Finite Group Databasebeta

← D43×#1686 #25079185

Subgroups — D43×#1686 #25079185

Order 11008.

766 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
4#446×D43C211yesmaximal, characteristic, complemented
5#19134070C211yesmaximal, characteristic, complemented
6#19134069C211yesmaximal, characteristic, complemented
7#19134068C211yesmaximal, characteristic, complemented
8#19134067C211yesmaximal, characteristic, complemented
9#19134066C211yesmaximal, characteristic, complemented
10#19134065C211yesmaximal, characteristic, complemented
11#19134064C211yesmaximal, characteristic, complemented
12#335×D43C211yesmaximal, characteristic, complemented
13#332×D43C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic
15C43×#1686C211yesmaximal, 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
37#14583030C2211yescharacteristic, complemented
38#14583029C2211yescharacteristic, complemented
39#14583028—21no—
40#14583027—21no—
41#14583026C2211yescharacteristic, 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—
49#97×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×#492C2211yescharacteristic
61C43×#475C2211yescharacteristic, complemented
62C43×#460C2211yescharacteristic
63C43×#446C2211yescharacteristic, 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×#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—
126#13063236—21no—
127#13063235—21no—
128#13063235—21no—
129C4×C43⋊C8C2311yescharacteristic
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—
145#97×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—22no—
158Q8×D43—42no—
159Q8×D43—42no—
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—21no—
234Q8×C43—41no—
235Q8×C43—41no—
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—22no—
262C4×D43—42no—
263C4×D43—42no—
264C4×D43—82no—
265C4×D43C2×SD1612yes—
266C4×D43AGL(1,ℤ/8)12yes—
267C4×D43AGL(1,ℤ/8)12yes—
268C4×D43#13712yes—
269Dic86—21no—
270Dic86—21no—
271Dic86—42no—
272Dic86—41no—
273Dic86—41no—
274Dic86—82no—
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×#1686—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#46812yes—
296C2×D43#47112yes—
297C4×C43—21no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43C22×SD1611yescharacteristic
302C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
303C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C43C2×#13711yescharacteristic
305Dic43—21no—
306Dic43—41no—
307Dic43—41no—
308Dic43—81no—
309Dic43#46012yes—
310Dic43#46812yes—
311C2×#492—431no—
312C2×#475—431no—
313C2×#460—431no—
314C2×#446—431no—
315#1686—431no—
316#1686—431no—
317#1686—431no—
318#1686—431no—
319#1686—431no—
320#1686—431no—
321#1686—431no—
322#1686D4311yescharacteristic, direct product factor
323C2×#335—431no—
324C2×#332—431no—
325C2×#331—431no—
326C2×C43—161no—
327C2×C43C2×#46011yescharacteristic
328C2×C43C2×#46811yescharacteristic
329C2×C43C2×#47111yescharacteristic
330D43—161no—
331D43#168614yesdirect 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
356#446—431no—
357#446—431no—
358#446—431no—
359#446—861no—
360#446—861no—
361#446C2×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×#97—861no—
370C2×C4×C8—431no—
371#335—431no—
372#335—431no—
373#335—431no—
374#335C2×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×#168611yescharacteristic, 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—
456#97—21no—
457#97—861no—
458#97—861no—
459#97—861no—
460C4×C8—431no—
461C4×C8—431no—
462C4×C8—431no—
463C4×C8C22×D4311yescharacteristic
464C24—1721no—
465C2×Q8—21no—
466C2×Q8—431no—
467C2×Q8—861no—
468C2×Q8—862no—
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—21no—
551Q8—41no—
552Q8—41no—
553Q8—861no—
554Q8—861no—
555Q8—3442no—
556Q8—1722no—
557Q8—1721no—
558Q8—1721no—
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—861no—
584C2×C4—861no—
585C2×C4—3442no—
586C2×C4—1722no—
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—41no—
615C4—41no—
616C4—81no—
617C4—432no—
618C4—432no—
619C4—861no—
620C4—3441no—
621C4—1721no—
622C4—1721no—
623C4C2×SD16×D4311yescharacteristic
624C4AGL(1,ℤ/8)×D4311yescharacteristic
625C4AGL(1,ℤ/8)×D4311yescharacteristic
626C4#137×D4311yescharacteristic
627C2—161no—
628C2—434no—
629C2—6881no—
630C2#460×D4311yescharacteristic
631C2#468×D4311yescharacteristic
632C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1686C2
socleC22×C43C2×#121
prime radical#127×D43C22
hypercenter#1686D43
hypocenterC43C2×#1686
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1686

Complements

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

NH ≅ G/Ntype
2. #475×D43C2semidirect
4. #446×D43C2semidirect
5. #19134070C2semidirect
6. #19134069C2semidirect
7. #19134068C2semidirect
8. #19134067C2semidirect
9. #19134066C2semidirect
10. #19134065C2semidirect
11. #19134064C2semidirect
12. #335×D43C2semidirect
13. #332×D43C2semidirect
15. C43×#1686C2semidirect
27. #14583185C22semidirect
28. #14583184C22semidirect
31. #14583181C22semidirect
37. #14583030C22semidirect
38. #14583029C22semidirect
41. #14583026C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
61. C43×#475C22semidirect
63. C43×#446C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
225. C8×D43SD16semidirect
279. C8×C43C2×SD16semidirect
284. C43⋊C8C2×SD16semidirect
322. #1686D43direct (N × H)
331. D43#1686direct (N × H)
349. #475C2×D43semidirect
361. #446C2×D43semidirect
374. #335C2×D43semidirect
378. #332C2×D43semidirect
383. C43C2×#1686semidirect
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
#446×D432
#191340702
#191340692
#191340682
#191340672
#191340662
#191340652
#191340642
#335×D432
#332×D432
#331×D432
C43×#16862
C2×#168643