Finite Group Databasebeta

← C43×#20208 #24940225

Subgroups — C43×#20208 #24940225

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3400C211yesmaximal, characteristic, complemented
2C43×#3386C211yesmaximal, characteristic, complemented
3C43×#3373C211yesmaximal, characteristic
4D4×Q16×C43C211yesmaximal, characteristic, complemented
5C43×#1722C211yesmaximal, characteristic, complemented
6C43×#1702C211yesmaximal, characteristic, complemented
7C43×#1694C211yesmaximal, characteristic, complemented
8C43×#1690C211yesmaximal, characteristic, complemented
9C43×#1665C211yesmaximal, characteristic
10C43×#1649C211yesmaximal, characteristic, complemented
11C43×#1648C211yesmaximal, characteristic, complemented
12C43×#1640C211yesmaximal, characteristic, complemented
13C43×#1627C211yesmaximal, characteristic
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1582C211yesmaximal, characteristic, complemented
16C22×Q16×C43—21no—
17C43×#559C2211yescharacteristic
18C43×#557C2211yescharacteristic
19D4×Q8×C43C2211yescharacteristic
20D4×Q8×C43C2211yescharacteristic
21C43×#501—21no—
22C43×#500C2211yescharacteristic
23C43×#500C2211yescharacteristic
24C43×#497—21no—
25C43×#494C2211yescharacteristic
26C43×#492C2211yescharacteristic
27C43×#489—21no—
28C43×#486C2211yescharacteristic
29C43×#486C2211yescharacteristic
30C43×#478—21no—
31C43×#477—21no—
32C43×#476—21no—
33C43×#475C2211yescharacteristic
34C43×#475C2211yescharacteristic
35C43×#474C2211yescharacteristic
36C43×#467—21no—
37C43×#464—21no—
38C43×#463—21no—
39C43×#462C2211yescharacteristic
40C43×#462C2211yescharacteristic
41C43×#462C2211yescharacteristic
42C43×#461—21no—
43C43×#460C2211yescharacteristic
44C43×#459C2211yescharacteristic
45C43×#451—21no—
46C43×#451—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C43×#446C2211yescharacteristic
50C43×#442—21no—
51C43×#440—21no—
52C43×#440—21no—
53C4×Q16×C43C2211yescharacteristic
54C4×SD16×C43C2211yescharacteristic
55C8×D4×C43C2211yescharacteristic
56C43×#334C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#332C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C22×Q8×C43—21no—
68C22×Q8×C43—21no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×Q16×C43—21no—
72C2×Q16×C43—21no—
73C2×Q16×C43—21no—
74C2×Q16×C43—44no—
75C2×Q16×C43D411yescharacteristic
76C2×SD16×C43—21no—
77C2×SD16×C43—21no—
78C2×SD16×C43—21no—
79C2×SD16×C43D411yescharacteristic
80C2×D8×C43—21no—
81C22×C8×C43—21no—
82C4⋊Q8×C43—21no—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43—21no—
85C4⋊Q8×C43C2311yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43C2311yescharacteristic
89#125×C43—21no—
90#125×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—41no—
97C22⋊Q8×C43—41no—
98C4×Q8×C43—21no—
99C4×Q8×C43—21no—
100C4×Q8×C43C2311yescharacteristic
101C4×Q8×C43C2311yescharacteristic
102C4×Q8×C43C2311yescharacteristic
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43—21no—
107C4×D4×C43C2311yescharacteristic
108#107×C43—21no—
109#107×C43—21no—
110#107×C43—21no—
111#107×C43—41no—
112#107×C43D411yescharacteristic
113#106×C43—21no—
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×C43—21no—
126#103×C43—21no—
127#103×C43—21no—
128#103×C43D411yescharacteristic
129#103×C43D411yescharacteristic
130#103×C43D411yescharacteristic
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—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—41no—
150C2×Q8×C43—42no—
151C2×Q8×C43—42no—
152C2×Q8×C43—81no—
153C2×Q8×C43—81no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×Q8×C43C2×D411yescharacteristic
156C2×Q8×C43C2×D411yescharacteristic
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43C2×D411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164C22×C4×C43—41no—
165Q16×C43—22no—
166Q16×C43—42no—
167Q16×C43—42no—
168Q16×C43—42no—
169Q16×C43—81no—
170Q16×C43—81no—
171SD16×C43—22no—
172SD16×C43—42no—
173SD16×C43—81no—
