D43—21no—
68C2×D4×D43—21no—
69C2×Dic172—22no—
70C2×#10621885—22no—
71C2×#10621885—22no—
72Q16×D43—48no—
73C2×C8×D43D412yes—
74C2×C8×D43D412yes—
75C2×C8×D43D412yes—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063324—21no—
81#13063324—21no—
82#13063324—21no—
83#13063324—21no—
84#13063324—21no—
85#13063323—21no—
86#13063323—21no—
87#13063323—21no—
88#13063322C2311yescharacteristic
89#13063321—21no—
90#13063321—21no—
91#13063321—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C42×D43C2311yescharacteristic
99#13063257—22no—
100#13063256—22no—
101#13063256—22no—
102#13063250—22no—
103#13063249—22no—
104#13063248—22no—
105#13063247—22no—
106#13063247—22no—
107#13063247—22no—
108#13063246—22no—
109#13063246—22no—
110#13063246—22no—
111#13063245—22no—
112#13063245—22no—
113#13063245—22no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C8×Dic43D412yes—
118C8×Dic43D412yes—
119C8×Dic43D412yes—
120C2×Q16×C43—22no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124#127×C43C2311yescharacteristic
125#106×C43—22no—
126#103×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C4×C8×C43C2311yescharacteristic
133C23×D43—41no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×C22⋊D43—41no—
141C2×C22⋊D43—41no—
142C2×C22⋊D43—41no—
143Q8×D43—44no—
144Q8×D43—44no—
145Q8×D43—44no—
146D4×D43—44no—
147D4×D43—44no—
148D4×D43—44no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×C4×D43—41no—
153C2×C4×D43—41no—
154C2×C4×D43—41no—
155C2×C4×D43C2×D411yescharacteristic
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86—41no—
163C2×Dic86—41no—
164Q16×C43—44no—
165C2×C8×C43C2×D412yes—
166C2×C8×C43C2×D412yes—
167C2×C8×C43C2×D412yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C42×C43C2411yescharacteristic
175#10621885—44no—
176#10621885—44no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183Dic43⋊C4—41no—
184Dic43⋊C4—41no—
185Dic43⋊C4—41no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189C4×Dic43C2×D411yescharacteristic
190C4×Dic43C2×D411yescharacteristic
191C4×Dic43C2×D411yescharacteristic
192C2×C43⋊C8C2×D412yes—
193C2×C43⋊C8C2×D412yes—
194C2×C43⋊C8C2×D412yes—
195Dic172—44no—
196C8×D43—24no—
197C8×D43—24no—
198C8×D43—24no—
199C23×C43—41no—
200C22×D43—41no—
201C22×D43—82no—
202C22×D43—82no—
203C22×D43—82no—
204C22×D43#12711yescharacteristic
205Q8×C43—42no—
206Q8×C43—42no—
207Q8×C43—42no—
208D4×C43—42no—
209D4×C43—42no—
210D4×C43—42no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C22⋊D43—82no—
218C22⋊D43—82no—
219C22⋊D43—82no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43#12711yescharacteristic
224C2×Dic43#12711yescharacteristic
225C2×Dic43#12711yescharacteristic
226D172—42no—
227D172—42no—
228D172—42no—
229C4×D43—82no—
230C4×D43—82no—
231C4×D43—82no—
232C4×D43#13514yes—
233C4×D43AGL(1,ℤ/8)14yes—
234C4×D43#13714yes—
235Dic86—42no—
236Dic86—42no—
237Dic86—42no—
238Dic86—82no—
239Dic86—82no—
240Dic86—82no—
241C8×C43—22no—
242C8×C43—22no—
243C8×C43—22no—
244C43⋊C8—22no—
245C43⋊C8—22no—
246C43⋊C8—22no—
247C2×#1720—431nomaximal, Sylow
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43C2×#12711yescharacteristic
252C2×D43—81no—
253C2×D43—81no—
254C2×D43—81no—
255C2×D43—164no—
256C2×D43#49512yes—
257C2×D43#49612yes—
258C2×D43#49712yes—
259C4×C43—81no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43C2×#13512yes—
263C4×C43C2×AGL(1,ℤ/8)12yes—
264C4×C43C2×#13712yes—
265Dic43—81no—
266Dic43—81no—
267Dic43—81no—
268Dic43#49512yes—
269Dic43#49612yes—
270Dic43#49712yes—
271C2×#498—431no—
272C2×#494—431no—
273C2×#487—431no—
274C2×#486—431no—
275C2×#486—431no—
276C2×#486—431no—
277#1720—431no—
278#1720—431no—
279#1720—431no—
280#1720—431no—
281#1720—431no—
282#1720—431no—
283#1720—431no—
284#1720D4311yescharacteristic, direct product factor
285C2×#322—431no—
286C2×C43—161no—
287C2×C43C2×#49511yescharacteristic
288C2×C43C2×#49611yescharacteristic
289C2×C43C2×#49711yescharacteristic
290D43—161no—
291D43#172014yesdirect product factor
292C22×Q16—862no—
293C2×C4⋊Q8—431no—
294C2×C4⋊Q8—431no—
295C2×C4⋊Q8—431no—
296C2×#127—431no—
297#498—431no—
298#498—431no—
299#498—431no—
300#498—862no—
301#498C2×D4311yescharacteristic, complemented
302#494—431no—
303#494—431no—
304#494—431no—
305#494—862no—
