Finite Group Databasebeta

← D43×#1671 #25078842

Subgroups — D43×#1671 #25078842

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#498×D43C211yesmaximal, characteristic, complemented
2#476×D43C211yesmaximal, characteristic
3#461×D43C211yesmaximal, characteristic
4C8×D4×D43C211yesmaximal, characteristic
5#19133973C211yesmaximal, characteristic, complemented
6#19133972C211yesmaximal, characteristic, complemented
7#19133971C211yesmaximal, characteristic, complemented
8#19133970C211yesmaximal, characteristic, complemented
9#19133969C211yesmaximal, characteristic, complemented
10#19133968C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic, complemented
13#333×D43C211yesmaximal, characteristic, complemented
14#332×D43C211yesmaximal, characteristic, complemented
15C43×#1671C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C22×C8×D43—21no—
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20C4×D4×D43C2211yescharacteristic
21#14583297C2211yescharacteristic, complemented
22#14583296—21no—
23#14583296—21no—
24#14583295C2211yescharacteristic, complemented
25#14583295C2211yescharacteristic, complemented
26#14583190C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583188—21no—
29#14583187—21no—
30#14583186C2211yescharacteristic
31#14583105C2211yescharacteristic
32#14583104C2211yescharacteristic
33#14583103—21no—
34#14583102—21no—
35#14583101C2211yescharacteristic
36C8×D172C2211yescharacteristic
37D4×C43⋊C8C2211yescharacteristic
38#14582964C2211yescharacteristic
39C8×C22⋊D43—21no—
40(C22⋊D43)⋊C8—21no—
41#106×D43—21no—
42#106×D43—21no—
43#106×D43—21no—
44C4⋊C8×D43C2211yescharacteristic
45C4⋊C8×D43C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#103×D43—21no—
48#102×D43—21no—
49C22⋊C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582646C2211yescharacteristic, complemented
58#14582645C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#498C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#332C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C2×Q8×D43—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74SD16×D43—44no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81C2×C8×D43—44no—
82C2×C8×D43D411yescharacteristic
83C2×C8×D43D411yescharacteristic
84#13063325C2311yescharacteristic
85#13063325C2311yescharacteristic
86#13063324—21no—
87#13063324—21no—
88#13063324—21no—
89#13063324—21no—
90#13063323—21no—
91#13063323—21no—
92C4×D172C2311yescharacteristic
93D4×Dic43D411yescharacteristic
94#13063287D411yescharacteristic
95C4×C22⋊D43—21no—
96(C22⋊D43)⋊C4—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43D411yescharacteristic
102C22⋊C4×D43—21no—
103C42×D43C2311yescharacteristic
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256—21no—
110#13063256—21no—
111#13063256—21no—
112#13063256—21no—
113C4⋊(C43⋊C8)C2311yescharacteristic
114C4⋊(C43⋊C8)C2311yescharacteristic
115C4⋊(C43⋊C8)C2311yescharacteristic
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118Dic43⋊C8—21no—
119#13063250—21no—
120#13063249—21no—
121#13063248—21no—
122#13063247—21no—
123#13063246—21no—
124#13063245—21no—
125C22⋊(C43⋊C8)—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C2×SD16×C43—21no—
132C22×C8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134C4⋊Q8×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#106×C43—21no—
137#106×C43—21no—
138#106×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142#103×C43—21no—
143#102×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C22×Dic43—21no—
153Q8×D43—42no—
154Q8×D43—42no—
155Q8×D43—82no—
156D4×D43—22no—
157D4×D43SD1614yes—
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—41no—
165C2×C4×D43—41no—
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43#4111yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—41no—
172C2×Dic86—41no—
173SD16×C43—42no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—42no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—21no—
186C42×C43C2411yescharacteristic
187C22⋊Dic43—21no—
188#10621884—42no—
189#10621883—42no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43#4111yescharacteristic
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—42no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211#10621873—42no—
212C8×D43—22no—
213C8×D43—42no—
214C8×D43—42no—
215C8×D43—42no—
216C8×D43—42no—
217C8×D43—42no—
218C8×D43SD1614yescomplemented
219C23×C43—21no—
220C22×D43—21no—
221C22×D43—24no—
222C22×D43—42no—
223C22×D43—42no—
224C22×D43#12111yescharacteristic
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—81no—
228D4×C43—21no—
229D4×C43C2×SD1612yes—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—24no—
239C2×Dic43—21no—
240C2×Dic43—42no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43#12111yescharacteristic
244C2×Dic43#12111yescharacteristic
245C2×Dic43#12111yescharacteristic
246D172—21no—
247D172C2×SD1612yes—
248C4×D43—22no—
249C4×D43—42no—
250C4×D43—41no—
251C4×D43—41no—
252C4×D43—42no—
253C4×D43—82no—
254C4×D43—82no—
255C4×D43C2×SD1612yes—
256C4×D43C2×SD1612yes—
257C4×D43#13512yes—
258C4×D43#13712yes—
259Dic86—41no—
260Dic86—41no—
261Dic86—82no—
262Dic86—82no—
263Dic86—81no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43C2×SD1612yescomplemented
269C43⋊C8—21no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273C43⋊C8C2×SD1612yescomplemented
274C2×#1671—431nomaximal, Sylow
275C22×C43—22no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43C2×#12111yescharacteristic
279C2×D43—22no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—48no—
283C2×D43#46112yes—
284C2×D43#46512yes—
285C2×D43#47112yes—
286C4×C43—21no—
287C4×C43—41no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43C22×SD1611yescharacteristic
