Finite Group Databasebeta

← D43×#2401 #25262892

Subgroups — D43×#2401 #25262892

Order 11008.

2294 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137898C211yesmaximal, characteristic, complemented
2#19137897C211yesmaximal, characteristic, complemented
3#19137896C213yesmaximal, complemented
4#19137895C213yesmaximal, complemented
5#19137894C213yesmaximal, complemented
6#19137893C211yesmaximal, characteristic, complemented
7#19137892C213yesmaximal, complemented
8#401×D43C211yesmaximal, characteristic, complemented
9#400×D43C213yesmaximal, complemented
10#397×D43C213yesmaximal
11#396×D43C211yesmaximal, characteristic
12C4×C4⋊C4×D43C213yesmaximal, complemented
13C4×C22⋊C4×D43C213yesmaximal
14#376×D43C211yesmaximal, characteristic, complemented
15C43×#2401C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C2×C4⋊C4×D43C2213yes—
18C2×C4⋊C4×D43C2213yes—
19C2×C22⋊C4×D43C2213yes—
20C2×C22⋊C4×D43C2213yes—
21C2×C42×D43C2213yes—
22C2×C42×D43C2213yes—
23C43⋊#401C2213yescomplemented
24C43⋊#401C2211yescharacteristic, complemented
25C43⋊#401C2213yescomplemented
26#14582841C2213yescomplemented
27#14582841C2213yescomplemented
28#14582840C2213yescomplemented
29#14582840C2213yescomplemented
30#14582839C2213yescomplemented
31#14582838C2213yescomplemented
32#14582837C2213yescomplemented
33#14582828C2213yes—
34#14582828C2213yes—
35#14582827C2213yes—
36#14582827C2213yes—
37#14582826C2213yes—
38#14582825C2213yes—
39#14582824C2213yes—
40#14582823C2211yescharacteristic
41#14582822C2213yes—
42#14582821C2213yes—
43C4⋊C4×Dic43C2213yescomplemented
44C4⋊C4×Dic43C2213yescomplemented
45C4×Dic43⋊C4C2213yescomplemented
46C4×Dic43⋊C4C2213yescomplemented
47C4×C4⋊Dic43C2213yescomplemented
48#14582750C2213yescomplemented
49#14582750C2213yescomplemented
50C22⋊C4×Dic43C2213yes—
51C22⋊C4×Dic43C2213yes—
52C4×(C2×D43)⋊C4C2213yes—
53C4×(C2×D43)⋊C4C2213yes—
54C4×C22⋊Dic43C2213yes—
55#14582746C2213yes—
56#14582746C2213yes—
57#14582745C2213yescomplemented
58#14582744C2213yescomplemented
59#14582744C2211yescharacteristic, complemented
60#95×D43C2211yescharacteristic
61#95×D43C2213yes—
62#95×D43C2213yes—
63#95×D43C2213yes—
64#95×D43C2213yes—
65#95×D43C2213yes—
66C43×#401C2211yescharacteristic, complemented
67C43×#400C2213yescomplemented
68C43×#397C2213yes—
69C43×#396C2211yescharacteristic
70C4×C4⋊C4×C43C2213yescomplemented
71C4×C22⋊C4×C43C2213yes—
72C43×#376C2211yescharacteristic, complemented
73C24×D43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C22×C4×D43—212no—
76C22×C4×D43C2313yes—
77C22×C4×D43C2313yes—
78C22×C4×D43C2313yes—
79C22×C4×D43C2311yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C22×C4×D43C2311yescharacteristic
82C22×C4×D43C2313yes—
83C22×C4×D43C2311yescharacteristic
84C2×C4⋊Dic43C2313yes—
85C2×C4⋊Dic43C2313yes—
86C2×Dic43⋊C4C2313yes—
87C2×Dic43⋊C4C2313yes—
88C2×Dic43⋊C4C2313yes—
89C2×Dic43⋊C4C2313yes—
90C4⋊C4×D43—212no—
91C4⋊C4×D43—212no—
92C2×C22⋊Dic43C2313yes—
93C2×C22⋊Dic43C2313yes—
94C2×(C2×D43)⋊C4C2313yes—
95C2×(C2×D43)⋊C4C2313yes—