306#494C2×D4311yescharacteristic, complemented
307#487—431no—
308#487—431no—
309#487—431no—
310#487—862no—
311#487C2×D4311yescharacteristic, complemented
312#486—431no—
313#486—431no—
314#486—431no—
315#486—431no—
316#486—431no—
317#486—431no—
318#486—431no—
319#486—431no—
320#486—431no—
321#486—862no—
322#486—862no—
323#486—862no—
324#486C2×D4311yescharacteristic
325#486C2×D4311yescharacteristic
326#486C2×D4311yescharacteristic
327C2×#106—862no—
328C2×#103—862no—
329C2×#102—862no—
330C2×#102—862no—
331C2×#102—862no—
332C2×C4×C8—431no—
333C2×C4×C8—431no—
334C2×C4×C8—431no—
335#322—431no—
336#322—431no—
337#322—431no—
338#322C2×D4311yescharacteristic, complemented
339C43C2×#172011yescharacteristic, complemented, Sylow
340C22×Q8—861no—
341C22×Q8—861no—
342C22×Q8—861no—
343C22×D4—861no—
344C22×D4—861no—
345C22×D4—861no—
346C2×Q16—22no—
347C2×Q16—862no—
348C2×Q16—862no—
349C2×Q16—862no—
350C2×Q16—1728no—
351C22×C8—432no—
352C22×C8—432no—
353C22×C8—432no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—861no—
358C4⋊Q8—861no—
359C4⋊Q8—861no—
360C4⋊Q8—861no—
361C4⋊Q8—861no—
362C4⋊Q8—861no—
363C4⋊Q8—861no—
364C4⋊Q8—861no—
365C4⋊Q8—861no—
366C4⋊Q8C22×D4311yescharacteristic
367C4⋊Q8C22×D4311yescharacteristic
368C4⋊Q8C22×D4311yescharacteristic
369#127—431no—
370#127—861no—
371#127—861no—
372#127—861no—
373#127C22×D4311yescharacteristic
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C42—431no—
381#106—22no—
382#106—862no—
383#106—862no—
384#106—862no—
385#103—22no—
386#103—862no—
387#103—862no—
388#103—862no—
389#102—22no—
390#102—22no—
391#102—22no—
392#102—862no—
393#102—862no—
394#102—862no—
395#102—862no—
396#102—862no—
397#102—862no—
398#102—862no—
399#102—862no—
400#102—862no—
401C4×C8—432no—
402C4×C8—432no—
403C4×C8—432no—
404C4×C8—431no—
405C4×C8—431no—
406C4×C8—431no—
407C4×C8C22×D4311yescharacteristic
408C4×C8C22×D4311yescharacteristic
409C4×C8C22×D4311yescharacteristic
410C24—1721no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—861no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×Q8—1721no—
418C2×Q8—1721no—
419C2×Q8—1721no—
420C2×Q8—1724no—
421C2×Q8—1724no—
422C2×Q8—1724no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—861no—
427C2×D4—861no—
428C2×D4—861no—
429C2×D4—1724no—
430C2×D4—1724no—
431C2×D4—1724no—
432C2×D4—1721no—
433C2×D4—1721no—
434C2×D4—1721no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—1721no—
439C22×C4—1721no—
440C22×C4—1721no—
441Q16—44no—
442Q16—1724no—
443Q16—1724no—
444Q16—1724no—
445C2×C8—432no—
446C2×C8—432no—
447C2×C8—432no—
448C2×C8—864no—
449C2×C8—864no—
450C2×C8—864no—
451C2×C8D4×D4312yes—
452C2×C8D4×D4312yes—
453C2×C8D4×D4312yes—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C42—431no—
473C42—431no—
474C42—431no—
475C42C23×D4311yescharacteristic
476C23—41no—
477C23—431no—
478C23—3442no—
479C23—3442no—
480C23—3442no—
481C23—1721no—
482Q8—42no—
483Q8—42no—
484Q8—42no—
485Q8—3442no—
486Q8—3442no—
487Q8—3442no—
488Q8—1722no—
489Q8—1722no—
490Q8—1722no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—3442no—
495D4—3442no—
496D4—3442no—
497D4—1722no—
498D4—1722no—
499D4—1722no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—431no—
504C2×C4—431no—
505C2×C4—431no—
506C2×C4—434no—
507C2×C4—434no—
508C2×C4—434no—
509C2×C4—3442no—
510C2×C4—3442no—
511C2×C4—3442no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C2×D4×D4311yescharacteristic
517C2×C4C2×D4×D4311yescharacteristic
518C8—22no—
519C8—22no—
520C8—22no—
521C8—862no—
522C8—862no—
523C8—862no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—432no—
528C22—432no—
529C22—432no—
530C22—3441no—
531C22—3441no—
532C22—3441no—
533C22—6884no—
534C22#127×D4311yescharacteristic
535C4—81no—
536C4—81no—
537C4—81no—
538C4—432no—
539C4—432no—
540C4—432no—
541C4—3441no—
542C4—3441no—
543C4—3441no—
544C4#135×D4312yes—
545C4AGL(1,ℤ/8)×D4312yes—
546C4#137×D4312yes—
547C2—161no—
548C2—434no—
549C2—6881no—
550C2#495×D4311yescharacteristic
551C2#496×D4311yescharacteristic
552C2#497×D4311yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1720C2
socleC22×C43C2×#127
prime radical#127×D43C22
hypercenter#1720D43
hypocenterC43C2×#1720
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1720

