Finite Group Databasebeta

← C43×#19587 #24939604

Subgroups — C43×#19587 #24939604

Order 11008.

550 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3252C211yesmaximal, characteristic
2C43×#3233C211yesmaximal, characteristic
3C43×#3231C211yesmaximal, characteristic, complemented
4C43×#2994C211yesmaximal, characteristic
5C43×#1703C211yesmaximal, characteristic, complemented
6C43×#1700C211yesmaximal, characteristic, complemented
7C43×#1696C211yesmaximal, characteristic, complemented
8C43×#1691C211yesmaximal, characteristic, complemented
9C43×#1684C211yesmaximal, characteristic, complemented
10C43×#1679C211yesmaximal, characteristic, complemented
11C43×#1675C211yesmaximal, characteristic, complemented
12C43×#1672C211yesmaximal, characteristic, complemented
13C43×#1574C211yesmaximal, characteristic, complemented
14C43×#1550C211yesmaximal, characteristic, complemented
15C43×#1542C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#533C2211yescharacteristic
18C43×#529C2211yescharacteristic
19C43×#500C2211yescharacteristic
20C43×#499—21no—
21C43×#498C2211yescharacteristic
22C43×#488—21no—
23C43×#487C2211yescharacteristic
24C43×#487C2211yescharacteristic
25C43×#485—21no—
26C43×#485—21no—
27C43×#485—21no—
28C43×#482—21no—
29C43×#479—21no—
30C43×#479—21no—
31C43×#479—21no—
32C43×#477C2211yescharacteristic
33C43×#477C2211yescharacteristic
34C43×#476C2211yescharacteristic
35C43×#476C2211yescharacteristic
36C43×#475C2211yescharacteristic
37C43×#474C2211yescharacteristic
38C43×#470—21no—
39C43×#468—21no—
40C43×#464—21no—
41C43×#462C2211yescharacteristic
42C43×#461C2211yescharacteristic
43C43×#446C2211yescharacteristic
44C8×Q8×C43C2211yescharacteristic
45C43×#436C2211yescharacteristic
46C43×#435—21no—
47C8×D4×C43—21no—
48C8×D4×C43C2211yescharacteristic
49C43×#433—21no—
50C43×#431C2211yescharacteristic
51C43×#431C2211yescharacteristic
52C43×#424—21no—
53C43×#423C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#334C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#333C2211yescharacteristic
62C43×#333C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×SD16×C43—21no—
69C2×M16×C43—21no—
70C2×M16×C43—21no—
71C22×C8×C43—21no—
72C22×C8×C43—21no—
73C4⋊Q8×C43C2311yescharacteristic
74C4⋊Q8×C43C2311yescharacteristic
75C4⋊Q8×C43C2311yescharacteristic
76C4⋊Q8×C43C2311yescharacteristic
77#126×C43—21no—
78#125×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×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43D411yescharacteristic
88#121×C43D411yescharacteristic
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43C2311yescharacteristic
94C4×D4×C43—21no—
95C4×D4×C43C2311yescharacteristic
96#117×C43—21no—
97#117×C43—21no—
98#117×C43—21no—
99C2×C42×C43C2311yescharacteristic
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—
109#106×C43—21no—
110C4⋊C8×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43D411yescharacteristic
115C4⋊C8×C43D411yescharacteristic
116C4⋊C8×C43C2311yescharacteristic
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
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×C43—21no—
129#103×C43—21no—
130#103×C43—21no—
131#102×C43—21no—
132#102×C43—21no—
133#102×C43—21no—
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43D411yescharacteristic
138C22⋊C8×C43D411yescharacteristic
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×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155Q16×C43—81no—
156SD16×C43—81no—
157M16×C43—81no—
158M16×C43—81no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—81no—
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—
195C22⋊C4×C43—41no—
196C42×C43—21no—
197C42×C43—41no—
198C42×C43—41no—
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43#4111yescharacteristic
202C42×C43C2411yescharacteristic
203C23×C43—21no—
204C23×C43#12111yescharacteristic
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—41no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—81no—
212Q8×C43—81no—
213D4×C43—21no—
214D4×C43—21no—
215D4×C43—42no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—21no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246#19587C4311yesmaximal, characteristic, direct product factor, Sylow
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43C2×#12111yescharacteristic
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43#57711yescharacteristic
266C4×C43#57711yescharacteristic
267C4×C43#57811yescharacteristic
268C4×C43#57811yescharacteristic
269#3252C2×C4311yescharacteristic
270#3233C2×C4311yescharacteristic
271#3231C2×C4311yescharacteristic, complemented
272#2994C2×C4311yescharacteristic
273#1703C2×C4311yescharacteristic, complemented
274#1700C2×C4311yescharacteristic, complemented
275#1696C2×C4311yescharacteristic, complemented
276#1691C2×C4311yescharacteristic, complemented
277#1684C2×C4311yescharacteristic, complemented
278#1679C2×C4311yescharacteristic, complemented
279#1675C2×C4311yescharacteristic, complemented
280#1672C2×C4311yescharacteristic, complemented
281#1574C2×C4311yescharacteristic, complemented
282#1550C2×C4311yescharacteristic, complemented
283#1542C2×C4311yescharacteristic, complemented
284C2×C43—41no—
285C2×C43—81no—
286C2×C43#304611yescharacteristic
287C2×C43#306311yescharacteristic
