Finite Group Databasebeta

← C43×#20233 #24940250

Subgroups — C43×#20233 #24940250

Order 11008.

556 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×#3398C211yesmaximal, characteristic
2C43×#3381C211yesmaximal, characteristic
3C43×#3374C211yesmaximal, characteristic, complemented
4C43×#3356C211yesmaximal, characteristic
5C43×#1716C211yesmaximal, characteristic, complemented
6C43×#1699C211yesmaximal, characteristic
7C43×#1692C211yesmaximal, characteristic, complemented
8C43×#1692C211yesmaximal, characteristic, complemented
9C43×#1670C211yesmaximal, characteristic, complemented
10C43×#1653C211yesmaximal, characteristic, complemented
11C43×#1652C211yesmaximal, characteristic
12C43×#1643C211yesmaximal, characteristic
13C43×#1636C211yesmaximal, characteristic, complemented
14C43×#1592C211yesmaximal, characteristic
15C43×#1584C211yesmaximal, characteristic, complemented
16C43×#557C2211yescharacteristic
17C43×#557C2211yescharacteristic
18C43×#556C2211yescharacteristic
19C43×#554C2211yescharacteristic
20C43×#499—21no—
21C43×#498C2211yescharacteristic
22C43×#498C2211yescharacteristic
23C43×#498C2211yescharacteristic
24C43×#497—21no—
25C43×#494C2211yescharacteristic
26C43×#491—21no—
27C43×#487C2211yescharacteristic
28C43×#487C2211yescharacteristic
29C43×#485—21no—
30C43×#483—21no—
31C43×#479—21no—
32C43×#479—21no—
33C43×#478—21no—
34C43×#477C2211yescharacteristic
35C43×#477C2211yescharacteristic
36C43×#475C2211yescharacteristic
37C43×#475C2211yescharacteristic
38C43×#474C2211yescharacteristic
39C43×#470—21no—
40C43×#464—21no—
41C43×#462—21no—
42C43×#462—21no—
43C43×#462C2211yescharacteristic
44C43×#462C2211yescharacteristic
45C43×#461C2211yescharacteristic
46C43×#446C2211yescharacteristic
47C43×#446C2211yescharacteristic
48C8×Q8×C43C2211yescharacteristic
49C43×#441—21no—
50C43×#441—21no—
51C4×Q16×C43C2211yescharacteristic
52C4×SD16×C43—21no—
53C4×SD16×C43C2211yescharacteristic
54C43×#436C2211yescharacteristic
55C43×#428—21no—
56C43×#335C2211yescharacteristic
57C43×#335C2211yescharacteristic
58C43×#333C2211yescharacteristic
59C43×#332C2211yescharacteristic
60C43×#332C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×Q8⋊C8C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q16×C43—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43—21no—
70C2×Q16×C43—21no—
71C2×Q16×C43D411yescharacteristic
72C2×SD16×C43—21no—
73C2×SD16×C43D411yescharacteristic
74C2×M16×C43—21no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43—21no—
77C4⋊Q8×C43C2311yescharacteristic
78C4⋊Q8×C43C2311yescharacteristic
79C4⋊Q8×C43C2311yescharacteristic
80C4⋊Q8×C43C2311yescharacteristic
81#126×C43—41no—
82#125×C43—21no—
83#125×C43—21no—
84#125×C43—21no—
85#125×C43—41no—
86#125×C43—41no—
87#124×C43—21no—
88C22⋊Q8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—41no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43C2311yescharacteristic
97C4×Q8×C43C2311yescharacteristic
98C4×Q8×C43C2311yescharacteristic
99C4×D4×C43—21no—
100C4×D4×C43C2311yescharacteristic
101#117×C43—21no—
102C2×C4⋊C4×C43—21no—
103#107×C43—21no—
104#107×C43—21no—
105#107×C43—21no—
106#107×C43D411yescharacteristic
107#106×C43—21no—
108#106×C43—21no—
109#106×C43—21no—
110#106×C43—21no—
111#106×C43—21no—
112#106×C43—21no—
113#106×C43—41no—
114#106×C43D411yescharacteristic
115C4⋊C8×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#103×C43D411yescharacteristic
135#102×C43—21no—
136#102×C43D411yescharacteristic
