Finite Group Databasebeta

← C43×#20216 #24940233

Subgroups — C43×#20216 #24940233

Order 11008.

560 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3387C211yesmaximal, characteristic, complemented
2C43×#3375C211yesmaximal, characteristic
3C43×#3375C211yesmaximal, characteristic
4C43×#3363C211yesmaximal, characteristic, complemented
5C43×#1720C211yesmaximal, characteristic
6C43×#1704C211yesmaximal, characteristic, complemented
7C43×#1698C211yesmaximal, characteristic
8C43×#1692C211yesmaximal, characteristic, complemented
9C43×#1678C211yesmaximal, characteristic
10C43×#1640C211yesmaximal, characteristic
11C43×#1633C211yesmaximal, characteristic, complemented
12C43×#1633C211yesmaximal, characteristic, complemented
13C43×#1626C211yesmaximal, characteristic
14C43×#1593C211yesmaximal, characteristic, complemented
15C43×#1584C211yesmaximal, characteristic, complemented
16C43×#559C2211yescharacteristic
17Q82×C43C2211yescharacteristic
18Q82×C43C2211yescharacteristic
19C43×#557C2211yescharacteristic
20C43×#501—21no—
21C43×#498C2211yescharacteristic
22C43×#494C2211yescharacteristic
23C43×#489—21no—
24C43×#489—21no—
25C43×#487—21no—
26C43×#487C2211yescharacteristic
27C43×#486C2211yescharacteristic
28C43×#486C2211yescharacteristic
29C43×#486C2211yescharacteristic
30C43×#479—21no—
31C43×#477—21no—
32C43×#477C2211yescharacteristic
33C43×#477C2211yescharacteristic
34C43×#477C2211yescharacteristic
35C43×#477C2211yescharacteristic
36C43×#475—21no—
37C43×#475C2211yescharacteristic
38C43×#474—21no—
39C43×#474—21no—
40C43×#464—21no—
41C43×#464—21no—
42C43×#462—21no—
43C43×#462C2211yescharacteristic
44C43×#460C2211yescharacteristic
45C43×#460C2211yescharacteristic
46C43×#446C2211yescharacteristic
47C43×#446C2211yescharacteristic
48C43×#446C2211yescharacteristic
49C8×Q8×C43C2211yescharacteristic
50C43×#441—21no—
51C43×#440—21no—
52C43×#440—21no—
53C4×Q16×C43—21no—
54C4×Q16×C43C2211yescharacteristic
55C4×Q16×C43C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#331C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×Q16×C43—41no—
69C2×Q16×C43D411yescharacteristic
70C2×Q16×C43D411yescharacteristic
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C4⋊Q8×C43—21no—
74C4⋊Q8×C43—21no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43—41no—
79C4⋊Q8×C43—41no—
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83#127×C43C2311yescharacteristic
84#125×C43—21no—
85#125×C43—41no—
86#124×C43—21no—
87#124×C43—21no—
88#123×C43—41no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43C2311yescharacteristic
96C4×Q8×C43C2311yescharacteristic
97C4×Q8×C43C2311yescharacteristic
98C4×Q8×C43C2311yescharacteristic
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101#107×C43—21no—
102#107×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#107×C43D411yescharacteristic
106#107×C43D411yescharacteristic
107#106×C43—21no—
108#106×C43—21no—
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—21no—
123#103×C43—21no—
124#103×C43—21no—
125#103×C43—21no—
126#103×C43D411yescharacteristic
127#103×C43D411yescharacteristic
128#103×C43D411yescharacteristic
129#103×C43D411yescharacteristic
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—41no—
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—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—41no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C22×C4×C43—41no—
157Q16×C43—22no—
158Q16×C43—41no—
159Q16×C43—42no—
160Q16×C43—82no—
161SD16×C43—42no—
162SD16×C43—42no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C22⋊C4×C43—41no—
194C22⋊C4×C43—41no—
195C22⋊C4×C43—41no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—41no—
201C42×C43—41no—
202C42×C43—41no—
203C42×C43C2411yescharacteristic
204C23×C43—41no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215Q8×C43—81no—
216Q8×C43—161no—
217Q8×C43—161no—
218Q8×C43#13712yes—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—81no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—161no—
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248#20216C4311yesmaximal, characteristic, direct product factor, Sylow
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43D4211yescharacteristic
253C4×C43—22no—
254C4×C43—21no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43C2×#13711yescharacteristic
266C4×C43#57511yescharacteristic
267C4×C43#57811yescharacteristic
268C4×C43#57811yescharacteristic
269#3387C2×C4311yescharacteristic, complemented
270#3375C2×C4311yescharacteristic
271#3375C2×C4311yescharacteristic
272#3363C2×C4311yescharacteristic, complemented
273#1720C2×C4311yescharacteristic
274#1704C2×C4311yescharacteristic, complemented
275#1698C2×C4311yescharacteristic
276#1692C2×C4311yescharacteristic, complemented
277#1678C2×C4311yescharacteristic
278#1640C2×C4311yescharacteristic
279#1633C2×C4311yescharacteristic, complemented
280#1633C2×C4311yescharacteristic, complemented
281#1626C2×C4311yescharacteristic
282#1593C2×C4311yescharacteristic, complemented
283#1584C2×C4311yescharacteristic, complemented
284C2×C43—161no—
285C2×C43#327011yescharacteristic
286C2×C43#327711yescharacteristic
287C2×C43#328811yescharacteristic
288#559C22×C4311yescharacteristic
