Finite Group Databasebeta

← D43×#1665 #25078814

Subgroups — D43×#1665 #25078814

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#492×D43C211yesmaximal, characteristic, complemented
2#474×D43C211yesmaximal, characteristic, complemented
3#459×D43C211yesmaximal, characteristic
4C8×D4×D43C211yesmaximal, characteristic, complemented
5#19133939C211yesmaximal, characteristic, complemented
6#19133938C211yesmaximal, characteristic, complemented
7#19133937C211yesmaximal, characteristic, complemented
8#19133936C211yesmaximal, characteristic, complemented
9#19133935C211yesmaximal, characteristic, complemented
10#19133934C211yesmaximal, characteristic, complemented
11#19133933C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic, complemented
13#332×D43C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C2×SD16×D43—21no—
18C2×D8×D43—21no—
19C22×C8×D43—21no—
20C4⋊Q8×D43C2211yescharacteristic
21#127×D43C2211yescharacteristic
22C4×D4×D43C2211yescharacteristic
23#14583273C2211yescharacteristic, complemented
24#14583272C2211yescharacteristic, complemented
25#14583271C2211yescharacteristic, complemented
26#14583270—21no—
27#14583270—21no—
28#14583180C2211yescharacteristic, complemented
29#14583179C2211yescharacteristic, complemented
30#14583178—21no—
31#14583177—21no—
32#14583176C2211yescharacteristic, complemented
33#14583095C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583093—21no—
36#14583092—21no—
37#14583091C2211yescharacteristic
38C8×D172C2211yescharacteristic, complemented
39D4×C43⋊C8C2211yescharacteristic, complemented
40#14582964C2211yescharacteristic, complemented
41C8×C22⋊D43—21no—
42(C22⋊D43)⋊C8—21no—
43#107×D43—21no—
44C4⋊C8×D43C2211yescharacteristic
45C4⋊C8×D43C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#102×D43—21no—
48#102×D43—21no—
49C22⋊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, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#492C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic, complemented
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×Q8×D43—21no—
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43D411yescharacteristic
72C22×C4×D43—21no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×#10621883—21no—
76C2×#10621883—21no—
77C2×#10621884—21no—
78C2×#10621884—21no—
79SD16×D43—44no—
80SD16×D43—44no—
81C2×D344—21no—
82C2×#10621882—21no—
83C2×#10621882—21no—
84D8×D43—44no—
85C22×C43⋊C8—21no—
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88C2×C8×D43—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91C2×C8×D43—44no—
92C2×C8×D43D411yescharacteristic
93C2×C8×D43D411yescharacteristic
94#13063325C2311yescharacteristic
95#13063324—21no—
96#13063324—21no—
97#13063323—21no—
98#13063322C2311yescharacteristic
99#13063321—21no—
100#13063321—21no—
101#13063321—21no—
102C4×D172C2311yescharacteristic
103D4×Dic43D411yescharacteristic
104#13063287D411yescharacteristic
105C4×C22⋊D43—21no—
106(C22⋊D43)⋊C4—21no—
107C4⋊C4×D43—21no—
108C4⋊C4×D43—21no—
109C4⋊C4×D43D411yescharacteristic
110C22⋊C4×D43—21no—
111C42×D43C2311yescharacteristic
112#13063259—21no—
113#13063258—21no—
114#13063258—21no—
115C4⋊(C43⋊C8)C2311yescharacteristic
116C4⋊(C43⋊C8)C2311yescharacteristic
117C4⋊(C43⋊C8)C2311yescharacteristic
118Dic43⋊C8—21no—
119Dic43⋊C8—21no—
120Dic43⋊C8—21no—
121#13063247—21no—
122#13063247—21no—
123#13063246—21no—
124#13063246—21no—
125#13063245—21no—
126#13063245—21no—
127C22⋊(C43⋊C8)—21no—
128(C2×D43)⋊C8—21no—
129(C2×D43)⋊C8—21no—
130C4×C43⋊C8C2311yescharacteristic
131C8×Dic43D411yescharacteristic
132C8×Dic43D411yescharacteristic
133C2×SD16×C43—21no—
134C2×SD16×C43—21no—
135C2×D8×C43—21no—
136C22×C8×C43—21no—
137C4⋊Q8×C43C2311yescharacteristic
138#127×C43C2311yescharacteristic
139C4×D4×C43C2311yescharacteristic
140#107×C43—21no—
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143C4⋊C8×C43C2311yescharacteristic
144#102×C43—21no—
145#102×C43—21no—
146C22⋊C8×C43—21no—
147C4×C8×C43C2311yescharacteristic
148C23×D43—21no—
149C23×D43—41no—
150C2×Q8×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C2×C22⋊D43—21no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160C22×Dic43—21no—
161Q8×D43—42no—
162Q8×D43—42no—
163D4×D43—22no—
164D4×D43—42no—
165D4×D43—42no—
166D4×D43—42no—
167D4×D43—42no—
168D4×D43—82no—
169D4×D43SD1614yescomplemented
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172C2×D411yescharacteristic
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43—41no—
180C2×C4×D43C2×D411yescharacteristic
181C2×C4×D43C2×D411yescharacteristic
182C2×C4×D43#4111yescharacteristic
