Finite Group Databasebeta

← D43×#2060 #25124692

Subgroups — D43×#2060 #25124692

Order 11008.

1218 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#544×D43C211yesmaximal, characteristic
2#428×D43C212yesmaximal
3#384×D43C211yesmaximal, characteristic
4#19135941C211yesmaximal, characteristic, complemented
5#19135940C211yesmaximal, characteristic, complemented
6#19135939C212yesmaximal, complemented
7#19135938C212yesmaximal, complemented
8#19135937C211yesmaximal, characteristic, complemented
9#343×D43C211yesmaximal, characteristic
10#339×D43C212yesmaximal
11C43×#2060C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583530C2211yescharacteristic
14#14583529—22no—
15#14583528—22no—
16#14583527C2212yes—
17#14583526—22no—
18C4⋊Q8×D43—22no—
19#125×D43—22no—
20C22⋊Q8×D43—22no—
21#117×D43C2212yes—
22C2×C4⋊C4×D43—22no—
23C2×C4⋊C4×D43C2211yescharacteristic
24C2×C4⋊C4×D43C2211yescharacteristic
25C2×C42×D43C2211yescharacteristic
26#14582942C2212yes—
27#14582941C2212yes—
28#14582940—22no—
29#14582939C2212yes—
30#14582938—22no—
31#107×D43—22no—
32#106×D43—22no—
33#14582769C2211yescharacteristic
34#14582768—22no—
35#14582768C2211yescharacteristic
36#14582768C2211yescharacteristic
37#14582668C2211yescharacteristic
38#14582667C2212yes—
39#14582660C2212yes—
40#14582659C2212yes—
41#14582658C2212yes—
42C43×#544C2211yescharacteristic
43C43×#428C2212yes—
44C43×#384C2211yescharacteristic
45C43×#343C2211yescharacteristic
46C43×#339C2212yes—
47C2×Q8×D43—22no—
48C22×C4×D43—21no—
49C22×C4×D43—21no—
50C22×C4×D43D412yes—
51C22×C4×D43C2311yescharacteristic
52C2×#10621877C2312yes—
53C2×#10621872—22no—
54M16×D43—24no—
55M16×D43Q818yescomplemented
56C2×C8×D43—22no—
57#13063325—22no—
58#13063324—24no—
59#13063324—22no—
60#13063324—22no—
61#13063323—24no—
62#13063317—22no—
63#13063316—22no—
64#13063316—22no—
65#13063315—24no—
66#13063315—24no—
67#13063305—22no—
68#13063304—22no—
69#13063303—24no—
70#13063302—24no—
71#13063301—22no—
72#13063284C2312yes—
73#13063283D412yes—
74#13063283D412yes—
75#13063282—22no—
76#13063281—22no—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—22no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4D412yes—
84C4⋊C4×D43—22no—
85C4⋊C4×D43—24no—
86C4⋊C4×D43—22no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43—48no—
91C4⋊C4×D43D412yes—
92C4⋊C4×D43D412yes—
93C22⋊C4×D43—22no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C42×D43—22no—
97C42×D43—22no—
98C42×D43Q814yescomplemented
99#13063259—22no—
100#13063258—22no—
101#13063258—22no—
102#13063257—22no—
103#13063256—22no—
104#13063256—22no—
105C2×M16×C43C2312yes—
106C4⋊Q8×C43—22no—
107#125×C43—22no—
108C22⋊Q8×C43—22no—
109#117×C43C2312yes—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114#107×C43—22no—
115#106×C43—22no—
116C23×D43C2×D411yescharacteristic
117C2×Q8×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43C2×D412yes—