174SD16×C43—81no—
175D8×C43—42no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—42no—
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—21no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43—41no—
197C4⋊C4×C43—41no—
198C4⋊C4×C43—41no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43C2×D411yescharacteristic
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C22⋊C4×C43—21no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—41no—
214C42×C43C2411yescharacteristic
215C23×C43—21no—
216C23×C43—41no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—21no—
221Q8×C43—21no—
222Q8×C43—21no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—82no—
230Q8×C43—82no—
231D4×C43—21no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—81no—
237D4×C43#13712yes—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—82no—
251C2×C4×C43—82no—
252C2×C4×C43—161no—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C8×C43AGL(1,ℤ/8)12yes—
265#20208C4311yesmaximal, characteristic, direct product factor, Sylow
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43D4211yescharacteristic
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C43C2×#13711yescharacteristic
286C4×C43#57611yescharacteristic
287C4×C43#57811yescharacteristic
288#3400C2×C4311yescharacteristic, complemented
289#3386C2×C4311yescharacteristic, complemented
290#3373C2×C4311yescharacteristic
291D4×Q16C2×C4311yescharacteristic, complemented
292#1722C2×C4311yescharacteristic, complemented
293#1702C2×C4311yescharacteristic, complemented
294#1694C2×C4311yescharacteristic, complemented
295#1690C2×C4311yescharacteristic, complemented
296#1665C2×C4311yescharacteristic
297#1649C2×C4311yescharacteristic, complemented
298#1648C2×C4311yescharacteristic, complemented
299#1640C2×C4311yescharacteristic, complemented
300#1627C2×C4311yescharacteristic
301#1593C2×C4311yescharacteristic, complemented
302#1582C2×C4311yescharacteristic, complemented
303C2×C43—42no—
304C2×C43—161no—
305C2×C43#327011yescharacteristic
306C2×C43#327411yescharacteristic
307C2×C43#328911yescharacteristic
308C22×Q16—21no—
309#559C22×C4311yescharacteristic
310#557C22×C4311yescharacteristic
311D4×Q8C22×C4311yescharacteristic
312D4×Q8C22×C4311yescharacteristic
313#501—21no—
314#500C22×C4311yescharacteristic
315#500C22×C4311yescharacteristic
316#497—21no—
317#494C22×C4311yescharacteristic
318#492C22×C4311yescharacteristic
319#489—21no—
320#486C22×C4311yescharacteristic
321#486C22×C4311yescharacteristic
322#478—21no—
323#477—21no—
324#476—21no—
325#475C22×C4311yescharacteristic
326#475C22×C4311yescharacteristic
327#474C22×C4311yescharacteristic
328#467—21no—
329#464—21no—
330#463—21no—
331#462C22×C4311yescharacteristic
332#462C22×C4311yescharacteristic
333#462C22×C4311yescharacteristic
334#461—21no—
335#460C22×C4311yescharacteristic
336#459C22×C4311yescharacteristic
337#451—21no—
338#451—21no—
339#446C22×C4311yescharacteristic
340#446C22×C4311yescharacteristic
341#446C22×C4311yescharacteristic
342#442—21no—
343#440—21no—
344#440—21no—
345C4×Q16C22×C4311yescharacteristic
346C4×SD16C22×C4311yescharacteristic
347C8×D4C22×C4311yescharacteristic
348#334C22×C4311yescharacteristic
349#334C22×C4311yescharacteristic
350#332C22×C4311yescharacteristic
351#332C22×C4311yescharacteristic
352#332C22×C4311yescharacteristic
353#331C22×C4311yescharacteristic
354Q8⋊C8C22×C4311yescharacteristic
355Q8⋊C8C22×C4311yescharacteristic
356Q8⋊C8C22×C4311yescharacteristic
357D4⋊C8C22×C4311yescharacteristic
358#322C22×C4311yescharacteristic
359C43#2020811yescharacteristic, direct product factor, Sylow
360C22×Q8—21no—
361C22×Q8—21no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×Q16—44no—
368C2×Q16D4×C4311yescharacteristic
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16D4×C4311yescharacteristic
373C2×D8—21no—
374C22×C8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C4311yescharacteristic
