Finite Group Databasebeta

← C43×#19866 #24939883

Subgroups — C43×#19866 #24939883

Order 11008.

570 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3393C211yesmaximal, characteristic
2C43×#3360C211yesmaximal, characteristic
3C43×#3356C211yesmaximal, characteristic, complemented
4C43×#3342C211yesmaximal, characteristic, complemented
5C43×#1723C211yesmaximal, characteristic, complemented
6C43×#1693C211yesmaximal, characteristic, complemented
7C43×#1684C211yesmaximal, characteristic, complemented
8C43×#1671C211yesmaximal, characteristic, complemented
9C43×#1670C211yesmaximal, characteristic, complemented
10C43×#1650C211yesmaximal, characteristic, complemented
11C43×#1650C211yesmaximal, characteristic, complemented
12C43×#1643C211yesmaximal, characteristic, complemented
13C43×#1638C211yesmaximal, characteristic, complemented
14C43×#1581C211yesmaximal, characteristic
15C43×#1579C211yesmaximal, characteristic, complemented
16C43×#556C2211yescharacteristic
17C43×#556C2211yescharacteristic
18C43×#556C2211yescharacteristic
19C43×#554C2211yescharacteristic
20C43×#500C2211yescharacteristic
21C43×#500C2211yescharacteristic
22C43×#498C2211yescharacteristic
23C43×#495—21no—
24C43×#494C2211yescharacteristic
25C43×#488—21no—
26C43×#487C2211yescharacteristic
27C43×#487C2211yescharacteristic
28C43×#485—21no—
29C43×#485—21no—
30C43×#485—21no—
31C43×#483—21no—
32C43×#479—21no—
33C43×#477C2211yescharacteristic
34C43×#476C2211yescharacteristic
35C43×#475C2211yescharacteristic
36C43×#475C2211yescharacteristic
37C43×#475C2211yescharacteristic
38C43×#470—21no—
39C43×#467—21no—
40C43×#464—21no—
41C43×#464—21no—
42C43×#463—21no—
43C43×#461C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#461C2211yescharacteristic
46C8×Q8×C43C2211yescharacteristic
47C8×Q8×C43C2211yescharacteristic
48C4×Q16×C43—21no—
49C4×Q16×C43C2211yescharacteristic
50C4×SD16×C43—21no—
51C4×D8×C43C2211yescharacteristic
52C43×#436C2211yescharacteristic
53C8×D4×C43C2211yescharacteristic
54C43×#428—21no—
55C43×#427—21no—
56C43×#335C2211yescharacteristic
57C43×#334C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43D411yescharacteristic
70C2×SD16×C43—21no—
71C2×SD16×C43—21no—
72C2×SD16×C43—21no—
73C2×D8×C43D411yescharacteristic
74C2×M16×C43—21no—
75C22×C8×C43—21no—
76C4⋊Q8×C43C2311yescharacteristic
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80#126×C43—41no—
81#126×C43—41no—
82#126×C43—41no—
83#125×C43—21no—
84#124×C43—21no—
85#124×C43—21no—
86#124×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—41no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43C2311yescharacteristic
96C4×Q8×C43C2311yescharacteristic
97C4×D4×C43—21no—
98C4×D4×C43C2311yescharacteristic
99C4×D4×C43C2311yescharacteristic
100#117×C43—21no—
101#117×C43—21no—
102#117×C43—21no—
103C2×C4⋊C4×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43—21no—
107#107×C43—41no—
108#107×C43D411yescharacteristic
109#107×C43D411yescharacteristic
110#106×C43—21no—
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—21no—
114#106×C43—21no—
115#106×C43—21no—
116C4⋊C8×C43—21no—
117C4⋊C8×C43—21no—
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#103×C43—41no—
132#103×C43D411yescharacteristic
133#103×C43D411yescharacteristic
134#102×C43—21no—
135#102×C43D411yescharacteristic
136#102×C43D411yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C4×C8×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—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155Q16×C43—22no—
156Q16×C43—42no—
157Q16×C43—81no—
158SD16×C43—42no—
159SD16×C43—81no—
160SD16×C43—81no—
161D8×C43—41no—
162M16×C43—42no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—42no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
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×C43—41no—
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—41no—
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—41no—
204C42×C43—41no—
205C42×C43—41no—
206C42×C43C2411yescharacteristic
207C23×C43—21no—
208C23×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—81no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
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—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—161no—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43#13512yes—
251#19866C4311yesmaximal, characteristic, direct product factor, Sylow
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43D4211yescharacteristic
259C4×C43—21no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43C2×#13511yescharacteristic
271C4×C43#57511yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274#3393C2×C4311yescharacteristic
275#3360C2×C4311yescharacteristic
276#3356C2×C4311yescharacteristic, complemented
277#3342C2×C4311yescharacteristic, complemented
278#1723C2×C4311yescharacteristic, complemented
279#1693C2×C4311yescharacteristic, complemented
280#1684C2×C4311yescharacteristic, complemented
281#1671C2×C4311yescharacteristic, complemented
282#1670C2×C4311yescharacteristic, complemented
283#1650C2×C4311yescharacteristic, complemented
284#1650C2×C4311yescharacteristic, complemented
285#1643C2×C4311yescharacteristic, complemented
286#1638C2×C4311yescharacteristic, complemented
287#1581C2×C4311yescharacteristic
288#1579C2×C4311yescharacteristic, complemented
