Finite Group Databasebeta

← C43×#20250 #24940267

Subgroups — C43×#20250 #24940267

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3393C211yesmaximal, characteristic, complemented
2C43×#3353C211yesmaximal, characteristic, complemented
3C43×#3324C211yesmaximal, characteristic, complemented
4C43×#3272C211yesmaximal, characteristic
5C43×#1722C211yesmaximal, characteristic, complemented
6C43×#1701C211yesmaximal, characteristic, complemented
7C43×#1693C211yesmaximal, characteristic, complemented
8C43×#1689C211yesmaximal, characteristic, complemented
9C43×#1666C211yesmaximal, characteristic, complemented
10C43×#1650C211yesmaximal, characteristic, complemented
11C43×#1647C211yesmaximal, characteristic, complemented
12C43×#1639C211yesmaximal, characteristic, complemented
13C43×#1628C211yesmaximal, characteristic, complemented
14C43×#1594C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C43—21no—
17C43×#556C2211yescharacteristic
18C43×#556C2211yescharacteristic, complemented
19C43×#547C2211yescharacteristic
20D42×C43C2211yescharacteristic
21C43×#500C2211yescharacteristic, complemented
22C43×#500C2211yescharacteristic, complemented
23C43×#495—21no—
24C43×#494C2211yescharacteristic, complemented
25C43×#492C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#484—21no—
29C43×#482—21no—
30C43×#482—21no—
31C43×#475C2211yescharacteristic, complemented
32C43×#474C2211yescharacteristic
33C43×#474C2211yescharacteristic
34C43×#468—21no—
35C43×#468—21no—
36C43×#468—21no—
37C43×#464—21no—
38C43×#464—21no—
39C43×#461C2211yescharacteristic
40C43×#461C2211yescharacteristic
41C43×#461C2211yescharacteristic, complemented
42C43×#460C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#450—21no—
45C43×#450—21no—
46C43×#449—21no—
47C8×Q8×C43C2211yescharacteristic, complemented
48C4×Q16×C43—21no—
49C4×SD16×C43C2211yescharacteristic
50C4×D8×C43C2211yescharacteristic
51C43×#436C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C43×#436C2211yescharacteristic, complemented
54C43×#428—21no—
55C43×#418—21no—
56C43×#334C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#332C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#332C2211yescharacteristic, complemented
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70AGL(1,ℤ/8)×C43—44no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43—21no—
78C2×SD16×C43—21no—
79C2×SD16×C43D411yescharacteristic
80C2×D8×C43—21no—
81C2×D8×C43D411yescharacteristic
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C4⋊Q8×C43C2311yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43C2311yescharacteristic
89#126×C43—41no—
90#126×C43—41no—
91#124×C43—21no—
92#124×C43—21no—
93#123×C43—41no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—21no—
96C22⋊Q8×C43—21no—
97#121×C43—21no—
98#121×C43—21no—
99#121×C43—21no—
100#120×C43—41no—
101C4×Q8×C43—21no—
102C4×Q8×C43—21no—
103C4×Q8×C43C2311yescharacteristic
104C4×D4×C43C2311yescharacteristic
105C4×D4×C43C2311yescharacteristic
106C4×D4×C43C2311yescharacteristic
107#117×C43—21no—
108#117×C43—21no—
109C2×C4⋊C4×C43—21no—
110#107×C43—21no—
111#107×C43—21no—
112#107×C43—21no—
113#107×C43—21no—
114#107×C43—41no—
115#107×C43D411yescharacteristic
116#106×C43—21no—
117#106×C43D411yescharacteristic
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×C43—21no—
126#103×C43—21no—
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—41no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C2×D4×C43C2×D411yescharacteristic
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—41no—
169Q16×C43—42no—
170Q16×C43—81no—
171SD16×C43—41no—
172SD16×C43—42no—
173SD16×C43—42no—
174SD16×C43—81no—
175SD16×C43—81no—
176SD16×C43—81no—
177SD16×C43—81no—
178D8×C43—22no—
179D8×C43—42no—
180M16×C43—42no—
181M16×C43—42no—
182M16×C43—81no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C22⋊C4×C43—41no—
215C42×C43—21no—
216C42×C43—41no—
217C42×C43—41no—
218C42×C43C2411yescharacteristic
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—41no—
223C23×C43—82no—
224C23×C43—82no—
225C23×C43—161no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—21no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—81no—
