Finite Group Databasebeta

← C43×#20288 #24940305

Subgroups — C43×#20288 #24940305

Order 11008.

670 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×#3398C211yesmaximal, characteristic, complemented
2C43×#3368C211yesmaximal, characteristic, complemented
3C43×#3324C211yesmaximal, characteristic, complemented
4C43×#3274C211yesmaximal, characteristic
5C43×#1709C211yesmaximal, characteristic, complemented
6C43×#1702C211yesmaximal, characteristic, complemented
7C43×#1701C211yesmaximal, characteristic, complemented
8C43×#1689C211yesmaximal, characteristic, complemented
9C43×#1688C211yesmaximal, characteristic, complemented
10C43×#1641C211yesmaximal, characteristic, complemented
11C43×#1639C211yesmaximal, characteristic, complemented
12C43×#1628C211yesmaximal, characteristic, complemented
13C43×#1626C211yesmaximal, characteristic, complemented
14C43×#1590C211yesmaximal, characteristic, complemented
15C43×#1590C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C43—21no—
17C43×#557C2211yescharacteristic, complemented
18C43×#556C2211yescharacteristic
19C43×#550C2211yescharacteristic
20D42×C43C2211yescharacteristic
21C43×#497—21no—
22C43×#494C2211yescharacteristic, complemented
23C43×#493C2211yescharacteristic
24C43×#490—21no—
25C43×#486C2211yescharacteristic
26C43×#486C2211yescharacteristic
27C43×#486C2211yescharacteristic, complemented
28C43×#486C2211yescharacteristic, complemented
29C43×#482—21no—
30C43×#478—21no—
31C43×#474C2211yescharacteristic
32C43×#474C2211yescharacteristic
33C43×#469—21no—
34C43×#468—21no—
35C43×#464—21no—
36C43×#462—21no—
37C43×#462C2211yescharacteristic, complemented
38C43×#461C2211yescharacteristic
39C43×#460—21no—
40C43×#460C2211yescharacteristic
41C43×#460C2211yescharacteristic
42C43×#460C2211yescharacteristic, complemented
43C43×#459C2211yescharacteristic
44C43×#450—21no—
45C43×#449—21no—
46C43×#447—21no—
47C43×#446C2211yescharacteristic, complemented
48C43×#446C2211yescharacteristic, complemented
49C43×#441—21no—
50C43×#440—21no—
51C4×SD16×C43C2211yescharacteristic
52C4×SD16×C43C2211yescharacteristic
53C43×#436C2211yescharacteristic
54C43×#436C2211yescharacteristic
55C43×#418—21no—
56C43×#334C2211yescharacteristic, complemented
57C43×#334C2211yescharacteristic, complemented
58C43×#332C2211yescharacteristic, complemented
59C43×#332C2211yescharacteristic, complemented
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic, complemented
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×Q8⋊C8C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic, 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×Q16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43—21no—
78C2×SD16×C43D411yescharacteristic
79C2×SD16×C43D411yescharacteristic
80C2×D8×C43—21no—
81C2×D8×C43—21no—
82C2×D8×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C4⋊Q8×C43—21no—
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43—21no—
89#127×C43C2311yescharacteristic
90#127×C43C2311yescharacteristic
91#126×C43—41no—
92#125×C43—21no—
93#125×C43—41no—
94#124×C43—21no—
95C22⋊Q8×C43—21no—
96#121×C43—21no—
97#121×C43—21no—
98#121×C43—21no—
99#121×C43—41no—
100#120×C43—41no—
101C4×Q8×C43—21no—
102C4×Q8×C43—21no—
103C4×Q8×C43—21no—
104C4×Q8×C43C2311yescharacteristic
105C4×Q8×C43C2311yescharacteristic
106C4×D4×C43—21no—
107C4×D4×C43C2311yescharacteristic
108C4×D4×C43C2311yescharacteristic
109#117×C43—21no—
110#107×C43—21no—
111#107×C43—21no—
112#106×C43D411yescharacteristic
113#106×C43D411yescharacteristic
114C4⋊C8×C43—21no—
115C4⋊C8×C43—21no—
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120#103×C43—21no—
121#103×C43—21no—
122#103×C43D411yescharacteristic
123#103×C43D411yescharacteristic
124#102×C43—21no—
125#102×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
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×C43—41no—
136#102×C43D411yescharacteristic
137#102×C43D411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#97×C43—21no—
141#97×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×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43C2×D411yescharacteristic
167C2×D4×C43C2×D411yescharacteristic
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—41no—
171Q16×C43—42no—
172Q16×C43—81no—
173Q16×C43—81no—
174SD16×C43—22no—
175SD16×C43—41no—
176SD16×C43—42no—
177SD16×C43—42no—
178SD16×C43—81no—
179SD16×C43—81no—
180D8×C43—42no—
181D8×C43—42no—
182D8×C43—81no—
183M16×C43—42no—
184M16×C43—81no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43C2×D411yescharacteristic
