Finite Group Databasebeta

← C43×#20282 #24940299

Subgroups — C43×#20282 #24940299

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3399C211yesmaximal, characteristic, complemented
2C43×#3396C211yesmaximal, characteristic, complemented
3C43×#3373C211yesmaximal, characteristic, complemented
4C43×#3278C211yesmaximal, characteristic, complemented
5C43×#1721C211yesmaximal, characteristic, complemented
6C43×#1702C211yesmaximal, characteristic, complemented
7C43×#1688C211yesmaximal, characteristic, complemented
8C43×#1687C211yesmaximal, characteristic, complemented
9C43×#1666C211yesmaximal, characteristic, complemented
10C43×#1640C211yesmaximal, characteristic, complemented
11C43×#1627C211yesmaximal, characteristic, complemented
12C43×#1621C211yesmaximal, characteristic, complemented
13C43×#1620C211yesmaximal, characteristic, complemented
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17C43×#559C2211yescharacteristic
18C43×#559C2211yescharacteristic
19C43×#550C2211yescharacteristic
20D4×Q8×C43C2211yescharacteristic
21C43×#496—21no—
22C43×#495—21no—
23C43×#493C2211yescharacteristic
24C43×#493C2211yescharacteristic
25C43×#493C2211yescharacteristic
26C43×#492C2211yescharacteristic
27C43×#489—21no—
28C43×#486C2211yescharacteristic
29C43×#486C2211yescharacteristic
30C43×#476—21no—
31C43×#475C2211yescharacteristic
32C43×#468—21no—
33C43×#463—21no—
34C43×#463—21no—
35C43×#463—21no—
36C43×#463—21no—
37C43×#462C2211yescharacteristic
38C43×#460C2211yescharacteristic
39C43×#460C2211yescharacteristic
40C43×#460C2211yescharacteristic
41C43×#460C2211yescharacteristic
42C43×#459—21no—
43C43×#459C2211yescharacteristic
44C43×#459C2211yescharacteristic
45C43×#452—21no—
46C43×#448—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C8×Q8×C43C2211yescharacteristic
50C43×#442—21no—
51C43×#442—21no—
52C4×Q16×C43C2211yescharacteristic
53C4×SD16×C43C2211yescharacteristic
54C4×D8×C43—21no—
55C43×#436C2211yescharacteristic
56C43×#334C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#332C2211yescharacteristic
59C43×#331C2211yescharacteristic
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C22×Q8×C43—21no—
69#137×C43—44no—
70C2×Q16×C43—21no—
71C2×Q16×C43D411yescharacteristic
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43—21no—
78C2×SD16×C43D411yescharacteristic
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×D8×C43—21no—
82C2×D8×C43—21no—
83C2×D8×C43—21no—
84C2×D8×C43—21no—
85C2×D8×C43—41no—
86C2×M16×C43—21no—
87C4⋊Q8×C43—21no—
88C4⋊Q8×C43C2311yescharacteristic
89#127×C43—21no—
90#127×C43C2311yescharacteristic
91#127×C43C2311yescharacteristic
92#127×C43C2311yescharacteristic
93#124×C43—21no—
94#124×C43—21no—
95#124×C43—21no—
96#124×C43—21no—
97#123×C43—41no—
98#123×C43—41no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—41no—
101#121×C43—21no—
102#121×C43—41no—
103C4×Q8×C43C2311yescharacteristic
104C4×Q8×C43C2311yescharacteristic
105C4×Q8×C43C2311yescharacteristic
106C4×D4×C43—21no—
107C4×D4×C43—21no—
108C4×D4×C43—21no—
109C4×D4×C43—21no—
110C4×D4×C43—21no—
111C4×D4×C43—21no—
112C4×D4×C43C2311yescharacteristic
113#107×C43D411yescharacteristic
114#106×C43—21no—
115#106×C43D411yescharacteristic
116C4⋊C8×C43—21no—
117C4⋊C8×C43—21no—
118C4⋊C8×C43—21no—
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123#103×C43—21no—
124#103×C43—21no—
125#103×C43D411yescharacteristic
126#103×C43D411yescharacteristic
127#103×C43D411yescharacteristic
128#102×C43—21no—
129#102×C43—21no—
130#102×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134#102×C43—21no—
135#102×C43—21no—
136#102×C43—41no—
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139#97×C43—21no—
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—41no—
164C2×D4×C43—41no—
165C2×D4×C43C2×D411yescharacteristic
166C22×C4×C43—21no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171Q16×C43—22no—
172Q16×C43—42no—
173SD16×C43—41no—
174SD16×C43—42no—
175SD16×C43—42no—
176SD16×C43—81no—
177SD16×C43—81no—
178SD16×C43—81no—
179SD16×C43—81no—
180D8×C43—42no—
181D8×C43—42no—
182D8×C43—42no—
183D8×C43—81no—
