Finite Group Databasebeta

← D43×#2383 #25259254

Subgroups — D43×#2383 #25259254

Order 11008.

2502 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D43C211yesmaximal, characteristic
2#19137788C211yesmaximal, characteristic, complemented
3#19137787C211yesmaximal, characteristic, complemented
4#19137786C213yesmaximal, complemented
5#19137785C213yesmaximal, complemented
6#19137784C211yesmaximal, characteristic, complemented
7#19137783C213yesmaximal, complemented
8#19137782C213yesmaximal, complemented
9#389×D43C213yesmaximal, complemented
10#388×D43C213yesmaximal
11#387×D43C213yesmaximal, complemented
12#385×D43C213yesmaximal
13#384×D43C211yesmaximal, characteristic, complemented
14#383×D43C211yesmaximal, characteristic, complemented
15C43×#2383C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C2×#13063320C2213yes—
18C2×#13063319C2211yescharacteristic
19C2×#13063318C2213yes—
20#126×D43C4116yescomplemented
21C2×C4⋊C4×D43C2213yes—
22C2×C4⋊C4×D43C2213yes—
23C2×C4⋊C4×D43C2213yes—
24C2×C4⋊C4×D43C2213yes—
25C2×C22⋊C4×D43C2213yes—
26C2×C22⋊C4×D43C2213yes—
27C2×C42×D43C2213yes—
28C2×C42×D43C2211yescharacteristic
29#14582798C2213yescomplemented
30#14582797C2213yescomplemented
31#14582796C2213yescomplemented
32#14582796C2213yescomplemented
33#14582795C2213yescomplemented
34#14582794C2213yescomplemented
35#14582794C2213yescomplemented
36#14582793C2213yes—
37#14582792C2213yes—
38#14582791C2213yes—
39#14582790C2213yes—
40#14582789C2213yes—
41#14582788C2213yes—
42#14582787C2213yes—
43#14582786C2213yescomplemented
44#14582785C2213yescomplemented
45#14582784C2213yescomplemented
46#14582783C2213yescomplemented
47#14582782C2213yescomplemented
48#14582781C2213yescomplemented
49#14582780C2213yescomplemented
50#14582774C2213yes—
51#14582773C2213yes—
52#14582773C2213yes—
53#14582772C2213yes—
54#14582771C2213yes—
55#14582770C2213yes—
56#14582770C2213yes—
57#14582769C2211yescharacteristic, complemented
58#14582768C2213yescomplemented
59#14582768C2213yescomplemented
60#14582767C2211yescharacteristic, complemented
61#14582766C2213yescomplemented
62#14582766C2213yescomplemented
63#95×D43C2213yes—
64#95×D43C2213yes—
65#95×D43C2213yes—
66#95×D43C2213yes—
67C2×#126×C43C2211yescharacteristic
68C43×#389C2213yescomplemented
69C43×#388C2213yes—
70C43×#387C2213yescomplemented
71C43×#385C2213yes—
72C43×#384C2211yescharacteristic, complemented
73C43×#383C2211yescharacteristic, complemented
74C24×D43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C22×C4×D43—46no—
77C22×C4×D43C2313yes—
78C22×C4×D43C2313yes—
79C22×C4×D43C2311yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C22×C4×D43C2313yes—
82C22×C4×D43C2313yes—
83C22×C4×D43C2311yescharacteristic
84C22×C4×D43C2311yescharacteristic
85#13063320C2×C4124yescomplemented
86#13063319C2×C418yescomplemented
87#13063318C2×C4124yescomplemented
88C2×C4⋊Dic43C2313yes—
89C2×C4⋊Dic43C2313yes—
90C2×C4⋊Dic43C2313yes—
91C2×C4⋊Dic43C2313yes—
