Finite Group Databasebeta

← D43×#1701 #25079158

Subgroups — D43×#1701 #25079158

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#486×D43C211yesmaximal, characteristic, complemented
2#461×D43C211yesmaximal, characteristic, complemented
3#459×D43C211yesmaximal, characteristic
4#436×D43C211yesmaximal, characteristic, complemented
5#19134159C211yesmaximal, characteristic, complemented
6#19134158C211yesmaximal, characteristic, complemented
7#19134157C211yesmaximal, characteristic, complemented
8#19134156C211yesmaximal, characteristic, complemented
9#19134155C211yesmaximal, characteristic, complemented
10#19134154C211yesmaximal, characteristic, complemented
11#19134153C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic, complemented
13#332×D43C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic, complemented
15C43×#1701C211yesmaximal, characteristic, complemented
16C2×SD16×D43—21no—
17C2×D8×D43—21no—
18C2×M16×D43—21no—
19C4⋊Q8×D43C2211yescharacteristic
20#127×D43C2211yescharacteristic
21C4×D4×D43C2211yescharacteristic
22#14583247C2211yescharacteristic, complemented
23#14583246C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic, complemented
25#14583244—21no—
26#14583244—21no—
27#14583105C2211yescharacteristic, complemented
28#14583104C2211yescharacteristic, complemented
29#14583103—21no—
30#14583102—21no—
31#14583101C2211yescharacteristic, complemented
32#14583095C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583093—21no—
35#14583092—21no—
36#14583091C2211yescharacteristic
37#14582978C2211yescharacteristic, complemented
38#14582977C2211yescharacteristic, complemented
39#14582976C2211yescharacteristic, complemented
40#14582975—21no—
41#14582974—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—
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×#486C2211yescharacteristic, complemented
61C43×#461C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C43×#436C2211yescharacteristic, 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×#10621883—21no—
75C2×#10621884—21no—
76SD16×D43—44no—
77C2×D344—21no—
78C2×#10621882—21no—
79C2×#10621882—21no—
80D8×D43—44no—
81C2×#10621877—21no—
82C2×#10621872—21no—
83C2×#10621872—21no—
84M16×D43—44no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88C2×C8×D43D411yescharacteristic
89C2×C8×D43D411yescharacteristic
90#13063325C2311yescharacteristic
91#13063324—21no—
92#13063324—21no—
93#13063323—21no—
94#13063322C2311yescharacteristic
95#13063321—21no—
96#13063321—21no—
97#13063321—21no—
98C4×D172C2311yescharacteristic
99D4×Dic43D411yescharacteristic
100#13063287D411yescharacteristic
101C4×C22⋊D43—21no—
102(C22⋊D43)⋊C4—21no—
103C4⋊C4×D43—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43D411yescharacteristic
106C22⋊C4×D43—21no—
107C42×D43C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114#13063250—21no—
115#13063249—21no—
116#13063248—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063246—21no—
121#13063246—21no—
122#13063246—21no—
123#13063245—21no—
124#13063245—21no—
125#13063245—21no—
126C22⋊(C43⋊C8)—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129C4×C43⋊C8C2311yescharacteristic
130C8×Dic43D411yescharacteristic
131C8×Dic43D411yescharacteristic
132C2×SD16×C43—21no—
133C2×D8×C43—21no—
134C2×M16×C43—21no—
135C4⋊Q8×C43C2311yescharacteristic
136#127×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#102×C43—21no—
145C22⋊C8×C43—21no—
146C4×C8×C43C2311yescharacteristic
147C23×D43—21no—
148C23×D43—41no—
149C2×Q8×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C2×C22⋊D43—21no—
156C2×C22⋊D43—41no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C22×Dic43—21no—
160Q8×D43—42no—
161Q8×D43—42no—
162D4×D43—22no—
163D4×D43—22no—
164D4×D43—42no—
165D4×D43—42no—
166D4×D43—42no—
167D4×D43—42no—
168D4×D43—82no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172C2×D411yescharacteristic
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43—41no—
179C2×C4×D43C2×D411yescharacteristic
180C2×C4×D43C2×D411yescharacteristic
181C2×C4×D43#4111yescharacteristic
182C2×Dic86—21no—
183C2×Dic86—41no—
184SD16×C43—42no—
185D8×C43—42no—
186M16×C43—42no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43C2×D411yescharacteristic
195C22⋊C4×C43—21no—