245D4×C43—82no—
246D4×C43—82no—
247D4×C43—82no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—82no—
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43AGL(1,ℤ/8)12yes—
275#20250C4311yesmaximal, characteristic, direct product factor, Sylow
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—164no—
289C22×C43D4211yescharacteristic
290C4×C43—21no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C43#57511yescharacteristic
301C4×C43#57611yescharacteristic
302C4×C43#57711yescharacteristic
303#3393C2×C4311yescharacteristic, complemented
304#3353C2×C4311yescharacteristic, complemented
305#3324C2×C4311yescharacteristic, complemented
306#3272C2×C4311yescharacteristic
307#1722C2×C4311yescharacteristic, complemented
308#1701C2×C4311yescharacteristic, complemented
309#1693C2×C4311yescharacteristic, complemented
310#1689C2×C4311yescharacteristic, complemented
311#1666C2×C4311yescharacteristic, complemented
312#1650C2×C4311yescharacteristic, complemented
313#1647C2×C4311yescharacteristic, complemented
314#1639C2×C4311yescharacteristic, complemented
315#1628C2×C4311yescharacteristic, complemented
316#1594C2×C4311yescharacteristic, complemented
317#1583C2×C4311yescharacteristic, complemented
318C2×C43—81no—
319C2×C43—81no—
320C2×C43—81no—
321C2×C43—161no—
322C2×C43#326711yescharacteristic
323C2×C43#327411yescharacteristic
324C2×C43#328911yescharacteristic
325C2×AGL(1,ℤ/8)—21no—
326#556C22×C4311yescharacteristic
327#556C22×C4311yescharacteristic, complemented
328#547C22×C4311yescharacteristic
329D42C22×C4311yescharacteristic
330#500C22×C4311yescharacteristic, complemented
331#500C22×C4311yescharacteristic, complemented
332#495—21no—
333#494C22×C4311yescharacteristic, complemented
334#492C22×C4311yescharacteristic
335#486C22×C4311yescharacteristic
336#486C22×C4311yescharacteristic
337#484—21no—
338#482—21no—
339#482—21no—
340#475C22×C4311yescharacteristic, complemented
341#474C22×C4311yescharacteristic
342#474C22×C4311yescharacteristic
343#468—21no—
344#468—21no—
345#468—21no—
346#464—21no—
347#464—21no—
348#461C22×C4311yescharacteristic
349#461C22×C4311yescharacteristic
350#461C22×C4311yescharacteristic, complemented
351#460C22×C4311yescharacteristic
352#459C22×C4311yescharacteristic
353#450—21no—
354#450—21no—
355#449—21no—
356C8×Q8C22×C4311yescharacteristic, complemented
357C4×Q16—21no—
358C4×SD16C22×C4311yescharacteristic
359C4×D8C22×C4311yescharacteristic
360#436C22×C4311yescharacteristic
361#436C22×C4311yescharacteristic
362#436C22×C4311yescharacteristic, complemented
363#428—21no—
364#418—21no—
365#334C22×C4311yescharacteristic, complemented
366#334C22×C4311yescharacteristic, complemented
367#332C22×C4311yescharacteristic, complemented
368#332C22×C4311yescharacteristic, complemented
369#332C22×C4311yescharacteristic, complemented
370#331C22×C4311yescharacteristic
371Q8⋊C8C22×C4311yescharacteristic, complemented
372D4⋊C8C22×C4311yescharacteristic
373D4⋊C8C22×C4311yescharacteristic
374D4⋊C8C22×C4311yescharacteristic, complemented
375#322C22×C4311yescharacteristic, complemented
376C43#2025011yescharacteristic, direct product factor, Sylow
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380AGL(1,ℤ/8)—44no—
381C2×Q16—21no—
382C2×Q16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16D4×C4311yescharacteristic
390C2×D8—21no—
391C2×D8D4×C4311yescharacteristic
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C4⋊Q8C23×C4311yescharacteristic
396C4⋊Q8C23×C4311yescharacteristic
397C4⋊Q8C23×C4311yescharacteristic
398#127C23×C4311yescharacteristic
399#126—41no—
400#126—41no—
401#124—21no—
402#124—21no—
403#123—41no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8C23×C4311yescharacteristic
414C4×D4C23×C4311yescharacteristic
415C4×D4C23×C4311yescharacteristic
416C4×D4C23×C4311yescharacteristic
417#117—21no—
418#117—21no—
419C2×C4⋊C4—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#107—41no—
425#107D4×C4311yescharacteristic
426#106—21no—
427#106D4×C4311yescharacteristic
428C4⋊C8—21no—
429C4⋊C8C23×C4311yescharacteristic
430C4⋊C8C23×C4311yescharacteristic
