Finite Group Databasebeta

← D43×#1666 #25078913

Subgroups — D43×#1666 #25078913

Order 11008.

786 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#492×D43C211yesmaximal, characteristic
2#475×D43C211yesmaximal, characteristic, complemented
3#460×D43C211yesmaximal, characteristic
4C8×Q8×D43C211yesmaximal, characteristic, complemented
5#19133946C211yesmaximal, characteristic, complemented
6#19133945C211yesmaximal, characteristic, complemented
7#19133944C211yesmaximal, characteristic, complemented
8#19133943C211yesmaximal, characteristic, complemented
9#19133942C211yesmaximal, characteristic, complemented
10#19133941C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic, complemented
13#332×D43C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic
15C43×#1666C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C2×SD16×D43—21no—
18C2×SD16×D43—21no—
19C4⋊Q8×D43C2211yescharacteristic
20#127×D43C2211yescharacteristic
21C4×Q8×D43C2211yescharacteristic
22#14583273C2211yescharacteristic
23#14583272C2211yescharacteristic
24#14583271C2211yescharacteristic
25#14583270—21no—
26#14583270—21no—
27#14583185C2211yescharacteristic, complemented
28#14583184C2211yescharacteristic, complemented
29#14583183—21no—
30#14583182—21no—
31#14583181C2211yescharacteristic, complemented
32#14583100C2211yescharacteristic
33#14583099C2211yescharacteristic
34#14583098—21no—
35#14583097—21no—
36#14583096C2211yescharacteristic
37Q8×C43⋊C8C2211yescharacteristic, complemented
38C8×Dic86—21no—
39C8×Dic86C2211yescharacteristic, complemented
40#14583023—21no—
41#14583023C2211yescharacteristic, complemented
42#106×D43—21no—
43C4⋊C8×D43—21no—
44C4⋊C8×D43C2211yescharacteristic
45C4⋊C8×D43C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#103×D43—21no—
48#102×D43—21no—
49C4×C8×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×#492C2211yescharacteristic
61C43×#475C2211yescharacteristic, complemented
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic, 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×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×#10621883—21no—
76C2×#10621883—21no—
77C2×#10621883—21no—
78C2×#10621884—21no—
79C2×#10621884—21no—
80C2×#10621884—21no—
81SD16×D43—44no—
82SD16×D43—44no—
83SD16×D43—44no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87C2×C8×D43D411yescharacteristic
88C2×C8×D43D411yescharacteristic
89#13063325C2311yescharacteristic
90#13063324—21no—
91#13063324—21no—
92#13063323—21no—
93#13063322C2311yescharacteristic
94#13063321—21no—
95#13063321—21no—
96#13063321—21no—
97Q8×Dic43D411yescharacteristic
98C4×Dic86—21no—
99C4×Dic86C2311yescharacteristic
100#13063290—21no—
101#13063290D411yescharacteristic
102C4⋊C4×D43—21no—
103C4⋊C4×D43—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43D411yescharacteristic
106C42×D43—21no—
107C42×D43C2311yescharacteristic
108#13063257—21no—
109#13063256—21no—
110#13063256—21no—
111C4⋊(C43⋊C8)—21no—
112C4⋊(C43⋊C8)C2311yescharacteristic
113C4⋊(C43⋊C8)C2311yescharacteristic
114C4⋊(C43⋊C8)C2311yescharacteristic
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118Dic43⋊C8—21no—
119Dic43⋊C8—21no—
120#13063250—21no—
121#13063249—21no—
122#13063248—21no—
123#13063247—21no—
124#13063246—21no—
125#13063245—21no—
126C4×C43⋊C8—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
130C8×Dic43D411yescharacteristic
131C8×Dic43D411yescharacteristic
132C2×SD16×C43—21no—
133C2×SD16×C43—21no—
134C2×SD16×C43—21no—
135C4⋊Q8×C43C2311yescharacteristic
136#127×C43C2311yescharacteristic
137C4×Q8×C43C2311yescharacteristic
138#106×C43—21no—
139C4⋊C8×C43—21no—
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143#103×C43—21no—
144#102×C43—21no—
145C4×C8×C43—21no—
146C4×C8×C43C2311yescharacteristic
147C23×D43—41no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156Q8×D43—22no—
157Q8×D43—42no—
158Q8×D43—42no—
159Q8×D43SD1614yescomplemented
160D4×D43—42no—
161D4×D43—42no—
162D4×D43—42no—
163D4×D43—42no—
164D4×D43—82no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—41no—
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43#4111yescharacteristic
