Finite Group Databasebeta

← D43×#1718 #25084341

Subgroups — D43×#1718 #25084341

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D43C211yesmaximal, characteristic
2#498×D43C211yesmaximal, characteristic
3#487×D43C211yesmaximal, characteristic
4#487×D43C211yesmaximal, characteristic
5#487×D43C211yesmaximal, characteristic
6#487×D43C211yesmaximal, characteristic
7#19134244C211yesmaximal, characteristic, complemented
8#19134243C211yesmaximal, characteristic, complemented
9#19134242C211yesmaximal, characteristic, complemented
10#19134241C211yesmaximal, characteristic, complemented
11#19134240C211yesmaximal, characteristic, complemented
12#19134239C211yesmaximal, characteristic, complemented
13#19134238C211yesmaximal, characteristic, complemented
14#322×D43C211yesmaximal, characteristic
15C43×#1718C211yesmaximal, characteristic, complemented
16C4⋊Q8×D43C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583303—22no—
22#14583302C2211yescharacteristic
23#14583302C2211yescharacteristic
24#14583297C2211yescharacteristic
25#14583296—22no—
26#14583295C2211yescharacteristic
27#14583295C2211yescharacteristic
28#14583251C2211yescharacteristic
29#14583251C2211yescharacteristic
30#14583251C2211yescharacteristic
31#14583251C2211yescharacteristic
32#14583250C2211yescharacteristic
33#14583250C2211yescharacteristic
34#14583250C2211yescharacteristic
35#14583250C2211yescharacteristic
36#14583249C2211yescharacteristic
37#14583249C2211yescharacteristic
38#14583249C2211yescharacteristic
39#14583249C2211yescharacteristic
40#14583248—22no—
41#14583248—22no—
42#14583248—22no—
43#14583248—22no—
44#107×D43—22no—
45#106×D43—22no—
46#103×D43—22no—
47#103×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×#498C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#487C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#322C2211yescharacteristic
63C2×Q8×D43—21no—
64C2×Q8×D43—21no—
65C2×Q8×D43—21no—
66C2×Q8×D43—21no—
67C2×C8×D43D412yes—
68C2×C8×D43D412yes—
69C2×C8×D43D412yes—
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063324—21no—
75#13063324—21no—
76#13063324—21no—
77#13063324—21no—
78#13063324—21no—
79#13063324—21no—
80#13063324—21no—
81#13063324—21no—
82#13063323—21no—
83#13063323—21no—
84#13063323—21no—
85#13063323—21no—
86C4⋊C4×D43—21no—
87C4⋊C4×D43—21no—
88C4⋊C4×D43—21no—
89C4⋊C4×D43—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C42×D43C2311yescharacteristic
95#13063259—22no—
96#13063258—22no—
97#13063258—22no—
98#13063257—22no—
99#13063256—22no—
100#13063256—22no—
101#13063250—22no—
102#13063250—22no—
103#13063250—22no—
104#13063250—22no—
105#13063249—22no—
106#13063249—22no—
107#13063249—22no—
108#13063249—22no—
109#13063248—22no—
110#13063248—22no—
111#13063248—22no—
112#13063248—22no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C8×Dic43D412yes—
117C8×Dic43D412yes—
118C8×Dic43D412yes—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#107×C43—22no—
124#106×C43—22no—
125#103×C43—22no—
126#103×C43—22no—
127#103×C43—22no—
128#103×C43—22no—
129C4×C8×C43C2311yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136Q8×D43—44no—
137Q8×D43—44no—
138Q8×D43—44no—
139Q8×D43—44no—
140C2×C4×D43—41no—
141C2×C4×D43—41no—
142C2×C4×D43—41no—
143C2×C4×D43—41no—
144C2×C4×D43C2×D411yescharacteristic
145C2×C4×D43C2×D411yescharacteristic
146C2×C4×D43C2×D411yescharacteristic
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—41no—
152C2×Dic86—41no—
153C2×Dic86—41no—