137C22⋊C8×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—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154Q16×C43—41no—
155Q16×C43—42no—
156Q16×C43—42no—
157Q16×C43—81no—
158Q16×C43—81no—
159SD16×C43—22no—
160SD16×C43—81no—
161M16×C43—42no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
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—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×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C22⋊C4×C43—21no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—41no—
203C42×C43—41no—
204C42×C43—41no—
205C42×C43C2411yescharacteristic
206C23×C43—21no—
207Q8×C43—21no—
208Q8×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—
222C2×C4×C43—21no—
223C2×C4×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—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
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—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43#13712yes—
248#20233C4311yesmaximal, characteristic, direct product factor, Sylow
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43D4211yescharacteristic
253C4×C43—21no—
254C4×C43—41no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43C2×#13711yescharacteristic
266C4×C43#57511yescharacteristic
267C4×C43#57711yescharacteristic
268C4×C43#57811yescharacteristic
269#3398C2×C4311yescharacteristic
270#3381C2×C4311yescharacteristic
271#3374C2×C4311yescharacteristic, complemented
272#3356C2×C4311yescharacteristic
273#1716C2×C4311yescharacteristic, complemented
274#1699C2×C4311yescharacteristic
275#1692C2×C4311yescharacteristic, complemented
276#1692C2×C4311yescharacteristic, complemented
277#1670C2×C4311yescharacteristic, complemented
278#1653C2×C4311yescharacteristic, complemented
279#1652C2×C4311yescharacteristic
280#1643C2×C4311yescharacteristic
281#1636C2×C4311yescharacteristic, complemented
282#1592C2×C4311yescharacteristic
283#1584C2×C4311yescharacteristic, complemented
284C2×C43—81no—
285C2×C43#326911yescharacteristic
286C2×C43#327811yescharacteristic
287C2×C43#328911yescharacteristic
288#557C22×C4311yescharacteristic
289#557C22×C4311yescharacteristic
290#556C22×C4311yescharacteristic
291#554C22×C4311yescharacteristic
292#499—21no—
293#498C22×C4311yescharacteristic
294#498C22×C4311yescharacteristic
295#498C22×C4311yescharacteristic
296#497—21no—
297#494C22×C4311yescharacteristic
298#491—21no—
299#487C22×C4311yescharacteristic
300#487C22×C4311yescharacteristic
301#485—21no—
302#483—21no—
303#479—21no—
304#479—21no—
305#478—21no—
306#477C22×C4311yescharacteristic
307#477C22×C4311yescharacteristic
308#475C22×C4311yescharacteristic
309#475C22×C4311yescharacteristic
310#474C22×C4311yescharacteristic
311#470—21no—
312#464—21no—
313#462—21no—
314#462—21no—
315#462C22×C4311yescharacteristic
316#462C22×C4311yescharacteristic
317#461C22×C4311yescharacteristic
318#446C22×C4311yescharacteristic
319#446C22×C4311yescharacteristic
320C8×Q8C22×C4311yescharacteristic
321#441—21no—
322#441—21no—
323C4×Q16C22×C4311yescharacteristic
324C4×SD16—21no—
325C4×SD16C22×C4311yescharacteristic
326#436C22×C4311yescharacteristic
327#428—21no—
328#335C22×C4311yescharacteristic
329#335C22×C4311yescharacteristic
330#333C22×C4311yescharacteristic
331#332C22×C4311yescharacteristic
332#332C22×C4311yescharacteristic
333#332C22×C4311yescharacteristic
334Q8⋊C8C22×C4311yescharacteristic
335Q8⋊C8C22×C4311yescharacteristic
336Q8⋊C8C22×C4311yescharacteristic
337D4⋊C8C22×C4311yescharacteristic
338#322C22×C4311yescharacteristic
339C43#2023311yescharacteristic, direct product factor, Sylow