196C42×C43C2411yescharacteristic
197C22⋊Dic43—21no—
198#10621884—42no—
199#10621883—42no—
200#10621882—42no—
201#10621882—42no—
202(C2×D43)⋊C4—21no—
203(C2×D43)⋊C4—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—21no—
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210C4×Dic43C2×D411yescharacteristic
211C4×Dic43C2×D411yescharacteristic
212C4×Dic43#4111yescharacteristic
213#10621877—42no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219D344—42no—
220#10621873—42no—
221#10621872—42no—
222#10621872—42no—
223C8×D43—22no—
224C8×D43—22no—
225C8×D43—42no—
226C8×D43—42no—
227C8×D43—42no—
228C23×C43—21no—
229C23×C43—41no—
230C22×D43—21no—
231C22×D43—42no—
232C22×D43—42no—
233C22×D43—42no—
234C22×D43—41no—
235C22×D43—82no—
236C22×D43—82no—
237C22×D43—82no—
238C22×D43#12111yescharacteristic
239Q8×C43—41no—
240Q8×C43—41no—
241D4×C43—21no—
242D4×C43—21no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—81no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C22⋊D43—42no—
256C22⋊D43—82no—
257C22⋊D43—82no—
258C22⋊D43—82no—
259C2×Dic43—21no—
260C2×Dic43—42no—
261C2×Dic43—41no—
262C2×Dic43#12111yescharacteristic
263C2×Dic43#12111yescharacteristic
264C2×Dic43#12111yescharacteristic
265D172—21no—
266D172—21no—
267D172—41no—
268D172—41no—
269D172—41no—
270D172—41no—
271D172—81no—
272C4×D43—22no—
273C4×D43—42no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—42no—
277C4×D43—82no—
278C4×D43#13512yes—
279C4×D43AGL(1,ℤ/8)12yes—
280C4×D43AGL(1,ℤ/8)12yes—
281C4×D43AGL(1,ℤ/8)12yes—
282Dic86—41no—
283Dic86—41no—
284Dic86—82no—
285C8×C43—21no—
286C8×C43—21no—
287C8×C43—41no—
288C8×C43—41no—
289C8×C43—41no—
290C43⋊C8—21no—
291C43⋊C8—21no—
292C43⋊C8—41no—
293C43⋊C8—41no—
294C43⋊C8—41no—
295C2×#1701—431nomaximal, Sylow
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43C2×#12111yescharacteristic
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—84no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—164no—
311C2×D43#46312yes—
312C2×D43#46912yes—
313C2×D43#47112yes—
314C4×C43—21no—
315C4×C43—41no—
316C4×C43—81no—
317C4×C43C2×#13511yescharacteristic
318C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
319C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
320C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
321Dic43—21no—
322Dic43—41no—
323Dic43—81no—
324Dic43#46312yes—
325Dic43#46912yes—
326C2×#486—431no—
327C2×#461—431no—
328C2×#459—431no—
329C2×#436—431no—
330#1701—431no—
331#1701—431no—
332#1701—431no—
333#1701—431no—
334#1701—431no—
335#1701—431no—
336#1701—431no—
337#1701D4311yescharacteristic, direct product factor
338C2×#334—431no—
339C2×#332—431no—
340C2×#331—431no—
341C2×C43—81no—
342C2×C43—161no—
343C2×C43C2×#46311yescharacteristic
344C2×C43C2×#46911yescharacteristic
345C2×C43C2×#47111yescharacteristic
346D43—81no—
347D43—161no—
348D43#170114yesdirect product factor
349C22×SD16—861no—
350C22×D8—861no—
351C22×M16—861no—
352C2×C4⋊Q8—431no—
353C2×#127—431no—
354C2×C4×D4—431no—
355#486—431no—
356#486—431no—
357#486—431no—
358#486—861no—
359#486—861no—
360#486C2×D4311yescharacteristic, complemented
361#461—431no—
362#461—431no—
363#461—431no—
364#461—861no—
365#461—861no—
366#461C2×D4311yescharacteristic, complemented
367#459—431no—
368#459—431no—
369#459—431no—
370#459—861no—
371#459—861no—
372#459C2×D4311yescharacteristic
373#436—431no—
374#436—431no—
375#436—431no—
376#436—861no—
377#436—861no—
378#436C2×D4311yescharacteristic, complemented
379C2×C4⋊C8—431no—
380C2×C4⋊C8—431no—
381C2×C4⋊C8—431no—
382C2×#103—861no—
383C2×#102—861no—
384C2×#102—861no—
385C2×#102—861no—
386C2×C22⋊C8—861no—
387C2×C4×C8—431no—
388#334—431no—
389#334—431no—
390#334—431no—
391#334C2×D4311yescharacteristic, complemented
392#332—431no—
393#332—431no—
394#332—431no—
395#332C2×D4311yescharacteristic, complemented
396#331—431no—
397#331—431no—
398#331—431no—
399#331C2×D4311yescharacteristic, complemented
400C43C2×#170111yescharacteristic, complemented, Sylow
401C22×Q8—861no—
402C22×D4—431no—
403C22×D4—861no—
404C22×D4—861no—
405C22×D4—861no—
406C23×C4—861no—
407C2×SD16—21no—
408C2×SD16—861no—
409C2×SD16—861no—
410C2×SD16—861no—
411C2×SD16—1724no—
412C2×D8—21no—
413C2×D8—861no—
414C2×D8—861no—
415C2×D8—861no—
