Finite Group Databasebeta

← D43×#1723 #25084391

Subgroups — D43×#1723 #25084391

Order 11008.

798 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D43C211yesmaximal, characteristic
2#500×D43C211yesmaximal, characteristic
3#498×D43C211yesmaximal, characteristic
4#494×D43C211yesmaximal, characteristic
5#487×D43C211yesmaximal, characteristic
6#487×D43C211yesmaximal, characteristic
7#19134275C211yesmaximal, characteristic, complemented
8#19134274C211yesmaximal, characteristic, complemented
9#19134273C211yesmaximal, characteristic, complemented
10#19134272C211yesmaximal, characteristic, complemented
11#19134271C211yesmaximal, characteristic, complemented
12#19134270C211yesmaximal, characteristic, complemented
13#19134269C211yesmaximal, characteristic, complemented
14#322×D43C211yesmaximal, characteristic
15C43×#1723C211yesmaximal, characteristic, complemented
16C2×Q16×D43—22no—
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20C4⋊Q8×D43C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583304C2211yescharacteristic
23#14583303—22no—
24#14583303—22no—
25#14583302C2211yescharacteristic
26#14583302C2211yescharacteristic
27#14583302C2211yescharacteristic
28#14583302C2211yescharacteristic
29#14583297C2211yescharacteristic
30#14583296—22no—
31#14583295C2211yescharacteristic
32#14583295C2211yescharacteristic
33#14583279C2211yescharacteristic
34#14583278C2211yescharacteristic
35#14583278C2211yescharacteristic
36#14583277—22no—
37#14583251C2211yescharacteristic
38#14583251C2211yescharacteristic
39#14583250C2211yescharacteristic
40#14583250C2211yescharacteristic
41#14583249C2211yescharacteristic
42#14583249C2211yescharacteristic
43#14583248—22no—
44#14583248—22no—
45#107×D43—22no—
46#107×D43—22no—
47#106×D43—22no—
48#103×D43—22no—
49#103×D43—22no—
50C4×C8×D43C2211yescharacteristic
51C4×C8×D43C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic
54#14582621C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#500C2211yescharacteristic
57C43×#500C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#322C2211yescharacteristic
63C2×Q8×D43—21no—
64C2×Q8×D43—21no—
65C2×Q8×D43—21no—
66C2×Q8×D43—21no—
67C2×Dic172—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70Q16×D43—48no—
71C2×C8×D43D412yes—
72C2×C8×D43D412yes—
73C2×C8×D43D412yes—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063324—21no—
79#13063324—21no—
80#13063324—21no—
81#13063324—21no—
82#13063324—21no—
83#13063324—21no—
84#13063324—21no—
85#13063324—21no—
86#13063323—21no—
87#13063323—21no—
88#13063323—21no—
89#13063323—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C42×D43C2311yescharacteristic
99#13063259—22no—
100#13063259—22no—
101#13063258—22no—
102#13063258—22no—
103#13063258—22no—
104#13063258—22no—
105#13063257—22no—
106#13063256—22no—
107#13063256—22no—
108#13063250—22no—
109#13063250—22no—
110#13063249—22no—
111#13063249—22no—
112#13063248—22no—
113#13063248—22no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C8×Dic43D412yes—
118C8×Dic43D412yes—
119C8×Dic43D412yes—
120C2×Q16×C43—22no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124C4⋊Q8×C43C2311yescharacteristic
125#107×C43—22no—
126#107×C43—22no—
127#106×C43—22no—
128#103×C43—22no—
129#103×C43—22no—
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C4×C8×C43C2311yescharacteristic
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137Q8×D43—44no—
138Q8×D43—44no—
139Q8×D43—44no—
140Q8×D43—44no—
141C2×C4×D43—41no—
142C2×C4×D43—41no—
143C2×C4×D43—41no—
144C2×C4×D43—41no—
145C2×C4×D43C2×D411yescharacteristic
146C2×C4×D43C2×D411yescharacteristic
147C2×C4×D43C2×D411yescharacteristic
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—41no—
153C2×Dic86—41no—
154C2×Dic86—41no—
