Finite Group Databasebeta

← D43×#1697 #25079142

Subgroups — D43×#1697 #25079142

Order 11008.

778 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#486×D43C211yesmaximal, characteristic, complemented
2#476×D43C211yesmaximal, characteristic, complemented
3#459×D43C211yesmaximal, characteristic
4#436×D43C211yesmaximal, characteristic, complemented
5#19134131C211yesmaximal, characteristic, complemented
6#19134130C211yesmaximal, characteristic, complemented
7#19134129C211yesmaximal, characteristic, complemented
8#19134128C211yesmaximal, characteristic, complemented
9#19134127C211yesmaximal, characteristic, complemented
10#19134126C211yesmaximal, characteristic, complemented
11#19134125C211yesmaximal, characteristic, complemented
12#335×D43C211yesmaximal, characteristic, complemented
13#333×D43C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic, complemented
15C43×#1697C211yesmaximal, characteristic, complemented
16C2×D8×D43—21no—
17C2×M16×D43—21no—
18C4⋊Q8×D43C2211yescharacteristic
19#127×D43C2211yescharacteristic
20C4×D4×D43C2211yescharacteristic
21#14583247C2211yescharacteristic, complemented
22#14583246C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic, complemented
24#14583244—21no—
25#14583244—21no—
26#14583190C2211yescharacteristic, complemented
27#14583189C2211yescharacteristic, complemented
28#14583188—21no—
29#14583187—21no—
30#14583186C2211yescharacteristic, complemented
31#14583095C2211yescharacteristic
32#14583094C2211yescharacteristic
33#14583093—21no—
34#14583092—21no—
35#14583091C2211yescharacteristic
36#14582978C2211yescharacteristic, complemented
37#14582977C2211yescharacteristic, complemented
38#14582976C2211yescharacteristic, complemented
39#14582975—21no—
40#14582974—21no—
41#106×D43—21no—
42C4⋊C8×D43C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#102×D43—21no—
46#102×D43—21no—
47#102×D43—21no—
48#102×D43—21no—
49C22⋊C8×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, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C43×#436C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, 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×D344—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76D8×D43—44no—
77C2×#10621877—21no—
78C2×#10621872—21no—
79C2×#10621872—21no—
80M16×D43—44no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83C2×C8×D43—21no—
84C2×C8×D43D411yescharacteristic
85C2×C8×D43D411yescharacteristic
86#13063325C2311yescharacteristic
87#13063324—21no—
88#13063324—21no—
89#13063323—21no—
90#13063322C2311yescharacteristic
91#13063321—21no—
92#13063321—21no—
93#13063321—21no—
94C4×D172C2311yescharacteristic
95D4×Dic43D411yescharacteristic
96#13063287D411yescharacteristic
97C4×C22⋊D43—21no—
98(C22⋊D43)⋊C4—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43D411yescharacteristic
102C22⋊C4×D43—21no—
103C42×D43C2311yescharacteristic
104#13063257—21no—
105#13063256—21no—
106#13063256—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063247—21no—
114#13063247—21no—
115#13063247—21no—
116#13063247—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063245—21no—
122#13063245—21no—
123#13063245—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×D8×C43—21no—
132C2×M16×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C23×D43—41no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C2×C22⋊D43—21no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C2×C22⋊D43—41no—
158C22×Dic43—21no—
159Q8×D43—82no—
160D4×D43—22no—
161D4×D43—22no—
162D4×D43—42no—
163D4×D43—42no—
164D4×D43—42no—
165D4×D43—42no—
166D4×D43—82no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172C2×D411yescharacteristic
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—42no—
175C2×C4×D43—42no—
176C2×C4×D43—41no—
177C2×C4×D43C2×D411yescharacteristic
178C2×C4×D43C2×D411yescharacteristic
179C2×C4×D43#4111yescharacteristic
180C2×Dic86—21no—
181C2×Dic86—41no—
182D8×C43—42no—
183M16×C43—42no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43C2×D411yescharacteristic
192C22⋊C4×C43—21no—
193C42×C43C2411yescharacteristic
194C22⋊Dic43—21no—
195#10621882—42no—
196#10621882—42no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205C4×Dic43C2×D411yescharacteristic
206C4×Dic43C2×D411yescharacteristic
207C4×Dic43#4111yescharacteristic
208#10621877—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214D344—42no—
215#10621872—42no—
216#10621872—42no—
217C8×D43—22no—
218C8×D43—22no—
219C8×D43—42no—
220C8×D43—42no—
221C8×D43—42no—
222C23×C43—21no—
223C23×C43—41no—
224C22×D43—21no—
225C22×D43—42no—
226C22×D43—42no—
227C22×D43—42no—
228C22×D43—41no—
229C22×D43—82no—
230C22×D43—82no—
231C22×D43—82no—
232C22×D43#12111yescharacteristic
233Q8×C43—81no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—81no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C22⋊D43—42no—
249C22⋊D43—82no—
250C22⋊D43—82no—
251C22⋊D43—82no—
252C2×Dic43—21no—
253C2×Dic43—42no—
254C2×Dic43—41no—
255C2×Dic43#12111yescharacteristic
256C2×Dic43#12111yescharacteristic
257C2×Dic43#12111yescharacteristic
258D172—21no—
259D172—21no—
260D172—41no—
261D172—41no—
262D172—41no—
263D172—41no—
264D172—81no—
265C4×D43—22no—
266C4×D43—42no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—42no—
270C4×D43—82no—
271C4×D43#13512yes—
272C4×D43AGL(1,ℤ/8)12yes—
273C4×D43AGL(1,ℤ/8)12yes—
274C4×D43#13712yes—
275Dic86—82no—
276Dic86—81no—
277C8×C43—21no—
278C8×C43—21no—
279C8×C43—41no—
280C8×C43—41no—
281C8×C43—41no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C2×#1697—431nomaximal, Sylow
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43C2×#12111yescharacteristic
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—84no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—164no—
303C2×D43#46312yes—
304C2×D43#46812yes—
305C2×D43#47212yes—
306C4×C43—21no—
307C4×C43—41no—
308C4×C43—81no—
309C4×C43C2×#13511yescharacteristic