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—41no—
177C2×Dic86C2×D411yescharacteristic
178SD16×C43—42no—
179SD16×C43—42no—
180SD16×C43—42no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43C2×D411yescharacteristic
190C42×C43—21no—
191C42×C43C2411yescharacteristic
192#10621884—42no—
193#10621884—42no—
194#10621884—42no—
195#10621883—42no—
196#10621883—42no—
197#10621883—42no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43C2×D411yescharacteristic
211C4×Dic43C2×D411yescharacteristic
212C4×Dic43#4111yescharacteristic
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8C2×D411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218#10621873—42no—
219#10621873—42no—
220#10621873—42no—
221C8×D43—22no—
222C8×D43—42no—
223C8×D43—42no—
224C8×D43—42no—
225C8×D43SD1614yescomplemented
226C23×C43—41no—
227C22×D43—41no—
228C22×D43—82no—
229C22×D43—82no—
230C22×D43—82no—
231C22×D43#12111yescharacteristic
232Q8×C43—21no—
233Q8×C43—41no—
234Q8×C43—41no—
235Q8×C43C2×SD1612yescomplemented
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—81no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C22⋊D43—82no—
248C22⋊D43—82no—
249C22⋊D43—82no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—41no—
253C2×Dic43#12111yescharacteristic
254C2×Dic43#12111yescharacteristic
255C2×Dic43#12111yescharacteristic
256D172—41no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—81no—
261C4×D43—24no—
262C4×D43—22no—
263C4×D43—42no—
264C4×D43—82no—
265C4×D43C2×SD1612yes—
266C4×D43C2×SD1612yes—
267C4×D43#13512yes—
268C4×D43AGL(1,ℤ/8)12yes—
269Dic86—21no—
270Dic86—24no—
271Dic86—41no—
272Dic86—41no—
273Dic86—82no—
274Dic86C2×SD1612yescomplemented
275C8×C43—21no—
276C8×C43—41no—
277C8×C43—41no—
278C8×C43—41no—
279C8×C43C2×SD1612yescomplemented
280C43⋊C8—21no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284C43⋊C8C2×SD1612yescomplemented
285C2×#1666—431nomaximal, Sylow
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43C2×#12111yescharacteristic
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—164no—
294C2×D43#46012yes—
295C2×D43#46512yes—
296C2×D43#47112yes—
297C4×C43—22no—
298C4×C43—21no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43C22×SD1611yescharacteristic
302C4×C43C22×SD1611yescharacteristic
303C4×C43C2×#13511yescharacteristic
304C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
305Dic43—22no—
306Dic43—21no—
307Dic43—41no—
308Dic43—81no—
309Dic43#46012yes—
310Dic43#46512yes—
311C2×#492—431no—
312C2×#475—431no—
313C2×#460—431no—
314C2×C8×Q8—431no—
315#1666—431no—
316#1666—431no—
317#1666—431no—
318#1666—431no—
319#1666—431no—
320#1666—431no—
321#1666—431no—
322#1666D4311yescharacteristic, direct product factor
323C2×#334—431no—
324C2×#332—431no—
325C2×#331—431no—
326C2×C43—161no—
327C2×C43C2×#46011yescharacteristic
328C2×C43C2×#46511yescharacteristic
329C2×C43C2×#47111yescharacteristic
330D43—161no—
331D43#166614yesdirect product factor
332C22×SD16—861no—
333C22×SD16—861no—
334C22×SD16—861no—
335C2×C4⋊Q8—431no—
336C2×#127—431no—
337C2×C4×Q8—431no—
338#492—431no—
339#492—431no—
340#492—431no—
341#492—861no—
342#492—861no—
343#492C2×D4311yescharacteristic
344#475—431no—
345#475—431no—
346#475—431no—
347#475—861no—
348#475—861no—
349#475C2×D4311yescharacteristic, complemented
350#460—431no—
351#460—431no—
352#460—431no—
353#460—861no—
354#460—861no—
355#460C2×D4311yescharacteristic
356C8×Q8—431no—
357C8×Q8—431no—
358C8×Q8—431no—
359C8×Q8—861no—
360C8×Q8—861no—
361C8×Q8C2×D4311yescharacteristic, complemented
362C2×#106—861no—
363C2×C4⋊C8—431no—
364C2×C4⋊C8—431no—
365C2×C4⋊C8—431no—
366C2×C4⋊C8—861no—
367C2×#103—861no—
368C2×#102—861no—
369C2×C4×C8—431no—
370C2×C4×C8—861no—
371#334—431no—
372#334—431no—
373#334—431no—
374#334C2×D4311yescharacteristic, complemented
375#332—431no—
376#332—431no—
377#332—431no—
378#332C2×D4311yescharacteristic, complemented
379#331—431no—
380#331—431no—
381#331—431no—
382#331C2×D4311yescharacteristic
383C43C2×#166611yescharacteristic, complemented, Sylow
384C22×Q8—431no—
385C22×Q8—861no—
386C22×D4—861no—
387C22×D4—861no—
388C22×D4—861no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16—21no—