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43C2×D412yes—
125C22×Dic43C2×D411yescharacteristic
126Q8×D43—84no—
127C2×C4×D43—24no—
128C2×C4×D43—24no—
129C2×C4×D43—22no—
130C2×C4×D43—22no—
131C2×C4×D43—22no—
132C2×C4×D43—22no—
133C2×C4×D43—24no—
134C2×C4×D43—44no—
135C2×C4×D43—44no—
136C2×C4×D43—41no—
137C2×C4×D43—41no—
138C2×C4×D43C2×D412yes—
139C2×C4×D43C2×D412yes—
140C2×C4×D43C2×Q812yes—
141C2×C4×D43C2×Q814yes—
142C2×C4×D43#4112yes—
143C2×Dic86—24no—
144C2×Dic86—22no—
145M16×C43—22no—
146M16×C43C2×Q814yescomplemented
147C2×C8×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—24no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—44no—
153C4⋊C4×C43C2×D412yes—
154C4⋊C4×C43C2×D412yes—
155C22⋊C4×C43—22no—
156C42×C43—22no—
157C42×C43—21no—
158C42×C43C2×Q812yescomplemented
159C22⋊Dic43—22no—
160(C2×D43)⋊C4—22no—
161(C2×D43)⋊C4—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43—24no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43—44no—
167C4⋊Dic43C2×D412yes—
168C4⋊Dic43C2×D412yes—
169Dic43⋊C4—24no—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175Dic43⋊C4—44no—
176Dic43⋊C4—44no—
177Dic43⋊C4—42no—
178C4×Dic43—22no—
179C4×Dic43—21no—
180C4×Dic43—22no—
181C4×Dic43—22no—
182C4×Dic43—24no—
183C4×Dic43C2×Q812yescomplemented
184#10621877—22no—
185#10621877C2×Q814yescomplemented
186C2×C43⋊C8—22no—
187#10621872—28no—
188C8×D43—28no—
189C23×C43C22×D411yescharacteristic
190C22×D43—22no—
191C22×D43—22no—
192C22×D43#12011yescharacteristic
193C22×D43#12011yescharacteristic
194C22×D43C22⋊Q812yes—
195C22×D43C4⋊Q812yes—
196Q8×C43—82no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—41no—
206C2×C4×C43C22×D412yes—
207C2×C4×C43C22×Q812yes—
208C2×C4×C43C22×Q811yescharacteristic
209C2×C4×C43C2×#4111yescharacteristic
210C2×Dic43—22no—
211C2×Dic43—22no—
212C2×Dic43—22no—
213C2×Dic43—22no—
214C2×Dic43—22no—
215C2×Dic43—22no—
216C2×Dic43—42no—
217C2×Dic43—42no—
218C2×Dic43—41no—
219C2×Dic43#12012yes—
220C2×Dic43C22⋊Q812yes—
221C2×Dic43C4⋊Q812yes—
222C4×D43—216no—
223C4×D43—44no—
224C4×D43—44no—
225C4×D43—44no—
226C4×D43—82no—
227C4×D43—82no—
228C4×D43—82no—
229C4×D43C22⋊Q814yes—
230C4×D43C22⋊Q814yes—
231C4×D43C4⋊Q814yes—
232C4×D43C4⋊Q814yes—
233Dic86—82no—
234Dic86—84no—
235C8×C43—24no—
236C43⋊C8—24no—
237C2×#2060—431nomaximal, Sylow
238C22×C43—21no—
239C22×C43—21no—
240C22×C43C2×#12011yescharacteristic
241C22×C43C2×C22⋊Q811yescharacteristic
242C22×C43C2×C4⋊Q811yescharacteristic
243C2×D43—21no—
244C2×D43—21no—
245C2×D43—24no—
246C2×D43—24no—
247C2×D43#39512yes—
248C2×D43#39512yes—
249C2×D43#45312yes—
250C2×D43#45612yes—
251C4×C43—24no—
252C4×C43—42no—
253C4×C43—42no—
254C4×C43—42no—
255C4×C43—81no—
256C4×C43C2×C22⋊Q812yes—
257C4×C43C2×C4⋊Q812yes—
258Dic43—24no—
259Dic43—42no—
260Dic43—42no—
261Dic43—42no—
262Dic43—81no—
263Dic43#39514yes—
264C2×#544—431no—
265C2×#428—432no—
266C2×#384—431no—
267#2060—432no—
268#2060—431no—