183C2×Dic86—21no—
184C2×Dic86—41no—
185SD16×C43—42no—
186SD16×C43—42no—
187D8×C43—42no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—42no—
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43C2×D411yescharacteristic
197C22⋊C4×C43—21no—
198C42×C43C2411yescharacteristic
199C22⋊Dic43—21no—
200#10621884—42no—
201#10621884—42no—
202#10621883—42no—
203#10621883—42no—
204#10621882—42no—
205#10621882—42no—
206(C2×D43)⋊C4—21no—
207(C2×D43)⋊C4—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43C2×D411yescharacteristic
211Dic43⋊C4—21no—
212Dic43⋊C4—41no—
213Dic43⋊C4—41no—
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43#4111yescharacteristic
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—42no—
221C2×C43⋊C8C2×D411yescharacteristic
222C2×C43⋊C8C2×D411yescharacteristic
223D344—42no—
224#10621873—42no—
225#10621873—42no—
226C8×D43—22no—
227C8×D43—42no—
228C8×D43—42no—
229C8×D43—42no—
230C8×D43—42no—
231C8×D43—42no—
232C8×D43D814yescomplemented
233C23×C43—21no—
234C23×C43—41no—
235C22×D43—21no—
236C22×D43—24no—
237C22×D43—42no—
238C22×D43—42no—
239C22×D43—41no—
240C22×D43—82no—
241C22×D43—82no—
242C22×D43—82no—
243C22×D43#12111yescharacteristic
244Q8×C43—41no—
245Q8×C43—41no—
246D4×C43—21no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—81no—
252D4×C43C2×SD1612yescomplemented
253C2×C4×C43—21no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C22⋊D43—24no—
261C22⋊D43—82no—
262C22⋊D43—82no—
263C22⋊D43—82no—
264C2×Dic43—21no—
265C2×Dic43—42no—
266C2×Dic43—41no—
267C2×Dic43#12111yescharacteristic
268C2×Dic43#12111yescharacteristic
269C2×Dic43#12111yescharacteristic
270D172—21no—
271D172—41no—
272D172—41no—
273D172—41no—
274D172—41no—
275D172—81no—
276D172C2×SD1612yescomplemented
277C4×D43—22no—
278C4×D43—42no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—42no—
282C4×D43—82no—
283C4×D43C2×D812yes—
284C4×D43C2×SD1612yes—
285C4×D43#13512yes—
286C4×D43AGL(1,ℤ/8)12yes—
287Dic86—41no—
288Dic86—41no—
289Dic86—82no—
290C8×C43—21no—
291C8×C43—41no—
292C8×C43—41no—
293C8×C43—41no—
294C8×C43C2×D812yescomplemented
295C43⋊C8—21no—
296C43⋊C8—41no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299C43⋊C8C2×D812yescomplemented
300C2×#1665—431nomaximal, Sylow
301C22×C43—22no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43C2×#12111yescharacteristic
308C2×D43—22no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—48no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C2×D43—164no—
316C2×D43#45912yes—
317C2×D43#46512yes—
318C2×D43#47112yes—
319C4×C43—21no—
320C4×C43—41no—
321C4×C43—81no—
322C4×C43C22×D811yescharacteristic
323C4×C43C22×SD1611yescharacteristic
324C4×C43C2×#13511yescharacteristic
325C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
326Dic43—21no—
327Dic43—41no—
328Dic43—81no—
329Dic43#45912yes—
330Dic43#46512yes—
331C2×#492—431no—
332C2×#474—431no—
333C2×#459—431no—
334C2×C8×D4—431no—
335#1665—431no—
336#1665—431no—
337#1665—431no—
338#1665—431no—
339#1665—431no—
340#1665—431no—
341#1665—431no—
342#1665D4311yescharacteristic, direct product factor
343C2×#334—431no—
344C2×#332—431no—
345C2×#331—431no—
346C2×C43—42no—
347C2×C43—161no—
348C2×C43C2×#45911yescharacteristic
349C2×C43C2×#46511yescharacteristic
350C2×C43C2×#47111yescharacteristic
351D43—42no—
352D43—161no—
353D43#166514yesdirect product factor
354C22×SD16—861no—
355C22×SD16—861no—
356C22×D8—861no—
357C23×C8—861no—
358C2×C4⋊Q8—431no—
359C2×#127—431no—
360C2×C4×D4—431no—
361#492—431no—
362#492—431no—
363#492—431no—
364#492—861no—
365#492—861no—
366#492C2×D4311yescharacteristic, complemented
367#474—431no—
368#474—431no—
369#474—431no—
370#474—861no—
371#474—861no—
372#474C2×D4311yescharacteristic, complemented
373#459—431no—
374#459—431no—
375#459—431no—
376#459—861no—
377#459—861no—
378#459C2×D4311yescharacteristic
379C8×D4—431no—
380C8×D4—431no—
381C8×D4—431no—
382C8×D4—861no—
383C8×D4—861no—
384C8×D4C2×D4311yescharacteristic, complemented
385C2×#107—861no—
386C2×C4⋊C8—431no—
387C2×C4⋊C8—431no—
388C2×C4⋊C8—431no—
389C2×#102—861no—
390C2×#102—861no—
391C2×C22⋊C8—861no—
392C2×C4×C8—431no—
393#334—431no—
394#334—431no—
395#334—431no—
396#334C2×D4311yescharacteristic, complemented
397#332—431no—
398#332—431no—
399#332—431no—
400#332C2×D4311yescharacteristic, complemented
401#331—431no—
402#331—431no—
403#331—431no—
404#331C2×D4311yescharacteristic, complemented
405C43C2×#166511yescharacteristic, complemented, Sylow
406C22×Q8—861no—
407C22×D4—431no—
408C22×D4—861no—
409C22×D4—861no—
410C22×D4—861no—
411C23×C4—861no—
412C2×SD16—21no—
413C2×SD16—21no—