92C2×Dic43⋊C4C2313yes—
93C2×Dic43⋊C4C2313yes—
94C2×Dic43⋊C4C2313yes—
95C2×Dic43⋊C4C2313yes—
96C2×Dic43⋊C4C2313yes—
97C2×Dic43⋊C4C2313yes—
98C2×Dic43⋊C4C2313yes—
99C2×Dic43⋊C4C2313yes—
100C4⋊C4×D43—46no—
101C4⋊C4×D43—46no—
102C4⋊C4×D43—46no—
103C4⋊C4×D43C2×C4124yescomplemented
104C2×C22⋊Dic43C2313yes—
105C2×C22⋊Dic43C2313yes—
106C2×(C2×D43)⋊C4C2313yes—
107C2×(C2×D43)⋊C4C2313yes—
108C2×(C2×D43)⋊C4C2313yes—
109C2×(C2×D43)⋊C4C2313yes—
110C22⋊C4×D43—46no—
111C22⋊C4×D43C2×C4124yes—
112C2×C4×Dic43C2313yes—
113C2×C4×Dic43C2313yes—
114C2×C4×Dic43C2313yes—
115C2×C4×Dic43C2313yes—
116C42×D43—46no—
117C42×D43C2×C418yescomplemented
118C43⋊#95C2313yes—
119C43⋊#95C2313yes—
120C43⋊#95C2313yes—
121C43⋊#95C2313yes—
122C43⋊#95C2313yes—
123C43⋊#95C2313yes—
124C43⋊#95C2313yes—
125C43⋊#95C2313yes—
126C43⋊#95C2313yes—
127C43⋊#95C2313yes—
128C43⋊#95C2313yes—
129C43⋊#95C2313yes—
130C23×C4×C43C2311yescharacteristic
131#126×C43C2×C418yescomplemented
132C2×C4⋊C4×C43C2313yes—
133C2×C4⋊C4×C43C2313yes—
134C2×C4⋊C4×C43C2313yes—
135C2×C4⋊C4×C43C2313yes—
136C2×C22⋊C4×C43C2313yes—
137C2×C22⋊C4×C43C2313yes—
138C2×C42×C43C2313yes—
139C2×C42×C43C2311yescharacteristic
140#95×C43C2313yes—
141#95×C43C2313yes—
142#95×C43C2313yes—
143#95×C43C2313yes—
144C24×C43C2411yescharacteristic
145C23×D43—26no—
146C23×D43—26no—
147C23×D43C22×C414yes—
148C23×D43C2411yescharacteristic
149C23×D43C2411yescharacteristic
150C22×C4×C43—43no—
151C22×C4×C43C2413yes—
152C22×C4×C43C2411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×C4×C43C2413yes—
155C22×C4×C43C2413yes—
156C22×C4×C43C2413yes—
157C22×Dic43—43no—
158C22×Dic43C2413yes—
159C22×Dic43C2411yescharacteristic
160C22×Dic43C2411yescharacteristic
161C22×Dic43C2413yes—
162C22×Dic43C2413yes—
163C22×Dic43C2413yes—
164C2×C4×D43—26no—
165C2×C4×D43—26no—
166C2×C4×D43—26no—
167C2×C4×D43—26no—
168C2×C4×D43—26no—
169C2×C4×D43—26no—
170C2×C4×D43—26no—
171C2×C4×D43—26no—
172C2×C4×D43—26no—
173C2×C4×D43—26no—
174C2×C4×D43—212no—
175C2×C4×D43—43no—
176C2×C4×D43—43no—
177C2×C4×D43—416no—
178C2×C4×D43C22×C4112yes—
179C2×C4×D43C22×C4112yes—
180C4⋊C4×C43—43no—
181C4⋊C4×C43—43no—
182C4⋊C4×C43—43no—
183C4⋊C4×C43C22×C4112yescomplemented
184C22⋊C4×C43—43no—
185C22⋊C4×C43C22×C4112yes—
186C42×C43—43no—
187C42×C43C22×C414yescomplemented
188C22⋊Dic43—43no—
189C22⋊Dic43C22×C4112yes—
190(C2×D43)⋊C4—43no—
191(C2×D43)⋊C4—43no—
192(C2×D43)⋊C4C22×C4112yes—
193(C2×D43)⋊C4C22×C4112yes—
194C4⋊Dic43—43no—
195C4⋊Dic43—43no—
196C4⋊Dic43—43no—
197C4⋊Dic43C22×C4112yescomplemented
198Dic43⋊C4—43no—
199Dic43⋊C4—43no—
200Dic43⋊C4—43no—
201Dic43⋊C4—43no—
202Dic43⋊C4—43no—
203Dic43⋊C4—43no—
204Dic43⋊C4C22×C4112yescomplemented
205Dic43⋊C4C22×C4112yescomplemented
206C4×Dic43—43no—
207C4×Dic43—43no—
208C4×Dic43—43no—
209C4×Dic43C22×C4112yescomplemented
210C23×C43—23no—
211C23×C43—23no—
212C23×C43C23×C412yes—
213C23×C43C2511yescharacteristic
214C22×D43—23no—
215C22×D43—23no—
216C22×D43—224no—
217C22×D43—44no—