154C2×Dic86—41no—
155C2×C8×C43C2×D412yes—
156C2×C8×C43C2×D412yes—
157C2×C8×C43C2×D412yes—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C42×C43C2411yescharacteristic
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175Dic43⋊C4—41no—
176Dic43⋊C4—41no—
177Dic43⋊C4—41no—
178Dic43⋊C4—41no—
179Dic43⋊C4—41no—
180Dic43⋊C4—41no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183C4×Dic43C2×D411yescharacteristic
184C4×Dic43C2×D411yescharacteristic
185C4×Dic43C2×D411yescharacteristic
186C2×C43⋊C8C2×D412yes—
187C2×C43⋊C8C2×D412yes—
188C2×C43⋊C8C2×D412yes—
189C8×D43—24no—
190C8×D43—24no—
191C8×D43—24no—
192C22×D43#12711yescharacteristic
193Q8×C43—42no—
194Q8×C43—42no—
195Q8×C43—42no—
196Q8×C43—42no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43#12711yescharacteristic
209C2×Dic43#12711yescharacteristic
210C2×Dic43#12711yescharacteristic
211C4×D43—82no—
212C4×D43—82no—
213C4×D43—82no—
214C4×D43—82no—
215C4×D43#13514yes—
216C4×D43#13714yes—
217C4×D43#13714yes—
218Dic86—42no—
219Dic86—42no—
220Dic86—42no—
221Dic86—42no—
222Dic86—82no—
223Dic86—82no—
224Dic86—82no—
225Dic86—82no—
226C8×C43—22no—
227C8×C43—22no—
228C8×C43—22no—
229C43⋊C8—22no—
230C43⋊C8—22no—
231C43⋊C8—22no—
232C2×#1718—431nomaximal, Sylow
233C22×C43C2×#12711yescharacteristic
234C2×D43#49512yes—
235C2×D43#49712yes—
236C2×D43#49712yes—
237C4×C43—81no—
238C4×C43—81no—
239C4×C43—81no—
240C4×C43—81no—
241C4×C43C2×#13512yes—
242C4×C43C2×#13712yes—
243C4×C43C2×#13712yes—
244Dic43—81no—
245Dic43—81no—
246Dic43—81no—
247Dic43—81no—
248Dic43#49512yes—
249Dic43#49712yes—
250Dic43#49712yes—
251C2×#500—431no—
252C2×#498—431no—
253C2×#487—431no—
254C2×#487—431no—
255C2×#487—431no—
256C2×#487—431no—
257#1718—431no—
258#1718—431no—
259#1718—431no—
260#1718—431no—
261#1718—431no—
262#1718—431no—
263#1718—431no—
264#1718D4311yescharacteristic, direct product factor
265C2×#322—431no—
266C2×C43C2×#49511yescharacteristic
267C2×C43C2×#49711yescharacteristic
268C2×C43C2×#49711yescharacteristic
269D43#171814yesdirect product factor
270C2×C4⋊Q8—431no—
271C2×C4⋊Q8—431no—
272C2×C4⋊Q8—431no—
273C2×C4⋊Q8—431no—
274#500—431no—
275#500—431no—
276#500—431no—
277#500—862no—
278#500C2×D4311yescharacteristic
279#498—431no—
280#498—431no—
281#498—431no—
282#498—862no—
283#498C2×D4311yescharacteristic
284#487—431no—
285#487—431no—
286#487—431no—
287#487—431no—
288#487—431no—
289#487—431no—
290#487—431no—
291#487—431no—
292#487—431no—
293#487—431no—
294#487—431no—
295#487—431no—
296#487—862no—
297#487—862no—
298#487—862no—
299#487—862no—
300#487C2×D4311yescharacteristic
301#487C2×D4311yescharacteristic
302#487C2×D4311yescharacteristic
303#487C2×D4311yescharacteristic
304C2×#107—862no—
305C2×#106—862no—
306C2×#103—862no—
307C2×#103—862no—
308C2×#103—862no—
309C2×#103—862no—
310C2×C4×C8—431no—
311C2×C4×C8—431no—
312C2×C4×C8—431no—
313#322—431no—
314#322—431no—
315#322—431no—
316#322C2×D4311yescharacteristic
317C43C2×#171811yescharacteristic, complemented, Sylow
318C22×Q8—861no—
319C22×Q8—861no—
320C22×Q8—861no—
321C22×Q8—861no—
322C22×C8—432no—
323C22×C8—432no—
324C22×C8—432no—
325C4⋊Q8—431no—
326C4⋊Q8—431no—
327C4⋊Q8—431no—
328C4⋊Q8—431no—
329C4⋊Q8—861no—
330C4⋊Q8—861no—
331C4⋊Q8—861no—
332C4⋊Q8—861no—
333C4⋊Q8—861no—
334C4⋊Q8—861no—
335C4⋊Q8—861no—
336C4⋊Q8—861no—
337C4⋊Q8—861no—
338C4⋊Q8—861no—
339C4⋊Q8—861no—
340C4⋊Q8—861no—
341C4⋊Q8C22×D4311yescharacteristic
342C4⋊Q8C22×D4311yescharacteristic
343C4⋊Q8C22×D4311yescharacteristic