392C2×SD16—861no—
393C2×SD16—861no—
394C2×SD16—861no—
395C2×SD16—861no—
396C2×SD16—861no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16—861no—
401C2×SD16—1724no—
402C2×SD16—1724no—
403C2×SD16—1724no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8—861no—
407C22×C8—861no—
408C22×C8—861no—
409C4⋊Q8—431no—
410C4⋊Q8—861no—
411C4⋊Q8—861no—
412C4⋊Q8—861no—
413C4⋊Q8C22×D4311yescharacteristic
414#127—431no—
415#127—861no—
416#127—861no—
417#127—861no—
418#127C22×D4311yescharacteristic
419C4×Q8—431no—
420C4×Q8—431no—
421C4×Q8—431no—
422C4×Q8—861no—
423C4×Q8—861no—
424C4×Q8C22×D4311yescharacteristic
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C42—431no—
430C2×C42—861no—
431#106—21no—
432#106—861no—
433#106—861no—
434#106—861no—
435C4⋊C8—21no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—861no—
440C4⋊C8—861no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8C22×D4311yescharacteristic
446C4⋊C8C22×D4311yescharacteristic
447C4⋊C8C22×D4311yescharacteristic
448#103—21no—
449#103—861no—
450#103—861no—
451#103—861no—
452#102—21no—
453#102—861no—
454#102—861no—
455#102—861no—
456C4×C8—21no—
457C4×C8—431no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8—861no—
461C4×C8—861no—
462C4×C8—861no—
463C4×C8C22×D4311yescharacteristic
464C24—1721no—
465C2×Q8—21no—
466C2×Q8—434no—
467C2×Q8—431no—
468C2×Q8—861no—
469C2×Q8—862no—
470C2×Q8—861no—
471C2×Q8—1721no—
472C2×Q8—1722no—
473C2×Q8—1722no—
474C2×Q8D4×D4311yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—3442no—
482C2×D4—1722no—
483C2×D4—1722no—
484C2×D4—1722no—
485C2×D4—1722no—
486C2×D4—1721no—
487C2×D4—1721no—
488C2×D4—1721no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—1721no—
495SD16—42no—
496SD16—42no—
497SD16—42no—
498SD16—1722no—
499SD16—1722no—
500SD16—1722no—
501SD16—1722no—
502SD16—1722no—
503SD16—1722no—
504SD16—1722no—
505SD16—1722no—
506SD16—1722no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—431no—
511C2×C8—434no—
512C2×C8—431no—
513C2×C8—862no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—1722no—
518C2×C8—1722no—
519C2×C8—1722no—
520C2×C8D4×D4311yescharacteristic
521C2×C8D4×D4311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—431no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—1721no—
533C4⋊C4—1721no—
534C4⋊C4D4×D4311yescharacteristic
535C42—21no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—861no—
540C42—861no—
541C42—861no—
542C42C23×D4311yescharacteristic
543C23—41no—
544C23—431no—
545C23—3442no—
546C23—3442no—
547C23—3442no—
548C23—1721no—
549Q8—21no—
550Q8—41no—
551Q8—41no—
552Q8—432no—
553Q8—864no—
554Q8—861no—
555Q8—3442no—
556Q8—1721no—
557Q8—1721no—
558Q8SD16×D4312yescomplemented
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—81no—
564D4—3441no—
565D4—3442no—
566D4—3442no—
567D4—3442no—
568D4—1721no—
569D4—1721no—
570D4—1721no—
571D4—1721no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—432no—
578C2×C4—432no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—431no—
582C2×C4—862no—
583C2×C4—864no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—3442no—
587C2×C4—1722no—
588C2×C4—1721no—
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C8—21no—
593C8—41no—
594C8—41no—
595C8—41no—
596C8—432no—
597C8—861no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C8SD16×D4312yescomplemented
602C22—81no—
603C22—81no—
604C22—81no—
605C22—432no—
606C22—432no—
607C22—432no—
608C22—3441no—
609C22—3441no—
610C22—3441no—
611C22—6884no—
612C22#121×D4311yescharacteristic
613C4—21no—
614C4—22no—
615C4—41no—
616C4—81no—
617C4—432no—
618C4—432no—
619C4—861no—
620C4—862no—
621C4—3441no—
622C4—1721no—
623C4C2×SD16×D4311yescharacteristic
624C4C2×SD16×D4311yescharacteristic
625C4#135×D4311yescharacteristic
626C4AGL(1,ℤ/8)×D4311yescharacteristic
627C2—161no—
628C2—434no—
629C2—6881no—
630C2#460×D4311yescharacteristic
631C2#465×D4311yescharacteristic
632C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1666C2
socleC22×C43C2×#121
prime radical#127×D43C22
hypercenter#1666D43
hypocenterC43C2×#1666
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1666