218C22×D43—412no—
219C22×D43C23×C412yes—
220C22×D43C23×C412yes—
221C22×D43H(5,𝔽2)16yes—
222C22×D432−1+416yes—
223C2×C4×C43—23no—
224C2×C4×C43—23no—
225C2×C4×C43—23no—
226C2×C4×C43—23no—
227C2×C4×C43—23no—
228C2×C4×C43—23no—
229C2×C4×C43—23no—
230C2×C4×C43—23no—
231C2×C4×C43—23no—
232C2×C4×C43—23no—
233C2×C4×C43—26no—
234C2×C4×C43—44no—
235C2×C4×C43C23×C416yes—
236C2×C4×C43C23×C416yes—
237C2×Dic43—23no—
238C2×Dic43—23no—
239C2×Dic43—23no—
240C2×Dic43—23no—
241C2×Dic43—23no—
242C2×Dic43—23no—
243C2×Dic43—23no—
244C2×Dic43—23no—
245C2×Dic43—23no—
246C2×Dic43—23no—
247C2×Dic43—26no—
248C2×Dic43—44no—
249C2×Dic43C23×C416yes—
250C2×Dic43C23×C416yes—
251C4×D43—224no—
252C4×D43—224no—
253C4×D43—44no—
254C4×D43—44no—
255C4×D43—412no—
256C4×D43—44no—
257C4×D43—44no—
258C4×D43—412no—
259C2×#2383—431nomaximal, Sylow
260C22×C43—26no—
261C22×C43—41no—
262C22×C43—43no—
263C22×C43C24×C411yescharacteristic
264C22×C43C2×H(5,𝔽2)13yes—
265C22×C43C2×2−1+413yes—
266C2×D43—26no—
267C2×D43—41no—
268C2×D43—43no—
269C2×D43—416no—
270C2×D43#520112yes—
271C2×D43#56014yes—
272C2×D43#563112yes—
273C4×C43—26no—
274C4×C43—26no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—43no—
278C4×C43—43no—
279Dic43—26no—
280Dic43—26no—
281Dic43—41no—
282Dic43—41no—
283Dic43—43no—
284Dic43—43no—
285C22×#126—431no—
286#2383—433no—
287#2383—433no—
288#2383—433no—
289#2383—433no—
290#2383—431no—
291#2383—431no—
292#2383—431no—
293#2383D4311yescharacteristic, direct product factor
294C2×#389—433no—
295C2×#388—433no—
296C2×#387—433no—
297C2×#385—433no—
298C2×#384—431no—
299C2×#383—431no—
300C2×C43—42no—
301C2×C43C2×#52013yes—
302C2×C43C2×#56011yescharacteristic
303C2×C43C2×#56313yes—
304D43—42no—
305D43#238318yesdirect product factor
306C24×C4—431no—
307C2×#126—4316no—
308C2×#126—433no—
309C2×#126—433no—
310C2×#126—431no—
311C2×#126C2×D4311yescharacteristic
312C22×C4⋊C4—433no—
313C22×C4⋊C4—433no—
314C22×C4⋊C4—433no—
315C22×C4⋊C4—433no—
316C22×C22⋊C4—433no—
317C22×C22⋊C4—433no—
318C22×C42—431no—
319C22×C42—433no—
320#389—433no—
321#389—433no—
322#389—433no—
323#389—433no—
324#389—433no—
325#389—433no—
326#389—433no—
327#389C2×D4313yescomplemented
328#388—433no—
329#388—433no—
330#388—433no—
331#388—433no—
332#388—433no—
333#388—433no—
334#388—433no—
335#388C2×D4313yes—
336#387—433no—
337#387—433no—
338#387—433no—
339#387—433no—
340#387—433no—
341#387—433no—
342#387—433no—
343#387C2×D4313yescomplemented
344#385—433no—
345#385—433no—
346#385—433no—
347#385—433no—
348#385—433no—
349#385—433no—
350#385—433no—
351#385C2×D4313yes—
352#384—433no—
353#384—433no—
354#384—431no—
355#384C2×D4311yescharacteristic, complemented
356#383—431no—
357#383—433no—
358#383—433no—
359#383C2×D4311yescharacteristic, complemented
360C2×#95—433no—
361C2×#95—433no—
362C2×#95—433no—
363C2×#95—433no—
364C43C2×#238311yescharacteristic, complemented, Sylow
365C25—431no—
366C23×C4—433no—
367C23×C4—433no—
368C23×C4—431no—
369C23×C4—433no—