155C2×Dic86—41no—
156Q16×C43—44no—
157C2×C8×C43C2×D412yes—
158C2×C8×C43C2×D412yes—
159C2×C8×C43C2×D412yes—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C42×C43C2411yescharacteristic
169#10621885—44no—
170#10621885—44no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179Dic43⋊C4—41no—
180Dic43⋊C4—41no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183Dic43⋊C4—41no—
184Dic43⋊C4—41no—
185Dic43⋊C4—41no—
186Dic43⋊C4—41no—
187C4×Dic43C2×D411yescharacteristic
188C4×Dic43C2×D411yescharacteristic
189C4×Dic43C2×D411yescharacteristic
190C2×C43⋊C8C2×D412yes—
191C2×C43⋊C8C2×D412yes—
192C2×C43⋊C8C2×D412yes—
193Dic172—44no—
194C8×D43—24no—
195C8×D43—24no—
196C8×D43Q1618yescomplemented
197C22×D43#12711yescharacteristic
198Q8×C43—42no—
199Q8×C43—42no—
200Q8×C43—42no—
201Q8×C43—42no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43C22×D411yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43#12711yescharacteristic
214C2×Dic43#12711yescharacteristic
215C2×Dic43#12711yescharacteristic
216C4×D43—82no—
217C4×D43—82no—
218C4×D43—82no—
219C4×D43—82no—
220C4×D43C2×Q1614yes—
221C4×D43AGL(1,ℤ/8)14yes—
222C4×D43#13714yes—
223Dic86—42no—
224Dic86—42no—
225Dic86—42no—
226Dic86—42no—
227Dic86—82no—
228Dic86—82no—
229Dic86—82no—
230Dic86—82no—
231C8×C43—22no—
232C8×C43—22no—
233C8×C43C2×Q1614yescomplemented
234C43⋊C8—22no—
235C43⋊C8—22no—
236C43⋊C8C2×Q1614yescomplemented
237C2×#1723—431nomaximal, Sylow
238C22×C43C2×#12711yescharacteristic
239C2×D43#49412yes—
240C2×D43#49612yes—
241C2×D43#49712yes—
242C4×C43—81no—
243C4×C43—81no—
244C4×C43—81no—
245C4×C43—81no—
246C4×C43C22×Q1612yes—
247C4×C43C2×AGL(1,ℤ/8)12yes—
248C4×C43C2×#13712yes—
249Dic43—81no—
250Dic43—81no—
251Dic43—81no—
252Dic43—81no—
253Dic43#49412yes—
254Dic43#49612yes—
255Dic43#49712yes—
256C2×#500—431no—
257C2×#500—431no—
258C2×#498—431no—
259C2×#494—431no—
260C2×#487—431no—
261C2×#487—431no—
262#1723—431no—
263#1723—431no—
264#1723—431no—
265#1723—431no—
266#1723—431no—
267#1723—431no—
268#1723—431no—
269#1723D4311yescharacteristic, direct product factor
270C2×#322—431no—
271C2×C43C2×#49411yescharacteristic
272C2×C43C2×#49611yescharacteristic
273C2×C43C2×#49711yescharacteristic
274D43#172314yesdirect product factor
275C22×Q16—862no—
276C2×C4⋊Q8—431no—
277C2×C4⋊Q8—431no—
278C2×C4⋊Q8—431no—
279C2×C4⋊Q8—431no—
280#500—431no—
281#500—431no—
282#500—431no—
283#500—431no—
284#500—431no—
285#500—431no—
286#500—862no—
287#500—862no—
288#500C2×D4311yescharacteristic
289#500C2×D4311yescharacteristic
290#498—431no—
291#498—431no—
292#498—431no—
293#498—862no—
294#498C2×D4311yescharacteristic
295#494—431no—
296#494—431no—
297#494—431no—
298#494—862no—
299#494C2×D4311yescharacteristic
300#487—431no—
301#487—431no—
302#487—431no—
303#487—431no—
304#487—431no—
305#487—431no—
306#487—862no—
307#487—862no—
308#487C2×D4311yescharacteristic
309#487C2×D4311yescharacteristic
310C2×#107—862no—
311C2×#107—862no—
312C2×#106—862no—
313C2×#103—862no—
314C2×#103—862no—
315C2×C4×C8—431no—
316C2×C4×C8—431no—
317C2×C4×C8—431no—
318#322—431no—
319#322—431no—
320#322—431no—
321#322C2×D4311yescharacteristic
322C43C2×#172311yescharacteristic, complemented, Sylow
323C22×Q8—861no—
324C22×Q8—861no—
325C22×Q8—861no—
326C22×Q8—861no—
327C2×Q16—22no—
328C2×Q16—862no—
329C2×Q16—862no—
330C2×Q16—862no—
331C2×Q16—1728no—
332C22×C8—432no—
333C22×C8—432no—
334C22×C8—432no—
335C4⋊Q8—431no—
336C4⋊Q8—431no—
337C4⋊Q8—431no—
338C4⋊Q8—431no—
339C4⋊Q8—861no—
340C4⋊Q8—861no—
341C4⋊Q8—861no—
342C4⋊Q8—861no—
343C4⋊Q8—861no—
344C4⋊Q8—861no—
345C4⋊Q8—861no—
346C4⋊Q8—861no—
347C4⋊Q8—861no—
348C4⋊Q8—861no—
349C4⋊Q8—861no—
350C4⋊Q8—861no—
351C4⋊Q8C22×D4311yescharacteristic
352C4⋊Q8C22×D4311yescharacteristic
353C4⋊Q8C22×D4311yescharacteristic
