Finite Group Databasebeta

← C43×#19547 #24939564

Subgroups — C43×#19547 #24939564

Order 11008.

552 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×#3238C211yesmaximal, characteristic
2C43×#3233C211yesmaximal, characteristic
3C43×#3230C211yesmaximal, characteristic, complemented
4C43×#2993C211yesmaximal, characteristic
5C43×#1704C211yesmaximal, characteristic, complemented
6C43×#1703C211yesmaximal, characteristic, complemented
7C43×#1696C211yesmaximal, characteristic, complemented
8C43×#1695C211yesmaximal, characteristic, complemented
9C43×#1684C211yesmaximal, characteristic, complemented
10C43×#1683C211yesmaximal, characteristic, complemented
11C43×#1676C211yesmaximal, characteristic, complemented
12C43×#1675C211yesmaximal, characteristic, complemented
13C43×#1572C211yesmaximal, characteristic, complemented
14C43×#1559C211yesmaximal, characteristic, complemented
15C43×#1548C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C2×C4⋊Q8×C43C2211yescharacteristic
18C43×#529C2211yescharacteristic
19C43×#501—21no—
20C43×#500C2211yescharacteristic
21C43×#500C2211yescharacteristic
22C43×#499—21no—
23C43×#489—21no—
24C43×#488—21no—
25C43×#487C2211yescharacteristic
26C43×#487C2211yescharacteristic
27C43×#485—21no—
28C43×#484—21no—
29C43×#484—21no—
30C43×#483—21no—
31C43×#482—21no—
32C43×#480—21no—
33C43×#477—21no—
34C43×#477—21no—
35C43×#477C2211yescharacteristic
36C43×#477C2211yescharacteristic
37C43×#477C2211yescharacteristic
38C43×#476C2211yescharacteristic
39C43×#476C2211yescharacteristic
40C43×#476C2211yescharacteristic
41C43×#475C2211yescharacteristic
42C43×#474C2211yescharacteristic
43C43×#446C2211yescharacteristic
44C8×Q8×C43C2211yescharacteristic
45C43×#436—21no—
46C43×#436C2211yescharacteristic
47C43×#435—21no—
48C8×D4×C43C2211yescharacteristic
49C43×#433—21no—
50C43×#432C2211yescharacteristic
51C43×#431C2211yescharacteristic
52C43×#431C2211yescharacteristic
53C43×#424—21no—
54C43×#423C2211yescharacteristic
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#334C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#333C2211yescharacteristic
62C43×#333C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C22×Q8×C43—21no—
68C2×M16×C43—21no—
69C2×M16×C43—21no—
70C22×C8×C43—21no—
71C4⋊Q8×C43—21no—
72C4⋊Q8×C43—21no—
73C4⋊Q8×C43—21no—
74C4⋊Q8×C43C2311yescharacteristic
75C4⋊Q8×C43C2311yescharacteristic
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78#126×C43—21no—
79#125×C43—21no—
80#125×C43D411yescharacteristic
81#124×C43D411yescharacteristic
82#123×C43—21no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43D411yescharacteristic
86#121×C43D411yescharacteristic
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43C2311yescharacteristic
90C4×D4×C43—21no—
91C4×D4×C43C2311yescharacteristic
92#117×C43—21no—
93#117×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C42×C43C2311yescharacteristic
97#107×C43—21no—
98#107×C43—21no—
99#107×C43—21no—
100#107×C43—21no—
101#107×C43—21no—
102#107×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#106×C43—21no—
106#106×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#103×C43—21no—
127#103×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—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—82no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158M16×C43—81no—
159M16×C43—81no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
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—21no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—41no—
195C42×C43—21no—
196C42×C43—41no—
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C42×C43#4111yescharacteristic
200C42×C43C2411yescharacteristic