370C23×C4—433no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—1726no—
376C23×C4C22×D4311yescharacteristic
377#126—4324no—
378#126—4324no—
379#126—438no—
380#126C4×D4318yescomplemented
381C2×C4⋊C4—433no—
382C2×C4⋊C4—433no—
383C2×C4⋊C4—433no—
384C2×C4⋊C4—4324no—
385C2×C4⋊C4—433no—
386C2×C4⋊C4—433no—
387C2×C4⋊C4—433no—
388C2×C4⋊C4—433no—
389C2×C4⋊C4—433no—
390C2×C4⋊C4—433no—
391C2×C4⋊C4—433no—
392C2×C4⋊C4—433no—
393C2×C4⋊C4—433no—
394C2×C4⋊C4—1726no—
395C2×C4⋊C4—1726no—
396C2×C4⋊C4—1726no—
397C2×C4⋊C4C22×D4313yes—
398C2×C4⋊C4C22×D4313yes—
399C2×C4⋊C4C22×D4313yes—
400C2×C4⋊C4C22×D4313yes—
401C2×C22⋊C4—433no—
402C2×C22⋊C4—433no—
403C2×C22⋊C4—433no—
404C2×C22⋊C4—4324no—
405C2×C22⋊C4—433no—
406C2×C22⋊C4—433no—
407C2×C22⋊C4—433no—
408C2×C22⋊C4—1726no—
409C2×C22⋊C4C22×D4313yes—
410C2×C22⋊C4C22×D4313yes—
411C2×C42—433no—
412C2×C42—438no—
413C2×C42—433no—
414C2×C42—433no—
415C2×C42—433no—
416C2×C42—1726no—
417C2×C42C22×D4313yes—
418C2×C42C22×D4311yescharacteristic
419#95—433no—
420#95—433no—
421#95—433no—
422#95—433no—
423#95—433no—
424#95—433no—
425#95—433no—
426#95—433no—
427#95—433no—
428#95—433no—
429#95—433no—
430#95—433no—
431#95C22×D4313yes—
432#95C22×D4313yes—
433#95C22×D4313yes—
434#95C22×D4313yes—
435C24—431no—
436C24—434no—
437C24—431no—
438C24—866no—
439C24—866no—
440C24C23×D4311yescharacteristic
441C22×C4—43no—
442C22×C4—433no—
443C22×C4—433no—
444C22×C4—4312no—
445C22×C4—4312no—
446C22×C4—433no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—433no—
450C22×C4—866no—
451C22×C4—866no—
452C22×C4—866no—
453C22×C4—866no—
454C22×C4—866no—
455C22×C4—866no—
456C22×C4—866no—
457C22×C4—866no—
458C22×C4—866no—
459C22×C4—866no—
460C22×C4—8612no—
461C22×C4—1723no—
462C22×C4—1723no—
463C22×C4—17216no—
464C22×C4—1723no—
465C22×C4C23×D4313yes—
466C22×C4C23×D4311yescharacteristic
467C22×C4C23×D4311yescharacteristic
468C22×C4C23×D4313yes—
469C22×C4C23×D4313yes—
470C22×C4C23×D4313yes—
471C4⋊C4—43no—
472C4⋊C4—43no—
473C4⋊C4—43no—
474C4⋊C4—4312no—
475C4⋊C4—4312no—
476C4⋊C4—4312no—
477C4⋊C4—1723no—
478C4⋊C4—1723no—
479C4⋊C4—1723no—
480C4⋊C4—1723no—
481C4⋊C4—1723no—
482C4⋊C4—1723no—
483C4⋊C4—1723no—
484C4⋊C4—1723no—
485C4⋊C4—1723no—
486C4⋊C4C2×C4×D43112yescomplemented
487C22⋊C4—43no—
488C22⋊C4—4312no—
489C22⋊C4—4312no—
490C22⋊C4—4312no—
491C22⋊C4—1723no—
492C22⋊C4—1723no—
493C22⋊C4—1723no—
494C22⋊C4C2×C4×D43112yes—
495C42—43no—
496C42—4312no—
497C42—1723no—
498C42—1723no—
499C42—1723no—
500C42C2×C4×D4314yescomplemented
501C23—23no—
502C23—23no—
503C23—432no—
504C23—436no—
505C23—436no—
506C23—432no—
507C23—8624no—
508C23—863no—
509C23—863no—
510C23—1724no—
511C23—17212no—
512C23C22×C4×D4312yes—
513C23C24×D4311yescharacteristic
514C2×C4—23no—
515C2×C4—23no—
516C2×C4—23no—
517C2×C4—23no—
518C2×C4—23no—
519C2×C4—23no—
520C2×C4—23no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—26no—
525C2×C4—44no—
526C2×C4—436no—
527C2×C4—436no—
528C2×C4—8624no—
529C2×C4—8624no—