Complements

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

NH ≅ G/Ntype
2. #475×D43C2semidirect
4. C8×Q8×D43C2semidirect
5. #19133946C2semidirect
6. #19133945C2semidirect
7. #19133944C2semidirect
8. #19133943C2semidirect
9. #19133942C2semidirect
10. #19133941C2semidirect
11. #19133940C2semidirect
12. #334×D43C2semidirect
13. #332×D43C2semidirect
15. C43×#1666C2semidirect
27. #14583185C22semidirect
28. #14583184C22semidirect
31. #14583181C22semidirect
37. Q8×C43⋊C8C22semidirect
39. C8×Dic86C22semidirect
41. #14583023C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
61. C43×#475C22semidirect
63. C8×Q8×C43C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
159. Q8×D43SD16semidirect
225. C8×D43SD16semidirect
235. Q8×C43C2×SD16semidirect
274. Dic86C2×SD16semidirect
279. C8×C43C2×SD16semidirect
284. C43⋊C8C2×SD16semidirect
322. #1666D43direct (N × H)
331. D43#1666direct (N × H)
349. #475C2×D43semidirect
361. C8×Q8C2×D43semidirect
374. #334C2×D43semidirect
378. #332C2×D43semidirect
383. C43C2×#1666semidirect
558. Q8SD16×D43semidirect
601. C8SD16×D43semidirect

Maximal subgroups

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

subgroupindex
#492×D432
#475×D432
#460×D432
C8×Q8×D432
#191339462
#191339452
#191339442
#191339432
#191339422
#191339412
#191339402
#334×D432
#332×D432
#331×D432
C43×#16662
C2×#166643