269#2060—431no—
270#2060—432no—
271#2060—431no—
272#2060D4311yescharacteristic, direct product factor
273C2×#343—431no—
274C2×#339—432no—
275C2×C43—21no—
276C2×C43—21no—
277C2×C43C2×#39511yescharacteristic
278C2×C43C2×#45311yescharacteristic
279C2×C43C2×#45611yescharacteristic
280D43—22no—
281D43#206014yesdirect product factor
282C22×M16—432no—
283#544—432no—
284#544—431no—
285#544—862no—
286#544—862no—
287#544—862no—
288#544C2×D4311yescharacteristic
289C2×C4⋊Q8—862no—
290C2×#125—862no—
291C2×C22⋊Q8—862no—
292C2×#117—432no—
293C22×C4⋊C4—431no—
294C22×C4⋊C4—431no—
295C22×C4⋊C4—862no—
296C22×C42—431no—
297#428—432no—
298#428—432no—
299#428—432no—
300#428—862no—
301#428—862no—
302#428C2×D4312yes—
303C2×#107—862no—
304C2×#106—862no—
305#384—431no—
306#384—431no—
307#384—431no—
308#384—862no—
309#384C2×D4311yescharacteristic
310#343—432no—
311#343—431no—
312#343C2×D4311yescharacteristic
313#339—432no—
314#339—432no—
315#339—432no—
316#339C2×D4312yes—
317C43C2×#206011yescharacteristic, complemented, Sylow
318C22×Q8—862no—
319C23×C4—431no—
320C23×C4—432no—
321C23×C4—861no—
322C23×C4—861no—
323C2×M16—432no—
324C2×M16—438no—
325C2×M16—862no—
326C2×M16—864no—
327C2×M16C22×D4312yes—
328C22×C8—862no—
329C4⋊Q8—22no—
330C4⋊Q8—862no—
331C4⋊Q8—862no—
332C4⋊Q8—864no—
333C4⋊Q8—864no—
334C4⋊Q8—862no—
335#125—22no—
336#125—862no—
337#125—862no—
338#125—864no—
339#125—864no—
340#125—862no—
341C22⋊Q8—22no—
342C22⋊Q8—864no—
343C22⋊Q8—864no—
344C22⋊Q8—862no—
345C22⋊Q8—862no—
346C22⋊Q8—862no—
347#117—432no—
348#117—432no—
349#117—432no—
350#117—862no—
351#117—862no—
352#117C22×D4312yes—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—432no—
355C2×C4⋊C4—432no—
356C2×C4⋊C4—432no—
357C2×C4⋊C4—431no—
358C2×C4⋊C4—431no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4—862no—
361C2×C4⋊C4—862no—
362C2×C4⋊C4—864no—
363C2×C4⋊C4—862no—
364C2×C4⋊C4—862no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—862no—
367C2×C4⋊C4—862no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—1728no—
370C2×C4⋊C4C22×D4311yescharacteristic
371C2×C4⋊C4C22×D4311yescharacteristic
372C2×C22⋊C4—862no—
373C2×C42—431no—
374C2×C42—434no—
375C2×C42—862no—
376C2×C42—862no—
377C2×C42—861no—
378C2×C42C22×D4311yescharacteristic
379#107—22no—
380#107—862no—
381#107—862no—
382#107—862no—
383#106—22no—
384#106—862no—
385#106—862no—
386#106—862no—
387C24—431no—
388C2×Q8—22no—
389C2×Q8—864no—
390C2×Q8—862no—
391C2×Q8—3444no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—431no—
395C22×C4—432no—
396C22×C4—432no—
397C22×C4—432no—
398C22×C4—434no—
399C22×C4—432no—
400C22×C4—432no—
401C22×C4—864no—
402C22×C4—864no—
403C22×C4—864no—
404C22×C4—862no—
405C22×C4—862no—
406C22×C4—862no—
407C22×C4—862no—
408C22×C4—861no—
409C22×C4—861no—
410C22×C4—1721no—
411C22×C4—1721no—
412C22×C4—1724no—
413C22×C4—1724no—
414C22×C4D4×D4312yes—
415C22×C4C23×D4311yescharacteristic