310C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
311C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
312C4×C43C2×#13711yescharacteristic
313Dic43—21no—
314Dic43—41no—
315Dic43—81no—
316Dic43#46312yes—
317Dic43#46812yes—
318C2×#486—431no—
319C2×#476—431no—
320C2×#459—431no—
321C2×#436—431no—
322#1697—431no—
323#1697—431no—
324#1697—431no—
325#1697—431no—
326#1697—431no—
327#1697—431no—
328#1697—431no—
329#1697D4311yescharacteristic, direct product factor
330C2×#335—431no—
331C2×#333—431no—
332C2×#331—431no—
333C2×C43—81no—
334C2×C43—161no—
335C2×C43C2×#46311yescharacteristic
336C2×C43C2×#46811yescharacteristic
337C2×C43C2×#47211yescharacteristic
338D43—81no—
339D43—161no—
340D43#169714yesdirect product factor
341C22×D8—861no—
342C22×M16—861no—
343C2×C4⋊Q8—431no—
344C2×#127—431no—
345C2×C4×D4—431no—
346#486—431no—
347#486—431no—
348#486—431no—
349#486—861no—
350#486—861no—
351#486C2×D4311yescharacteristic, complemented
352#476—431no—
353#476—431no—
354#476—431no—
355#476—861no—
356#476—861no—
357#476C2×D4311yescharacteristic, complemented
358#459—431no—
359#459—431no—
360#459—431no—
361#459—861no—
362#459—861no—
363#459C2×D4311yescharacteristic
364#436—431no—
365#436—431no—
366#436—431no—
367#436—861no—
368#436—861no—
369#436C2×D4311yescharacteristic, complemented
370C2×#106—861no—
371C2×C4⋊C8—431no—
372C2×C4⋊C8—431no—
373C2×C4⋊C8—431no—
374C2×#102—861no—
375C2×#102—861no—
376C2×#102—861no—
377C2×#102—861no—
378C2×C22⋊C8—861no—
379C2×C4×C8—431no—
380#335—431no—
381#335—431no—
382#335—431no—
383#335C2×D4311yescharacteristic, complemented
384#333—431no—
385#333—431no—
386#333—431no—
387#333C2×D4311yescharacteristic, complemented
388#331—431no—
389#331—431no—
390#331—431no—
391#331C2×D4311yescharacteristic, complemented
392C43C2×#169711yescharacteristic, complemented, Sylow
393C22×Q8—861no—
394C22×D4—431no—
395C22×D4—861no—
396C22×D4—861no—
397C22×D4—861no—
398C23×C4—861no—
399C2×D8—21no—
400C2×D8—861no—
401C2×D8—861no—
402C2×D8—861no—
403C2×D8—1724no—
404C2×M16—21no—
405C2×M16—861no—
406C2×M16—861no—
407C2×M16—861no—
408C2×M16—1724no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8—861no—
412C22×C8—861no—
413C22×C8—861no—
414C4⋊Q8—431no—
415C4⋊Q8—861no—
416C4⋊Q8—861no—
417C4⋊Q8—861no—
418C4⋊Q8C22×D4311yescharacteristic
419#127—431no—
420#127—861no—
421#127—861no—
422#127—861no—
423#127C22×D4311yescharacteristic
424C4×D4—431no—
425C4×D4—431no—
426C4×D4—431no—
427C4×D4—861no—
428C4×D4—861no—
429C4×D4C22×D4311yescharacteristic
430C2×C4⋊C4—431no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C42—431no—
435#106—21no—
436#106—861no—
437#106—861no—
438#106—861no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8C22×D4311yescharacteristic
446C4⋊C8C22×D4311yescharacteristic
447C4⋊C8C22×D4311yescharacteristic
448#102—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102—861no—
458#102—861no—
459#102—861no—
460#102—861no—
461#102—861no—
462#102—861no—
463#102—861no—
464C22⋊C8—21no—
465C22⋊C8—861no—
466C22⋊C8—861no—
467C22⋊C8—861no—
468C4×C8—431no—
469C4×C8—431no—
470C4×C8—431no—
471C4×C8C22×D4311yescharacteristic
472C24—861no—
473C24—1721no—
474C2×Q8—21no—
475C2×Q8—861no—
476C2×Q8—3442no—
477C2×Q8—1721no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—431no—
482C2×D4—862no—
483C2×D4—862no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—3442no—
489C2×D4—1722no—
490C2×D4—1722no—
491C2×D4—1722no—
492C2×D4—1722no—
493C2×D4—1721no—
494C2×D4—1721no—
495C2×D4—1721no—
496C2×D4D4×D4311yescharacteristic
497C22×C4—21no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4—1721no—
508D8—42no—
509D8—1722no—
510D8—1722no—
511D8—1722no—
512M16—42no—
513M16—1722no—
514M16—1722no—
515M16—1722no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—431no—
520C2×C8—431no—
521C2×C8—862no—
522C2×C8—862no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—1722no—
527C2×C8—1722no—
528C2×C8—1722no—
529C2×C8D4×D4311yescharacteristic
530C2×C8D4×D4311yescharacteristic
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—431no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—1721no—
538C4⋊C4—1721no—
539C4⋊C4D4×D4311yescharacteristic
540C22⋊C4—21no—
541C22⋊C4—861no—
542C22⋊C4—861no—
543C22⋊C4—861no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42C23×D4311yescharacteristic
548C23—21no—
549C23—41no—
550C23—431no—
551C23—861no—
552C23—3442no—
553C23—3442no—
554C23—3442no—
555C23—1722no—
556C23—1722no—
557C23—1722no—
558C23—1721no—
559Q8—81no—
560Q8—3441no—
561Q8—3442no—
562D4—21no—
563D4—21no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—81no—
569D4—861no—
570D4—861no—
571D4—3441no—
572D4—3442no—
573D4—3442no—
574D4—3442no—
575D4—1722no—
576D4—1721no—
577D4—1721no—
578D4—1721no—
579D4—1721no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—431no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—3442no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C8—21no—
604C8—21no—
605C8—41no—
606C8—41no—
607C8—41no—
608C8—861no—
609C8—861no—
610C8—1721no—
611C8—1721no—
612C8—1721no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—432no—
620C22—432no—
621C22—432no—
622C22—3444no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—1721no—
627C22—1721no—
628C22—1721no—
629C22—6884no—
630C22#121×D4311yescharacteristic
631C4—21no—
632C4—41no—
633C4—81no—
634C4—432no—
635C4—432no—
636C4—861no—
637C4—3441no—
638C4—1721no—
639C4#135×D4311yescharacteristic
640C4AGL(1,ℤ/8)×D4311yescharacteristic
641C4AGL(1,ℤ/8)×D4311yescharacteristic
642C4#137×D4311yescharacteristic
643C2—81no—
644C2—161no—
645C2—434no—
646C2—3441no—
647C2—6881no—
648C2#463×D4311yescharacteristic
649C2#468×D4311yescharacteristic
650C2#472×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1697C2
socleC22×C43C2×#121
prime radical#459×D43C2
hypercenter#1697D43
hypocenterC43C2×#1697
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1697