288C2×C43#306711yescharacteristic
289#533C22×C4311yescharacteristic
290#533C22×C4311yescharacteristic
291#529C22×C4311yescharacteristic
292#500C22×C4311yescharacteristic
293#499—21no—
294#498C22×C4311yescharacteristic
295#488—21no—
296#487C22×C4311yescharacteristic
297#487C22×C4311yescharacteristic
298#485—21no—
299#485—21no—
300#485—21no—
301#482—21no—
302#479—21no—
303#479—21no—
304#479—21no—
305#477C22×C4311yescharacteristic
306#477C22×C4311yescharacteristic
307#476C22×C4311yescharacteristic
308#476C22×C4311yescharacteristic
309#475C22×C4311yescharacteristic
310#474C22×C4311yescharacteristic
311#470—21no—
312#468—21no—
313#464—21no—
314#462C22×C4311yescharacteristic
315#461C22×C4311yescharacteristic
316#446C22×C4311yescharacteristic
317C8×Q8C22×C4311yescharacteristic
318#436C22×C4311yescharacteristic
319#435—21no—
320C8×D4—21no—
321C8×D4C22×C4311yescharacteristic
322#433—21no—
323#431C22×C4311yescharacteristic
324#431C22×C4311yescharacteristic
325#424—21no—
326#423C22×C4311yescharacteristic
327C2×C4⋊C8C22×C4311yescharacteristic
328#335C22×C4311yescharacteristic
329#335C22×C4311yescharacteristic
330#334C22×C4311yescharacteristic
331#334C22×C4311yescharacteristic
332#333C22×C4311yescharacteristic
333#333C22×C4311yescharacteristic
334#333C22×C4311yescharacteristic
335#333C22×C4311yescharacteristic
336#332C22×C4311yescharacteristic
337#332C22×C4311yescharacteristic
338#332C22×C4311yescharacteristic
339#332C22×C4311yescharacteristic
340C43#1958711yescharacteristic, direct product factor, Sylow
341C2×Q16—21no—
342C2×SD16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C22×C8—21no—
346C22×C8—21no—
347C4⋊Q8C23×C4311yescharacteristic
348C4⋊Q8C23×C4311yescharacteristic
349C4⋊Q8C23×C4311yescharacteristic
350C4⋊Q8C23×C4311yescharacteristic
351#126—21no—
352#125—21no—
353#125—21no—
354#125D4×C4311yescharacteristic
355#124D4×C4311yescharacteristic
356#123—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8D4×C4311yescharacteristic
362#121D4×C4311yescharacteristic
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C23×C4311yescharacteristic
368C4×D4—21no—
369C4×D4C23×C4311yescharacteristic
370#117—21no—
371#117—21no—
372#117—21no—
373C2×C42C23×C4311yescharacteristic
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#106—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8D4×C4311yescharacteristic
389C4⋊C8D4×C4311yescharacteristic
390C4⋊C8C23×C4311yescharacteristic
391C4⋊C8C23×C4311yescharacteristic
392C4⋊C8C23×C4311yescharacteristic
393C4⋊C8C23×C4311yescharacteristic
394C4⋊C8C23×C4311yescharacteristic
395C4⋊C8C23×C4311yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8D4×C4311yescharacteristic
412C22⋊C8D4×C4311yescharacteristic
413#97—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C4311yescharacteristic
417C4×C8C23×C4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C2×D4×C4311yescharacteristic
423C2×D4—21no—
424C2×D4C2×D4×C4311yescharacteristic
425C22×C4—21no—
426C22×C4C2×D4×C4311yescharacteristic
427C22×C4C2×D4×C4311yescharacteristic
428C22×C4#41×C4311yescharacteristic
429Q16—81no—
430SD16—81no—
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×C8—81no—
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—21no—
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4C2×D4×C4311yescharacteristic
462C4⋊C4C2×D4×C4311yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C42—21no—
471C42—41no—
472C42—41no—
473C42C2×D4×C4311yescharacteristic
474C42C2×D4×C4311yescharacteristic
475C42#41×C4311yescharacteristic
476C42C24×C4311yescharacteristic
477C23—21no—
478C23#121×C4311yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—81no—
486Q8—81no—
487D4—21no—
488D4—21no—
489D4—42no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4#121×C4311yescharacteristic
505C2×C4#121×C4311yescharacteristic
506C2×C4#121×C4311yescharacteristic
507C2×C4C22×D4×C4311yescharacteristic
508C2×C4C22×D4×C4311yescharacteristic
509C2×C4C2×#41×C4311yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×#121×C4311yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4C43×#57711yescharacteristic
539C4C43×#57711yescharacteristic
540C4C43×#57811yescharacteristic
541C4C43×#57811yescharacteristic
542C2—41no—
543C2—81no—
544C2C43×#304611yescharacteristic
545C2C43×#306311yescharacteristic
546C2C43×#306711yescharacteristic
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×#3231C2semidirect
5. C43×#1703C2semidirect
6. C43×#1700C2semidirect
7. C43×#1696C2semidirect
8. C43×#1691C2semidirect
9. C43×#1684C2semidirect
10. C43×#1679C2semidirect
11. C43×#1675C2semidirect
12. C43×#1672C2semidirect
13. C43×#1574C2semidirect
14. C43×#1550C2semidirect
15. C43×#1542C2semidirect
246. #19587C43direct (N × H)
271. #3231C2×C43semidirect
273. #1703C2×C43semidirect
274. #1700C2×C43semidirect
275. #1696C2×C43semidirect
276. #1691C2×C43semidirect
277. #1684C2×C43semidirect
278. #1679C2×C43semidirect
279. #1675C2×C43semidirect
280. #1672C2×C43semidirect
281. #1574C2×C43semidirect
282. #1550C2×C43semidirect
283. #1542C2×C43semidirect
340. C43#19587direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32522
C43×#32332
C43×#32312
C43×#29942
C43×#17032
C43×#17002
C43×#16962
C43×#16912
C43×#16842
C43×#16792
C43×#16752
C43×#16722
C43×#15742
C43×#15502
C43×#15422
#1958743