416C2×D8—1724no—
417C2×M16—21no—
418C2×M16—861no—
419C2×M16—861no—
420C2×M16—861no—
421C2×M16—1724no—
422C22×C8—431no—
423C22×C8—431no—
424C22×C8—861no—
425C22×C8—861no—
426C22×C8—861no—
427C4⋊Q8—431no—
428C4⋊Q8—861no—
429C4⋊Q8—861no—
430C4⋊Q8—861no—
431C4⋊Q8C22×D4311yescharacteristic
432#127—431no—
433#127—861no—
434#127—861no—
435#127—861no—
436#127C22×D4311yescharacteristic
437C4×D4—431no—
438C4×D4—431no—
439C4×D4—431no—
440C4×D4—861no—
441C4×D4—861no—
442C4×D4C22×D4311yescharacteristic
443C2×C4⋊C4—431no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C42—431no—
448C4⋊C8—431no—
449C4⋊C8—431no—
450C4⋊C8—431no—
451C4⋊C8—861no—
452C4⋊C8—861no—
453C4⋊C8—861no—
454C4⋊C8C22×D4311yescharacteristic
455C4⋊C8C22×D4311yescharacteristic
456C4⋊C8C22×D4311yescharacteristic
457#103—21no—
458#103—861no—
459#103—861no—
460#103—861no—
461#102—21no—
462#102—21no—
463#102—21no—
464#102—861no—
465#102—861no—
466#102—861no—
467#102—861no—
468#102—861no—
469#102—861no—
470#102—861no—
471#102—861no—
472#102—861no—
473C22⋊C8—21no—
474C22⋊C8—861no—
475C22⋊C8—861no—
476C22⋊C8—861no—
477C4×C8—431no—
478C4×C8—431no—
479C4×C8—431no—
480C4×C8C22×D4311yescharacteristic
481C24—861no—
482C24—1721no—
483C2×Q8—21no—
484C2×Q8—861no—
485C2×Q8—1721no—
486C2×Q8—1722no—
487C2×Q8—1722no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—431no—
492C2×D4—862no—
493C2×D4—862no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—3442no—
499C2×D4—1722no—
500C2×D4—1722no—
501C2×D4—1722no—
502C2×D4—1722no—
503C2×D4—1721no—
504C2×D4—1721no—
505C2×D4—1721no—
506C2×D4D4×D4311yescharacteristic
507C22×C4—21no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—1722no—
516C22×C4—1722no—
517C22×C4—1721no—
518SD16—42no—
519SD16—1722no—
520SD16—1722no—
521SD16—1722no—
522D8—42no—
523D8—1722no—
524D8—1722no—
525D8—1722no—
526M16—42no—
527M16—1722no—
528M16—1722no—
529M16—1722no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—431no—
534C2×C8—431no—
535C2×C8—862no—
536C2×C8—862no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—1722no—
541C2×C8—1722no—
542C2×C8—1722no—
543C2×C8D4×D4311yescharacteristic
544C2×C8D4×D4311yescharacteristic
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—431no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—1721no—
552C4⋊C4—1721no—
553C4⋊C4D4×D4311yescharacteristic
554C22⋊C4—21no—
555C22⋊C4—861no—
556C22⋊C4—861no—
557C22⋊C4—861no—
558C42—431no—
559C42—431no—
560C42—431no—
561C42C23×D4311yescharacteristic
562C23—21no—
563C23—41no—
564C23—431no—
565C23—861no—
566C23—3442no—
567C23—3442no—
568C23—3442no—
569C23—1722no—
570C23—1722no—
571C23—1722no—
572C23—1721no—
573Q8—41no—
574Q8—41no—
575Q8—3442no—
576Q8—1721no—
577Q8—1721no—
578D4—21no—
579D4—21no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—81no—
585D4—861no—
586D4—861no—
587D4—3441no—
588D4—3442no—
589D4—3442no—
590D4—3442no—
591D4—1722no—
592D4—1721no—
593D4—1721no—
594D4—1721no—
595D4—1721no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—431no—
601C2×C4—431no—
602C2×C4—432no—
603C2×C4—432no—
604C2×C4—432no—
605C2×C4—432no—
606C2×C4—431no—
607C2×C4—862no—
608C2×C4—861no—
609C2×C4—3442no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4C2×D4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C8—21no—
620C8—21no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—861no—
625C8—861no—
626C8—1721no—
627C8—1721no—
628C8—1721no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—432no—
636C22—432no—
637C22—432no—
638C22—3444no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—1721no—
643C22—1721no—
644C22—1721no—
645C22—6884no—
646C22#121×D4311yescharacteristic
647C4—21no—
648C4—41no—
649C4—81no—
650C4—432no—
651C4—432no—
652C4—861no—
653C4—3441no—
654C4—1721no—
655C4#135×D4311yescharacteristic
656C4AGL(1,ℤ/8)×D4311yescharacteristic
657C4AGL(1,ℤ/8)×D4311yescharacteristic
658C4AGL(1,ℤ/8)×D4311yescharacteristic
659C2—81no—
660C2—161no—
661C2—434no—
662C2—3441no—
663C2—6881no—
664C2#463×D4311yescharacteristic
665C2#469×D4311yescharacteristic
666C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1701C2
socleC22×C43C2×#121
prime radical#459×D43C2
hypercenter#1701D43
hypocenterC43C2×#1701
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1701

