Finite Group Databasebeta

← C43×#20200 #24940217

Subgroups — C43×#20200 #24940217

Order 11008.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3374C211yesmaximal, characteristic, complemented
2C43×#3368C211yesmaximal, characteristic
3C43×#3359C211yesmaximal, characteristic, complemented
4C43×#3278C211yesmaximal, characteristic
5C43×#1719C211yesmaximal, characteristic, complemented
6C43×#1700C211yesmaximal, characteristic, complemented
7C43×#1699C211yesmaximal, characteristic, complemented
8C43×#1686C211yesmaximal, characteristic, complemented
9C43×#1682C211yesmaximal, characteristic, complemented
10C43×#1649C211yesmaximal, characteristic, complemented
11C43×#1648C211yesmaximal, characteristic, complemented
12C43×#1642C211yesmaximal, characteristic
13C43×#1626C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic, complemented
15C43×#1584C211yesmaximal, characteristic, complemented
16C2×#137×C43—21no—
17C43×#557C2211yescharacteristic
18C43×#557C2211yescharacteristic
19C43×#550C2211yescharacteristic
20D4×Q8×C43C2211yescharacteristic
21C43×#500C2211yescharacteristic
22C43×#492C2211yescharacteristic
23C43×#491—21no—
24C43×#490—21no—
25C43×#487—21no—
26C43×#487C2211yescharacteristic
27C43×#487C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#486C2211yescharacteristic
30C43×#479—21no—
31C43×#478—21no—
32C43×#475—21no—
33C43×#475C2211yescharacteristic
34C43×#475C2211yescharacteristic
35C43×#474C2211yescharacteristic
36C43×#468—21no—
37C43×#462—21no—
38C43×#462C2211yescharacteristic
39C43×#462C2211yescharacteristic
40C43×#461—21no—
41C43×#461C2211yescharacteristic
42C43×#460—21no—
43C43×#460C2211yescharacteristic
44C43×#460C2211yescharacteristic
45C43×#452—21no—
46C43×#448—21no—
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C8×Q8×C43C2211yescharacteristic
50C43×#441—21no—
51C43×#440—21no—
52C4×Q16×C43C2211yescharacteristic
53C4×SD16×C43—21no—
54C4×SD16×C43C2211yescharacteristic
55C43×#436C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
58C43×#332C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#41×C43—21no—
68C22×Q8×C43—21no—
69#137×C43—44no—
70C2×Q16×C43—21no—
71C2×Q16×C43—21no—
72C2×Q16×C43D411yescharacteristic
73C2×SD16×C43—21no—
74C2×SD16×C43—21no—
75C2×SD16×C43—21no—
76C2×SD16×C43—21no—
77C2×SD16×C43—21no—
78C2×SD16×C43D411yescharacteristic
79C2×M16×C43—21no—
80C4⋊Q8×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43—21no—
83C4⋊Q8×C43C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43—21no—
87#127×C43C2311yescharacteristic
88#125×C43—21no—
89#125×C43—21no—
90#125×C43—41no—
91#125×C43—41no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—41no—
94#121×C43—21no—
95#121×C43—41no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
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×C43C2311yescharacteristic
106#107×C43—21no—
107#107×C43—41no—
108#107×C43D411yescharacteristic
109#106×C43—21no—
110#106×C43—21no—
111#106×C43D411yescharacteristic
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43—21no—
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119#103×C43—21no—
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#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—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—41no—
151C2×Q8×C43—42no—
152C2×Q8×C43—81no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×Q8×C43C2×D411yescharacteristic
155C2×Q8×C43C2×D411yescharacteristic
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—
165Q16×C43—22no—
166Q16×C43—42no—
167Q16×C43—42no—
168SD16×C43—41no—
169SD16×C43—42no—
170SD16×C43—42no—
171SD16×C43—42no—
172SD16×C43—42no—
173SD16×C43—81no—
174M16×C43—42no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