201C23×C43—21no—
202C23×C43#12111yescharacteristic
203Q8×C43—21no—
204Q8×C43—21no—
205Q8×C43—41no—
206Q8×C43—41no—
207Q8×C43—81no—
208Q8×C43—81no—
209Q8×C43—81no—
210Q8×C43—82no—
211D4×C43—21no—
212D4×C43—21no—
213D4×C43—81no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—82no—
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C8×C43—21no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245#19547C4311yesmaximal, characteristic, direct product factor, Sylow
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43C2×#12111yescharacteristic
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43#57711yescharacteristic
265C4×C43#57811yescharacteristic
266C4×C43#57811yescharacteristic
267C4×C43#57811yescharacteristic
268#3238C2×C4311yescharacteristic
269#3233C2×C4311yescharacteristic
270#3230C2×C4311yescharacteristic, complemented
271#2993C2×C4311yescharacteristic
272#1704C2×C4311yescharacteristic, complemented
273#1703C2×C4311yescharacteristic, complemented
274#1696C2×C4311yescharacteristic, complemented
275#1695C2×C4311yescharacteristic, complemented
276#1684C2×C4311yescharacteristic, complemented
277#1683C2×C4311yescharacteristic, complemented
278#1676C2×C4311yescharacteristic, complemented
279#1675C2×C4311yescharacteristic, complemented
280#1572C2×C4311yescharacteristic, complemented
281#1559C2×C4311yescharacteristic, complemented
282#1548C2×C4311yescharacteristic, complemented
283C2×C43—41no—
284C2×C43—81no—
285C2×C43#304611yescharacteristic
286C2×C43#305911yescharacteristic
287C2×C43#306811yescharacteristic
288#533C22×C4311yescharacteristic
289C2×C4⋊Q8C22×C4311yescharacteristic
290#529C22×C4311yescharacteristic
291#501—21no—
292#500C22×C4311yescharacteristic
293#500C22×C4311yescharacteristic
294#499—21no—
295#489—21no—
296#488—21no—
297#487C22×C4311yescharacteristic
298#487C22×C4311yescharacteristic
299#485—21no—
300#484—21no—
301#484—21no—
302#483—21no—
303#482—21no—
304#480—21no—
305#477—21no—
306#477—21no—
307#477C22×C4311yescharacteristic
308#477C22×C4311yescharacteristic
309#477C22×C4311yescharacteristic
310#476C22×C4311yescharacteristic
311#476C22×C4311yescharacteristic
312#476C22×C4311yescharacteristic
313#475C22×C4311yescharacteristic
314#474C22×C4311yescharacteristic
315#446C22×C4311yescharacteristic
316C8×Q8C22×C4311yescharacteristic
317#436—21no—
318#436C22×C4311yescharacteristic
319#435—21no—
320C8×D4C22×C4311yescharacteristic
321#433—21no—
322#432C22×C4311yescharacteristic
323#431C22×C4311yescharacteristic
324#431C22×C4311yescharacteristic
325#424—21no—
326#423C22×C4311yescharacteristic
327#335C22×C4311yescharacteristic
328#335C22×C4311yescharacteristic
329#334C22×C4311yescharacteristic
330#334C22×C4311yescharacteristic
331#333C22×C4311yescharacteristic
332#333C22×C4311yescharacteristic
333#333C22×C4311yescharacteristic
334#333C22×C4311yescharacteristic
335#333C22×C4311yescharacteristic
336#333C22×C4311yescharacteristic
337#332C22×C4311yescharacteristic
338#332C22×C4311yescharacteristic
339C43#1954711yescharacteristic, direct product factor, Sylow
340C22×Q8—21no—
341C2×M16—21no—
342C2×M16—21no—
343C22×C8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8C23×C4311yescharacteristic
348C4⋊Q8C23×C4311yescharacteristic
349C4⋊Q8C23×C4311yescharacteristic
350C4⋊Q8C23×C4311yescharacteristic
351#126—21no—
352#125—21no—
353#125D4×C4311yescharacteristic
354#124D4×C4311yescharacteristic
355#123—21no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8D4×C4311yescharacteristic
359#121D4×C4311yescharacteristic
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8C23×C4311yescharacteristic
363C4×D4—21no—
364C4×D4C23×C4311yescharacteristic
