Finite Group Databasebeta

← D43×#1699 #25079150

Subgroups — D43×#1699 #25079150

Order 11008.

726 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#487×D43C211yesmaximal, characteristic, complemented
2#474×D43C211yesmaximal, characteristic
3#461×D43C211yesmaximal, characteristic
4#436×D43C211yesmaximal, characteristic
5#19134145C211yesmaximal, characteristic, complemented
6#19134144C211yesmaximal, characteristic, complemented
7#19134143C211yesmaximal, characteristic, complemented
8#19134142C211yesmaximal, characteristic, complemented
9#19134141C211yesmaximal, characteristic, complemented
10#19134140C211yesmaximal, characteristic, complemented
11#19134139C211yesmaximal, characteristic, complemented
12#335×D43C211yesmaximal, characteristic, complemented
13#332×D43C211yesmaximal, characteristic, complemented
14#332×D43C211yesmaximal, characteristic, complemented
15C43×#1699C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C2×M16×D43—21no—
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20C4×D4×D43C2211yescharacteristic
21#14583251C2211yescharacteristic, complemented
22#14583250C2211yescharacteristic, complemented
23#14583249C2211yescharacteristic, complemented
24#14583248—21no—
25#14583248—21no—
26#14583180C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583178—21no—
29#14583177—21no—
30#14583176C2211yescharacteristic
31#14583105C2211yescharacteristic
32#14583104C2211yescharacteristic
33#14583103—21no—
34#14583102—21no—
35#14583101C2211yescharacteristic
36#14582978C2211yescharacteristic
37#14582977C2211yescharacteristic
38#14582976C2211yescharacteristic
39#14582975—21no—
40#14582974—21no—
41#107×D43—21no—
42C4⋊C8×D43C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#103×D43—21no—
46#103×D43—21no—
47#103×D43—21no—
48#102×D43—21no—
49C22⋊C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582645C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582644C2211yescharacteristic, complemented
60C43×#487C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#335C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, 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—
75C2×#10621877—21no—
76C2×#10621872—21no—
77C2×#10621872—21no—
78M16×D43—44no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
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#13063259—21no—
105#13063258—21no—
106#13063258—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063249—21no—
117#13063249—21no—
118#13063249—21no—
119#13063248—21no—
120#13063248—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—
132C2×M16×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134C4⋊Q8×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
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—42no—
156Q8×D43—42no—
157D4×D43—22no—
158D4×D43—22no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—41no—
166C2×C4×D43—41no—
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43#4111yescharacteristic
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—41no—
173C2×Dic86—41no—
174SD16×C43—42no—
175M16×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×C43—21no—
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C42×C43C2411yescharacteristic
188C22⋊Dic43—21no—
189#10621884—42no—
190#10621883—42no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43#4111yescharacteristic
206#10621877—42no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212#10621873—42no—
213#10621872—42no—
214#10621872—42no—
215C8×D43—22no—
216C8×D43—22no—
217C8×D43—42no—
218C8×D43—42no—
219C8×D43—42no—
220C23×C43—21no—
221C22×D43—21no—
222C22×D43—42no—
223C22×D43—42no—
224C22×D43—42no—
225C22×D43#12111yescharacteristic
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230D4×C43—21no—
231D4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—42no—
241C2×Dic43—21no—
242C2×Dic43—42no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43#12111yescharacteristic
246C2×Dic43#12111yescharacteristic
247C2×Dic43#12111yescharacteristic
248D172—21no—
249D172—21no—
250C4×D43—22no—
251C4×D43—42no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—42no—
255C4×D43—82no—
256C4×D43—82no—
257C4×D43#13512yes—
258C4×D43AGL(1,ℤ/8)12yes—
259C4×D43AGL(1,ℤ/8)12yes—
260C4×D43#13712yes—
261Dic86—41no—
262Dic86—41no—
263Dic86—41no—
264Dic86—41no—
265Dic86—82no—
266Dic86—82no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272C43⋊C8—21no—
273C43⋊C8—21no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C2×#1699—431nomaximal, Sylow
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43C2×#12111yescharacteristic
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—84no—
286C2×D43#46312yes—
287C2×D43#46812yes—
288C2×D43#47312yes—
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43C2×#13511yescharacteristic
294C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C43C2×#13711yescharacteristic
297Dic43—21no—
298Dic43—41no—
299Dic43—81no—
300Dic43—81no—
301Dic43#46312yes—
302Dic43#46812yes—
303C2×#487—431no—
304C2×#474—431no—
305C2×#461—431no—
306C2×#436—431no—
307#1699—431no—
308#1699—431no—
309#1699—431no—
310#1699—431no—
311#1699—431no—
312#1699—431no—