354C4⋊Q8C22×D4311yescharacteristic
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—861no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4—861no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4—861no—
363C2×C42—431no—
364#107—22no—
365#107—22no—
366#107—862no—
367#107—862no—
368#107—862no—
369#107—862no—
370#107—862no—
371#107—862no—
372#106—22no—
373#106—862no—
374#106—862no—
375#106—862no—
376#103—22no—
377#103—22no—
378#103—862no—
379#103—862no—
380#103—862no—
381#103—862no—
382#103—862no—
383#103—862no—
384C4×C8—432no—
385C4×C8—432no—
386C4×C8—432no—
387C4×C8—431no—
388C4×C8—431no—
389C4×C8—431no—
390C4×C8C22×D4311yescharacteristic
391C4×C8C22×D4311yescharacteristic
392C4×C8C22×D4311yescharacteristic
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—861no—
398C2×Q8—861no—
399C2×Q8—861no—
400C2×Q8—861no—
401C2×Q8—1721no—
402C2×Q8—1721no—
403C2×Q8—1721no—
404C2×Q8—1721no—
405C2×Q8—1724no—
406C2×Q8—1724no—
407C2×Q8—1724no—
408C2×Q8—1724no—
409C22×C4—431no—
410C22×C4—431no—
411C22×C4—431no—
412C22×C4—1721no—
413C22×C4—1721no—
414C22×C4—1721no—
415C22×C4—1721no—
416Q16—44no—
417Q16—1724no—
418Q16—1724no—
419Q16—1724no—
420C2×C8—432no—
421C2×C8—438no—
422C2×C8—432no—
423C2×C8—432no—
424C2×C8—864no—
425C2×C8—864no—
426C2×C8D4×D4312yes—
427C2×C8D4×D4312yes—
428C2×C8D4×D4312yes—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—861no—
438C4⋊C4—861no—
439C4⋊C4—861no—
440C4⋊C4—861no—
441C4⋊C4—861no—
442C4⋊C4—861no—
443C4⋊C4—861no—
444C4⋊C4—861no—
445C4⋊C4—1721no—
446C4⋊C4—1721no—
447C4⋊C4—1721no—
448C4⋊C4—1721no—
449C4⋊C4—1721no—
450C4⋊C4—1721no—
451C4⋊C4—1721no—
452C4⋊C4—1721no—
453C42—431no—
454C42—431no—
455C42—431no—
456C42C23×D4311yescharacteristic
457C23—431no—
458Q8—42no—
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—3442no—
463Q8—3442no—
464Q8—3442no—
465Q8—3442no—
466Q8—1722no—
467Q8—1722no—
468Q8—1722no—
469Q8—1722no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—431no—
475C2×C4—431no—
476C2×C4—431no—
477C2×C4—434no—
478C2×C4—434no—
479C2×C4—434no—
480C2×C4—3442no—
481C2×C4—3442no—
482C2×C4—3442no—
483C2×C4—3442no—
484C2×C4—1721no—
485C2×C4—1721no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4C2×D4×D4311yescharacteristic
489C2×C4C2×D4×D4311yescharacteristic
490C2×C4C2×D4×D4311yescharacteristic
491C8—22no—
492C8—22no—
493C8—434no—
494C8—862no—
495C8—862no—
496C8Q16×D4314yescomplemented
497C22—432no—
498C22—432no—
499C22—432no—
500C22#127×D4311yescharacteristic
501C4—81no—
502C4—81no—
503C4—81no—
504C4—81no—
505C4—432no—
506C4—432no—
507C4—432no—
508C4—3441no—
509C4—3441no—
510C4—3441no—
511C4—3441no—
512C4C2×Q16×D4312yes—
513C4AGL(1,ℤ/8)×D4312yes—
514C4#137×D4312yes—
515C2—434no—
516C2#494×D4311yescharacteristic
517C2#496×D4311yescharacteristic
518C2#497×D4311yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1723C2
socleC22×C43C2×#127
prime radicalC22×D43#127
hypercenter#1723D43
hypocenterC43C2×#1723
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1723

Complements

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

NH ≅ G/Ntype
7. #19134275C2semidirect
8. #19134274C2semidirect
9. #19134273C2semidirect
10. #19134272C2semidirect
11. #19134271C2semidirect
12. #19134270C2semidirect
13. #19134269C2semidirect
15. C43×#1723C2semidirect
196. C8×D43Q16semidirect
233. C8×C43C2×Q16semidirect
236. C43⋊C8C2×Q16semidirect
269. #1723D43direct (N × H)
274. D43#1723direct (N × H)
322. C43C2×#1723semidirect
496. C8Q16×D43semidirect

Maximal subgroups

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

subgroupindex
#500×D432
#498×D432
#494×D432
#487×D432
#191342752
#191342742
#191342732
#191342722
#191342712
#191342702
#191342692
#322×D432
C43×#17232
C2×#172343