414C2×SD16—861no—
415C2×SD16—861no—
416C2×SD16—861no—
417C2×SD16—861no—
418C2×SD16—861no—
419C2×SD16—861no—
420C2×SD16—1724no—
421C2×SD16—1724no—
422C2×D8—21no—
423C2×D8—861no—
424C2×D8—861no—
425C2×D8—861no—
426C2×D8—1724no—
427C22×C8—21no—
428C22×C8—431no—
429C22×C8—431no—
430C22×C8—861no—
431C22×C8—861no—
432C22×C8—861no—
433C22×C8—861no—
434C22×C8—861no—
435C22×C8—861no—
436C22×C8—1724no—
437C4⋊Q8—431no—
438C4⋊Q8—861no—
439C4⋊Q8—861no—
440C4⋊Q8—861no—
441C4⋊Q8C22×D4311yescharacteristic
442#127—431no—
443#127—861no—
444#127—861no—
445#127—861no—
446#127C22×D4311yescharacteristic
447C4×D4—431no—
448C4×D4—431no—
449C4×D4—431no—
450C4×D4—861no—
451C4×D4—861no—
452C4×D4C22×D4311yescharacteristic
453C2×C4⋊C4—431no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C42—431no—
458#107—21no—
459#107—861no—
460#107—861no—
461#107—861no—
462C4⋊C8—431no—
463C4⋊C8—431no—
464C4⋊C8—431no—
465C4⋊C8—861no—
466C4⋊C8—861no—
467C4⋊C8—861no—
468C4⋊C8C22×D4311yescharacteristic
469C4⋊C8C22×D4311yescharacteristic
470C4⋊C8C22×D4311yescharacteristic
471#102—21no—
472#102—21no—
473#102—861no—
474#102—861no—
475#102—861no—
476#102—861no—
477#102—861no—
478#102—861no—
479C22⋊C8—21no—
480C22⋊C8—861no—
481C22⋊C8—861no—
482C22⋊C8—861no—
483C4×C8—431no—
484C4×C8—431no—
485C4×C8—431no—
486C4×C8C22×D4311yescharacteristic
487C24—861no—
488C24—1721no—
489C2×Q8—21no—
490C2×Q8—861no—
491C2×Q8—1721no—
492C2×Q8—1722no—
493C2×Q8—1722no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—434no—
498C2×D4—431no—
499C2×D4—862no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4—861no—
503C2×D4—861no—
504C2×D4—3442no—
505C2×D4—1722no—
506C2×D4—1722no—
507C2×D4—1722no—
508C2×D4—1722no—
509C2×D4—1721no—
510C2×D4—1721no—
511C2×D4—1721no—
512C2×D4D4×D4311yescharacteristic
513C22×C4—21no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—1722no—
522C22×C4—1722no—
523C22×C4—1721no—
524SD16—42no—
525SD16—42no—
526SD16—1722no—
527SD16—1722no—
528SD16—1722no—
529SD16—1722no—
530SD16—1722no—
531SD16—1722no—
532D8—42no—
533D8—1722no—
534D8—1722no—
535D8—1722no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—42no—
540C2×C8—431no—
541C2×C8—434no—
542C2×C8—431no—
543C2×C8—862no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—1722no—
548C2×C8—1722no—
549C2×C8—1722no—
550C2×C8—1722no—
551C2×C8—1722no—
552C2×C8—1722no—
553C2×C8D4×D4311yescharacteristic
554C2×C8D4×D4311yescharacteristic
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—431no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—1721no—
562C4⋊C4—1721no—
563C4⋊C4D4×D4311yescharacteristic
564C22⋊C4—21no—
565C22⋊C4—861no—
566C22⋊C4—861no—
567C22⋊C4—861no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42C23×D4311yescharacteristic
572C23—21no—
573C23—41no—
574C23—431no—
575C23—864no—
576C23—861no—
577C23—3442no—
578C23—3442no—
579C23—3442no—
580C23—1722no—
581C23—1722no—
582C23—1721no—
583Q8—41no—
584Q8—41no—
585Q8—3442no—
586Q8—1721no—
587Q8—1721no—
588D4—21no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—41no—
593D4—81no—
594D4—432no—
595D4—864no—
596D4—861no—
597D4—3441no—
598D4—3442no—
599D4—3442no—
600D4—3442no—
601D4—1721no—
602D4—1721no—
603D4—1721no—
604D4—1721no—
605D4SD16×D4312yescomplemented
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—431no—
611C2×C4—431no—
612C2×C4—432no—
613C2×C4—432no—
614C2×C4—432no—
615C2×C4—432no—
616C2×C4—431no—
617C2×C4—862no—
618C2×C4—861no—
619C2×C4—3442no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4C2×D4×D4311yescharacteristic
627C2×C4C2×D4×D4311yescharacteristic
628C2×C4#41×D4311yescharacteristic
629C8—21no—
630C8—41no—
631C8—41no—
632C8—41no—
633C8—432no—
634C8—861no—
635C8—1721no—
636C8—1721no—
637C8—1721no—
638C8D8×D4312yescomplemented
639C22—22no—
640C22—41no—
641C22—41no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—432no—
646C22—432no—
647C22—432no—
648C22—862no—
649C22—3441no—
650C22—3441no—
651C22—3441no—
652C22—1728no—
653C22—1721no—
654C22—1721no—
655C22—6884no—
656C22#121×D4311yescharacteristic
657C4—21no—
658C4—41no—
659C4—81no—
660C4—432no—
661C4—432no—
662C4—861no—
663C4—3441no—
664C4—1721no—
665C4C2×D8×D4311yescharacteristic
666C4C2×SD16×D4311yescharacteristic
667C4#135×D4311yescharacteristic
668C4AGL(1,ℤ/8)×D4311yescharacteristic
669C2—42no—
670C2—161no—
671C2—434no—
672C2—1722no—
673C2—6881no—
674C2#459×D4311yescharacteristic
675C2#465×D4311yescharacteristic
676C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#459×D43C2
hypercenter#1665D43
hypocenterC43C2×#1665
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1665

