Finite Group Databasebeta

← C43×#20280 #24940297

Subgroups — C43×#20280 #24940297

Order 11008.

578 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3400C211yesmaximal, characteristic, complemented
2C43×#3375C211yesmaximal, characteristic, complemented
3C43×#3375C211yesmaximal, characteristic, complemented
4C43×#3365C211yesmaximal, characteristic, complemented
5C43×#1717C211yesmaximal, characteristic
6C43×#1702C211yesmaximal, characteristic, complemented
7C43×#1698C211yesmaximal, characteristic, complemented
8C43×#1686C211yesmaximal, characteristic, complemented
9C43×#1678C211yesmaximal, characteristic, complemented
10C43×#1645C211yesmaximal, characteristic, complemented
11C43×#1636C211yesmaximal, characteristic, complemented
12C43×#1620C211yesmaximal, characteristic
13C43×#1620C211yesmaximal, characteristic
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1584C211yesmaximal, characteristic, complemented
16C43×#559C2211yescharacteristic
17C43×#559C2211yescharacteristic
18Q82×C43C2211yescharacteristic
19C43×#557C2211yescharacteristic
20C43×#497—21no—
21C43×#493C2211yescharacteristic
22C43×#492C2211yescharacteristic
23C43×#489—21no—
24C43×#489—21no—
25C43×#488—21no—
26C43×#487C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#486C2211yescharacteristic
30C43×#478—21no—
31C43×#477C2211yescharacteristic
32C43×#477C2211yescharacteristic
33C43×#475C2211yescharacteristic
34C43×#474—21no—
35C43×#474—21no—
36C43×#464—21no—
37C43×#464—21no—
38C43×#464—21no—
39C43×#464—21no—
40C43×#462C2211yescharacteristic
41C43×#461—21no—
42C43×#460C2211yescharacteristic
43C43×#460C2211yescharacteristic
44C43×#460C2211yescharacteristic
45C43×#460C2211yescharacteristic
46C43×#446C2211yescharacteristic
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C8×Q8×C43C2211yescharacteristic
50C43×#440—21no—
51C43×#440—21no—
52C43×#440—21no—
53C4×Q16×C43C2211yescharacteristic
54C4×Q16×C43C2211yescharacteristic
55C4×SD16×C43—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#331C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×Q16×C43D411yescharacteristic
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×D8×C43—41no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43—21no—
79C4⋊Q8×C43—21no—
80C4⋊Q8×C43—41no—
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43C2311yescharacteristic
84#127×C43C2311yescharacteristic
85#125×C43—21no—
86#125×C43—41no—
87#124×C43—21no—
88#124×C43—21no—
89#124×C43—21no—
90#124×C43—21no—
91#123×C43—41no—
92#123×C43—41no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43C2311yescharacteristic
98C4×Q8×C43C2311yescharacteristic
99C4×Q8×C43C2311yescharacteristic
100C4×Q8×C43C2311yescharacteristic
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43D411yescharacteristic
108#107×C43D411yescharacteristic
109#106×C43—21no—
110C4⋊C8×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43C2311yescharacteristic
115C4⋊C8×C43C2311yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118#103×C43—21no—
119#103×C43—21no—
120#103×C43—21no—
121#103×C43—21no—
122#103×C43—41no—
123#103×C43D411yescharacteristic
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—21no—
136#102×C43—21no—
137#97×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159Q16×C43—41no—
160Q16×C43—41no—
161Q16×C43—81no—
162SD16×C43—42no—
163SD16×C43—42no—
164SD16×C43—42no—
165SD16×C43—42no—
166SD16×C43—81no—
167SD16×C43—81no—
168D8×C43—82no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C22⋊C4×C43—41no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—41no—
206C42×C43—41no—
207C42×C43C2411yescharacteristic
208C23×C43—41no—
209C23×C43—41no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—81no—
221Q8×C43—161no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—81no—
231D4×C43—81no—
232C2×C4×C43—21no—
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—161no—
243C2×C4×C43—161no—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256#20280C4311yesmaximal, characteristic, direct product factor, Sylow
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43D4211yescharacteristic
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43#57511yescharacteristic
276C4×C43#57511yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57811yescharacteristic
279#3400C2×C4311yescharacteristic, complemented
280#3375C2×C4311yescharacteristic, complemented
281#3375C2×C4311yescharacteristic, complemented
282#3365C2×C4311yescharacteristic, complemented
283#1717C2×C4311yescharacteristic
284#1702C2×C4311yescharacteristic, complemented
285#1698C2×C4311yescharacteristic, complemented
286#1686C2×C4311yescharacteristic, complemented
287#1678C2×C4311yescharacteristic, complemented
288#1645C2×C4311yescharacteristic, complemented
289#1636C2×C4311yescharacteristic, complemented
290#1620C2×C4311yescharacteristic
291#1620C2×C4311yescharacteristic
292#1593C2×C4311yescharacteristic, complemented
293#1584C2×C4311yescharacteristic, complemented
294C2×C43—161no—
295C2×C43—161no—
296C2×C43#327111yescharacteristic
297C2×C43#327711yescharacteristic
298C2×C43#328811yescharacteristic
299#559C22×C4311yescharacteristic
300#559C22×C4311yescharacteristic
301Q82C22×C4311yescharacteristic
