Finite Group Databasebeta

← D43×#1698 #25079241

Subgroups — D43×#1698 #25079241

Order 11008.

702 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#486×D43C211yesmaximal, characteristic
2#477×D43C211yesmaximal, characteristic, complemented
3#460×D43C211yesmaximal, characteristic
4#446×D43C211yesmaximal, characteristic, complemented
5#19134138C211yesmaximal, characteristic, complemented
6#19134137C211yesmaximal, characteristic, complemented
7#19134136C211yesmaximal, characteristic, complemented
8#19134135C211yesmaximal, characteristic, complemented
9#19134134C211yesmaximal, characteristic, complemented
10#19134133C211yesmaximal, characteristic, complemented
11#19134132C211yesmaximal, characteristic, complemented
12#335×D43C211yesmaximal, characteristic, complemented
13#333×D43C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic
15C43×#1698C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C4⋊Q8×D43C2211yescharacteristic
18#127×D43C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583244—21no—
24#14583244—21no—
25#14583195C2211yescharacteristic, complemented
26#14583194C2211yescharacteristic, complemented
27#14583193—21no—
28#14583192—21no—
29#14583191C2211yescharacteristic, complemented
30#14583100C2211yescharacteristic
31#14583099C2211yescharacteristic
32#14583098—21no—
33#14583097—21no—
34#14583096C2211yescharacteristic
35#14583030C2211yescharacteristic, complemented
36#14583029C2211yescharacteristic, complemented
37#14583028—21no—
38#14583027—21no—
39#14583026C2211yescharacteristic, complemented
40#107×D43—21no—
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#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582647C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#477C2211yescharacteristic, complemented
62C43×#460C2211yescharacteristic
63C43×#446C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, 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×#10621883—21no—
74C2×#10621884—21no—
75SD16×D43—44no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43D411yescharacteristic
80C2×C8×D43D411yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063323—21no—
85#13063322C2311yescharacteristic
86#13063321—21no—
87#13063321—21no—
88#13063321—21no—
89Q8×Dic43D411yescharacteristic
90C4×Dic86—21no—
91C4×Dic86C2311yescharacteristic
92#13063290—21no—
93#13063290D411yescharacteristic
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43D411yescharacteristic
98C42×D43—21no—
99C42×D43C2311yescharacteristic
100#13063259—21no—
101#13063258—21no—
102#13063258—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112#13063250—21no—
113#13063249—21no—
114#13063248—21no—
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063245—21no—
122#13063245—21no—
123#13063245—21no—
124#13063236—21no—
125#13063235—21no—
126#13063235—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132#127×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#107×C43—21no—
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#97×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154Q8×D43—22no—
155Q8×D43—22no—
156Q8×D43—82no—
157D4×D43—42no—
158D4×D43—42no—
159D4×D43—42no—
160D4×D43—42no—
161D4×D43—82no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—41no—
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43#4111yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—41no—
174C2×Dic86C2×D411yescharacteristic
175SD16×C43—42no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C2×D411yescharacteristic
185C42×C43—21no—
186C42×C43C2411yescharacteristic
187#10621884—42no—
188#10621883—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43#4111yescharacteristic
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621873—42no—
210C8×D43—22no—
211C8×D43—22no—
212C8×D43—42no—
213C8×D43—42no—
214C8×D43—42no—
215C23×C43—41no—
216C22×D43—41no—
217C22×D43—82no—
218C22×D43—82no—
219C22×D43—82no—
220C22×D43#12111yescharacteristic
221Q8×C43—21no—
222Q8×C43—21no—
223Q8×C43—81no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—82no—
236C22⋊D43—82no—
237C22⋊D43—82no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43#12111yescharacteristic
242C2×Dic43#12111yescharacteristic
243C2×Dic43#12111yescharacteristic
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—81no—
249C4×D43—22no—
250C4×D43—42no—
251C4×D43—42no—
252C4×D43—82no—
253C4×D43#13512yes—
254C4×D43AGL(1,ℤ/8)12yes—
255C4×D43#13712yes—
256C4×D43#13712yes—
257Dic86—21no—
258Dic86—21no—
259Dic86—42no—
260Dic86—82no—
261Dic86—81no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C43⋊C8—21no—
268C43⋊C8—21no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C2×#1698—431nomaximal, Sylow
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43C2×#12111yescharacteristic
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—164no—
281C2×D43#46412yes—
282C2×D43#46812yes—
283C2×D43#47212yes—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43C2×#13511yescharacteristic
289C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
290C4×C43C2×#13711yescharacteristic
291C4×C43C2×#13711yescharacteristic
292Dic43—21no—
293Dic43—41no—
294Dic43—41no—
295Dic43—81no—
296Dic43#46412yes—
297Dic43#46812yes—
