Finite Group Databasebeta

← C43×#19550 #24939567

Subgroups — C43×#19550 #24939567

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3252C211yesmaximal, characteristic
2C43×#3248C211yesmaximal, characteristic
3C43×#3231C211yesmaximal, characteristic, complemented
4C43×#2993C211yesmaximal, characteristic
5C43×#1700C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic, complemented
7C43×#1692C211yesmaximal, characteristic, complemented
8C43×#1691C211yesmaximal, characteristic, complemented
9C43×#1684C211yesmaximal, characteristic, complemented
10C43×#1683C211yesmaximal, characteristic, complemented
11C43×#1674C211yesmaximal, characteristic, complemented
12C43×#1673C211yesmaximal, characteristic, complemented
13C43×#1571C211yesmaximal, characteristic, complemented
14C43×#1561C211yesmaximal, characteristic, complemented
15C43×#1550C211yesmaximal, characteristic, complemented
16C43×#533C2211yescharacteristic
17C43×#533C2211yescharacteristic
18C43×#529C2211yescharacteristic
19C43×#500C2211yescharacteristic
20C43×#498C2211yescharacteristic
21C43×#487C2211yescharacteristic
22C43×#487C2211yescharacteristic
23C43×#485—21no—
24C43×#485—21no—
25C43×#479—21no—
26C43×#479—21no—
27C43×#479—21no—
28C43×#479—21no—
29C43×#477C2211yescharacteristic
30C43×#476C2211yescharacteristic
31C43×#475C2211yescharacteristic
32C43×#474C2211yescharacteristic
33C43×#470—21no—
34C43×#468—21no—
35C43×#467—21no—
36C43×#465—21no—
37C43×#464—21no—
38C43×#464—21no—
39C43×#462C2211yescharacteristic
40C43×#462C2211yescharacteristic
41C43×#461C2211yescharacteristic
42C43×#461C2211yescharacteristic
43C43×#446C2211yescharacteristic
44C8×Q8×C43C2211yescharacteristic
45C43×#436—21no—
46C43×#436C2211yescharacteristic
47C43×#435—21no—
48C8×D4×C43C2211yescharacteristic
49C43×#433—21no—
50C43×#431C2211yescharacteristic
51C43×#424—21no—
52C43×#423C2211yescharacteristic
53C43×#423C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C43×#335C2211yescharacteristic
56C43×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
58C43×#335C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×Q16×C43—21no—
69C2×SD16×C43—21no—
70C2×SD16×C43—21no—
71C2×M16×C43—21no—
72C2×M16×C43—21no—
73C2×M16×C43—21no—
74C22×C8×C43—21no—
75C22×C8×C43—21no—
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80#126×C43—21no—
81#125×C43—21no—
82#125×C43—21no—
83#125×C43D411yescharacteristic
84#124×C43D411yescharacteristic
85#123×C43—21no—
86C22⋊Q8×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43D411yescharacteristic
91#121×C43D411yescharacteristic
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43C2311yescharacteristic
97C4×D4×C43—21no—
98C4×D4×C43C2311yescharacteristic
99#117×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#107×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#106×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111C4⋊C8×C43—21no—
112C4⋊C8×C43—21no—
113C4⋊C8×C43—21no—
114C4⋊C8×C43—21no—
115C4⋊C8×C43—21no—
116C4⋊C8×C43D411yescharacteristic
117C4⋊C8×C43D411yescharacteristic
118C4⋊C8×C43C2311yescharacteristic
119C4⋊C8×C43C2311yescharacteristic
120C4⋊C8×C43C2311yescharacteristic
121C4⋊C8×C43C2311yescharacteristic
122C4⋊C8×C43C2311yescharacteristic
123C4⋊C8×C43C2311yescharacteristic
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#103×C43—21no—
132#103×C43—21no—
133#103×C43—21no—
134#102×C43—21no—
135#102×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×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—
156Q16×C43—81no—
157SD16×C43—81no—
158SD16×C43—81no—
159M16×C43—81no—