344C4⋊Q8C22×D4311yescharacteristic
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4—861no—
348C2×C4⋊C4—861no—
349C2×C4⋊C4—861no—
350C2×C4⋊C4—861no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4—861no—
353C2×C42—431no—
354#107—22no—
355#107—862no—
356#107—862no—
357#107—862no—
358#106—22no—
359#106—862no—
360#106—862no—
361#106—862no—
362#103—22no—
363#103—22no—
364#103—22no—
365#103—22no—
366#103—862no—
367#103—862no—
368#103—862no—
369#103—862no—
370#103—862no—
371#103—862no—
372#103—862no—
373#103—862no—
374#103—862no—
375#103—862no—
376#103—862no—
377#103—862no—
378C4×C8—432no—
379C4×C8—432no—
380C4×C8—432no—
381C4×C8—431no—
382C4×C8—431no—
383C4×C8—431no—
384C4×C8C22×D4311yescharacteristic
385C4×C8C22×D4311yescharacteristic
386C4×C8C22×D4311yescharacteristic
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—861no—
392C2×Q8—861no—
393C2×Q8—861no—
394C2×Q8—861no—
395C2×Q8—1721no—
396C2×Q8—1721no—
397C2×Q8—1721no—
398C2×Q8—1721no—
399C2×Q8—1724no—
400C2×Q8—1724no—
401C2×Q8—1724no—
402C2×Q8—1724no—
403C22×C4—431no—
404C22×C4—431no—
405C22×C4—431no—
406C22×C4—1721no—
407C22×C4—1721no—
408C22×C4—1721no—
409C22×C4—1721no—
410C2×C8—432no—
411C2×C8—432no—
412C2×C8—432no—
413C2×C8—864no—
414C2×C8—864no—
415C2×C8—864no—
416C2×C8D4×D4312yes—
417C2×C8D4×D4312yes—
418C2×C8D4×D4312yes—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C4⋊C4—861no—
433C4⋊C4—861no—
434C4⋊C4—861no—
435C4⋊C4—1721no—
436C4⋊C4—1721no—
437C4⋊C4—1721no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4—1721no—
441C4⋊C4—1721no—
442C4⋊C4—1721no—
443C42—431no—
444C42—431no—
445C42—431no—
446C42C23×D4311yescharacteristic
447C23—431no—
448Q8—42no—
449Q8—42no—
450Q8—42no—
451Q8—42no—
452Q8—3442no—
453Q8—3442no—
454Q8—3442no—
455Q8—3442no—
456Q8—1722no—
457Q8—1722no—
458Q8—1722no—
459Q8—1722no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—431no—
465C2×C4—431no—
466C2×C4—431no—
467C2×C4—434no—
468C2×C4—434no—
469C2×C4—434no—
470C2×C4—3442no—
471C2×C4—3442no—
472C2×C4—3442no—
473C2×C4—3442no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—1721no—
478C2×C4C2×D4×D4311yescharacteristic
479C2×C4C2×D4×D4311yescharacteristic
480C2×C4C2×D4×D4311yescharacteristic
481C8—22no—
482C8—22no—
483C8—22no—
484C8—862no—
485C8—862no—
486C8—862no—
487C22—432no—
488C22—432no—
489C22—432no—
490C22#127×D4311yescharacteristic
491C4—81no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4—432no—
496C4—432no—
497C4—432no—
498C4—3441no—
499C4—3441no—
500C4—3441no—
501C4—3441no—
502C4#135×D4312yes—
503C4#137×D4312yes—
504C4#137×D4312yes—
505C2—434no—
506C2#495×D4311yescharacteristic
507C2#497×D4311yescharacteristic
508C2#497×D4311yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1718C2
socleC22×C43C2×#127
prime radicalC22×D43#127
hypercenter#1718D43
hypocenterC43C2×#1718
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1718

Complements

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

NH ≅ G/Ntype
7. #19134244C2semidirect
8. #19134243C2semidirect
9. #19134242C2semidirect
10. #19134241C2semidirect
11. #19134240C2semidirect
12. #19134239C2semidirect
13. #19134238C2semidirect
15. C43×#1718C2semidirect
264. #1718D43direct (N × H)
269. D43#1718direct (N × H)
317. C43C2×#1718semidirect

Maximal subgroups

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

subgroupindex
#500×D432
#498×D432
#487×D432
#191342442
#191342432
#191342422
#191342412
#191342402
#191342392
#191342382
#322×D432
C43×#17182
C2×#171843