205C4⋊C4×C43C2×D411yescharacteristic
206C4⋊C4×C43C2×D411yescharacteristic
207C4⋊C4×C43C2×D411yescharacteristic
208C22⋊C4×C43—21no—
209C22⋊C4×C43—21no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—41no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43—41no—
217C42×C43—41no—
218C42×C43C2411yescharacteristic
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—82no—
224C23×C43—82no—
225C23×C43—161no—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—21no—
229Q8×C43—21no—
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—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—81no—
247D4×C43—81no—
248D4×C43—82no—
249D4×C43—82no—
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—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—82no—
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43AGL(1,ℤ/8)12yes—
277#20288C4311yesmaximal, characteristic, direct product factor, Sylow
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—164no—
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—81no—
300C4×C43—81no—
301C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C43#57511yescharacteristic
303C4×C43#57611yescharacteristic
304C4×C43#57711yescharacteristic
305#3398C2×C4311yescharacteristic, complemented
306#3368C2×C4311yescharacteristic, complemented
307#3324C2×C4311yescharacteristic, complemented
308#3274C2×C4311yescharacteristic
309#1709C2×C4311yescharacteristic, complemented
310#1702C2×C4311yescharacteristic, complemented
311#1701C2×C4311yescharacteristic, complemented
312#1689C2×C4311yescharacteristic, complemented
313#1688C2×C4311yescharacteristic, complemented
314#1641C2×C4311yescharacteristic, complemented
315#1639C2×C4311yescharacteristic, complemented
316#1628C2×C4311yescharacteristic, complemented
317#1626C2×C4311yescharacteristic, complemented
318#1590C2×C4311yescharacteristic, complemented
319#1590C2×C4311yescharacteristic, complemented
320C2×C43—81no—
321C2×C43—81no—
322C2×C43—161no—
323C2×C43—161no—
324C2×C43#327411yescharacteristic
325C2×C43#327511yescharacteristic
326C2×C43#329011yescharacteristic
327C2×AGL(1,ℤ/8)—21no—
328#557C22×C4311yescharacteristic, complemented
329#556C22×C4311yescharacteristic
330#550C22×C4311yescharacteristic
331D42C22×C4311yescharacteristic
332#497—21no—
333#494C22×C4311yescharacteristic, complemented
334#493C22×C4311yescharacteristic
335#490—21no—
336#486C22×C4311yescharacteristic
337#486C22×C4311yescharacteristic
338#486C22×C4311yescharacteristic, complemented
339#486C22×C4311yescharacteristic, complemented
340#482—21no—
341#478—21no—
342#474C22×C4311yescharacteristic
343#474C22×C4311yescharacteristic
344#469—21no—
345#468—21no—
346#464—21no—
347#462—21no—
348#462C22×C4311yescharacteristic, complemented
349#461C22×C4311yescharacteristic
350#460—21no—
351#460C22×C4311yescharacteristic
352#460C22×C4311yescharacteristic
353#460C22×C4311yescharacteristic, complemented
354#459C22×C4311yescharacteristic
355#450—21no—
356#449—21no—
357#447—21no—
358#446C22×C4311yescharacteristic, complemented
359#446C22×C4311yescharacteristic, complemented
360#441—21no—
361#440—21no—
362C4×SD16C22×C4311yescharacteristic
363C4×SD16C22×C4311yescharacteristic
364#436C22×C4311yescharacteristic
365#436C22×C4311yescharacteristic
366#418—21no—
367#334C22×C4311yescharacteristic, complemented
368#334C22×C4311yescharacteristic, complemented
369#332C22×C4311yescharacteristic, complemented
370#332C22×C4311yescharacteristic, complemented
371#331C22×C4311yescharacteristic
372#331C22×C4311yescharacteristic, complemented
373Q8⋊C8C22×C4311yescharacteristic, complemented
374Q8⋊C8C22×C4311yescharacteristic, complemented
375D4⋊C8C22×C4311yescharacteristic
376D4⋊C8C22×C4311yescharacteristic
377C82C22×C4311yescharacteristic, complemented
378C43#2028811yescharacteristic, direct product factor, Sylow
379C2×#41—21no—
380C22×D4—21no—
381C22×D4—21no—
382AGL(1,ℤ/8)—44no—
383C2×Q16—21no—
384C2×Q16—21no—
385C2×Q16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16D4×C4311yescharacteristic
391C2×SD16D4×C4311yescharacteristic
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×M16—21no—
396C2×M16—21no—
397C4⋊Q8—21no—
398C4⋊Q8C23×C4311yescharacteristic
399C4⋊Q8C23×C4311yescharacteristic
400#127—21no—
401#127C23×C4311yescharacteristic
402#127C23×C4311yescharacteristic
403#126—41no—
404#125—21no—
405#125—41no—
406#124—21no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—41no—
412#120—41no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8C23×C4311yescharacteristic