160M16×C43—81no—
161M16×C43—81no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C2×C8×C43—81no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
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—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×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C42×C43—21no—
200C42×C43—41no—
201C42×C43—41no—
202C42×C43C2×D411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C42×C43#4111yescharacteristic
205C42×C43C2411yescharacteristic
206C23×C43—21no—
207C23×C43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—81no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—81no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250#19550C4311yesmaximal, characteristic, direct product factor, Sylow
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43C2×#12111yescharacteristic
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43#57611yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272C4×C43#57811yescharacteristic
273#3252C2×C4311yescharacteristic
274#3248C2×C4311yescharacteristic
275#3231C2×C4311yescharacteristic, complemented
276#2993C2×C4311yescharacteristic
277#1700C2×C4311yescharacteristic, complemented
278#1699C2×C4311yescharacteristic, complemented
279#1692C2×C4311yescharacteristic, complemented
280#1691C2×C4311yescharacteristic, complemented
281#1684C2×C4311yescharacteristic, complemented
282#1683C2×C4311yescharacteristic, complemented
283#1674C2×C4311yescharacteristic, complemented
284#1673C2×C4311yescharacteristic, complemented
285#1571C2×C4311yescharacteristic, complemented
286#1561C2×C4311yescharacteristic, complemented
287#1550C2×C4311yescharacteristic, complemented
288C2×C43—41no—
289C2×C43—81no—
290C2×C43#304611yescharacteristic
291C2×C43#306111yescharacteristic
292C2×C43#306911yescharacteristic
293#533C22×C4311yescharacteristic
294#533C22×C4311yescharacteristic
295#529C22×C4311yescharacteristic
296#500C22×C4311yescharacteristic
297#498C22×C4311yescharacteristic
298#487C22×C4311yescharacteristic
299#487C22×C4311yescharacteristic
300#485—21no—
301#485—21no—
302#479—21no—
303#479—21no—
304#479—21no—
305#479—21no—
306#477C22×C4311yescharacteristic
307#476C22×C4311yescharacteristic
308#475C22×C4311yescharacteristic
309#474C22×C4311yescharacteristic
310#470—21no—
311#468—21no—
312#467—21no—
313#465—21no—
314#464—21no—
315#464—21no—
316#462C22×C4311yescharacteristic
317#462C22×C4311yescharacteristic
318#461C22×C4311yescharacteristic
319#461C22×C4311yescharacteristic
320#446C22×C4311yescharacteristic
321C8×Q8C22×C4311yescharacteristic
322#436—21no—
323#436C22×C4311yescharacteristic
324#435—21no—
325C8×D4C22×C4311yescharacteristic
326#433—21no—
327#431C22×C4311yescharacteristic
328#424—21no—
329#423C22×C4311yescharacteristic
330#423C22×C4311yescharacteristic
331C2×C4⋊C8C22×C4311yescharacteristic
332#335C22×C4311yescharacteristic
333#335C22×C4311yescharacteristic
334#335C22×C4311yescharacteristic
335#335C22×C4311yescharacteristic
336#333C22×C4311yescharacteristic
337#333C22×C4311yescharacteristic
338#332C22×C4311yescharacteristic
339#332C22×C4311yescharacteristic
340#332C22×C4311yescharacteristic
341#332C22×C4311yescharacteristic
342#332C22×C4311yescharacteristic
343#332C22×C4311yescharacteristic
344C43#1955011yescharacteristic, direct product factor, Sylow
345C2×Q16—21no—
346C2×Q16—21no—
347C2×SD16—21no—
348C2×SD16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C22×C8—21no—
353C22×C8—21no—
354C4⋊Q8C23×C4311yescharacteristic
355C4⋊Q8C23×C4311yescharacteristic