Complements

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

NH ≅ G/Ntype
1. #498×D43C2semidirect
2. #494×D43C2semidirect
3. #487×D43C2semidirect
7. #19134258C2semidirect
8. #19134257C2semidirect
9. #19134256C2semidirect
10. #19134255C2semidirect
11. #19134254C2semidirect
12. #19134253C2semidirect
13. #19134252C2semidirect
14. #322×D43C2semidirect
15. C43×#1720C2semidirect
21. #14583297C22semidirect
23. #14583295C22semidirect
24. #14583295C22semidirect
25. #14583279C22semidirect
26. #14583278C22semidirect
27. #14583278C22semidirect
29. #14583251C22semidirect
30. #14583250C22semidirect
31. #14583249C22semidirect
53. #14582621C22semidirect
54. #14582621C22semidirect
55. #14582620C22semidirect
56. C43×#498C22semidirect
57. C43×#494C22semidirect
58. C43×#487C22semidirect
62. C43×#322C22semidirect
284. #1720D43direct (N × H)
291. D43#1720direct (N × H)
301. #498C2×D43semidirect
306. #494C2×D43semidirect
311. #487C2×D43semidirect
338. #322C2×D43semidirect
339. C43C2×#1720semidirect

Maximal subgroups

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

subgroupindex
#498×D432
#494×D432
#487×D432
#486×D432
#191342582
#191342572
#191342562
#191342552
#191342542
#191342532
#191342522
#322×D432
C43×#17202
C2×#172043