417C4×Q8C23×C4311yescharacteristic
418C4×D4—21no—
419C4×D4C23×C4311yescharacteristic
420C4×D4C23×C4311yescharacteristic
421#117—21no—
422#107—21no—
423#107—21no—
424#106D4×C4311yescharacteristic
425#106D4×C4311yescharacteristic
426C4⋊C8—21no—
427C4⋊C8—21no—
428C4⋊C8C23×C4311yescharacteristic
429C4⋊C8C23×C4311yescharacteristic
430C4⋊C8C23×C4311yescharacteristic
431C4⋊C8C23×C4311yescharacteristic
432#103—21no—
433#103—21no—
434#103D4×C4311yescharacteristic
435#103D4×C4311yescharacteristic
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—41no—
447#102—41no—
448#102D4×C4311yescharacteristic
449#102D4×C4311yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97—21no—
453#97—21no—
454C4×C8C23×C4311yescharacteristic
455C4×C8C23×C4311yescharacteristic
456C4×C8C23×C4311yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C4311yescharacteristic
463C2×Q8C2×D4×C4311yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C4311yescharacteristic
479C2×D4C2×D4×C4311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483Q16—42no—
484Q16—81no—
485Q16—81no—
486SD16—22no—
487SD16—41no—
488SD16—42no—
489SD16—42no—
490SD16—81no—
491SD16—81no—
492D8—42no—
493D8—42no—
494D8—81no—
495M16—42no—
496M16—81no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8C2×D4×C4311yescharacteristic
503C2×C8C2×D4×C4311yescharacteristic
504C2×C8C2×D4×C4311yescharacteristic
505C2×C8C2×D4×C4311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4C2×D4×C4311yescharacteristic
517C4⋊C4C2×D4×C4311yescharacteristic
518C4⋊C4C2×D4×C4311yescharacteristic
519C4⋊C4C2×D4×C4311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C42—21no—
527C42—21no—
528C42—41no—
529C42—41no—
530C42C24×C4311yescharacteristic
531C23—21no—
532C23—21no—
533C23—41no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—21no—
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—81no—
559D4—81no—
560D4—82no—
561D4—82no—
562D4—82no—
563D4—161no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4C22×D4×C4311yescharacteristic
578C2×C4C22×D4×C4311yescharacteristic
579C2×C4H(5,𝔽2)×C4311yescharacteristic
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8AGL(1,ℤ/8)×C4312yes—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—164no—
602C22D42×C4311yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
613C4C43×#57511yescharacteristic
614C4C43×#57611yescharacteristic
615C4C43×#57711yescharacteristic
616C2—81no—
617C2—81no—
618C2—161no—
619C2—161no—
620C2C43×#327411yescharacteristic
621C2C43×#327511yescharacteristic
622C2C43×#329011yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3274C2
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×#3398C2semidirect
2. C43×#3368C2semidirect
3. C43×#3324C2semidirect
5. C43×#1709C2semidirect
6. C43×#1702C2semidirect
7. C43×#1701C2semidirect
8. C43×#1689C2semidirect
9. C43×#1688C2semidirect
10. C43×#1641C2semidirect
11. C43×#1639C2semidirect
12. C43×#1628C2semidirect
13. C43×#1626C2semidirect
14. C43×#1590C2semidirect
15. C43×#1590C2semidirect
17. C43×#557C22semidirect
22. C43×#494C22semidirect
27. C43×#486C22semidirect
28. C43×#486C22semidirect
37. C43×#462C22semidirect
42. C43×#460C22semidirect
47. C43×#446C22semidirect
48. C43×#446C22semidirect
56. C43×#334C22semidirect
57. C43×#334C22semidirect
58. C43×#332C22semidirect
59. C43×#332C22semidirect
61. C43×#331C22semidirect
62. C43×Q8⋊C8C22semidirect
63. C43×Q8⋊C8C22semidirect
66. C82×C43C22semidirect
277. #20288C43direct (N × H)
305. #3398C2×C43semidirect
306. #3368C2×C43semidirect
307. #3324C2×C43semidirect
309. #1709C2×C43semidirect
310. #1702C2×C43semidirect
311. #1701C2×C43semidirect
312. #1689C2×C43semidirect
313. #1688C2×C43semidirect
314. #1641C2×C43semidirect
315. #1639C2×C43semidirect
316. #1628C2×C43semidirect
317. #1626C2×C43semidirect
318. #1590C2×C43semidirect
319. #1590C2×C43semidirect
328. #557C22×C43semidirect
333. #494C22×C43semidirect
338. #486C22×C43semidirect
339. #486C22×C43semidirect
348. #462C22×C43semidirect
353. #460C22×C43semidirect
358. #446C22×C43semidirect
359. #446C22×C43semidirect
367. #334C22×C43semidirect
368. #334C22×C43semidirect
369. #332C22×C43semidirect
370. #332C22×C43semidirect
372. #331C22×C43semidirect
373. Q8⋊C8C22×C43semidirect
374. Q8⋊C8C22×C43semidirect
377. C82C22×C43semidirect
378. C43#20288direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33982
C43×#33682
C43×#33242
C43×#32742
C43×#17092
C43×#17022
C43×#17012
C43×#16892
C43×#16882
C43×#16412
C43×#16392
C43×#16282
C43×#16262
C43×#15902
#2028843