313#1699—431no—
314#1699D4311yescharacteristic, direct product factor
315C2×#335—431no—
316C2×#332—431no—
317C2×#332—431no—
318C2×C43—81no—
319C2×C43C2×#46311yescharacteristic
320C2×C43C2×#46811yescharacteristic
321C2×C43C2×#47311yescharacteristic
322D43—81no—
323D43#169914yesdirect product factor
324C22×SD16—861no—
325C22×M16—861no—
326C2×C4⋊Q8—431no—
327C2×C4⋊Q8—431no—
328C2×C4×D4—431no—
329#487—431no—
330#487—431no—
331#487—431no—
332#487—861no—
333#487—861no—
334#487C2×D4311yescharacteristic, complemented
335#474—431no—
336#474—431no—
337#474—431no—
338#474—861no—
339#474—861no—
340#474C2×D4311yescharacteristic
341#461—431no—
342#461—431no—
343#461—431no—
344#461—861no—
345#461—861no—
346#461C2×D4311yescharacteristic
347#436—431no—
348#436—431no—
349#436—431no—
350#436—861no—
351#436—861no—
352#436C2×D4311yescharacteristic
353C2×#107—861no—
354C2×C4⋊C8—431no—
355C2×C4⋊C8—431no—
356C2×C4⋊C8—431no—
357C2×#103—861no—
358C2×#103—861no—
359C2×#103—861no—
360C2×#102—861no—
361C2×C22⋊C8—861no—
362C2×C4×C8—431no—
363#335—431no—
364#335—431no—
365#335—431no—
366#335C2×D4311yescharacteristic, complemented
367#332—431no—
368#332—431no—
369#332—431no—
370#332—431no—
371#332—431no—
372#332—431no—
373#332C2×D4311yescharacteristic, complemented
374#332C2×D4311yescharacteristic, complemented
375C43C2×#169911yescharacteristic, complemented, Sylow
376C22×Q8—861no—
377C22×Q8—861no—
378C22×D4—431no—
379C23×C4—861no—
380C2×SD16—21no—
381C2×SD16—861no—
382C2×SD16—861no—
383C2×SD16—861no—
384C2×SD16—1724no—
385C2×M16—21no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16—1724no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—861no—
393C22×C8—861no—
394C22×C8—861no—
395C4⋊Q8—431no—
396C4⋊Q8—431no—
397C4⋊Q8—861no—
398C4⋊Q8—861no—
399C4⋊Q8—861no—
400C4⋊Q8—861no—
401C4⋊Q8—861no—
402C4⋊Q8—861no—
403C4⋊Q8C22×D4311yescharacteristic
404C4⋊Q8C22×D4311yescharacteristic
405C4×D4—431no—
406C4×D4—431no—
407C4×D4—431no—
408C4×D4—861no—
409C4×D4—861no—
410C4×D4C22×D4311yescharacteristic
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C42—431no—
418#107—21no—
419#107—861no—
420#107—861no—
421#107—861no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—861no—
426C4⋊C8—861no—
427C4⋊C8—861no—
428C4⋊C8C22×D4311yescharacteristic
429C4⋊C8C22×D4311yescharacteristic
430C4⋊C8C22×D4311yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—861no—
435#103—861no—
436#103—861no—
437#103—861no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#103—861no—
443#102—21no—
444#102—861no—
445#102—861no—
446#102—861no—
447C22⋊C8—21no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8C22×D4311yescharacteristic
455C24—861no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—861no—
459C2×Q8—861no—
460C2×Q8—1721no—
461C2×Q8—1721no—
462C2×Q8—1722no—
463C2×Q8—1722no—
464C2×Q8—1722no—
465C2×Q8—1722no—
466C2×D4—431no—
467C2×D4—862no—
468C2×D4—862no—
469C2×D4—861no—
470C2×D4D4×D4311yescharacteristic
471C22×C4—21no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4—1721no—
482C22×C4—1721no—
483SD16—42no—
484SD16—1722no—
485SD16—1722no—
486SD16—1722no—
487M16—42no—
488M16—1722no—
489M16—1722no—
490M16—1722no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—431no—
495C2×C8—431no—
496C2×C8—862no—
497C2×C8—862no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—1722no—
502C2×C8—1722no—
503C2×C8—1722no—
504C2×C8D4×D4311yescharacteristic
505C2×C8D4×D4311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—431no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—1721no—
517C4⋊C4—1721no—
518C4⋊C4—1721no—
519C4⋊C4—1721no—
520C4⋊C4D4×D4311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C22⋊C4—861no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42C23×D4311yescharacteristic
529C23—21no—
530C23—431no—
531C23—861no—
532C23—1722no—
533C23—1722no—
534C23—1722no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—3442no—
540Q8—3442no—
541Q8—1721no—
542Q8—1721no—
543Q8—1721no—
544Q8—1721no—
545D4—21no—
546D4—21no—
547D4—861no—
548D4—861no—
549D4—1722no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—431no—
556C2×C4—431no—
557C2×C4—432no—
558C2×C4—432no—
559C2×C4—432no—
560C2×C4—432no—
561C2×C4—431no—
562C2×C4—862no—
563C2×C4—861no—
564C2×C4—3442no—
565C2×C4—3442no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—861no—
582C8—861no—
583C8—1721no—
584C8—1721no—
585C8—1721no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—432no—
590C22—432no—
591C22—432no—
592C22—3444no—
593C22—1721no—
594C22—1721no—
595C22—1721no—
596C22#121×D4311yescharacteristic
597C4—21no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—432no—
602C4—432no—
603C4—861no—
604C4—3441no—
605C4—3441no—
606C4—1721no—
607C4#135×D4311yescharacteristic
608C4AGL(1,ℤ/8)×D4311yescharacteristic
609C4AGL(1,ℤ/8)×D4311yescharacteristic
610C4#137×D4311yescharacteristic
611C2—81no—
612C2—434no—
613C2—3441no—
614C2#463×D4311yescharacteristic
615C2#468×D4311yescharacteristic
616C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1699C2
socleC22×C43C2×#121
prime radicalC2×D4×D43D4
hypercenter#1699D43
hypocenterC43C2×#1699
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1699

