Finite Group Databasebeta

← D43×#1682 #25078985

Subgroups — D43×#1682 #25078985

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#486×D43C211yesmaximal, characteristic
2#462×D43C211yesmaximal, characteristic, complemented
3#460×D43C211yesmaximal, characteristic
4C8×Q8×D43C211yesmaximal, characteristic, complemented
5#19134042C211yesmaximal, characteristic, complemented
6#19134041C211yesmaximal, characteristic, complemented
7#19134040C211yesmaximal, characteristic, complemented
8#19134039C211yesmaximal, characteristic, complemented
9#19134038C211yesmaximal, characteristic, complemented
10#19134037C211yesmaximal, characteristic, complemented
11#19134036C211yesmaximal, characteristic, complemented
12#335×D43C211yesmaximal, characteristic, complemented
13#332×D43C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic
15C43×#1682C211yesmaximal, characteristic, complemented
16C2×Q16×D43—21no—
17C2×SD16×D43—21no—
18C4⋊Q8×D43C2211yescharacteristic
19#127×D43C2211yescharacteristic
20C4×Q8×D43C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583244—21no—
25#14583244—21no—
26#14583110C2211yescharacteristic, complemented
27#14583109C2211yescharacteristic, complemented
28#14583108—21no—
29#14583107—21no—
30#14583106C2211yescharacteristic, complemented
31#14583100C2211yescharacteristic
32#14583099C2211yescharacteristic
33#14583098—21no—
34#14583097—21no—
35#14583096C2211yescharacteristic
36Q8×C43⋊C8C2211yescharacteristic, complemented
37C8×Dic86—21no—
38C8×Dic86C2211yescharacteristic, complemented
39#14583023—21no—
40#14583023C2211yescharacteristic, complemented
41C4⋊C8×D43—21no—
42C4⋊C8×D43C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#103×D43—21no—
46#102×D43—21no—
47#102×D43—21no—
48#102×D43—21no—
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582645C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#462C2211yescharacteristic, complemented
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43D411yescharacteristic
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43—21no—
72C2×Dic172—21no—
73C2×#10621885—21no—
74C2×#10621885—21no—
75Q16×D43—44no—
76C2×#10621873—21no—
77C2×#10621883—21no—
78C2×#10621884—21no—
79SD16×D43—44no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83C2×C8×D43D411yescharacteristic
84C2×C8×D43D411yescharacteristic
85#13063325C2311yescharacteristic
86#13063324—21no—
87#13063324—21no—
88#13063323—21no—
89#13063322C2311yescharacteristic
90#13063321—21no—
91#13063321—21no—
92#13063321—21no—
93Q8×Dic43D411yescharacteristic
94C4×Dic86—21no—
95C4×Dic86C2311yescharacteristic
96#13063290—21no—
97#13063290D411yescharacteristic
98C4⋊C4×D43—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43D411yescharacteristic
102C42×D43—21no—
103C42×D43C2311yescharacteristic
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063250—21no—
114#13063249—21no—
115#13063248—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063246—21no—
120#13063246—21no—
121#13063246—21no—
122#13063245—21no—
123#13063245—21no—
124#13063245—21no—
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C2×Q16×C43—21no—
132C2×SD16×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×Q8×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144C4×C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155Q8×D43—22no—
156Q8×D43—42no—
157Q8×D43—42no—
158Q8×D43D814yes—
159D4×D43—42no—
160D4×D43—42no—
161D4×D43—42no—
162D4×D43—42no—
163D4×D43—82no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—41no—
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43#4111yescharacteristic
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—41no—
176C2×Dic86C2×D411yescharacteristic
177Q16×C43—42no—
178SD16×C43—42no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43C2×D411yescharacteristic
188C42×C43—21no—
189C42×C43C2411yescharacteristic
190#10621885—42no—
191#10621885—42no—
192#10621884—42no—
193#10621883—42no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43C2×D411yescharacteristic
207C4×Dic43C2×D411yescharacteristic
208C4×Dic43#4111yescharacteristic
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214Dic172—42no—
215#10621873—42no—
216C8×D43—22no—
217C8×D43—22no—
218C8×D43—42no—
219C8×D43—42no—
220C8×D43—42no—
221C23×C43—41no—
222C22×D43—41no—
223C22×D43—82no—
224C22×D43—82no—
225C22×D43—82no—
226C22×D43#12111yescharacteristic
227Q8×C43—21no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43C2×D812yes—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—81no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—82no—
243C22⋊D43—82no—
244C22⋊D43—82no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43#12111yescharacteristic
249C2×Dic43#12111yescharacteristic
250C2×Dic43#12111yescharacteristic
251D172—41no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—81no—
256C4×D43—24no—
257C4×D43—22no—
258C4×D43—42no—
259C4×D43—82no—
260C4×D43C2×D812yes—
261C4×D43#13512yes—
262C4×D43#13512yes—
263C4×D43#13712yes—
264Dic86—21no—
265Dic86—24no—
266Dic86—41no—
267Dic86—41no—
268Dic86—82no—
269Dic86C2×D812yes—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C43⋊C8—21no—
276C43⋊C8—21no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280C2×#1682—431nomaximal, Sylow
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43C2×#12111yescharacteristic
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—164no—
289C2×D43#46412yes—
290C2×D43#46612yes—
291C2×D43#47112yes—
292C4×C43—22no—
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43C22×D811yescharacteristic
297C4×C43C2×#13511yescharacteristic
298C4×C43C2×#13511yescharacteristic
299C4×C43C2×#13711yescharacteristic
300Dic43—22no—
301Dic43—21no—
302Dic43—41no—
303Dic43—81no—
