Finite Group Databasebeta

← C43×#19871 #24939888

Subgroups — C43×#19871 #24939888

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 614 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×#3394C211yesmaximal, characteristic, complemented
4C43×#3304C211yesmaximal, characteristic, complemented
5C43×#1721C211yesmaximal, characteristic, complemented
6C43×#1686C211yesmaximal, characteristic, complemented
7C43×#1682C211yesmaximal, characteristic, complemented
8C43×#1668C211yesmaximal, characteristic, complemented
9C43×#1667C211yesmaximal, characteristic, complemented
10C43×#1640C211yesmaximal, characteristic, complemented
11C43×#1628C211yesmaximal, characteristic, complemented
12C43×#1621C211yesmaximal, characteristic, complemented
13C43×#1620C211yesmaximal, characteristic, complemented
14C43×#1584C211yesmaximal, characteristic, complemented
15C43×SD16⋊C8C211yesmaximal, characteristic, complemented
16C43×#559C2211yescharacteristic
17C43×#559C2211yescharacteristic
18C43×#556C2211yescharacteristic
19C43×#550C2211yescharacteristic
20C43×#496—21no—
21C43×#495—21no—
22C43×#495—21no—
23C43×#493C2211yescharacteristic
24C43×#493C2211yescharacteristic
25C43×#493C2211yescharacteristic
26C43×#492C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#482—21no—
30C43×#475C2211yescharacteristic
31C43×#465—21no—
32C43×#464—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×#446C2211yescharacteristic
47C8×Q8×C43C2211yescharacteristic
48C8×Q8×C43C2211yescharacteristic
49C43×#442—21no—
50C4×Q16×C43C2211yescharacteristic
51C4×SD16×C43—21no—
52C4×SD16×C43C2211yescharacteristic
53C4×D8×C43—21no—
54C8×D4×C43C2211yescharacteristic
55C43×#416—21no—
56C43×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
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—
68C2×Q16×C43—21no—
69C2×Q16×C43D411yescharacteristic
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43D411yescharacteristic
77C2×D8×C43—21no—
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×D8×C43—21no—
82C2×D8×C43—21no—
83C2×D8×C43—41no—
84C22×C8×C43—21no—
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43—21no—
87#127×C43C2311yescharacteristic
88#127×C43C2311yescharacteristic
89#127×C43C2311yescharacteristic
90#126×C43—41no—
91#124×C43—21no—
92#124×C43—21no—
93#124×C43—21no—
94#124×C43—21no—
95#124×C43—21no—
96#123×C43—41no—
97#123×C43—41no—
98C22⋊Q8×C43—21no—
99#121×C43—21no—
100#121×C43—41no—
101C4×Q8×C43—21no—
102C4×Q8×C43C2311yescharacteristic
103C4×Q8×C43C2311yescharacteristic
104C4×Q8×C43C2311yescharacteristic
105C4×D4×C43—21no—
106C4×D4×C43—21no—
107C4×D4×C43—21no—
108C4×D4×C43—21no—
109C4×D4×C43—21no—
110C4×D4×C43C2311yescharacteristic
111#117×C43—21no—
112#107×C43D411yescharacteristic
113#106×C43—21no—
114#106×C43D411yescharacteristic
115C4⋊C8×C43—21no—
116C4⋊C8×C43—21no—
117C4⋊C8×C43—21no—
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122#103×C43—21no—
123#103×C43—21no—
124#103×C43D411yescharacteristic
125#103×C43D411yescharacteristic
126#103×C43D411yescharacteristic
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—21no—
135#102×C43—41no—
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138#97×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
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—21no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43C2×D411yescharacteristic
162C22×C4×C43—21no—
163C22×C4×C43—41no—
164C22×C4×C43—41no—
165C22×C4×C43—41no—
166Q16×C43—41no—
167Q16×C43—81no—
168SD16×C43—22no—
169SD16×C43—42no—
170SD16×C43—81no—
171SD16×C43—81no—
172SD16×C43—81no—
173SD16×C43—81no—
174SD16×C43—81no—
175D8×C43—42no—
176D8×C43—42no—
177D8×C43—81no—
178D8×C43—81no—
179D8×C43—81no—
180D8×C43—81no—
181D8×C43—82no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—81no—