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—41no—
194C4⋊C4×C43—41no—
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—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—21no—
210C42×C43—41no—
211C42×C43—41no—
212C42×C43C2411yescharacteristic
213C23×C43—21no—
214C23×C43—41no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—82no—
227Q8×C43AGL(1,ℤ/8)12yes—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—81no—
235D4×C43—82no—
236D4×C43—161no—
237C2×C4×C43—21no—
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—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—82no—
250C2×C4×C43—82no—
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
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—
263#20200C4311yesmaximal, characteristic, direct product factor, Sylow
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43D4211yescharacteristic
271C4×C43—22no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C43#57511yescharacteristic
284C4×C43#57711yescharacteristic
285C4×C43#57811yescharacteristic
286#3374C2×C4311yescharacteristic, complemented
287#3368C2×C4311yescharacteristic
288#3359C2×C4311yescharacteristic, complemented
289#3278C2×C4311yescharacteristic
290#1719C2×C4311yescharacteristic, complemented
291#1700C2×C4311yescharacteristic, complemented
292#1699C2×C4311yescharacteristic, complemented
293#1686C2×C4311yescharacteristic, complemented
294#1682C2×C4311yescharacteristic, complemented
295#1649C2×C4311yescharacteristic, complemented
296#1648C2×C4311yescharacteristic, complemented
297#1642C2×C4311yescharacteristic
298#1626C2×C4311yescharacteristic, complemented
299#1592C2×C4311yescharacteristic, complemented
300#1584C2×C4311yescharacteristic, complemented
301C2×C43—81no—
302C2×C43—161no—
303C2×C43#326511yescharacteristic
304C2×C43#327711yescharacteristic
305C2×C43#328911yescharacteristic
306C2×#137—21no—
307#557C22×C4311yescharacteristic
308#557C22×C4311yescharacteristic
309#550C22×C4311yescharacteristic
310D4×Q8C22×C4311yescharacteristic
311#500C22×C4311yescharacteristic
312#492C22×C4311yescharacteristic
313#491—21no—
314#490—21no—
315#487—21no—
316#487C22×C4311yescharacteristic
317#487C22×C4311yescharacteristic
318#486C22×C4311yescharacteristic
319#486C22×C4311yescharacteristic
320#479—21no—
321#478—21no—
322#475—21no—
323#475C22×C4311yescharacteristic
324#475C22×C4311yescharacteristic
325#474C22×C4311yescharacteristic
326#468—21no—
327#462—21no—
328#462C22×C4311yescharacteristic
329#462C22×C4311yescharacteristic
330#461—21no—
331#461C22×C4311yescharacteristic
332#460—21no—
333#460C22×C4311yescharacteristic
334#460C22×C4311yescharacteristic
335#452—21no—
336#448—21no—
337#446C22×C4311yescharacteristic
338#446C22×C4311yescharacteristic
339C8×Q8C22×C4311yescharacteristic
340#441—21no—
341#440—21no—
342C4×Q16C22×C4311yescharacteristic
343C4×SD16—21no—
344C4×SD16C22×C4311yescharacteristic
345#436C22×C4311yescharacteristic
346#335C22×C4311yescharacteristic
347#335C22×C4311yescharacteristic
348#332C22×C4311yescharacteristic
349#332C22×C4311yescharacteristic
350#332C22×C4311yescharacteristic
351#331C22×C4311yescharacteristic
352Q8⋊C8C22×C4311yescharacteristic
353Q8⋊C8C22×C4311yescharacteristic
354Q8⋊C8C22×C4311yescharacteristic
355D4⋊C8C22×C4311yescharacteristic
356#322C22×C4311yescharacteristic
357C43#2020011yescharacteristic, direct product factor, Sylow
358C2×#41—21no—
359C22×Q8—21no—
360#137—44no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16D4×C4311yescharacteristic
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16D4×C4311yescharacteristic
370C2×M16—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8C23×C4311yescharacteristic