365#117—21no—
366#117—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C42C23×C4311yescharacteristic
370#107—21no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#106—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8D4×C4311yescharacteristic
386C4⋊C8D4×C4311yescharacteristic
387C4⋊C8C23×C4311yescharacteristic
388C4⋊C8C23×C4311yescharacteristic
389C4⋊C8C23×C4311yescharacteristic
390C4⋊C8C23×C4311yescharacteristic
391C4⋊C8C23×C4311yescharacteristic
392C4⋊C8C23×C4311yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#102—21no—
402#102—21no—
403#102—21no—
404#102—21no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8D4×C4311yescharacteristic
410C22⋊C8D4×C4311yescharacteristic
411#97—21no—
412#97—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8C23×C4311yescharacteristic
416C4×C8C23×C4311yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—41no—
422C2×Q8—82no—
423C2×Q8C2×D4×C4311yescharacteristic
424C2×D4—21no—
425C2×D4C2×D4×C4311yescharacteristic
426C22×C4—21no—
427C22×C4—41no—
428C22×C4C2×D4×C4311yescharacteristic
429C22×C4C2×D4×C4311yescharacteristic
430C22×C4#41×C4311yescharacteristic
431M16—81no—
432M16—81no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—81no—
440C2×C8C2×D4×C4311yescharacteristic
441C2×C8C2×D4×C4311yescharacteristic
442C2×C8C2×D4×C4311yescharacteristic
443C2×C8C2×D4×C4311yescharacteristic
444C4⋊C4—21no—
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—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4C2×D4×C4311yescharacteristic
461C4⋊C4C2×D4×C4311yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—41no—
468C42—21no—
469C42—41no—
470C42C2×D4×C4311yescharacteristic
471C42C2×D4×C4311yescharacteristic
472C42#41×C4311yescharacteristic
473C42C24×C4311yescharacteristic
474C23—21no—
475C23#121×C4311yescharacteristic
476Q8—21no—
477Q8—21no—
478Q8—41no—
479Q8—41no—
480Q8—81no—
481Q8—81no—
482Q8—81no—
483Q8—82no—
484D4—21no—
485D4—21no—
486D4—81no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—82no—
502C2×C4#121×C4311yescharacteristic
503C2×C4#121×C4311yescharacteristic
504C2×C4#121×C4311yescharacteristic
505C2×C4C22×D4×C4311yescharacteristic
506C2×C4C22×D4×C4311yescharacteristic
507C2×C4C2×#41×C4311yescharacteristic
508C8—21no—
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22C2×#121×C4311yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4—81no—
536C4C43×#57711yescharacteristic
537C4C43×#57811yescharacteristic
538C4C43×#57811yescharacteristic
539C4C43×#57811yescharacteristic
540C2—41no—
541C2—81no—
542C2C43×#304611yescharacteristic
543C2C43×#305911yescharacteristic
544C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radical#121×C43D4
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
3. C43×#3230C2semidirect
5. C43×#1704C2semidirect
6. C43×#1703C2semidirect
7. C43×#1696C2semidirect
8. C43×#1695C2semidirect
9. C43×#1684C2semidirect
10. C43×#1683C2semidirect
11. C43×#1676C2semidirect
12. C43×#1675C2semidirect
13. C43×#1572C2semidirect
14. C43×#1559C2semidirect
15. C43×#1548C2semidirect
245. #19547C43direct (N × H)
270. #3230C2×C43semidirect
272. #1704C2×C43semidirect
273. #1703C2×C43semidirect
274. #1696C2×C43semidirect
275. #1695C2×C43semidirect
276. #1684C2×C43semidirect
277. #1683C2×C43semidirect
278. #1676C2×C43semidirect
279. #1675C2×C43semidirect
280. #1572C2×C43semidirect
281. #1559C2×C43semidirect
282. #1548C2×C43semidirect
339. C43#19547direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32382
C43×#32332
C43×#32302
C43×#29932
C43×#17042
C43×#17032
C43×#16962
C43×#16952
C43×#16842
C43×#16832
C43×#16762
C43×#16752
C43×#15722
C43×#15592
C43×#15482
#1954743