Complements

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

NH ≅ G/Ntype
1. #486×D43C2semidirect
2. #461×D43C2semidirect
4. #436×D43C2semidirect
5. #19134159C2semidirect
6. #19134158C2semidirect
7. #19134157C2semidirect
8. #19134156C2semidirect
9. #19134155C2semidirect
10. #19134154C2semidirect
11. #19134153C2semidirect
12. #334×D43C2semidirect
13. #332×D43C2semidirect
14. #331×D43C2semidirect
15. C43×#1701C2semidirect
22. #14583247C22semidirect
23. #14583246C22semidirect
24. #14583245C22semidirect
27. #14583105C22semidirect
28. #14583104C22semidirect
31. #14583101C22semidirect
37. #14582978C22semidirect
38. #14582977C22semidirect
39. #14582976C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
57. #14582643C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#486C22semidirect
61. C43×#461C22semidirect
63. C43×#436C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
66. C43×#331C22semidirect
337. #1701D43direct (N × H)
348. D43#1701direct (N × H)
360. #486C2×D43semidirect
366. #461C2×D43semidirect
378. #436C2×D43semidirect
391. #334C2×D43semidirect
395. #332C2×D43semidirect
399. #331C2×D43semidirect
400. C43C2×#1701semidirect

Maximal subgroups

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

subgroupindex
#486×D432
#461×D432
#459×D432
#436×D432
#191341592
#191341582
#191341572
#191341562
#191341552
#191341542
#191341532
#334×D432
#332×D432
#331×D432
C43×#17012
C2×#170143