96C2×(C2×D43)⋊C4C2313yes—
97C2×(C2×D43)⋊C4C2313yes—
98C22⋊C4×D43—212no—
99C22⋊C4×D43—212no—
100C2×C4×Dic43C2313yes—
101C2×C4×Dic43C2313yes—
102C2×C4×Dic43C2313yes—
103C2×C4×Dic43C2313yes—
104C2×C4×Dic43C2313yes—
105C2×C4×Dic43C2313yes—
106C42×D43—212no—
107C42×D43—212no—
108C43⋊#95C2313yes—
109C43⋊#95C2313yes—
110C43⋊#95C2313yes—
111C43⋊#95C2313yes—
112C43⋊#95C2313yes—
113C43⋊#95C2313yes—
114C43⋊#95C2313yes—
115C43⋊#95C2313yes—
116C43⋊#95C2313yes—
117C43⋊#95C2313yes—
118C43⋊#95C2313yes—
119C43⋊#95C2313yes—
120C43⋊#95C2313yes—
121C43⋊#95C2313yes—
122C43⋊#95C2313yes—
123C43⋊#95C2313yes—
124C23×C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2313yes—
126C2×C4⋊C4×C43C2313yes—
127C2×C22⋊C4×C43C2313yes—
128C2×C22⋊C4×C43C2313yes—
129C2×C42×C43C2313yes—
130C2×C42×C43C2313yes—
131#95×C43C2311yescharacteristic
132#95×C43C2313yes—
133#95×C43C2313yes—
134#95×C43C2313yes—
135#95×C43C2313yes—
136#95×C43C2313yes—
137C24×C43C2411yescharacteristic
138C23×D43—26no—
139C23×D43—26no—
140C23×D43#4114yes—
141C23×D43C2411yescharacteristic
142C23×D43C2411yescharacteristic
143C22×C4×C43—26no—
144C22×C4×C43C2411yescharacteristic
145C22×C4×C43C2413yes—
146C22×C4×C43C2413yes—
147C22×C4×C43C2413yes—
148C22×C4×C43C2413yes—
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—26no—
151C22×Dic43C2411yescharacteristic
152C22×Dic43C2413yes—
153C22×Dic43C2413yes—
154C22×Dic43C2413yes—
155C22×Dic43C2413yes—
156C22×Dic43C2411yescharacteristic
157C2×C4×D43—26no—
158C2×C4×D43—26no—
159C2×C4×D43—26no—
160C2×C4×D43—26no—
161C2×C4×D43—26no—
162C2×C4×D43—26no—
163C2×C4×D43—26no—
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—416no—
172C2×C4×D43#41112yes—
173C2×C4×D43#41112yes—
174C4⋊C4×C43—26no—
175C4⋊C4×C43—26no—
176C22⋊C4×C43—26no—
177C22⋊C4×C43—26no—
178C42×C43—26no—
179C42×C43—26no—
180C22⋊Dic43—26no—
181C22⋊Dic43—26no—
182(C2×D43)⋊C4—26no—
183(C2×D43)⋊C4—26no—
184(C2×D43)⋊C4—26no—
185(C2×D43)⋊C4—26no—
186C4⋊Dic43—26no—
187C4⋊Dic43—26no—
188Dic43⋊C4—26no—
189Dic43⋊C4—26no—
190Dic43⋊C4—26no—
191Dic43⋊C4—26no—
192C4×Dic43—26no—
193C4×Dic43—26no—
194C4×Dic43—26no—
195C4×Dic43—26no—
196C4×Dic43—26no—
197C4×Dic43—26no—
198C23×C43—23no—
199C23×C43—23no—
200C23×C43C2×#4112yes—
201C23×C43C2511yescharacteristic
202C22×D43—23no—
203C22×D43—23no—
204C22×D43—224no—
205C22×D43—44no—
206C22×D43—412no—
207C22×D43C2×#4112yes—
208C22×D43C2×#4116yes—
209C22×D43C2×#4112yes—
210C22×D43C2×#4116yes—
211C2×C4×C43—23no—
212C2×C4×C43—23no—
213C2×C4×C43—23no—
214C2×C4×C43—23no—
215C2×C4×C43—23no—
216C2×C4×C43—23no—
217C2×C4×C43—23no—
218C2×C4×C43—23no—
219C2×C4×C43—23no—
220C2×C4×C43—23no—
221C2×C4×C43—23no—
222C2×C4×C43—23no—
223C2×C4×C43—44no—
224C2×C4×C43C2×#4116yes—
225C2×C4×C43C2×#4116yes—
226C2×Dic43—23no—
227C2×Dic43—23no—
228C2×Dic43—23no—
229C2×Dic43—23no—
230C2×Dic43—23no—
231C2×Dic43—23no—
232C2×Dic43—23no—
233C2×Dic43—23no—
234C2×Dic43—23no—
235C2×Dic43—23no—
236C2×Dic43—23no—
237C2×Dic43—23no—
238C2×Dic43—44no—
239C2×Dic43C2×#4116yes—