298C2×#486—431no—
299C2×#477—431no—
300C2×#460—431no—
301C2×#446—431no—
302#1698—431no—
303#1698—431no—
304#1698—431no—
305#1698—431no—
306#1698—431no—
307#1698—431no—
308#1698—431no—
309#1698D4311yescharacteristic, direct product factor
310C2×#335—431no—
311C2×#333—431no—
312C2×#331—431no—
313C2×C43—161no—
314C2×C43C2×#46411yescharacteristic
315C2×C43C2×#46811yescharacteristic
316C2×C43C2×#47211yescharacteristic
317D43—161no—
318D43#169814yesdirect product factor
319C22×SD16—861no—
320C2×C4⋊Q8—431no—
321C2×#127—431no—
322C2×C4×Q8—431no—
323#486—431no—
324#486—431no—
325#486—431no—
326#486—861no—
327#486—861no—
328#486C2×D4311yescharacteristic
329#477—431no—
330#477—431no—
331#477—431no—
332#477—861no—
333#477—861no—
334#477C2×D4311yescharacteristic, complemented
335#460—431no—
336#460—431no—
337#460—431no—
338#460—861no—
339#460—861no—
340#460C2×D4311yescharacteristic
341#446—431no—
342#446—431no—
343#446—431no—
344#446—861no—
345#446—861no—
346#446C2×D4311yescharacteristic, complemented
347C2×#107—861no—
348C2×C4⋊C8—431no—
349C2×C4⋊C8—431no—
350C2×C4⋊C8—431no—
351C2×C4⋊C8—861no—
352C2×#103—861no—
353C2×#102—861no—
354C2×#102—861no—
355C2×#102—861no—
356C2×#97—861no—
357C2×C4×C8—431no—
358#335—431no—
359#335—431no—
360#335—431no—
361#335C2×D4311yescharacteristic, complemented
362#333—431no—
363#333—431no—
364#333—431no—
365#333C2×D4311yescharacteristic, complemented
366#331—431no—
367#331—431no—
368#331—431no—
369#331C2×D4311yescharacteristic
370C43C2×#169811yescharacteristic, complemented, Sylow
371C22×Q8—431no—
372C22×Q8—861no—
373C22×D4—861no—
374C22×D4—861no—
375C22×D4—861no—
376C2×SD16—21no—
377C2×SD16—861no—
378C2×SD16—861no—
379C2×SD16—861no—
380C2×SD16—1724no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8—861no—
384C22×C8—861no—
385C22×C8—861no—
386C4⋊Q8—431no—
387C4⋊Q8—861no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390C4⋊Q8C22×D4311yescharacteristic
391#127—431no—
392#127—861no—
393#127—861no—
394#127—861no—
395#127C22×D4311yescharacteristic
396C4×Q8—431no—
397C4×Q8—431no—
398C4×Q8—431no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8C22×D4311yescharacteristic
402C2×C4⋊C4—431no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C42—431no—
407C2×C42—861no—
408#107—21no—
409#107—861no—
410#107—861no—
411#107—861no—
412C4⋊C8—21no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8—861no—
421C4⋊C8—861no—
422C4⋊C8C22×D4311yescharacteristic
423C4⋊C8C22×D4311yescharacteristic
424C4⋊C8C22×D4311yescharacteristic
425#103—21no—
426#103—861no—
427#103—861no—
428#103—861no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#97—21no—
442#97—861no—
443#97—861no—
444#97—861no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—431no—
448C4×C8C22×D4311yescharacteristic
449C24—1721no—
450C2×Q8—21no—
451C2×Q8—431no—
452C2×Q8—861no—
453C2×Q8—862no—
454C2×Q8—862no—
455C2×Q8—861no—
456C2×Q8—3442no—
457C2×Q8—1721no—
458C2×Q8D4×D4311yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—3442no—
466C2×D4—1722no—
467C2×D4—1722no—
468C2×D4—1722no—
469C2×D4—1722no—
470C2×D4—1721no—
471C2×D4—1721no—
472C2×D4—1721no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—1721no—
479SD16—42no—
480SD16—1722no—
481SD16—1722no—
482SD16—1722no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—862no—
489C2×C8—862no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—1722no—
494C2×C8—1722no—
495C2×C8—1722no—
496C2×C8D4×D4311yescharacteristic
497C2×C8D4×D4311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—431no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4D4×D4311yescharacteristic
511C42—21no—
512C42—431no—
513C42—431no—
514C42—431no—
515C42—861no—
516C42—861no—
517C42—861no—
518C42C23×D4311yescharacteristic
519C23—41no—
520C23—431no—
521C23—3442no—
522C23—3442no—
523C23—3442no—
524C23—1721no—
525Q8—21no—
526Q8—21no—
527Q8—81no—
528Q8—861no—
529Q8—861no—
530Q8—3441no—
531Q8—3442no—
532Q8—1722no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—81no—
538D4—3441no—
539D4—3442no—
540D4—3442no—
541D4—3442no—
542D4—1721no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546C2×C4—21no—
547C2×C4—21no—
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—861no—
559C2×C4—3442no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1721no—
563C2×C4C2×D4×D4311yescharacteristic
564C2×C4C2×D4×D4311yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—861no—
572C8—861no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—432no—
580C22—432no—
581C22—432no—
582C22—3441no—
583C22—3441no—
584C22—3441no—
585C22—6884no—
586C22#121×D4311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—81no—
591C4—432no—
592C4—432no—
593C4—861no—
594C4—3441no—
595C4—1721no—
596C4—1721no—
597C4#135×D4311yescharacteristic
598C4AGL(1,ℤ/8)×D4311yescharacteristic
599C4#137×D4311yescharacteristic
600C4#137×D4311yescharacteristic
601C2—161no—
602C2—434no—
603C2—6881no—
604C2#464×D4311yescharacteristic
605C2#468×D4311yescharacteristic
606C2#472×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1698C2
socleC22×C43C2×#121
prime radical#127×D43C22
hypercenter#1698D43
hypocenterC43C2×#1698
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1698