184D8×C43—81no—
185D8×C43—81no—
186D8×C43—82no—
187M16×C43—42no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43C2×D411yescharacteristic
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43C2×D411yescharacteristic
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C4⋊C4×C43C2×D411yescharacteristic
207C22⋊C4×C43—21no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C22⋊C4×C43—41no—
215C22⋊C4×C43—41no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43C2411yescharacteristic
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—21no—
229Q8×C43—21no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—82no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—81no—
248D4×C43—81no—
249D4×C43—81no—
250D4×C43—82no—
251D4×C43—161no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—82no—
263C2×C4×C43—82no—
264C2×C4×C43—161no—
265C2×C4×C43—161no—
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43H(5,𝔽2)11yescharacteristic
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43—41no—
277C8×C43AGL(1,ℤ/8)12yes—
278#20282C4311yesmaximal, characteristic, direct product factor, Sylow
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43D4211yescharacteristic
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C43#57511yescharacteristic
303C4×C43#57611yescharacteristic
304C4×C43#57711yescharacteristic
305#3399C2×C4311yescharacteristic, complemented
306#3396C2×C4311yescharacteristic, complemented
307#3373C2×C4311yescharacteristic, complemented
308#3278C2×C4311yescharacteristic, complemented
309#1721C2×C4311yescharacteristic, complemented
310#1702C2×C4311yescharacteristic, complemented
311#1688C2×C4311yescharacteristic, complemented
312#1687C2×C4311yescharacteristic, complemented
313#1666C2×C4311yescharacteristic, complemented
314#1640C2×C4311yescharacteristic, complemented
315#1627C2×C4311yescharacteristic, complemented
316#1621C2×C4311yescharacteristic, complemented
317#1620C2×C4311yescharacteristic, complemented
318#1593C2×C4311yescharacteristic, complemented
319#1583C2×C4311yescharacteristic, complemented
320C2×C43—81no—
321C2×C43—161no—
322C2×C43—161no—
323C2×C43—161no—
324C2×C43#327111yescharacteristic
325C2×C43#327411yescharacteristic
326C2×C43#328811yescharacteristic
327C2×#137—21no—
328#559C22×C4311yescharacteristic
329#559C22×C4311yescharacteristic
330#550C22×C4311yescharacteristic
331D4×Q8C22×C4311yescharacteristic
332#496—21no—
333#495—21no—
334#493C22×C4311yescharacteristic
335#493C22×C4311yescharacteristic
336#493C22×C4311yescharacteristic
337#492C22×C4311yescharacteristic
338#489—21no—
339#486C22×C4311yescharacteristic
340#486C22×C4311yescharacteristic
341#476—21no—
342#475C22×C4311yescharacteristic
343#468—21no—
344#463—21no—
345#463—21no—
346#463—21no—
347#463—21no—
348#462C22×C4311yescharacteristic
349#460C22×C4311yescharacteristic
350#460C22×C4311yescharacteristic
351#460C22×C4311yescharacteristic
352#460C22×C4311yescharacteristic
353#459—21no—
354#459C22×C4311yescharacteristic
355#459C22×C4311yescharacteristic
356#452—21no—
357#448—21no—
358#446C22×C4311yescharacteristic
359#446C22×C4311yescharacteristic
360C8×Q8C22×C4311yescharacteristic
361#442—21no—
362#442—21no—
363C4×Q16C22×C4311yescharacteristic
364C4×SD16C22×C4311yescharacteristic
365C4×D8—21no—
366#436C22×C4311yescharacteristic
367#334C22×C4311yescharacteristic
368#334C22×C4311yescharacteristic
369#332C22×C4311yescharacteristic
370#331C22×C4311yescharacteristic
371#331C22×C4311yescharacteristic
372#331C22×C4311yescharacteristic
373Q8⋊C8C22×C4311yescharacteristic
374Q8⋊C8C22×C4311yescharacteristic
375Q8⋊C8C22×C4311yescharacteristic
376D4⋊C8C22×C4311yescharacteristic
377#322C22×C4311yescharacteristic
378C43#2028211yescharacteristic, direct product factor, Sylow
379C2×#41—21no—
380C22×Q8—21no—
381#137—44no—
382C2×Q16—21no—
383C2×Q16D4×C4311yescharacteristic
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16D4×C4311yescharacteristic
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×D8—21no—
396C2×D8—21no—
397C2×D8—41no—
398C2×M16—21no—
399C4⋊Q8—21no—
400C4⋊Q8C23×C4311yescharacteristic