379C4⋊Q8C23×C4311yescharacteristic
380C4⋊Q8C23×C4311yescharacteristic
381#127C23×C4311yescharacteristic
382#125—21no—
383#125—41no—
384#124—21no—
385#124—21no—
386#123—41no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—41no—
390C22⋊Q8—41no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8C23×C4311yescharacteristic
394C4×Q8C23×C4311yescharacteristic
395C4×Q8C23×C4311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4C23×C4311yescharacteristic
401#107—21no—
402#107—21no—
403#107—21no—
404#107—41no—
405#107D4×C4311yescharacteristic
406#106—21no—
407#106—21no—
408#106D4×C4311yescharacteristic
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8C23×C4311yescharacteristic
413C4⋊C8C23×C4311yescharacteristic
414C4⋊C8C23×C4311yescharacteristic
415C4⋊C8C23×C4311yescharacteristic
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103D4×C4311yescharacteristic
422#103D4×C4311yescharacteristic
423#103D4×C4311yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—41no—
430#102D4×C4311yescharacteristic
431C22⋊C8—21no—
432#97—21no—
433#97—21no—
434#97—21no—
435C4×C8C23×C4311yescharacteristic
436C4×C8C23×C4311yescharacteristic
437C4×C8C23×C4311yescharacteristic
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—81no—
446C2×Q8—81no—
447C2×Q8C2×D4×C4311yescharacteristic
448C2×Q8C2×D4×C4311yescharacteristic
449C2×Q8C2×D4×C4311yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4C2×D4×C4311yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458Q16—22no—
459Q16—42no—
460Q16—42no—
461Q16—42no—
462Q16—81no—
463Q16—81no—
464SD16—22no—
465SD16—42no—
466SD16—81no—
467SD16—81no—
468D8—42no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8C2×D4×C4311yescharacteristic
476C2×C8C2×D4×C4311yescharacteristic
477C2×C8C2×D4×C4311yescharacteristic
478C2×C8C2×D4×C4311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4C2×D4×C4311yescharacteristic
494C4⋊C4C2×D4×C4311yescharacteristic
495C4⋊C4C2×D4×C4311yescharacteristic
496C4⋊C4C2×D4×C4311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42C24×C4311yescharacteristic
508C23—21no—
509C23—41no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—21no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—82no—
523Q8—82no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—81no—
530D4#137×C4312yes—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—161no—
546C2×C4C22×D4×C4311yescharacteristic
547C2×C4C22×D4×C4311yescharacteristic
548C2×C4H(5,𝔽2)×C4311yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8AGL(1,ℤ/8)×C4312yes—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C4311yescharacteristic
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
577C4C2×#137×C4311yescharacteristic
578C4C43×#57611yescharacteristic
579C4C43×#57811yescharacteristic
580C2—42no—
581C2—161no—
582C2C43×#327011yescharacteristic
583C2C43×#327411yescharacteristic
584C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#459C22
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×#3400C2semidirect
2. C43×#3386C2semidirect
4. D4×Q16×C43C2semidirect
5. C43×#1722C2semidirect
6. C43×#1702C2semidirect
7. C43×#1694C2semidirect
8. C43×#1690C2semidirect
10. C43×#1649C2semidirect
11. C43×#1648C2semidirect
12. C43×#1640C2semidirect
14. C43×#1593C2semidirect
15. C43×#1582C2semidirect
265. #20208C43direct (N × H)
288. #3400C2×C43semidirect
289. #3386C2×C43semidirect
291. D4×Q16C2×C43semidirect
292. #1722C2×C43semidirect
293. #1702C2×C43semidirect
294. #1694C2×C43semidirect
295. #1690C2×C43semidirect
297. #1649C2×C43semidirect
298. #1648C2×C43semidirect
299. #1640C2×C43semidirect
301. #1593C2×C43semidirect
302. #1582C2×C43semidirect
359. C43#20208direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34002
C43×#33862
C43×#33732
D4×Q16×C432
C43×#17222
C43×#17022
C43×#16942
C43×#16902
C43×#16652
C43×#16492
C43×#16482
C43×#16402
C43×#16272
C43×#15932
C43×#15822
#2020843