Complements

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

NH ≅ G/Ntype
2. #477×D43C2semidirect
4. #446×D43C2semidirect
5. #19134138C2semidirect
6. #19134137C2semidirect
7. #19134136C2semidirect
8. #19134135C2semidirect
9. #19134134C2semidirect
10. #19134133C2semidirect
11. #19134132C2semidirect
12. #335×D43C2semidirect
13. #333×D43C2semidirect
15. C43×#1698C2semidirect
25. #14583195C22semidirect
26. #14583194C22semidirect
29. #14583191C22semidirect
35. #14583030C22semidirect
36. #14583029C22semidirect
39. #14583026C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
61. C43×#477C22semidirect
63. C43×#446C22semidirect
64. C43×#335C22semidirect
65. C43×#333C22semidirect
309. #1698D43direct (N × H)
318. D43#1698direct (N × H)
334. #477C2×D43semidirect
346. #446C2×D43semidirect
361. #335C2×D43semidirect
365. #333C2×D43semidirect
370. C43C2×#1698semidirect

Maximal subgroups

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

subgroupindex
#486×D432
#477×D432
#460×D432
#446×D432
#191341382
#191341372
#191341362
#191341352
#191341342
#191341332
#191341322
#335×D432
#333×D432
#331×D432
C43×#16982
C2×#169843