Finite Group Databasebeta

← D43×#1702 #25079257

Subgroups — D43×#1702 #25079257

Order 11008.

734 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
4#446×D43C211yesmaximal, characteristic, complemented
5#19134166C211yesmaximal, characteristic, complemented
6#19134165C211yesmaximal, characteristic, complemented
7#19134164C211yesmaximal, characteristic, complemented
8#19134163C211yesmaximal, characteristic, complemented
9#19134162C211yesmaximal, characteristic, complemented
10#19134161C211yesmaximal, characteristic, complemented
11#19134160C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic, complemented
13#332×D43C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic
15C43×#1702C211yesmaximal, 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
36#14583030C2211yescharacteristic, complemented
37#14583029C2211yescharacteristic, complemented
38#14583028—21no—
39#14583027—21no—
40#14583026C2211yescharacteristic, 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—
49#97×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582645C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#462C2211yescharacteristic, complemented
62C43×#460C2211yescharacteristic
63C43×#446C2211yescharacteristic, complemented
64C43×#334C2211yescharacteristic, 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—
125#13063236—21no—
126#13063235—21no—
127#13063235—21no—
128C4×C43⋊C8C2311yescharacteristic
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—
144#97×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—22no—
157Q8×D43—42no—
158Q8×D43—42no—
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—21no—
229Q8×C43—41no—
230Q8×C43—41no—
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—22no—
257C4×D43—42no—
258C4×D43—42no—
259C4×D43—82no—
260C4×D43#13512yes—
261C4×D43AGL(1,ℤ/8)12yes—
262C4×D43AGL(1,ℤ/8)12yes—
263C4×D43#13712yes—
264Dic86—21no—
265Dic86—21no—
266Dic86—42no—
267Dic86—41no—
268Dic86—41no—
269Dic86—82no—
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×#1702—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#46912yes—
291C2×D43#47112yes—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43C2×#13511yescharacteristic
297C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C43C2×#13711yescharacteristic
300Dic43—21no—
301Dic43—41no—
302Dic43—41no—
303Dic43—81no—
304Dic43#46412yes—
305Dic43#46912yes—
306C2×#486—431no—
307C2×#462—431no—
308C2×#460—431no—
309C2×#446—431no—
310#1702—431no—
311#1702—431no—
312#1702—431no—
313#1702—431no—
314#1702—431no—
315#1702—431no—
316#1702—431no—
317#1702D4311yescharacteristic, direct product factor
318C2×#334—431no—
319C2×#332—431no—
320C2×#331—431no—
321C2×C43—161no—
322C2×C43C2×#46411yescharacteristic
323C2×C43C2×#46911yescharacteristic
324C2×C43C2×#47111yescharacteristic
325D43—161no—
326D43#170214yesdirect 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
350#446—431no—
351#446—431no—
352#446—431no—
353#446—861no—
354#446—861no—
355#446C2×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×#97—861no—
365C2×C4×C8—431no—
366#334—431no—
367#334—431no—
368#334—431no—
369#334C2×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×#170211yescharacteristic, 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—
450#97—21no—
451#97—861no—
452#97—861no—
453#97—861no—
454C4×C8—431no—
455C4×C8—431no—
456C4×C8—431no—
457C4×C8C22×D4311yescharacteristic
458C24—1721no—
459C2×Q8—21no—
460C2×Q8—431no—
461C2×Q8—861no—
462C2×Q8—862no—
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—21no—
541Q8—41no—
542Q8—41no—
543Q8—861no—
544Q8—861no—
545Q8—3442no—
546Q8—1722no—
547Q8—1721no—
548Q8—1721no—
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—861no—
574C2×C4—861no—
575C2×C4—3442no—
576C2×C4—1722no—
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—41no—
605C4—41no—
606C4—81no—
607C4—432no—
608C4—432no—
609C4—861no—
610C4—3441no—
611C4—1721no—
612C4—1721no—
613C4#135×D4311yescharacteristic
614C4AGL(1,ℤ/8)×D4311yescharacteristic
615C4AGL(1,ℤ/8)×D4311yescharacteristic
616C4#137×D4311yescharacteristic
617C2—161no—
618C2—434no—
619C2—6881no—
620C2#464×D4311yescharacteristic
621C2#469×D4311yescharacteristic
622C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1702C2
socleC22×C43C2×#121
prime radical#127×D43C22
hypercenter#1702D43
hypocenterC43C2×#1702
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1702

Complements

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

NH ≅ G/Ntype
2. #462×D43C2semidirect
4. #446×D43C2semidirect
5. #19134166C2semidirect
6. #19134165C2semidirect
7. #19134164C2semidirect
8. #19134163C2semidirect
9. #19134162C2semidirect
10. #19134161C2semidirect
11. #19134160C2semidirect
12. #334×D43C2semidirect
13. #332×D43C2semidirect
15. C43×#1702C2semidirect
26. #14583110C22semidirect
27. #14583109C22semidirect
30. #14583106C22semidirect
36. #14583030C22semidirect
37. #14583029C22semidirect
40. #14583026C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
61. C43×#462C22semidirect
63. C43×#446C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
317. #1702D43direct (N × H)
326. D43#1702direct (N × H)
343. #462C2×D43semidirect
355. #446C2×D43semidirect
369. #334C2×D43semidirect
373. #332C2×D43semidirect
378. C43C2×#1702semidirect

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
#446×D432
#191341662
#191341652
#191341642
#191341632
#191341622
#191341612
#191341602
#334×D432
#332×D432
#331×D432
C43×#17022
C2×#170243