Finite Group Databasebeta

← C4×#126×D43 #25255074

Subgroups — C4×#126×D43 #25255074

Order 11008.

2838 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D43C211yesmaximal, characteristic
2#19137149C213yesmaximal, complemented
3C4×#13063320C213yesmaximal, complemented
4#126×Dic43C211yesmaximal, characteristic, complemented
5C4×#13063319C211yesmaximal, characteristic, complemented
6#19137145C213yesmaximal, complemented
7C4×#13063318C213yesmaximal, complemented
8#19137143C211yesmaximal, characteristic, complemented
9#388×D43C213yesmaximal
10#387×D43C213yesmaximal, complemented
11#383×D43C211yesmaximal, characteristic, complemented
12C4×C4⋊C4×D43C213yesmaximal, complemented
13C4×C22⋊C4×D43C213yesmaximal
14C43×D43C211yesmaximal, characteristic, complemented
15C4×#126×C43C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C2×#13063320C2213yes—
18C2×#13063319C2211yescharacteristic
19C2×#13063318C2213yes—
20#126×D43C4116yesdirect product factor
21C2×C4⋊C4×D43C2213yes—
22C2×C4⋊C4×D43C2213yes—
23C2×C22⋊C4×D43C2213yes—
24C2×C22⋊C4×D43C2213yes—
25C2×C42×D43C2213yes—
26C2×C42×D43C2213yes—
27C2×C42×D43C2213yes—
28C2×C42×D43C2211yescharacteristic
29#14582793C2213yes—
30#14582792C2213yes—
31#14582791C2213yes—
32#14582790C2213yes—
33#14582789C2213yes—
34#14582788C2213yes—
35#14582787C2213yes—
36#14582786C2213yescomplemented
37#14582785C2213yescomplemented
38#14582784C2213yescomplemented
39#14582783C2213yescomplemented
40#14582782C2213yescomplemented
41#14582781C2213yescomplemented
42#14582780C2213yescomplemented
43#14582767C2211yescharacteristic, complemented
44#14582766C2213yescomplemented
45#14582766C2213yescomplemented
46C4⋊C4×Dic43C2213yescomplemented
47C4⋊C4×Dic43C2213yescomplemented
48C4×Dic43⋊C4C2213yescomplemented
49C4×Dic43⋊C4C2213yescomplemented
50C4×C4⋊Dic43C2213yescomplemented
51#14582750C2213yescomplemented
52#14582750C2213yescomplemented
53C22⋊C4×Dic43C2213yes—
54C22⋊C4×Dic43C2213yes—
55C4×(C2×D43)⋊C4C2213yes—
56C4×(C2×D43)⋊C4C2213yes—
57C4×C22⋊Dic43C2213yes—
58#14582746C2213yes—
59#14582746C2213yes—
60#95×D43C2213yes—
61#95×D43C2213yes—
62#95×D43C2213yes—
63#95×D43C2213yes—
64C42×Dic43C2211yescharacteristic, complemented
65C42×Dic43C2213yescomplemented
66C42×Dic43C2213yescomplemented
67C2×#126×C43C2211yescharacteristic
68C43×#388C2213yes—
69C43×#387C2213yescomplemented
70C43×#383C2211yescharacteristic, complemented
71C4×C4⋊C4×C43C2213yescomplemented
72C4×C22⋊C4×C43C2213yes—
73C43×C43C2211yescharacteristic, complemented
74C24×D43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C22×C4×D43—212no—
77C22×C4×D43C2313yes—
78C22×C4×D43C2311yescharacteristic
79C22×C4×D43C2311yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C22×C4×D43C2313yes—
82C22×C4×D43C2313yes—
83C22×C4×D43C2313yes—
84C22×C4×D43C2311yescharacteristic
85#13063320C2×C4124yescomplemented
86#13063319C2×C418yescomplemented