Complements

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

NH ≅ G/Ntype
1. #492×D43C2semidirect
2. #474×D43C2semidirect
4. C8×D4×D43C2semidirect
5. #19133939C2semidirect
6. #19133938C2semidirect
7. #19133937C2semidirect
8. #19133936C2semidirect
9. #19133935C2semidirect
10. #19133934C2semidirect
11. #19133933C2semidirect
12. #334×D43C2semidirect
13. #332×D43C2semidirect
14. #331×D43C2semidirect
15. C43×#1665C2semidirect
23. #14583273C22semidirect
24. #14583272C22semidirect
25. #14583271C22semidirect
28. #14583180C22semidirect
29. #14583179C22semidirect
32. #14583176C22semidirect
38. C8×D172C22semidirect
39. D4×C43⋊C8C22semidirect
40. #14582964C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
57. #14582643C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#492C22semidirect
61. C43×#474C22semidirect
63. C8×D4×C43C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
66. C43×#331C22semidirect
169. D4×D43SD16semidirect
232. C8×D43D8semidirect
252. D4×C43C2×SD16semidirect
276. D172C2×SD16semidirect
294. C8×C43C2×D8semidirect
299. C43⋊C8C2×D8semidirect
342. #1665D43direct (N × H)
353. D43#1665direct (N × H)
366. #492C2×D43semidirect
372. #474C2×D43semidirect
384. C8×D4C2×D43semidirect
396. #334C2×D43semidirect
400. #332C2×D43semidirect
404. #331C2×D43semidirect
405. C43C2×#1665semidirect
605. D4SD16×D43semidirect
638. C8D8×D43semidirect

Maximal subgroups

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

subgroupindex
#492×D432
#474×D432
#459×D432
C8×D4×D432
#191339392
#191339382
#191339372
#191339362
#191339352
#191339342
#191339332
#334×D432
#332×D432
#331×D432
C43×#16652
C2×#166543