240C2×Dic43C2×#4116yes—
241C4×D43—224no—
242C4×D43—44no—
243C4×D43—412no—
244C4×D43—412no—
245C4×D43—412no—
246C4×D43—44no—
247C4×D43—44no—
248C4×D43#126116yes—
249C2×#2401—431nomaximal, Sylow
250C22×C43—26no—
251C22×C43—41no—
252C22×C43—43no—
253C22×C43C22×#4113yes—
254C22×C43C22×#4113yes—
255C22×C43C22×#4111yescharacteristic
256C2×D43—26no—
257C2×D43—41no—
258C2×D43—43no—
259C2×D43—416no—
260C2×D43C2×#12614yes—
261C2×D43#529112yes—
262C2×D43#529112yes—
263C4×C43—26no—
264C4×C43—41no—
265C4×C43—43no—
266C4×C43—43no—
267C4×C43—43no—
268C4×C43C2×#12614yes—
269Dic43—26no—
270Dic43—41no—
271Dic43—43no—
272Dic43—43no—
273Dic43—43no—
274Dic43C2×#12614yes—
275#2401—431no—
276#2401—433no—
277#2401—433no—
278#2401—431no—
279#2401—433no—
280#2401—433no—
281#2401—431no—
282#2401D4311yescharacteristic, direct product factor
283C2×#401—431no—
284C2×#400—433no—
285C2×#397—433no—
286C2×#396—431no—
287C2×C4×C4⋊C4—433no—
288C2×C4×C22⋊C4—433no—
289C2×#376—431no—
290C2×C43—42no—
291C2×C43C22×#12611yescharacteristic
292C2×C43C2×#52913yes—
293C2×C43C2×#52913yes—
294D43—42no—
295D43#240118yesdirect product factor
296C24×C4—431no—
297C22×C4⋊C4—433no—
298C22×C4⋊C4—433no—
299C22×C22⋊C4—433no—
300C22×C22⋊C4—433no—
301C22×C42—433no—
302C22×C42—433no—
303#401—433no—
304#401—433no—
305#401—431no—
306#401C2×D4311yescharacteristic, complemented
307#400—433no—
308#400—433no—
309#400—433no—
310#400—433no—
311#400—433no—
312#400—433no—
313#400—433no—
314#400C2×D4313yescomplemented
315#397—433no—
316#397—433no—
317#397—433no—
318#397—433no—
319#397—433no—
320#397—433no—
321#397—433no—
322#397C2×D4313yes—
323#396—433no—
324#396—433no—
325#396—431no—
326#396C2×D4311yescharacteristic
327C4×C4⋊C4—433no—
328C4×C4⋊C4—433no—
329C4×C4⋊C4—433no—
330C4×C4⋊C4—433no—
331C4×C4⋊C4—433no—
332C4×C4⋊C4—433no—
333C4×C4⋊C4—433no—
334C4×C4⋊C4C2×D4313yescomplemented
335C4×C22⋊C4—433no—
336C4×C22⋊C4—433no—
337C4×C22⋊C4—433no—
338C4×C22⋊C4—433no—
339C4×C22⋊C4—433no—
340C4×C22⋊C4—433no—
341C4×C22⋊C4—433no—
342C4×C22⋊C4C2×D4313yes—
343#376—433no—
344#376—433no—
345#376—431no—
346#376C2×D4311yescharacteristic, complemented
347C2×#95—431no—
348C2×#95—433no—
349C2×#95—433no—
350C2×#95—433no—
351C2×#95—433no—
352C2×#95—433no—
353C43C2×#240111yescharacteristic, complemented, Sylow
354C25—431no—
355C23×C4—431no—
356C23×C4—433no—
357C23×C4—431no—
358C23×C4—433no—
359C23×C4—433no—
360C23×C4—433no—
361C23×C4—431no—
362C23×C4—431no—
363C23×C4—431no—
364C23×C4—8612no—
365C23×C4C22×D4311yescharacteristic
366C2×C4⋊C4—433no—
367C2×C4⋊C4—433no—
368C2×C4⋊C4—433no—
369C2×C4⋊C4—433no—
370C2×C4⋊C4—433no—
371C2×C4⋊C4—433no—
372C2×C4⋊C4—8612no—
373C2×C4⋊C4—8612no—
374C2×C4⋊C4C22×D4313yes—
375C2×C4⋊C4C22×D4313yes—
376C2×C22⋊C4—433no—
377C2×C22⋊C4—433no—
378C2×C22⋊C4—433no—
379C2×C22⋊C4—433no—
380C2×C22⋊C4—433no—
381C2×C22⋊C4—433no—
382C2×C22⋊C4—8612no—
383C2×C22⋊C4—8612no—
384C2×C22⋊C4C22×D4313yes—
385C2×C22⋊C4C22×D4313yes—
386C2×C42—433no—
387C2×C42—433no—
388C2×C42—433no—
389C2×C42—433no—
390C2×C42—433no—