416M16—22no—
417M16—434no—
418M16—868no—
419M16—862no—
420M16Q8×D4314yescomplemented
421C2×C8—22no—
422C2×C8—868no—
423C2×C8—862no—
424C4⋊C4—22no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—44no—
429C4⋊C4—432no—
430C4⋊C4—432no—
431C4⋊C4—864no—
432C4⋊C4—862no—
433C4⋊C4—862no—
434C4⋊C4—864no—
435C4⋊C4—862no—
436C4⋊C4—864no—
437C4⋊C4—864no—
438C4⋊C4—864no—
439C4⋊C4—862no—
440C4⋊C4—862no—
441C4⋊C4—1724no—
442C4⋊C4—1722no—
443C4⋊C4—1724no—
444C4⋊C4—1724no—
445C4⋊C4D4×D4312yes—
446C4⋊C4D4×D4312yes—
447C22⋊C4—22no—
448C22⋊C4—862no—
449C22⋊C4—862no—
450C22⋊C4—862no—
451C42—22no—
452C42—21no—
453C42—432no—
454C42—864no—
455C42—862no—
456C42—862no—
457C42—862no—
458C42—861no—
459C42Q8×D4312yescomplemented
460C23—431no—
461C23—431no—
462C23—432no—
463C23—432no—
464C23—862no—
465C23—862no—
466C23C2×D4×D4311yescharacteristic
467Q8—82no—
468Q8—3442no—
469Q8—3444no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—432no—
480C2×C4—432no—
481C2×C4—432no—
482C2×C4—434no—
483C2×C4—434no—
484C2×C4—434no—
485C2×C4—434no—
486C2×C4—8616no—
487C2×C4—862no—
488C2×C4—862no—
489C2×C4—862no—
490C2×C4—862no—
491C2×C4—862no—
492C2×C4—862no—
493C2×C4—3442no—
494C2×C4—3442no—
495C2×C4—3442no—
496C2×C4—1724no—
497C2×C4—1724no—
498C2×C4—1724no—
499C2×C4—1722no—
500C2×C4—1721no—
501C2×C4—1722no—
502C2×C4C2×D4×D4312yes—
503C2×C4C2×Q8×D4312yes—
504C2×C4C2×Q8×D4311yescharacteristic
505C2×C4#41×D4311yescharacteristic
506C8—24no—
507C8—864no—
508C22—21no—
509C22—21no—
510C22—432no—
511C22—432no—
512C22—432no—
513C22—432no—
514C22—864no—
515C22—864no—
516C22—861no—
517C22—861no—
518C22#120×D4311yescharacteristic
519C22C22⋊Q8×D4311yescharacteristic
520C22C4⋊Q8×D4311yescharacteristic
521C4—24no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—81no—
526C4—434no—
527C4—864no—
528C4—3441no—
529C4—1722no—
530C4—1722no—
531C4—1722no—
532C4C22⋊Q8×D4312yes—
533C4C4⋊Q8×D4312yes—
534C2—21no—
535C2—21no—
536C2—434no—
537C2—862no—
538C2#395×D4311yescharacteristic
539C2#453×D4311yescharacteristic
540C2#456×D4311yescharacteristic
subgroupG/H
centerC22#120×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2060C2
socleC22×C43C2×#120
prime radicalC23×D43C2×D4
hypercenter#2060D43
hypocenterC43C2×#2060
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
4. #19135941C2semidirect
5. #19135940C2semidirect
6. #19135939C2semidirect
7. #19135938C2semidirect
8. #19135937C2semidirect
11. C43×#2060C2semidirect
55. M16×D43Q8semidirect
98. C42×D43Q8semidirect
146. M16×C43C2×Q8semidirect
158. C42×C43C2×Q8semidirect
183. C4×Dic43C2×Q8semidirect
185. #10621877C2×Q8semidirect
272. #2060D43direct (N × H)
281. D43#2060direct (N × H)
317. C43C2×#2060semidirect
420. M16Q8×D43semidirect
459. C42Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#544×D432
#428×D432
#384×D432
#191359412
#191359402
#191359392
#191359382
#191359372
#343×D432
#339×D432
C43×#20602
C2×#206043