87#13063318C2×C4124yescomplemented
88C2×C4⋊Dic43C2313yes—
89C2×C4⋊Dic43C2313yes—
90C2×Dic43⋊C4C2313yes—
91C2×Dic43⋊C4C2313yes—
92C2×Dic43⋊C4C2313yes—
93C2×Dic43⋊C4C2313yes—
94C4⋊C4×D43—212no—
95C4⋊C4×D43C2×C4124yescomplemented
96C2×C22⋊Dic43C2313yes—
97C2×C22⋊Dic43C2313yes—
98C2×(C2×D43)⋊C4C2313yes—
99C2×(C2×D43)⋊C4C2313yes—
100C2×(C2×D43)⋊C4C2313yes—
101C2×(C2×D43)⋊C4C2313yes—
102C22⋊C4×D43—212no—
103C22⋊C4×D43C2×C4124yes—
104C2×C4×Dic43C2313yes—
105C2×C4×Dic43C2313yes—
106C2×C4×Dic43C2313yes—
107C2×C4×Dic43C2313yes—
108C2×C4×Dic43C2313yes—
109C2×C4×Dic43C2313yes—
110C2×C4×Dic43C2313yes—
111C2×C4×Dic43C2313yes—
112C2×C4×Dic43C2313yes—
113C2×C4×Dic43C2313yes—
114C42×D43—212no—
115C42×D43—212no—
116C42×D43—212no—
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×C22⋊C4×C43C2313yes—
135C2×C22⋊C4×C43C2313yes—
136C2×C42×C43C2313yes—
137C2×C42×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—26no—
151C22×C4×C43C2411yescharacteristic
152C22×C4×C43C2413yes—
153C22×C4×C43C2413yes—
154C22×C4×C43C2413yes—
155C22×C4×C43C2413yes—
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—26no—
158C22×Dic43C2411yescharacteristic
159C22×Dic43C2413yes—
160C22×Dic43C2413yes—
161C22×Dic43C2413yes—
162C22×Dic43C2413yes—
163C22×Dic43C2411yescharacteristic
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—26no—
175C2×C4×D43—26no—
176C2×C4×D43—416no—
177C2×C4×D43C22×C4112yes—
178C2×C4×D43C22×C4112yes—
179C2×C4×D43#41112yes—
180C2×C4×D43#41112yes—
181C4⋊C4×C43—26no—
182C4⋊C4×C43C22×C4112yescomplemented
183C22⋊C4×C43—26no—
184C22⋊C4×C43C22×C4112yes—
185C42×C43—26no—
186C42×C43—26no—
187C42×C43—26no—
188C42×C43C22×C414yescomplemented
189C22⋊Dic43—26no—
190C22⋊Dic43C22×C4112yes—
191(C2×D43)⋊C4—26no—
192(C2×D43)⋊C4—26no—
193(C2×D43)⋊C4C22×C4112yes—
194(C2×D43)⋊C4C22×C4112yes—
195C4⋊Dic43—26no—
196C4⋊Dic43C22×C4112yescomplemented
197Dic43⋊C4—26no—
198Dic43⋊C4—26no—
199Dic43⋊C4C22×C4112yescomplemented
200Dic43⋊C4C22×C4112yescomplemented
201C4×Dic43—26no—
202C4×Dic43—26no—
203C4×Dic43—26no—
204C4×Dic43—26no—
205C4×Dic43—26no—
206C4×Dic43—26no—
207C4×Dic43—26no—
208C4×Dic43—26no—
209C4×Dic43—26no—
210C4×Dic43C22×C4112yescomplemented
211C23×C43—23no—
212C23×C43—23no—
213C23×C43C23×C412yes—
214C23×C43C2511yescharacteristic
215C22×D43—23no—
216C22×D43—23no—
217C22×D43—224no—
218C22×D43—44no—
219C22×D43—412no—
220C22×D43C23×C412yes—
221C22×D43C23×C412yes—
222C22×D43C2×#4116yes—
223C22×D43C2×#4116yes—
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—23no—
234C2×C4×C43—44no—
235C2×C4×C43C23×C416yes—
236C2×C4×C43C23×C416yes—
237C2×C4×C43C2×#4116yes—
238C2×C4×C43C2×#4116yes—
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—23no—
248C2×Dic43—23no—
249C2×Dic43—44no—
250C2×Dic43C23×C416yes—
251C2×Dic43C23×C416yes—
252C2×Dic43C2×#4116yes—
253C2×Dic43C2×#4116yes—
254C4×D43—224no—
255C4×D43—224no—
256C4×D43—224no—
257C4×D43—44no—