289Q82C22×C4311yescharacteristic
290Q82C22×C4311yescharacteristic
291#557C22×C4311yescharacteristic
292#501—21no—
293#498C22×C4311yescharacteristic
294#494C22×C4311yescharacteristic
295#489—21no—
296#489—21no—
297#487—21no—
298#487C22×C4311yescharacteristic
299#486C22×C4311yescharacteristic
300#486C22×C4311yescharacteristic
301#486C22×C4311yescharacteristic
302#479—21no—
303#477—21no—
304#477C22×C4311yescharacteristic
305#477C22×C4311yescharacteristic
306#477C22×C4311yescharacteristic
307#477C22×C4311yescharacteristic
308#475—21no—
309#475C22×C4311yescharacteristic
310#474—21no—
311#474—21no—
312#464—21no—
313#464—21no—
314#462—21no—
315#462C22×C4311yescharacteristic
316#460C22×C4311yescharacteristic
317#460C22×C4311yescharacteristic
318#446C22×C4311yescharacteristic
319#446C22×C4311yescharacteristic
320#446C22×C4311yescharacteristic
321C8×Q8C22×C4311yescharacteristic
322#441—21no—
323#440—21no—
324#440—21no—
325C4×Q16—21no—
326C4×Q16C22×C4311yescharacteristic
327C4×Q16C22×C4311yescharacteristic
328#335C22×C4311yescharacteristic
329#334C22×C4311yescharacteristic
330#333C22×C4311yescharacteristic
331#333C22×C4311yescharacteristic
332#332C22×C4311yescharacteristic
333#331C22×C4311yescharacteristic
334Q8⋊C8C22×C4311yescharacteristic
335Q8⋊C8C22×C4311yescharacteristic
336Q8⋊C8C22×C4311yescharacteristic
337Q8⋊C8C22×C4311yescharacteristic
338#322C22×C4311yescharacteristic
339C43#2021611yescharacteristic, direct product factor, Sylow
340C2×Q16—21no—
341C2×Q16—41no—
342C2×Q16D4×C4311yescharacteristic
343C2×Q16D4×C4311yescharacteristic
344C2×SD16—21no—
345C2×SD16—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—41no—
352C4⋊Q8—41no—
353C4⋊Q8C23×C4311yescharacteristic
354C4⋊Q8C23×C4311yescharacteristic
355C4⋊Q8C23×C4311yescharacteristic
356#127C23×C4311yescharacteristic
357#125—21no—
358#125—41no—
359#124—21no—
360#124—21no—
361#123—41no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C23×C4311yescharacteristic
369C4×Q8C23×C4311yescharacteristic
370C4×Q8C23×C4311yescharacteristic
371C4×Q8C23×C4311yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107D4×C4311yescharacteristic
379#107D4×C4311yescharacteristic
380#106—21no—
381#106—21no—
382#106—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8C23×C4311yescharacteristic
388C4⋊C8C23×C4311yescharacteristic
389C4⋊C8C23×C4311yescharacteristic
390C4⋊C8C23×C4311yescharacteristic
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103D4×C4311yescharacteristic
400#103D4×C4311yescharacteristic
401#103D4×C4311yescharacteristic
402#103D4×C4311yescharacteristic
403#102—21no—
404#102—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—41no—
410#97—21no—
411#97—21no—
412#97—21no—
413C4×C8—21no—
414C4×C8C23×C4311yescharacteristic
415C4×C8C23×C4311yescharacteristic
416C4×C8C23×C4311yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8C2×D4×C4311yescharacteristic
423C2×Q8C2×D4×C4311yescharacteristic
424C2×Q8C2×D4×C4311yescharacteristic
425C2×Q8C2×D4×C4311yescharacteristic
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C22×C4—41no—
430Q16—22no—
431Q16—41no—
432Q16—42no—
433Q16—82no—
434SD16—42no—
435SD16—42no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8C2×D4×C4311yescharacteristic
442C2×C8C2×D4×C4311yescharacteristic
443C2×C8C2×D4×C4311yescharacteristic
444C2×C8C2×D4×C4311yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×D4×C4311yescharacteristic
463C4⋊C4C2×D4×C4311yescharacteristic
464C4⋊C4C2×D4×C4311yescharacteristic
465C4⋊C4C2×D4×C4311yescharacteristic
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—41no—
474C42—41no—
475C42—41no—
476C42C24×C4311yescharacteristic
477C23—41no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—81no—
488Q8—81no—
489Q8—161no—
490Q8—161no—
491Q8#137×C4312yes—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—81no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—161no—
509C2×C4C22×D4×C4311yescharacteristic
510C2×C4C22×D4×C4311yescharacteristic
511C2×C4H(5,𝔽2)×C4311yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—41no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22D42×C4311yescharacteristic
525C4—22no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×#137×C4311yescharacteristic
538C4C43×#57511yescharacteristic
539C4C43×#57811yescharacteristic
540C4C43×#57811yescharacteristic
541C2—161no—
542C2C43×#327011yescharacteristic
543C2C43×#327711yescharacteristic
544C2C43×#328811yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radical#127×C43C23
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×#3387C2semidirect
4. C43×#3363C2semidirect
6. C43×#1704C2semidirect
8. C43×#1692C2semidirect
11. C43×#1633C2semidirect
12. C43×#1633C2semidirect
14. C43×#1593C2semidirect
15. C43×#1584C2semidirect
248. #20216C43direct (N × H)
269. #3387C2×C43semidirect
272. #3363C2×C43semidirect
274. #1704C2×C43semidirect
276. #1692C2×C43semidirect
279. #1633C2×C43semidirect
280. #1633C2×C43semidirect
282. #1593C2×C43semidirect
283. #1584C2×C43semidirect
339. C43#20216direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33872
C43×#33752
C43×#33632
C43×#17202
C43×#17042
C43×#16982
C43×#16922
C43×#16782
C43×#16402
C43×#16332
C43×#16262
C43×#15932
C43×#15842
#2021643