401#127—21no—
402#127C23×C4311yescharacteristic
403#127C23×C4311yescharacteristic
404#127C23×C4311yescharacteristic
405#124—21no—
406#124—21no—
407#124—21no—
408#124—21no—
409#123—41no—
410#123—41no—
411C22⋊Q8—21no—
412C22⋊Q8—41no—
413#121—21no—
414#121—41no—
415C4×Q8C23×C4311yescharacteristic
416C4×Q8C23×C4311yescharacteristic
417C4×Q8C23×C4311yescharacteristic
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4C23×C4311yescharacteristic
425#107D4×C4311yescharacteristic
426#106—21no—
427#106D4×C4311yescharacteristic
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8C23×C4311yescharacteristic
432C4⋊C8C23×C4311yescharacteristic
433C4⋊C8C23×C4311yescharacteristic
434C4⋊C8C23×C4311yescharacteristic
435#103—21no—
436#103—21no—
437#103D4×C4311yescharacteristic
438#103D4×C4311yescharacteristic
439#103D4×C4311yescharacteristic
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—41no—
449#102D4×C4311yescharacteristic
450C22⋊C8—21no—
451#97—21no—
452#97—21no—
453C4×C8—21no—
454C4×C8C23×C4311yescharacteristic
455C4×C8C23×C4311yescharacteristic
456C4×C8C23×C4311yescharacteristic
457#41—42no—
458#41—81no—
459C2×Q8—21no—
460C2×Q8—41no—
461C2×Q8—42no—
462C2×Q8—81no—
463C2×Q8C2×D4×C4311yescharacteristic
464C2×Q8C2×D4×C4311yescharacteristic
465C2×Q8C2×D4×C4311yescharacteristic
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4C2×D4×C4311yescharacteristic
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483Q16—22no—
484Q16—42no—
485SD16—41no—
486SD16—42no—
487SD16—42no—
488SD16—81no—
489SD16—81no—
490SD16—81no—
491SD16—81no—
492D8—42no—
493D8—42no—
494D8—42no—
495D8—81no—
496D8—81no—
497D8—81no—
498D8—82no—
499M16—42no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8C2×D4×C4311yescharacteristic
506C2×C8C2×D4×C4311yescharacteristic
507C2×C8C2×D4×C4311yescharacteristic
508C2×C8C2×D4×C4311yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C4311yescharacteristic
516C4⋊C4C2×D4×C4311yescharacteristic
517C4⋊C4C2×D4×C4311yescharacteristic
518C4⋊C4C2×D4×C4311yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42C24×C4311yescharacteristic
532C23—21no—
533C23—41no—
534C23—41no—
535C23—41no—
536Q8—21no—
537Q8—21no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—21no—
542Q8—41no—
543Q8—41no—
544Q8—82no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—81no—
560D4—81no—
561D4—81no—
562D4—82no—
563D4—161no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4—161no—
577C2×C4—161no—
578C2×C4C22×D4×C4311yescharacteristic
579C2×C4C22×D4×C4311yescharacteristic
580C2×C4H(5,𝔽2)×C4311yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8AGL(1,ℤ/8)×C4312yes—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22D42×C4311yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
613C4C43×#57511yescharacteristic
614C4C43×#57611yescharacteristic
615C4C43×#57711yescharacteristic
616C2—81no—
617C2—161no—
618C2—161no—
619C2—161no—
620C2C43×#327111yescharacteristic
621C2C43×#327411yescharacteristic
622C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3399C2semidirect
2. C43×#3396C2semidirect
3. C43×#3373C2semidirect
4. C43×#3278C2semidirect
5. C43×#1721C2semidirect
6. C43×#1702C2semidirect
7. C43×#1688C2semidirect
8. C43×#1687C2semidirect
9. C43×#1666C2semidirect
10. C43×#1640C2semidirect
11. C43×#1627C2semidirect
12. C43×#1621C2semidirect
13. C43×#1620C2semidirect
14. C43×#1593C2semidirect
15. C43×#1583C2semidirect
278. #20282C43direct (N × H)
305. #3399C2×C43semidirect
306. #3396C2×C43semidirect
307. #3373C2×C43semidirect
308. #3278C2×C43semidirect
309. #1721C2×C43semidirect
310. #1702C2×C43semidirect
311. #1688C2×C43semidirect
312. #1687C2×C43semidirect
313. #1666C2×C43semidirect
314. #1640C2×C43semidirect
315. #1627C2×C43semidirect
316. #1621C2×C43semidirect
317. #1620C2×C43semidirect
318. #1593C2×C43semidirect
319. #1583C2×C43semidirect
378. C43#20282direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33992
C43×#33962
C43×#33732
C43×#32782
C43×#17212
C43×#17022
C43×#16882
C43×#16872
C43×#16662
C43×#16402
C43×#16272
C43×#16212
C43×#16202
C43×#15932
C43×#15832
#2028243