391C2×C42—433no—
392C2×C42—8612no—
393C2×C42—8612no—
394C2×C42C22×D4313yes—
395C2×C42C22×D4313yes—
396#95—433no—
397#95—433no—
398#95—433no—
399#95—433no—
400#95—433no—
401#95—433no—
402#95—433no—
403#95—433no—
404#95—433no—
405#95—433no—
406#95—433no—
407#95—433no—
408#95—433no—
409#95—433no—
410#95—433no—
411#95—433no—
412#95C22×D4311yescharacteristic
413#95C22×D4313yes—
414#95C22×D4313yes—
415#95C22×D4313yes—
416#95C22×D4313yes—
417#95C22×D4313yes—
418C24—431no—
419C24—434no—
420C24—431no—
421C24—866no—
422C24—866no—
423C24C23×D4311yescharacteristic
424C22×C4—26no—
425C22×C4—431no—
426C22×C4—4312no—
427C22×C4—433no—
428C22×C4—4312no—
429C22×C4—431no—
430C22×C4—433no—
431C22×C4—433no—
432C22×C4—433no—
433C22×C4—866no—
434C22×C4—866no—
435C22×C4—866no—
436C22×C4—866no—
437C22×C4—866no—
438C22×C4—866no—
439C22×C4—866no—
440C22×C4—866no—
441C22×C4—866no—
442C22×C4—866no—
443C22×C4—866no—
444C22×C4—866no—
445C22×C4—866no—
446C22×C4—866no—
447C22×C4—866no—
448C22×C4—17216no—
449C22×C4C23×D4311yescharacteristic
450C22×C4C23×D4313yes—
451C22×C4C23×D4313yes—
452C22×C4C23×D4313yes—
453C22×C4C23×D4313yes—
454C22×C4C23×D4311yescharacteristic
455C4⋊C4—26no—
456C4⋊C4—26no—
457C4⋊C4—866no—
458C4⋊C4—866no—
459C4⋊C4—866no—
460C4⋊C4—866no—
461C4⋊C4—866no—
462C4⋊C4—866no—
463C22⋊C4—26no—
464C22⋊C4—26no—
465C22⋊C4—866no—
466C22⋊C4—866no—
467C22⋊C4—866no—
468C22⋊C4—866no—
469C22⋊C4—866no—
470C22⋊C4—866no—
471C42—26no—
472C42—26no—
473C42—866no—
474C42—866no—
475C42—866no—
476C42—866no—
477C42—866no—
478C42—866no—
479C23—23no—
480C23—23no—
481C23—436no—
482C23—436no—
483C23—432no—
484C23—432no—
485C23—8624no—
486C23—863no—
487C23—863no—
488C23—1724no—
489C23—17212no—
490C23#41×D4312yes—
491C23C24×D4311yescharacteristic
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—23no—
504C2×C4—44no—
505C2×C4—436no—
506C2×C4—4316no—
507C2×C4—436no—
508C2×C4—8624no—
509C2×C4—863no—
510C2×C4—863no—
511C2×C4—863no—
512C2×C4—863no—
513C2×C4—863no—
514C2×C4—863no—
515C2×C4—863no—
516C2×C4—863no—
517C2×C4—863no—
518C2×C4—863no—
519C2×C4—863no—
520C2×C4—863no—
521C2×C4—1724no—
522C2×C4—1724no—
523C2×C4—17212no—
524C2×C4—17212no—
525C2×C4—17212no—
526C2×C4—1724no—
527C2×C4—1724no—
528C2×C4#41×D4316yes—
529C2×C4#41×D4316yes—
530C22—26no—
531C22—41no—
532C22—43no—
533C22—434no—
534C22—4312no—
535C22—4312no—
536C22—866no—
537C22—17216no—
538C22—1721no—
539C22—1723no—
540C22C2×#41×D4313yes—
541C22C2×#41×D4311yescharacteristic
542C22C2×#41×D4313yes—
543C4—26no—
544C4—41no—
545C4—43no—
546C4—43no—
547C4—43no—
548C4—434no—
549C4—866no—
550C4—1721no—
551C4—1723no—
552C4—1723no—
553C4—1723no—
554C4#126×D4314yes—
555C2—42no—
556C2—438no—
557C2—1722no—
558C2C2×#126×D4311yescharacteristic
559C2#529×D4313yes—
560C2#529×D4313yes—
subgroupG/H
centerC22×C4C23×D43
commutator, socle, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC43×#2401C2
prime radicalC24×D43C23
hypercenter#2401D43
hypocenterC43C2×#2401
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #2401