375C4⋊Q8C23×C4311yescharacteristic
376C4⋊Q8C23×C4311yescharacteristic
377#127—21no—
378#127C23×C4311yescharacteristic
379#125—21no—
380#125—21no—
381#125—41no—
382#125—41no—
383C22⋊Q8—21no—
384C22⋊Q8—41no—
385#121—21no—
386#121—41no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8C23×C4311yescharacteristic
392C4×Q8C23×C4311yescharacteristic
393C4×Q8C23×C4311yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C4311yescharacteristic
397#107—21no—
398#107—41no—
399#107D4×C4311yescharacteristic
400#106—21no—
401#106—21no—
402#106D4×C4311yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C4311yescharacteristic
407C4⋊C8C23×C4311yescharacteristic
408C4⋊C8C23×C4311yescharacteristic
409C4⋊C8C23×C4311yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103D4×C4311yescharacteristic
420#103D4×C4311yescharacteristic
421#103D4×C4311yescharacteristic
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—41no—
428#102D4×C4311yescharacteristic
429C22⋊C8—21no—
430#97—21no—
431#97—21no—
432C4×C8—21no—
433C4×C8C23×C4311yescharacteristic
434C4×C8C23×C4311yescharacteristic
435C4×C8C23×C4311yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8C2×D4×C4311yescharacteristic
445C2×Q8C2×D4×C4311yescharacteristic
446C2×Q8C2×D4×C4311yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×D4×C4311yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456Q16—22no—
457Q16—42no—
458Q16—42no—
459SD16—41no—
460SD16—42no—
461SD16—42no—
462SD16—42no—
463SD16—42no—
464SD16—81no—
465M16—42no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×D4×C4311yescharacteristic
472C2×C8C2×D4×C4311yescharacteristic
473C2×C8C2×D4×C4311yescharacteristic
474C2×C8C2×D4×C4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C4311yescharacteristic
492C4⋊C4C2×D4×C4311yescharacteristic
493C4⋊C4C2×D4×C4311yescharacteristic
494C4⋊C4C2×D4×C4311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42—41no—
503C42C24×C4311yescharacteristic
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8AGL(1,ℤ/8)×C4312yes—
519D4—21no—
520D4—21no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—81no—
526D4—82no—
527D4—161no—
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—82no—
541C2×C4—82no—
542C2×C4C22×D4×C4311yescharacteristic
543C2×C4C22×D4×C4311yescharacteristic
544C2×C4H(5,𝔽2)×C4311yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22D42×C4311yescharacteristic
561C4—22no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
573C4C43×#57511yescharacteristic
574C4C43×#57711yescharacteristic
575C4C43×#57811yescharacteristic
576C2—81no—
577C2—161no—
578C2C43×#326511yescharacteristic
579C2C43×#327711yescharacteristic
580C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#550C22
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×#3374C2semidirect
3. C43×#3359C2semidirect
5. C43×#1719C2semidirect
6. C43×#1700C2semidirect
7. C43×#1699C2semidirect
8. C43×#1686C2semidirect
9. C43×#1682C2semidirect
10. C43×#1649C2semidirect
11. C43×#1648C2semidirect
13. C43×#1626C2semidirect
14. C43×#1592C2semidirect
15. C43×#1584C2semidirect
263. #20200C43direct (N × H)
286. #3374C2×C43semidirect
288. #3359C2×C43semidirect
290. #1719C2×C43semidirect
291. #1700C2×C43semidirect
292. #1699C2×C43semidirect
293. #1686C2×C43semidirect
294. #1682C2×C43semidirect
295. #1649C2×C43semidirect
296. #1648C2×C43semidirect
298. #1626C2×C43semidirect
299. #1592C2×C43semidirect
300. #1584C2×C43semidirect
357. C43#20200direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33742
C43×#33682
C43×#33592
C43×#32782
C43×#17192
C43×#17002
C43×#16992
C43×#16862
C43×#16822
C43×#16492
C43×#16482
C43×#16422
C43×#16262
C43×#15922
C43×#15842
#2020043