Finite Group Databasebeta

← C43×#19413 #24939430

Subgroups — C43×#19413 #24939430

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3210C211yesmaximal, characteristic, complemented
2C43×#3115C211yesmaximal, characteristic
3C43×#3107C211yesmaximal, characteristic, complemented
4C43×#2988C211yesmaximal, characteristic, complemented
5C43×#1682C211yesmaximal, characteristic, complemented
6C43×#1681C211yesmaximal, characteristic, complemented
7C43×#1680C211yesmaximal, characteristic, complemented
8C43×#1679C211yesmaximal, characteristic, complemented
9C43×#1670C211yesmaximal, characteristic, complemented
10C43×#1669C211yesmaximal, characteristic, complemented
11C43×#1666C211yesmaximal, characteristic, complemented
12C43×#1665C211yesmaximal, characteristic, complemented
13C43×#1572C211yesmaximal, characteristic, complemented
14C43×#1552C211yesmaximal, characteristic, complemented
15C43×#1540C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#532C2211yescharacteristic
18C4×#41×C43C2211yescharacteristic
19C43×#494C2211yescharacteristic
20C43×#492C2211yescharacteristic
21C43×#487C2211yescharacteristic
22C43×#486C2211yescharacteristic
23C43×#485—21no—
24C43×#482—21no—
25C43×#475C2211yescharacteristic
26C43×#475C2211yescharacteristic
27C43×#474C2211yescharacteristic
28C43×#474C2211yescharacteristic
29C43×#464—21no—
30C43×#464—21no—
31C43×#462C2211yescharacteristic
32C43×#461C2211yescharacteristic
33C43×#460C2211yescharacteristic
34C43×#459C2211yescharacteristic
35C43×#452—21no—
36C43×#452—21no—
37C43×#452—21no—
38C43×#449—21no—
39C8×Q8×C43C2211yescharacteristic
40C8×Q8×C43C2211yescharacteristic
41C43×#442—21no—
42C43×#440—21no—
43C4×Q16×C43—21no—
44C4×SD16×C43—21no—
45C8×D4×C43—21no—
46C8×D4×C43—21no—
47C8×D4×C43C2211yescharacteristic
48C8×D4×C43C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#431—21no—
51C43×#431C2211yescharacteristic
52C43×#431C2211yescharacteristic
53C2×C4⋊C8×C43—21no—
54C2×C4⋊C8×C43C2211yescharacteristic
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#334C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#41×C43—21no—
68C2×#41×C43D411yescharacteristic
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×Q16×C43—21no—
72C2×SD16×C43—21no—
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×D8×C43—21no—
77C22×C8×C43—21no—
78C22×C8×C43—21no—
79C22×C8×C43—21no—
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43C2311yescharacteristic
84#125×C43—21no—
85#124×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43D411yescharacteristic
93C4×Q8×C43C2311yescharacteristic
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43D411yescharacteristic
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101#117×C43—21no—
102#117×C43D411yescharacteristic
103C2×C42×C43—21no—
104C2×C42×C43C2311yescharacteristic
105#107×C43—21no—
106#107×C43—21no—
107#106×C43—21no—
108#106×C43—21no—
109C4⋊C8×C43—21no—
110C4⋊C8×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43D411yescharacteristic
113C4⋊C8×C43D411yescharacteristic
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120#103×C43—21no—
121#103×C43—21no—
122#103×C43—21no—
123#103×C43—21no—
124#103×C43—21no—
125#103×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—
132C22⋊C8×C43—21no—
133C22⋊C8×C43—21no—
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43D411yescharacteristic
137C22⋊C8×C43D411yescharacteristic
138#97×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—81no—
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—21no—
156C2×D4×C43—41no—
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4111yescharacteristic
165Q16×C43—42no—
166Q16×C43—81no—
167Q16×C43—81no—
168SD16×C43—42no—
169SD16×C43—42no—
170SD16×C43—81no—
171SD16×C43—81no—
172D8×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—81no—
180C2×C8×C43—81no—
181C2×C8×C43—81no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C22⋊C4×C43—21no—