289C2×C43—81no—
290C2×C43—81no—
291C2×C43#327111yescharacteristic
292C2×C43#328311yescharacteristic
293C2×C43#328911yescharacteristic
294#556C22×C4311yescharacteristic
295#556C22×C4311yescharacteristic
296#556C22×C4311yescharacteristic
297#554C22×C4311yescharacteristic
298#500C22×C4311yescharacteristic
299#500C22×C4311yescharacteristic
300#498C22×C4311yescharacteristic
301#495—21no—
302#494C22×C4311yescharacteristic
303#488—21no—
304#487C22×C4311yescharacteristic
305#487C22×C4311yescharacteristic
306#485—21no—
307#485—21no—
308#485—21no—
309#483—21no—
310#479—21no—
311#477C22×C4311yescharacteristic
312#476C22×C4311yescharacteristic
313#475C22×C4311yescharacteristic
314#475C22×C4311yescharacteristic
315#475C22×C4311yescharacteristic
316#470—21no—
317#467—21no—
318#464—21no—
319#464—21no—
320#463—21no—
321#461C22×C4311yescharacteristic
322#461C22×C4311yescharacteristic
323#461C22×C4311yescharacteristic
324C8×Q8C22×C4311yescharacteristic
325C8×Q8C22×C4311yescharacteristic
326C4×Q16—21no—
327C4×Q16C22×C4311yescharacteristic
328C4×SD16—21no—
329C4×D8C22×C4311yescharacteristic
330#436C22×C4311yescharacteristic
331C8×D4C22×C4311yescharacteristic
332#428—21no—
333#427—21no—
334#335C22×C4311yescharacteristic
335#334C22×C4311yescharacteristic
336#333C22×C4311yescharacteristic
337#332C22×C4311yescharacteristic
338#332C22×C4311yescharacteristic
339#332C22×C4311yescharacteristic
340Q8⋊C8C22×C4311yescharacteristic
341Q8⋊C8C22×C4311yescharacteristic
342D4⋊C8C22×C4311yescharacteristic
343D4⋊C8C22×C4311yescharacteristic
344#322C22×C4311yescharacteristic
345C43#1986611yescharacteristic, direct product factor, Sylow
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16D4×C4311yescharacteristic
349C2×SD16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C2×D8D4×C4311yescharacteristic
353C2×M16—21no—
354C22×C8—21no—
355C4⋊Q8C23×C4311yescharacteristic
356C4⋊Q8C23×C4311yescharacteristic
357C4⋊Q8C23×C4311yescharacteristic
358C4⋊Q8C23×C4311yescharacteristic
359#126—41no—
360#126—41no—
361#126—41no—
362#125—21no—
363#124—21no—
364#124—21no—
365#124—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C23×C4311yescharacteristic
375C4×Q8C23×C4311yescharacteristic
376C4×D4—21no—
377C4×D4C23×C4311yescharacteristic
378C4×D4C23×C4311yescharacteristic
379#117—21no—
380#117—21no—
381#117—21no—
382C2×C4⋊C4—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—41no—
387#107D4×C4311yescharacteristic
388#107D4×C4311yescharacteristic
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C4311yescharacteristic
398C4⋊C8C23×C4311yescharacteristic
399C4⋊C8C23×C4311yescharacteristic
400C4⋊C8C23×C4311yescharacteristic
401#103—21no—
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—41no—
411#103D4×C4311yescharacteristic
412#103D4×C4311yescharacteristic
413#102—21no—
414#102D4×C4311yescharacteristic
415#102D4×C4311yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C4311yescharacteristic
421C4×C8C23×C4311yescharacteristic
422C4×C8C23×C4311yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C2×D4×C4311yescharacteristic
428C2×Q8C2×D4×C4311yescharacteristic
429C2×D4C2×D4×C4311yescharacteristic
430C2×D4C2×D4×C4311yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434Q16—22no—
435Q16—42no—
436Q16—81no—
437SD16—42no—
438SD16—81no—
439SD16—81no—
440D8—41no—
441M16—42no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
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—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C4311yescharacteristic
468C4⋊C4C2×D4×C4311yescharacteristic
469C4⋊C4C2×D4×C4311yescharacteristic
470C4⋊C4C2×D4×C4311yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42C24×C4311yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—161no—
518C2×C4C22×D4×C4311yescharacteristic
519C2×C4C22×D4×C4311yescharacteristic
520C2×C4H(5,𝔽2)×C4311yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8#135×C4312yes—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22D42×C4311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4C2×#135×C4311yescharacteristic
549C4C43×#57511yescharacteristic
550C4C43×#57711yescharacteristic
551C4C43×#57811yescharacteristic
552C2—81no—
553C2—81no—
554C2C43×#327111yescharacteristic
555C2C43×#328311yescharacteristic
556C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC2×D8×C43D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C42×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C43×#3356C2semidirect
4. C43×#3342C2semidirect
5. C43×#1723C2semidirect
6. C43×#1693C2semidirect
7. C43×#1684C2semidirect
8. C43×#1671C2semidirect
9. C43×#1670C2semidirect
10. C43×#1650C2semidirect
11. C43×#1650C2semidirect
12. C43×#1643C2semidirect
13. C43×#1638C2semidirect
15. C43×#1579C2semidirect
251. #19866C43direct (N × H)
276. #3356C2×C43semidirect
277. #3342C2×C43semidirect
278. #1723C2×C43semidirect
279. #1693C2×C43semidirect
280. #1684C2×C43semidirect
281. #1671C2×C43semidirect
282. #1670C2×C43semidirect
283. #1650C2×C43semidirect
284. #1650C2×C43semidirect
285. #1643C2×C43semidirect
286. #1638C2×C43semidirect
288. #1579C2×C43semidirect
345. C43#19866direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33932
C43×#33602
C43×#33562
C43×#33422
C43×#17232
C43×#16932
C43×#16842
C43×#16712
C43×#16702
C43×#16502
C43×#16432
C43×#16382
C43×#15812
C43×#15792
#1986643