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—41no—
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C4⋊C4×C43C2×D411yescharacteristic
201C4⋊C4×C43C2×D411yescharacteristic
202C22⋊C4×C43—21no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—41no—
216C42×C43C2411yescharacteristic
217C23×C43—21no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221Q8×C43—21no—
222Q8×C43—21no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
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—81no—
244D4×C43—81no—
245D4×C43—81no—
246D4×C43—82no—
247D4×C43—161no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—82no—
259C2×C4×C43—161no—
260C2×C4×C43—161no—
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C8×C43—21no—
265C8×C43—21no—
266C8×C43—21no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43#13512yes—
273#19871C4311yesmaximal, characteristic, direct product factor, Sylow
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43D4211yescharacteristic
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43C2×#13511yescharacteristic
297C4×C43#57511yescharacteristic
298C4×C43#57611yescharacteristic
299C4×C43#57611yescharacteristic
300#3399C2×C4311yescharacteristic, complemented
301#3396C2×C4311yescharacteristic, complemented
302#3394C2×C4311yescharacteristic, complemented
303#3304C2×C4311yescharacteristic, complemented
304#1721C2×C4311yescharacteristic, complemented
305#1686C2×C4311yescharacteristic, complemented
306#1682C2×C4311yescharacteristic, complemented
307#1668C2×C4311yescharacteristic, complemented
308#1667C2×C4311yescharacteristic, complemented
309#1640C2×C4311yescharacteristic, complemented
310#1628C2×C4311yescharacteristic, complemented
311#1621C2×C4311yescharacteristic, complemented
312#1620C2×C4311yescharacteristic, complemented
313#1584C2×C4311yescharacteristic, complemented
314SD16⋊C8C2×C4311yescharacteristic, complemented
315C2×C43—81no—
316C2×C43—161no—
317C2×C43—161no—
318C2×C43—161no—
319C2×C43#326811yescharacteristic
320C2×C43#328711yescharacteristic
321C2×C43#328811yescharacteristic
322#559C22×C4311yescharacteristic
323#559C22×C4311yescharacteristic
324#556C22×C4311yescharacteristic
325#550C22×C4311yescharacteristic
326#496—21no—
327#495—21no—
328#495—21no—
329#493C22×C4311yescharacteristic
330#493C22×C4311yescharacteristic
331#493C22×C4311yescharacteristic
332#492C22×C4311yescharacteristic
333#486C22×C4311yescharacteristic
334#486C22×C4311yescharacteristic
335#482—21no—
336#475C22×C4311yescharacteristic
337#465—21no—
338#464—21no—
339#463—21no—
340#463—21no—
341#463—21no—
342#463—21no—
343#462C22×C4311yescharacteristic
344#460C22×C4311yescharacteristic
345#460C22×C4311yescharacteristic
346#460C22×C4311yescharacteristic
347#460C22×C4311yescharacteristic
348#459—21no—
349#459C22×C4311yescharacteristic
350#459C22×C4311yescharacteristic
351#452—21no—
352#446C22×C4311yescharacteristic
353C8×Q8C22×C4311yescharacteristic
354C8×Q8C22×C4311yescharacteristic
355#442—21no—
356C4×Q16C22×C4311yescharacteristic
357C4×SD16—21no—
358C4×SD16C22×C4311yescharacteristic
359C4×D8—21no—
360C8×D4C22×C4311yescharacteristic
361#416—21no—
362#335C22×C4311yescharacteristic
363#335C22×C4311yescharacteristic
364#332C22×C4311yescharacteristic
365#331C22×C4311yescharacteristic
366#331C22×C4311yescharacteristic
367#331C22×C4311yescharacteristic
368Q8⋊C8C22×C4311yescharacteristic
369Q8⋊C8C22×C4311yescharacteristic
370Q8⋊C8C22×C4311yescharacteristic
371D4⋊C8C22×C4311yescharacteristic
372#322C22×C4311yescharacteristic
373C43#1987111yescharacteristic, direct product factor, Sylow
374C2×#41—21no—
375C2×Q16—21no—
376C2×Q16D4×C4311yescharacteristic
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C4311yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—41no—