431C4⋊C8C23×C4311yescharacteristic
432C4⋊C8C23×C4311yescharacteristic
433#103—21no—
434#103—21no—
435#103—21no—
436#103—21no—
437#103D4×C4311yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—41no—
445#102D4×C4311yescharacteristic
446#102D4×C4311yescharacteristic
447#102D4×C4311yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C4×C8—21no—
452C4×C8C23×C4311yescharacteristic
453C4×C8C23×C4311yescharacteristic
454C4×C8C23×C4311yescharacteristic
455C24—41no—
456#41—42no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8C2×D4×C4311yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—41no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4C2×D4×C4311yescharacteristic
473C2×D4C2×D4×C4311yescharacteristic
474C2×D4C2×D4×C4311yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479Q16—42no—
480Q16—81no—
481SD16—41no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487SD16—81no—
488D8—22no—
489D8—42no—
490M16—42no—
491M16—42no—
492M16—81no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8C2×D4×C4311yescharacteristic
499C2×C8C2×D4×C4311yescharacteristic
500C2×C8C2×D4×C4311yescharacteristic
501C2×C8C2×D4×C4311yescharacteristic
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4C2×D4×C4311yescharacteristic
513C4⋊C4C2×D4×C4311yescharacteristic
514C4⋊C4C2×D4×C4311yescharacteristic
515C4⋊C4C2×D4×C4311yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C42—21no—
526C42—41no—
527C42—41no—
528C42C24×C4311yescharacteristic
529C23—21no—
530C23—21no—
531C23—21no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23—161no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4C22×D4×C4311yescharacteristic
574C2×C4C22×D4×C4311yescharacteristic
575C2×C4H(5,𝔽2)×C4311yescharacteristic
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C8AGL(1,ℤ/8)×C4312yes—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D42×C4311yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
609C4C43×#57511yescharacteristic
610C4C43×#57611yescharacteristic
611C4C43×#57711yescharacteristic
612C2—81no—
613C2—81no—
614C2—81no—
615C2—161no—
616C2C43×#326711yescharacteristic
617C2C43×#327411yescharacteristic
618C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3272C2
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×#3393C2semidirect
2. C43×#3353C2semidirect
3. C43×#3324C2semidirect
5. C43×#1722C2semidirect
6. C43×#1701C2semidirect
7. C43×#1693C2semidirect
8. C43×#1689C2semidirect
9. C43×#1666C2semidirect
10. C43×#1650C2semidirect
11. C43×#1647C2semidirect
12. C43×#1639C2semidirect
13. C43×#1628C2semidirect
14. C43×#1594C2semidirect
15. C43×#1583C2semidirect
18. C43×#556C22semidirect
21. C43×#500C22semidirect
22. C43×#500C22semidirect
24. C43×#494C22semidirect
31. C43×#475C22semidirect
41. C43×#461C22semidirect
47. C8×Q8×C43C22semidirect
53. C43×#436C22semidirect
56. C43×#334C22semidirect
57. C43×#334C22semidirect
58. C43×#332C22semidirect
59. C43×#332C22semidirect
60. C43×#332C22semidirect
62. C43×Q8⋊C8C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
275. #20250C43direct (N × H)
303. #3393C2×C43semidirect
304. #3353C2×C43semidirect
305. #3324C2×C43semidirect
307. #1722C2×C43semidirect
308. #1701C2×C43semidirect
309. #1693C2×C43semidirect
310. #1689C2×C43semidirect
311. #1666C2×C43semidirect
312. #1650C2×C43semidirect
313. #1647C2×C43semidirect
314. #1639C2×C43semidirect
315. #1628C2×C43semidirect
316. #1594C2×C43semidirect
317. #1583C2×C43semidirect
327. #556C22×C43semidirect
330. #500C22×C43semidirect
331. #500C22×C43semidirect
333. #494C22×C43semidirect
340. #475C22×C43semidirect
350. #461C22×C43semidirect
356. C8×Q8C22×C43semidirect
362. #436C22×C43semidirect
365. #334C22×C43semidirect
366. #334C22×C43semidirect
367. #332C22×C43semidirect
368. #332C22×C43semidirect
369. #332C22×C43semidirect
371. Q8⋊C8C22×C43semidirect
374. D4⋊C8C22×C43semidirect
375. #322C22×C43semidirect
376. C43#20250direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33932
C43×#33532
C43×#33242
C43×#32722
C43×#17222
C43×#17012
C43×#16932
C43×#16892
C43×#16662
C43×#16502
C43×#16472
C43×#16392
C43×#16282
C43×#15942
C43×#15832
#2025043