291C4×C43C22×SD1611yescharacteristic
292C4×C43C2×#13511yescharacteristic
293C4×C43C2×#13711yescharacteristic
294Dic43—21no—
295Dic43—41no—
296Dic43—81no—
297Dic43—81no—
298Dic43#46112yes—
299Dic43#46512yes—
300C2×#498—431no—
301C2×#476—431no—
302C2×#461—431no—
303C2×C8×D4—431no—
304#1671—431no—
305#1671—431no—
306#1671—431no—
307#1671—431no—
308#1671—431no—
309#1671—431no—
310#1671—431no—
311#1671D4311yescharacteristic, direct product factor
312C2×#334—431no—
313C2×#333—431no—
314C2×#332—431no—
315C2×C43—42no—
316C2×C43C2×#46111yescharacteristic
317C2×C43C2×#46511yescharacteristic
318C2×C43C2×#47111yescharacteristic
319D43—42no—
320D43#167114yesdirect product factor
321C22×SD16—861no—
322C23×C8—861no—
323C2×C4⋊Q8—431no—
324C2×C4⋊Q8—431no—
325C2×C4×D4—431no—
326#498—431no—
327#498—431no—
328#498—431no—
329#498—861no—
330#498—861no—
331#498C2×D4311yescharacteristic, complemented
332#476—431no—
333#476—431no—
334#476—431no—
335#476—861no—
336#476—861no—
337#476C2×D4311yescharacteristic
338#461—431no—
339#461—431no—
340#461—431no—
341#461—861no—
342#461—861no—
343#461C2×D4311yescharacteristic
344C8×D4—431no—
345C8×D4—431no—
346C8×D4—431no—
347C8×D4—861no—
348C8×D4—861no—
349C8×D4C2×D4311yescharacteristic
350C2×#106—861no—
351C2×#106—861no—
352C2×#106—861no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—431no—
355C2×C4⋊C8—431no—
356C2×#103—861no—
357C2×#102—861no—
358C2×C22⋊C8—861no—
359C2×C4×C8—431no—
360#334—431no—
361#334—431no—
362#334—431no—
363#334C2×D4311yescharacteristic, complemented
364#333—431no—
365#333—431no—
366#333—431no—
367#333C2×D4311yescharacteristic, complemented
368#332—431no—
369#332—431no—
370#332—431no—
371#332C2×D4311yescharacteristic, complemented
372C43C2×#167111yescharacteristic, complemented, Sylow
373C22×Q8—861no—
374C22×Q8—861no—
375C22×D4—431no—
376C23×C4—861no—
377C2×SD16—21no—
378C2×SD16—861no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×SD16—1724no—
382C22×C8—21no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8—861no—
386C22×C8—861no—
387C22×C8—861no—
388C22×C8—861no—
389C22×C8—861no—
390C22×C8—861no—
391C22×C8—1724no—
392C4⋊Q8—431no—
393C4⋊Q8—431no—
394C4⋊Q8—861no—
395C4⋊Q8—861no—
396C4⋊Q8—861no—
397C4⋊Q8—861no—
398C4⋊Q8—861no—
399C4⋊Q8—861no—
400C4⋊Q8C22×D4311yescharacteristic
401C4⋊Q8C22×D4311yescharacteristic
402C4×D4—431no—
403C4×D4—431no—
404C4×D4—431no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4C22×D4311yescharacteristic
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—431no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—861no—
419#106—861no—
420#106—861no—
421#106—861no—
422#106—861no—
423#106—861no—
424#106—861no—
425#106—861no—
426#106—861no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—861no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8C22×D4311yescharacteristic
434C4⋊C8C22×D4311yescharacteristic
435C4⋊C8C22×D4311yescharacteristic
436#103—21no—
437#103—861no—
438#103—861no—
439#103—861no—
440#102—21no—
441#102—861no—
442#102—861no—
443#102—861no—
444C22⋊C8—21no—
445C22⋊C8—861no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—431no—
451C4×C8C22×D4311yescharacteristic
452C24—861no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—3442no—
458C2×Q8—1721no—
459C2×Q8—1721no—
460C2×Q8—1722no—
461C2×Q8—1722no—
462C2×D4—434no—
463C2×D4—431no—
464C2×D4—862no—
465C2×D4—861no—
466C2×D4D4×D4311yescharacteristic
467C22×C4—21no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4—1721no—
478C22×C4—1721no—
479SD16—42no—
480SD16—1722no—
481SD16—1722no—
482SD16—1722no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—42no—
487C2×C8—431no—
488C2×C8—434no—
489C2×C8—431no—
490C2×C8—862no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—1722no—
495C2×C8—1722no—
496C2×C8—1722no—
497C2×C8—1722no—
498C2×C8—1722no—
499C2×C8—1722no—
500C2×C8D4×D4311yescharacteristic
501C2×C8D4×D4311yescharacteristic
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—431no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—1721no—
513C4⋊C4—1721no—
514C4⋊C4—1721no—
515C4⋊C4—1721no—
516C4⋊C4D4×D4311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—861no—
519C22⋊C4—861no—
520C22⋊C4—861no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42C23×D4311yescharacteristic
525C23—21no—
526C23—431no—
527C23—864no—
528C23—861no—
529C23—1722no—
530C23—1722no—
531Q8—41no—
532Q8—41no—
533Q8—81no—
534Q8—3441no—
535Q8—3442no—
536Q8—3442no—
537Q8—1721no—
538Q8—1721no—
539D4—21no—
540D4—432no—
541D4—864no—
542D4—861no—
543D4SD16×D4312yes—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—431no—
550C2×C4—431no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—431no—
556C2×C4—862no—
557C2×C4—861no—
558C2×C4—3442no—
559C2×C4—3442no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—432no—
575C8—861no—
576C8—1721no—
577C8—1721no—
578C8—1721no—
579C8SD16×D4312yescomplemented
580C22—22no—
581C22—41no—
582C22—41no—
583C22—432no—
584C22—432no—
585C22—432no—
586C22—862no—
587C22—1728no—
588C22—1721no—
589C22—1721no—
590C22#121×D4311yescharacteristic
591C4—21no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—432no—
596C4—432no—
597C4—861no—
598C4—3441no—
599C4—3441no—
600C4—1721no—
601C4C2×SD16×D4311yescharacteristic
602C4C2×SD16×D4311yescharacteristic
603C4#135×D4311yescharacteristic
604C4#137×D4311yescharacteristic
605C2—42no—
606C2—434no—
607C2—1722no—
608C2#461×D4311yescharacteristic
609C2#465×D4311yescharacteristic
610C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1671C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1671D43
hypocenterC43C2×#1671
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1671