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—41no—
208C42×C43C2×D411yescharacteristic
209C42×C43C2×D411yescharacteristic
210C42×C43#4111yescharacteristic
211C42×C43C2411yescharacteristic
212C23×C43—21no—
213C23×C43—41no—
214C23×C43#12111yescharacteristic
215Q8×C43—21no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43#13512yes—
223D4×C43—24no—
224D4×C43—21no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—81no—
230D4×C43—82no—
231D4×C43#13512yes—
232C2×C4×C43—24no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—81no—
247C2×C4×C43—82no—
248C2×C4×C43#12111yescharacteristic
249C2×C4×C43#12111yescharacteristic
250C2×C4×C43#12111yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264#19413C4311yesmaximal, characteristic, direct product factor, Sylow
265C22×C43—21no—
266C22×C43—22no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43C2×#12111yescharacteristic
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—22no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43C2×#13511yescharacteristic
286C4×C43C2×#13511yescharacteristic
287C4×C43#57611yescharacteristic
288C4×C43#57711yescharacteristic
289#3210C2×C4311yescharacteristic, complemented
290#3115C2×C4311yescharacteristic
291#3107C2×C4311yescharacteristic, complemented
292#2988C2×C4311yescharacteristic, complemented
293#1682C2×C4311yescharacteristic, complemented
294#1681C2×C4311yescharacteristic, complemented
295#1680C2×C4311yescharacteristic, complemented
296#1679C2×C4311yescharacteristic, complemented
297#1670C2×C4311yescharacteristic, complemented
298#1669C2×C4311yescharacteristic, complemented
299#1666C2×C4311yescharacteristic, complemented
300#1665C2×C4311yescharacteristic, complemented
301#1572C2×C4311yescharacteristic, complemented
302#1552C2×C4311yescharacteristic, complemented
303#1540C2×C4311yescharacteristic, complemented
304C2×C43—41no—
305C2×C43—42no—
306C2×C43—161no—
307C2×C43#304511yescharacteristic
308C2×C43#305011yescharacteristic
309C2×C43#306911yescharacteristic
310#533C22×C4311yescharacteristic
311#532C22×C4311yescharacteristic
312C4×#41C22×C4311yescharacteristic
313#494C22×C4311yescharacteristic
314#492C22×C4311yescharacteristic
315#487C22×C4311yescharacteristic
316#486C22×C4311yescharacteristic
317#485—21no—
318#482—21no—
319#475C22×C4311yescharacteristic
320#475C22×C4311yescharacteristic
321#474C22×C4311yescharacteristic
322#474C22×C4311yescharacteristic
323#464—21no—
324#464—21no—
325#462C22×C4311yescharacteristic
326#461C22×C4311yescharacteristic
327#460C22×C4311yescharacteristic
328#459C22×C4311yescharacteristic
329#452—21no—
330#452—21no—
331#452—21no—
332#449—21no—
333C8×Q8C22×C4311yescharacteristic
334C8×Q8C22×C4311yescharacteristic
335#442—21no—
336#440—21no—
337C4×Q16—21no—
338C4×SD16—21no—
339C8×D4—21no—
340C8×D4—21no—
341C8×D4C22×C4311yescharacteristic
342C8×D4C22×C4311yescharacteristic
343#432C22×C4311yescharacteristic
344#431—21no—
345#431C22×C4311yescharacteristic
346#431C22×C4311yescharacteristic
347C2×C4⋊C8—21no—
348C2×C4⋊C8C22×C4311yescharacteristic
349#335C22×C4311yescharacteristic
350#335C22×C4311yescharacteristic
351#334C22×C4311yescharacteristic
352#334C22×C4311yescharacteristic
353#332C22×C4311yescharacteristic
354#332C22×C4311yescharacteristic
355#332C22×C4311yescharacteristic
356#332C22×C4311yescharacteristic
357#332C22×C4311yescharacteristic
358#332C22×C4311yescharacteristic
359#331C22×C4311yescharacteristic
360#331C22×C4311yescharacteristic
361C43#1941311yescharacteristic, direct product factor, Sylow
362C2×#41—21no—
363C2×#41D4×C4311yescharacteristic
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×D8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C4⋊Q8C23×C4311yescharacteristic
376C4⋊Q8C23×C4311yescharacteristic
377C4⋊Q8C23×C4311yescharacteristic
378#127C23×C4311yescharacteristic
379#125—21no—