356C4⋊Q8C23×C4311yescharacteristic
357C4⋊Q8C23×C4311yescharacteristic
358#126—21no—
359#125—21no—
360#125—21no—
361#125D4×C4311yescharacteristic
362#124D4×C4311yescharacteristic
363#123—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8D4×C4311yescharacteristic
369#121D4×C4311yescharacteristic
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C4311yescharacteristic
375C4×D4—21no—
376C4×D4C23×C4311yescharacteristic
377#117—21no—
378#117—21no—
379#117—21no—
380C2×C42C23×C4311yescharacteristic
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8D4×C4311yescharacteristic
395C4⋊C8D4×C4311yescharacteristic
396C4⋊C8C23×C4311yescharacteristic
397C4⋊C8C23×C4311yescharacteristic
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—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#102—21no—
413#102—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8D4×C4311yescharacteristic
417C22⋊C8D4×C4311yescharacteristic
418#97—21no—
419C4×C8—21no—
420C4×C8C23×C4311yescharacteristic
421C4×C8C23×C4311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C4311yescharacteristic
427C2×D4—21no—
428C2×D4C2×D4×C4311yescharacteristic
429C22×C4—21no—
430C22×C4C2×D4×C4311yescharacteristic
431C22×C4C2×D4×C4311yescharacteristic
432C22×C4#41×C4311yescharacteristic
433Q16—81no—
434Q16—81no—
435SD16—81no—
436SD16—81no—
437M16—81no—
438M16—81no—
439M16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—81no—
448C2×C8C2×D4×C4311yescharacteristic
449C2×C8C2×D4×C4311yescharacteristic
450C2×C8C2×D4×C4311yescharacteristic
451C2×C8C2×D4×C4311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C4311yescharacteristic
469C4⋊C4C2×D4×C4311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42C2×D4×C4311yescharacteristic
481C42C2×D4×C4311yescharacteristic
482C42#41×C4311yescharacteristic
483C42C24×C4311yescharacteristic
484C23—21no—
485C23#121×C4311yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495D4—21no—
496D4—21no—
497D4—81no—
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—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4#121×C4311yescharacteristic
513C2×C4#121×C4311yescharacteristic
514C2×C4#121×C4311yescharacteristic
515C2×C4C22×D4×C4311yescharacteristic
516C2×C4C22×D4×C4311yescharacteristic
517C2×C4C2×#41×C4311yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×#121×C4311yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4C43×#57611yescharacteristic
547C4C43×#57711yescharacteristic
548C4C43×#57811yescharacteristic
549C4C43×#57811yescharacteristic
550C2—41no—
551C2—81no—
552C2C43×#304611yescharacteristic
553C2C43×#306111yescharacteristic
554C2C43×#306911yescharacteristic
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×#1700C2semidirect
6. C43×#1699C2semidirect
7. C43×#1692C2semidirect
8. C43×#1691C2semidirect
9. C43×#1684C2semidirect
10. C43×#1683C2semidirect
11. C43×#1674C2semidirect
12. C43×#1673C2semidirect
13. C43×#1571C2semidirect
14. C43×#1561C2semidirect
15. C43×#1550C2semidirect
250. #19550C43direct (N × H)
275. #3231C2×C43semidirect
277. #1700C2×C43semidirect
278. #1699C2×C43semidirect
279. #1692C2×C43semidirect
280. #1691C2×C43semidirect
281. #1684C2×C43semidirect
282. #1683C2×C43semidirect
283. #1674C2×C43semidirect
284. #1673C2×C43semidirect
285. #1571C2×C43semidirect
286. #1561C2×C43semidirect
287. #1550C2×C43semidirect
344. C43#19550direct (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×#32482
C43×#32312
C43×#29932
C43×#17002
C43×#16992
C43×#16922
C43×#16912
C43×#16842
C43×#16832
C43×#16742
C43×#16732
C43×#15712
C43×#15612
C43×#15502
#1955043