391C22×C8—21no—
392C4⋊Q8C23×C4311yescharacteristic
393#127—21no—
394#127C23×C4311yescharacteristic
395#127C23×C4311yescharacteristic
396#127C23×C4311yescharacteristic
397#126—41no—
398#124—21no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#123—41no—
404#123—41no—
405C22⋊Q8—21no—
406#121—21no—
407#121—41no—
408C4×Q8—21no—
409C4×Q8C23×C4311yescharacteristic
410C4×Q8C23×C4311yescharacteristic
411C4×Q8C23×C4311yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4C23×C4311yescharacteristic
418#117—21no—
419#107D4×C4311yescharacteristic
420#106—21no—
421#106D4×C4311yescharacteristic
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C4311yescharacteristic
426C4⋊C8C23×C4311yescharacteristic
427C4⋊C8C23×C4311yescharacteristic
428C4⋊C8C23×C4311yescharacteristic
429#103—21no—
430#103—21no—
431#103D4×C4311yescharacteristic
432#103D4×C4311yescharacteristic
433#103D4×C4311yescharacteristic
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C4311yescharacteristic
444C22⋊C8—21no—
445#97—21no—
446C4×C8—21no—
447C4×C8—21no—
448C4×C8C23×C4311yescharacteristic
449C4×C8C23×C4311yescharacteristic
450C4×C8C23×C4311yescharacteristic
451#41—42no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8C2×D4×C4311yescharacteristic
455C2×Q8C2×D4×C4311yescharacteristic
456C2×Q8C2×D4×C4311yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C4311yescharacteristic
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—41no—
474Q16—81no—
475SD16—22no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—42no—
483D8—42no—
484D8—81no—
485D8—81no—
486D8—81no—
487D8—81no—
488D8—82no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—81no—
495C2×C8C2×D4×C4311yescharacteristic
496C2×C8C2×D4×C4311yescharacteristic
497C2×C8C2×D4×C4311yescharacteristic
498C2×C8C2×D4×C4311yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C4311yescharacteristic
506C4⋊C4C2×D4×C4311yescharacteristic
507C4⋊C4C2×D4×C4311yescharacteristic
508C4⋊C4C2×D4×C4311yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42C24×C4311yescharacteristic
524C23—21no—
525C23—41no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—82no—
554D4—161no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C4311yescharacteristic
569C2×C4C22×D4×C4311yescharacteristic
570C2×C4H(5,𝔽2)×C4311yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8#135×C4312yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4C2×#135×C4311yescharacteristic
603C4C43×#57511yescharacteristic
604C4C43×#57611yescharacteristic
605C4C43×#57611yescharacteristic
606C2—81no—
607C2—161no—
608C2—161no—
609C2—161no—
610C2C43×#326811yescharacteristic
611C2C43×#328711yescharacteristic
612C2C43×#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×#3394C2semidirect
4. C43×#3304C2semidirect
5. C43×#1721C2semidirect
6. C43×#1686C2semidirect
7. C43×#1682C2semidirect
8. C43×#1668C2semidirect
9. C43×#1667C2semidirect
10. C43×#1640C2semidirect
11. C43×#1628C2semidirect
12. C43×#1621C2semidirect
13. C43×#1620C2semidirect
14. C43×#1584C2semidirect
15. C43×SD16⋊C8C2semidirect
273. #19871C43direct (N × H)
300. #3399C2×C43semidirect
301. #3396C2×C43semidirect
302. #3394C2×C43semidirect
303. #3304C2×C43semidirect
304. #1721C2×C43semidirect
305. #1686C2×C43semidirect
306. #1682C2×C43semidirect
307. #1668C2×C43semidirect
308. #1667C2×C43semidirect
309. #1640C2×C43semidirect
310. #1628C2×C43semidirect
311. #1621C2×C43semidirect
312. #1620C2×C43semidirect
313. #1584C2×C43semidirect
314. SD16⋊C8C2×C43semidirect
373. C43#19871direct (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×#33942
C43×#33042
C43×#17212
C43×#16862
C43×#16822
C43×#16682
C43×#16672
C43×#16402
C43×#16282
C43×#16212
C43×#16202
C43×#15842
C43×SD16⋊C82
#1987143