Complements

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

NH ≅ G/Ntype
1. #498×D43C2semidirect
5. #19133973C2semidirect
6. #19133972C2semidirect
7. #19133971C2semidirect
8. #19133970C2semidirect
9. #19133969C2semidirect
10. #19133968C2semidirect
11. #19133967C2semidirect
12. #334×D43C2semidirect
13. #333×D43C2semidirect
14. #332×D43C2semidirect
15. C43×#1671C2semidirect
21. #14583297C22semidirect
24. #14583295C22semidirect
25. #14583295C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
57. #14582646C22semidirect
58. #14582645C22semidirect
59. #14582644C22semidirect
60. C43×#498C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
66. C43×#332C22semidirect
218. C8×D43SD16semidirect
268. C8×C43C2×SD16semidirect
273. C43⋊C8C2×SD16semidirect
311. #1671D43direct (N × H)
320. D43#1671direct (N × H)
331. #498C2×D43semidirect
363. #334C2×D43semidirect
367. #333C2×D43semidirect
371. #332C2×D43semidirect
372. C43C2×#1671semidirect
579. C8SD16×D43semidirect

Maximal subgroups

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

subgroupindex
#498×D432
#476×D432
#461×D432
C8×D4×D432
#191339732
#191339722
#191339712
#191339702
#191339692
#191339682
#191339672
#334×D432
#333×D432
#332×D432
C43×#16712
C2×#167143