380#124—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383#121—21no—
384#121—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8D4×C4311yescharacteristic
388C4×Q8C23×C4311yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4D4×C4311yescharacteristic
394C4×D4C23×C4311yescharacteristic
395#117—21no—
396#117—21no—
397#117D4×C4311yescharacteristic
398C2×C42—21no—
399C2×C42C23×C4311yescharacteristic
400#107—21no—
401#107—21no—
402#106—21no—
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8D4×C4311yescharacteristic
408C4⋊C8D4×C4311yescharacteristic
409C4⋊C8C23×C4311yescharacteristic
410C4⋊C8C23×C4311yescharacteristic
411C4⋊C8C23×C4311yescharacteristic
412C4⋊C8C23×C4311yescharacteristic
413C4⋊C8C23×C4311yescharacteristic
414C4⋊C8C23×C4311yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8D4×C4311yescharacteristic
432C22⋊C8D4×C4311yescharacteristic
433#97—21no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C23×C4311yescharacteristic
438C4×C8C23×C4311yescharacteristic
439#41—22no—
440#41—22no—
441#41—81no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C2×D4×C4311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4C2×D4×C4311yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4C2×D4×C4311yescharacteristic
458C22×C4C2×D4×C4311yescharacteristic
459C22×C4#41×C4311yescharacteristic
460Q16—42no—
461Q16—81no—
462Q16—81no—
463SD16—42no—
464SD16—42no—
465SD16—81no—
466SD16—81no—
467D8—42no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8C2×D4×C4311yescharacteristic
478C2×C8C2×D4×C4311yescharacteristic
479C2×C8C2×D4×C4311yescharacteristic
480C2×C8C2×D4×C4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C4311yescharacteristic
492C4⋊C4C2×D4×C4311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C2×D4×C4311yescharacteristic
504C42C2×D4×C4311yescharacteristic
505C42#41×C4311yescharacteristic
506C42C24×C4311yescharacteristic
507C23—21no—
508C23—41no—
509C23#121×C4311yescharacteristic
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8#135×C4312yes—
518D4—24no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4#135×C4312yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—81no—
542C2×C4—82no—
543C2×C4#121×C4311yescharacteristic
544C2×C4#121×C4311yescharacteristic
545C2×C4#121×C4311yescharacteristic
546C2×C4C22×D4×C4311yescharacteristic
547C2×C4C22×D4×C4311yescharacteristic
548C2×C4C2×#41×C4311yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×#121×C4311yescharacteristic
569C4—21no—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×#135×C4311yescharacteristic
580C4C2×#135×C4311yescharacteristic
581C4C43×#57611yescharacteristic
582C4C43×#57711yescharacteristic
583C2—41no—
584C2—42no—
585C2—161no—
586C2C43×#304511yescharacteristic
587C2C43×#305011yescharacteristic
588C2C43×#306911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3115C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3210C2semidirect
3. C43×#3107C2semidirect
4. C43×#2988C2semidirect
5. C43×#1682C2semidirect
6. C43×#1681C2semidirect
7. C43×#1680C2semidirect
8. C43×#1679C2semidirect
9. C43×#1670C2semidirect
10. C43×#1669C2semidirect
11. C43×#1666C2semidirect
12. C43×#1665C2semidirect
13. C43×#1572C2semidirect
14. C43×#1552C2semidirect
15. C43×#1540C2semidirect
264. #19413C43direct (N × H)
289. #3210C2×C43semidirect
291. #3107C2×C43semidirect
292. #2988C2×C43semidirect
293. #1682C2×C43semidirect
294. #1681C2×C43semidirect
295. #1680C2×C43semidirect
296. #1679C2×C43semidirect
297. #1670C2×C43semidirect
298. #1669C2×C43semidirect
299. #1666C2×C43semidirect
300. #1665C2×C43semidirect
301. #1572C2×C43semidirect
302. #1552C2×C43semidirect
303. #1540C2×C43semidirect
361. C43#19413direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32102
C43×#31152
C43×#31072
C43×#29882
C43×#16822
C43×#16812
C43×#16802
C43×#16792
C43×#16702
C43×#16692
C43×#16662
C43×#16652
C43×#15722
C43×#15522
C43×#15402
#1941343