Complements

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

NH ≅ G/Ntype
1. #487×D43C2semidirect
5. #19134145C2semidirect
6. #19134144C2semidirect
7. #19134143C2semidirect
8. #19134142C2semidirect
9. #19134141C2semidirect
10. #19134140C2semidirect
11. #19134139C2semidirect
12. #335×D43C2semidirect
13. #332×D43C2semidirect
14. #332×D43C2semidirect
15. C43×#1699C2semidirect
21. #14583251C22semidirect
22. #14583250C22semidirect
23. #14583249C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582646C22semidirect
55. #14582646C22semidirect
56. #14582645C22semidirect
57. #14582645C22semidirect
58. #14582644C22semidirect
59. #14582644C22semidirect
60. C43×#487C22semidirect
64. C43×#335C22semidirect
65. C43×#332C22semidirect
66. C43×#332C22semidirect
314. #1699D43direct (N × H)
323. D43#1699direct (N × H)
334. #487C2×D43semidirect
366. #335C2×D43semidirect
373. #332C2×D43semidirect
374. #332C2×D43semidirect
375. C43C2×#1699semidirect

Maximal subgroups

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

subgroupindex
#487×D432
#474×D432
#461×D432
#436×D432
#191341452
#191341442
#191341432
#191341422
#191341412
#191341402
#191341392
#335×D432
#332×D432
C43×#16992
C2×#169943