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16D4×C4311yescharacteristic
345C2×SD16—21no—
346C2×SD16D4×C4311yescharacteristic
347C2×M16—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8C23×C4311yescharacteristic
351C4⋊Q8C23×C4311yescharacteristic
352C4⋊Q8C23×C4311yescharacteristic
353C4⋊Q8C23×C4311yescharacteristic
354#126—41no—
355#125—21no—
356#125—21no—
357#125—21no—
358#125—41no—
359#125—41no—
360#124—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—41no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C4311yescharacteristic
370C4×Q8C23×C4311yescharacteristic
371C4×Q8C23×C4311yescharacteristic
372C4×D4—21no—
373C4×D4C23×C4311yescharacteristic
374#117—21no—
375C2×C4⋊C4—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107D4×C4311yescharacteristic
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—41no—
387#106D4×C4311yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C4311yescharacteristic
392C4⋊C8C23×C4311yescharacteristic
393C4⋊C8C23×C4311yescharacteristic
394C4⋊C8C23×C4311yescharacteristic
395#103—21no—
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—41no—
405#103D4×C4311yescharacteristic
406#103D4×C4311yescharacteristic
407#103D4×C4311yescharacteristic
408#102—21no—
409#102D4×C4311yescharacteristic
410C22⋊C8—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—21no—
421C2×Q8C2×D4×C4311yescharacteristic
422C2×Q8C2×D4×C4311yescharacteristic
423C2×Q8C2×D4×C4311yescharacteristic
424C2×D4C2×D4×C4311yescharacteristic
425C22×C4—21no—
426C22×C4—41no—
427Q16—41no—
428Q16—42no—
429Q16—42no—
430Q16—81no—
431Q16—81no—
432SD16—22no—
433SD16—81no—
434M16—42no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
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—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C4311yescharacteristic
465C4⋊C4C2×D4×C4311yescharacteristic
466C4⋊C4C2×D4×C4311yescharacteristic
467C4⋊C4C2×D4×C4311yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—41no—
477C42—41no—
478C42C24×C4311yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493D4—21no—
494D4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
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—41no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8#137×C4312yes—
521C22—41no—
522C22—41no—
523C22—41no—
524C22D42×C4311yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—81no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×#137×C4311yescharacteristic
538C4C43×#57511yescharacteristic
539C4C43×#57711yescharacteristic
540C4C43×#57811yescharacteristic
541C2—81no—
542C2C43×#326911yescharacteristic
543C2C43×#327811yescharacteristic
544C2C43×#328911yescharacteristic
subgroupG/H
center, socleC22×C43D42
commutator, Frattini, cosocleC42C24×C43
prime radicalC2×D4×C43C2×D4
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×#3374C2semidirect
5. C43×#1716C2semidirect
7. C43×#1692C2semidirect
8. C43×#1692C2semidirect
9. C43×#1670C2semidirect
10. C43×#1653C2semidirect
13. C43×#1636C2semidirect
15. C43×#1584C2semidirect
248. #20233C43direct (N × H)
271. #3374C2×C43semidirect
273. #1716C2×C43semidirect
275. #1692C2×C43semidirect
276. #1692C2×C43semidirect
277. #1670C2×C43semidirect
278. #1653C2×C43semidirect
281. #1636C2×C43semidirect
283. #1584C2×C43semidirect
339. C43#20233direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#33982
C43×#33812
C43×#33742
C43×#33562
C43×#17162
C43×#16992
C43×#16922
C43×#16702
C43×#16532
C43×#16522
C43×#16432
C43×#16362
C43×#15922
C43×#15842
#2023343