302#557C22×C4311yescharacteristic
303#497—21no—
304#493C22×C4311yescharacteristic
305#492C22×C4311yescharacteristic
306#489—21no—
307#489—21no—
308#488—21no—
309#487C22×C4311yescharacteristic
310#486C22×C4311yescharacteristic
311#486C22×C4311yescharacteristic
312#486C22×C4311yescharacteristic
313#478—21no—
314#477C22×C4311yescharacteristic
315#477C22×C4311yescharacteristic
316#475C22×C4311yescharacteristic
317#474—21no—
318#474—21no—
319#464—21no—
320#464—21no—
321#464—21no—
322#464—21no—
323#462C22×C4311yescharacteristic
324#461—21no—
325#460C22×C4311yescharacteristic
326#460C22×C4311yescharacteristic
327#460C22×C4311yescharacteristic
328#460C22×C4311yescharacteristic
329#446C22×C4311yescharacteristic
330#446C22×C4311yescharacteristic
331#446C22×C4311yescharacteristic
332C8×Q8C22×C4311yescharacteristic
333#440—21no—
334#440—21no—
335#440—21no—
336C4×Q16C22×C4311yescharacteristic
337C4×Q16C22×C4311yescharacteristic
338C4×SD16—21no—
339#335C22×C4311yescharacteristic
340#334C22×C4311yescharacteristic
341#333C22×C4311yescharacteristic
342#332C22×C4311yescharacteristic
343#331C22×C4311yescharacteristic
344#331C22×C4311yescharacteristic
345Q8⋊C8C22×C4311yescharacteristic
346Q8⋊C8C22×C4311yescharacteristic
347Q8⋊C8C22×C4311yescharacteristic
348Q8⋊C8C22×C4311yescharacteristic
349#322C22×C4311yescharacteristic
350C43#2028011yescharacteristic, direct product factor, Sylow
351C2×Q16—21no—
352C2×Q16D4×C4311yescharacteristic
353C2×Q16D4×C4311yescharacteristic
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×D8—41no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—41no—
365C4⋊Q8C23×C4311yescharacteristic
366C4⋊Q8C23×C4311yescharacteristic
367#127C23×C4311yescharacteristic
368#127C23×C4311yescharacteristic
369#125—21no—
370#125—41no—
371#124—21no—
372#124—21no—
373#124—21no—
374#124—21no—
375#123—41no—
376#123—41no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C4311yescharacteristic
382C4×Q8C23×C4311yescharacteristic
383C4×Q8C23×C4311yescharacteristic
384C4×Q8C23×C4311yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389#107—21no—
390#107—21no—
391#107D4×C4311yescharacteristic
392#107D4×C4311yescharacteristic
393#106—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C23×C4311yescharacteristic
399C4⋊C8C23×C4311yescharacteristic
400C4⋊C8C23×C4311yescharacteristic
401C4⋊C8C23×C4311yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—41no—
407#103D4×C4311yescharacteristic
408#103D4×C4311yescharacteristic
409#103D4×C4311yescharacteristic
410#103D4×C4311yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#97—21no—
422#97—21no—
423#97—21no—
424C4×C8—21no—
425C4×C8C23×C4311yescharacteristic
426C4×C8C23×C4311yescharacteristic
427C4×C8C23×C4311yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8C2×D4×C4311yescharacteristic
432C2×Q8C2×D4×C4311yescharacteristic
433C2×Q8C2×D4×C4311yescharacteristic
434C2×Q8C2×D4×C4311yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C22×C4—41no—
442C22×C4—41no—
443Q16—41no—
444Q16—41no—
445Q16—81no—
446SD16—42no—
447SD16—42no—
448SD16—42no—
449SD16—42no—
450SD16—81no—
451SD16—81no—
452D8—82no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8C2×D4×C4311yescharacteristic
459C2×C8C2×D4×C4311yescharacteristic
460C2×C8C2×D4×C4311yescharacteristic
461C2×C8C2×D4×C4311yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C4311yescharacteristic
476C4⋊C4C2×D4×C4311yescharacteristic
477C4⋊C4C2×D4×C4311yescharacteristic
478C4⋊C4C2×D4×C4311yescharacteristic
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42—41no—
491C42C24×C4311yescharacteristic
492C23—41no—
493C23—41no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—161no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—81no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—161no—
527C2×C4—161no—
528C2×C4C22×D4×C4311yescharacteristic
529C2×C4C22×D4×C4311yescharacteristic
530C2×C4H(5,𝔽2)×C4311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22D42×C4311yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4C43×#57511yescharacteristic
559C4C43×#57511yescharacteristic
560C4C43×#57711yescharacteristic
561C4C43×#57811yescharacteristic
562C2—161no—
563C2—161no—
564C2C43×#327111yescharacteristic
565C2C43×#327711yescharacteristic
566C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#493C22
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×#3375C2semidirect
3. C43×#3375C2semidirect
4. C43×#3365C2semidirect
6. C43×#1702C2semidirect
7. C43×#1698C2semidirect
8. C43×#1686C2semidirect
9. C43×#1678C2semidirect
10. C43×#1645C2semidirect
11. C43×#1636C2semidirect
14. C43×#1593C2semidirect
15. C43×#1584C2semidirect
256. #20280C43direct (N × H)
279. #3400C2×C43semidirect
280. #3375C2×C43semidirect
281. #3375C2×C43semidirect
282. #3365C2×C43semidirect
284. #1702C2×C43semidirect
285. #1698C2×C43semidirect
286. #1686C2×C43semidirect
287. #1678C2×C43semidirect
288. #1645C2×C43semidirect
289. #1636C2×C43semidirect
292. #1593C2×C43semidirect
293. #1584C2×C43semidirect
350. C43#20280direct (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×#33752
C43×#33652
C43×#17172
C43×#17022
C43×#16982
C43×#16862
C43×#16782
C43×#16452
C43×#16362
C43×#16202
C43×#15932
C43×#15842
#2028043