530C2×C4—863no—
531C2×C4—863no—
532C2×C4—863no—
533C2×C4—863no—
534C2×C4—863no—
535C2×C4—863no—
536C2×C4—863no—
537C2×C4—863no—
538C2×C4—863no—
539C2×C4—863no—
540C2×C4—866no—
541C2×C4—1724no—
542C2×C4—1724no—
543C2×C4—17212no—
544C2×C4—17212no—
545C2×C4—1724no—
546C2×C4—1724no—
547C2×C4—1724no—
548C2×C4C22×C4×D4316yes—
549C2×C4C22×C4×D4316yes—
550C22—26no—
551C22—41no—
552C22—43no—
553C22—4312no—
554C22—434no—
555C22—4312no—
556C22—866no—
557C22—17216no—
558C22—1721no—
559C22—1723no—
560C22C23×C4×D4311yescharacteristic
561C22H(5,𝔽2)×D4313yes—
562C222−1+4×D4313yes—
563C4—26no—
564C4—26no—
565C4—41no—
566C4—41no—
567C4—43no—
568C4—43no—
569C4—866no—
570C4—866no—
571C4—1721no—
572C4—1721no—
573C4—1723no—
574C4—1723no—
575C2—42no—
576C2—438no—
577C2—1722no—
578C2#520×D4313yes—
579C2#560×D4311yescharacteristic
580C2#563×D4313yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2383C2
socle, cosocleC23×C43C25
prime radicalC24×D43C23
hypercenter#2383D43
hypocenterC43C2×#2383
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2383

Complements

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

NH ≅ G/Ntype
2. #19137788C2semidirect
3. #19137787C2semidirect
4. #19137786C2semidirect
5. #19137785C2semidirect
6. #19137784C2semidirect
7. #19137783C2semidirect
8. #19137782C2semidirect
9. #389×D43C2semidirect
11. #387×D43C2semidirect
13. #384×D43C2semidirect
14. #383×D43C2semidirect
15. C43×#2383C2semidirect
20. #126×D43C4semidirect
29. #14582798C22semidirect
30. #14582797C22semidirect
31. #14582796C22semidirect
32. #14582796C22semidirect
33. #14582795C22semidirect
34. #14582794C22semidirect
35. #14582794C22semidirect
43. #14582786C22semidirect
44. #14582785C22semidirect
45. #14582784C22semidirect
46. #14582783C22semidirect
47. #14582782C22semidirect
48. #14582781C22semidirect
49. #14582780C22semidirect
57. #14582769C22semidirect
58. #14582768C22semidirect
59. #14582768C22semidirect
60. #14582767C22semidirect
61. #14582766C22semidirect
62. #14582766C22semidirect
68. C43×#389C22semidirect
70. C43×#387C22semidirect
72. C43×#384C22semidirect
73. C43×#383C22semidirect
85. #13063320C2×C4semidirect
86. #13063319C2×C4semidirect
87. #13063318C2×C4semidirect
103. C4⋊C4×D43C2×C4semidirect
117. C42×D43C2×C4semidirect
131. #126×C43C2×C4semidirect
183. C4⋊C4×C43C22×C4semidirect
187. C42×C43C22×C4semidirect
197. C4⋊Dic43C22×C4semidirect
204. Dic43⋊C4C22×C4semidirect
205. Dic43⋊C4C22×C4semidirect
209. C4×Dic43C22×C4semidirect
293. #2383D43direct (N × H)
305. D43#2383direct (N × H)
327. #389C2×D43semidirect
343. #387C2×D43semidirect
355. #384C2×D43semidirect
359. #383C2×D43semidirect
364. C43C2×#2383semidirect
380. #126C4×D43semidirect
486. C4⋊C4C2×C4×D43semidirect
500. C42C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D432
#191377882
#191377872
#191377862
#191377852
#191377842
#191377832
#191377822
#389×D432
#388×D432
#387×D432
#385×D432
#384×D432
#383×D432
C43×#23832
C2×#238343