Complements

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

NH ≅ G/Ntype
1. #19137898C2semidirect
2. #19137897C2semidirect
3. #19137896C2semidirect
4. #19137895C2semidirect
5. #19137894C2semidirect
6. #19137893C2semidirect
7. #19137892C2semidirect
8. #401×D43C2semidirect
9. #400×D43C2semidirect
12. C4×C4⋊C4×D43C2semidirect
14. #376×D43C2semidirect
15. C43×#2401C2semidirect
23. C43⋊#401C22semidirect
24. C43⋊#401C22semidirect
25. C43⋊#401C22semidirect
26. #14582841C22semidirect
27. #14582841C22semidirect
28. #14582840C22semidirect
29. #14582840C22semidirect
30. #14582839C22semidirect
31. #14582838C22semidirect
32. #14582837C22semidirect
43. C4⋊C4×Dic43C22semidirect
44. C4⋊C4×Dic43C22semidirect
45. C4×Dic43⋊C4C22semidirect
46. C4×Dic43⋊C4C22semidirect
47. C4×C4⋊Dic43C22semidirect
48. #14582750C22semidirect
49. #14582750C22semidirect
57. #14582745C22semidirect
58. #14582744C22semidirect
59. #14582744C22semidirect
66. C43×#401C22semidirect
67. C43×#400C22semidirect
70. C4×C4⋊C4×C43C22semidirect
72. C43×#376C22semidirect
282. #2401D43direct (N × H)
295. D43#2401direct (N × H)
306. #401C2×D43semidirect
314. #400C2×D43semidirect
334. C4×C4⋊C4C2×D43semidirect
346. #376C2×D43semidirect
353. C43C2×#2401semidirect

Maximal subgroups

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

subgroupindex
#191378982
#191378972
#191378962
#191378952
#191378942
#191378932
#191378922
#401×D432
#400×D432
#397×D432
#396×D432
C4×C4⋊C4×D432
C4×C22⋊C4×D432
#376×D432
C43×#24012
C2×#240143