304Dic43#46412yes—
305Dic43#46612yes—
306C2×#486—431no—
307C2×#462—431no—
308C2×#460—431no—
309C2×C8×Q8—431no—
310#1682—431no—
311#1682—431no—
312#1682—431no—
313#1682—431no—
314#1682—431no—
315#1682—431no—
316#1682—431no—
317#1682D4311yescharacteristic, direct product factor
318C2×#335—431no—
319C2×#332—431no—
320C2×#331—431no—
321C2×C43—161no—
322C2×C43C2×#46411yescharacteristic
323C2×C43C2×#46611yescharacteristic
324C2×C43C2×#47111yescharacteristic
325D43—161no—
326D43#168214yesdirect product factor
327C22×Q16—861no—
328C22×SD16—861no—
329C2×C4⋊Q8—431no—
330C2×#127—431no—
331C2×C4×Q8—431no—
332#486—431no—
333#486—431no—
334#486—431no—
335#486—861no—
336#486—861no—
337#486C2×D4311yescharacteristic
338#462—431no—
339#462—431no—
340#462—431no—
341#462—861no—
342#462—861no—
343#462C2×D4311yescharacteristic, complemented
344#460—431no—
345#460—431no—
346#460—431no—
347#460—861no—
348#460—861no—
349#460C2×D4311yescharacteristic
350C8×Q8—431no—
351C8×Q8—431no—
352C8×Q8—431no—
353C8×Q8—861no—
354C8×Q8—861no—
355C8×Q8C2×D4311yescharacteristic, complemented
356C2×C4⋊C8—431no—
357C2×C4⋊C8—431no—
358C2×C4⋊C8—431no—
359C2×C4⋊C8—861no—
360C2×#103—861no—
361C2×#102—861no—
362C2×#102—861no—
363C2×#102—861no—
364C2×C4×C8—431no—
365C2×C4×C8—861no—
366#335—431no—
367#335—431no—
368#335—431no—
369#335C2×D4311yescharacteristic, complemented
370#332—431no—
371#332—431no—
372#332—431no—
373#332C2×D4311yescharacteristic, complemented
374#331—431no—
375#331—431no—
376#331—431no—
377#331C2×D4311yescharacteristic
378C43C2×#168211yescharacteristic, complemented, Sylow
379C22×Q8—431no—
380C22×Q8—861no—
381C22×D4—861no—
382C22×D4—861no—
383C22×D4—861no—
384C2×Q16—21no—
385C2×Q16—861no—
386C2×Q16—861no—
387C2×Q16—861no—
388C2×Q16—1724no—
389C2×SD16—21no—
390C2×SD16—861no—
391C2×SD16—861no—
392C2×SD16—861no—
393C2×SD16—1724no—
394C22×C8—431no—
395C22×C8—431no—
396C22×C8—861no—
397C22×C8—861no—
398C22×C8—861no—
399C4⋊Q8—431no—
400C4⋊Q8—861no—
401C4⋊Q8—861no—
402C4⋊Q8—861no—
403C4⋊Q8C22×D4311yescharacteristic
404#127—431no—
405#127—861no—
406#127—861no—
407#127—861no—
408#127C22×D4311yescharacteristic
409C4×Q8—431no—
410C4×Q8—431no—
411C4×Q8—431no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8C22×D4311yescharacteristic
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C42—431no—
420C2×C42—861no—
421C4⋊C8—21no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—861no—
426C4⋊C8—861no—
427C4⋊C8—861no—
428C4⋊C8—861no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8C22×D4311yescharacteristic
432C4⋊C8C22×D4311yescharacteristic
433C4⋊C8C22×D4311yescharacteristic
434#103—21no—
435#103—861no—
436#103—861no—
437#103—861no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—861no—
449#102—861no—
450C4×C8—21no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8—861no—
455C4×C8—861no—
456C4×C8—861no—
457C4×C8C22×D4311yescharacteristic
458C24—1721no—
459C2×Q8—21no—
460C2×Q8—434no—
461C2×Q8—431no—
462C2×Q8—861no—
463C2×Q8—862no—
464C2×Q8—861no—
465C2×Q8—1721no—
466C2×Q8—1722no—
467C2×Q8—1722no—
468C2×Q8D4×D4311yescharacteristic
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—3442no—
476C2×D4—1722no—
477C2×D4—1722no—
478C2×D4—1722no—
479C2×D4—1722no—
480C2×D4—1721no—
481C2×D4—1721no—
482C2×D4—1721no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—1721no—
489Q16—42no—
490Q16—1722no—
491Q16—1722no—
492Q16—1722no—
493SD16—42no—
494SD16—1722no—
495SD16—1722no—
496SD16—1722no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—431no—
501C2×C8—431no—
502C2×C8—862no—
503C2×C8—862no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—1722no—
508C2×C8—1722no—
509C2×C8—1722no—
510C2×C8D4×D4311yescharacteristic
511C2×C8D4×D4311yescharacteristic
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—431no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4D4×D4311yescharacteristic
525C42—21no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—861no—
530C42—861no—
531C42—861no—
532C42C23×D4311yescharacteristic
533C23—41no—
534C23—431no—
535C23—3442no—
536C23—3442no—
537C23—3442no—
538C23—1721no—
539Q8—21no—
540Q8—41no—
541Q8—41no—
542Q8—432no—
543Q8—864no—
544Q8—861no—
545Q8—3442no—
546Q8—1721no—
547Q8—1721no—
548Q8D8×D4312yes—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—81no—
554D4—3441no—
555D4—3442no—
556D4—3442no—
557D4—3442no—
558D4—1721no—
559D4—1721no—
560D4—1721no—
561D4—1721no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—431no—
566C2×C4—431no—
567C2×C4—432no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—432no—
571C2×C4—431no—
572C2×C4—862no—
573C2×C4—864no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—3442no—
577C2×C4—1722no—
578C2×C4—1721no—
579C2×C4C2×D4×D4311yescharacteristic
580C2×C4C2×D4×D4311yescharacteristic
581C2×C4#41×D4311yescharacteristic
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—861no—
588C8—861no—
589C8—1721no—
590C8—1721no—
591C8—1721no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—432no—
596C22—432no—
597C22—432no—
598C22—3441no—
599C22—3441no—
600C22—3441no—
601C22—6884no—
602C22#121×D4311yescharacteristic
603C4—21no—
604C4—22no—
605C4—41no—
606C4—81no—
607C4—432no—
608C4—432no—
609C4—861no—
610C4—862no—
611C4—3441no—
612C4—1721no—
613C4C2×D8×D4311yescharacteristic
614C4#135×D4311yescharacteristic
615C4#135×D4311yescharacteristic
616C4#137×D4311yescharacteristic
617C2—161no—
618C2—434no—
619C2—6881no—
620C2#464×D4311yescharacteristic
621C2#466×D4311yescharacteristic
622C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1682C2
socleC22×C43C2×#121
prime radical#127×D43C22
hypercenter#1682D43
hypocenterC43C2×#1682
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1682