Complements

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

NH ≅ G/Ntype
1. #486×D43C2semidirect
2. #476×D43C2semidirect
4. #436×D43C2semidirect
5. #19134131C2semidirect
6. #19134130C2semidirect
7. #19134129C2semidirect
8. #19134128C2semidirect
9. #19134127C2semidirect
10. #19134126C2semidirect
11. #19134125C2semidirect
12. #335×D43C2semidirect
13. #333×D43C2semidirect
14. #331×D43C2semidirect
15. C43×#1697C2semidirect
21. #14583247C22semidirect
22. #14583246C22semidirect
23. #14583245C22semidirect
26. #14583190C22semidirect
27. #14583189C22semidirect
30. #14583186C22semidirect
36. #14582978C22semidirect
37. #14582977C22semidirect
38. #14582976C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582648C22semidirect
55. #14582647C22semidirect
56. #14582647C22semidirect
57. #14582643C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#486C22semidirect
61. C43×#476C22semidirect
63. C43×#436C22semidirect
64. C43×#335C22semidirect
65. C43×#333C22semidirect
66. C43×#331C22semidirect
329. #1697D43direct (N × H)
340. D43#1697direct (N × H)
351. #486C2×D43semidirect
357. #476C2×D43semidirect
369. #436C2×D43semidirect
383. #335C2×D43semidirect
387. #333C2×D43semidirect
391. #331C2×D43semidirect
392. C43C2×#1697semidirect

Maximal subgroups

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

subgroupindex
#486×D432
#476×D432
#459×D432
#436×D432
#191341312
#191341302
#191341292
#191341282
#191341272
#191341262
#191341252
#335×D432
#333×D432
#331×D432
C43×#16972
C2×#169743