Complements

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

NH ≅ G/Ntype
2. #462×D43C2semidirect
4. C8×Q8×D43C2semidirect
5. #19134042C2semidirect
6. #19134041C2semidirect
7. #19134040C2semidirect
8. #19134039C2semidirect
9. #19134038C2semidirect
10. #19134037C2semidirect
11. #19134036C2semidirect
12. #335×D43C2semidirect
13. #332×D43C2semidirect
15. C43×#1682C2semidirect
26. #14583110C22semidirect
27. #14583109C22semidirect
30. #14583106C22semidirect
36. Q8×C43⋊C8C22semidirect
38. C8×Dic86C22semidirect
40. #14583023C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
61. C43×#462C22semidirect
63. C8×Q8×C43C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
317. #1682D43direct (N × H)
326. D43#1682direct (N × H)
343. #462C2×D43semidirect
355. C8×Q8C2×D43semidirect
369. #335C2×D43semidirect
373. #332C2×D43semidirect
378. C43C2×#1682semidirect

Maximal subgroups

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

subgroupindex
#486×D432
#462×D432
#460×D432
C8×Q8×D432
#191340422
#191340412
#191340402
#191340392
#191340382
#191340372
#191340362
#335×D432
#332×D432
#331×D432
C43×#16822
C2×#168243