258C4×D43—412no—
259C4×D43—44no—
260C4×D43—44no—
261C4×D43#126116yesdirect product factor
262C2×C4×#126—431nomaximal, Sylow
263C22×C43—26no—
264C22×C43—41no—
265C22×C43—43no—
266C22×C43C24×C411yescharacteristic
267C22×C43C22×#4113yes—
268C22×C43C22×#4113yes—
269C2×D43—26no—
270C2×D43—41no—
271C2×D43—43no—
272C2×D43—416no—
273C2×D43C4×#41112yes—
274C2×D43C2×#12614yes—
275C2×D43#529112yes—
276C4×C43—26no—
277C4×C43—26no—
278C4×C43—26no—
279C4×C43—41no—
280C4×C43—43no—
281C4×C43C2×#12614yescomplemented
282Dic43—26no—
283Dic43—26no—
284Dic43—26no—
285Dic43—41no—
286Dic43—43no—
287Dic43C2×#12614yescomplemented
288C22×#126—431no—
289C4×#126—433no—
290C4×#126—433no—
291C4×#126—431no—
292C4×#126—433no—
293C4×#126—433no—
294C4×#126—431no—
295C4×#126—431no—
296C4×#126D4311yescharacteristic, direct product factor
297C2×#388—433no—
298C2×#387—433no—
299C2×#383—431no—
300C2×C4×C4⋊C4—433no—
301C2×C4×C22⋊C4—433no—
302C2×C43—431no—
303C2×C43—42no—
304C2×C43C2×C4×#4113yes—
305C2×C43C22×#12611yescharacteristic
306C2×C43C2×#52913yes—
307D43—42no—
308D43C4×#12618yesdirect product factor
309C24×C4—431no—
310C2×#126—4316no—
311C2×#126—433no—
312C2×#126—433no—
313C2×#126—431no—
314C2×#126C2×D4311yescharacteristic
315C22×C4⋊C4—433no—
316C22×C4⋊C4—433no—
317C22×C22⋊C4—433no—
318C22×C22⋊C4—433no—
319C22×C42—431no—
320C22×C42—433no—
321C22×C42—433no—
322C22×C42—433no—
323#388—433no—
324#388—433no—
325#388—433no—
326#388—433no—
327#388—433no—
328#388—433no—
329#388—433no—
330#388C2×D4313yes—
331#387—433no—
332#387—433no—
333#387—433no—
334#387—433no—
335#387—433no—
336#387—433no—
337#387—433no—
338#387C2×D4313yescomplemented
339#383—431no—
340#383—433no—
341#383—433no—
342#383C2×D4311yescharacteristic, complemented
343C4×C4⋊C4—433no—
344C4×C4⋊C4—433no—
345C4×C4⋊C4—433no—
346C4×C4⋊C4—433no—
347C4×C4⋊C4—433no—
348C4×C4⋊C4—433no—
349C4×C4⋊C4—433no—
350C4×C4⋊C4C2×D4313yescomplemented
351C4×C22⋊C4—433no—
352C4×C22⋊C4—433no—
353C4×C22⋊C4—433no—
354C4×C22⋊C4—433no—
355C4×C22⋊C4—433no—
356C4×C22⋊C4—433no—
357C4×C22⋊C4—433no—
358C4×C22⋊C4C2×D4313yes—
359C2×#95—433no—
360C2×#95—433no—
361C2×#95—433no—
362C2×#95—433no—
363C43—433no—
364C43—433no—
365C43—431no—
366C43C2×D4311yescharacteristic, complemented
367C43C2×C4×#12611yescharacteristic, complemented, Sylow
368C25—431no—
369C23×C4—431no—
370C23×C4—433no—
371C23×C4—433no—
372C23×C4—433no—
373C23×C4—431no—
374C23×C4—433no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—431no—
378C23×C4—8612no—
379C23×C4C22×D4311yescharacteristic
380#126—4324no—
381#126—4324no—
382#126—438no—
383#126C4×D4318yesdirect product factor
384C2×C4⋊C4—433no—
385C2×C4⋊C4—433no—
386C2×C4⋊C4—433no—
387C2×C4⋊C4—4324no—
388C2×C4⋊C4—433no—
389C2×C4⋊C4—433no—
390C2×C4⋊C4—433no—
391C2×C4⋊C4—8612no—
392C2×C4⋊C4C22×D4313yes—
393C2×C4⋊C4C22×D4313yes—
394C2×C22⋊C4—433no—
395C2×C22⋊C4—433no—
396C2×C22⋊C4—433no—
397C2×C22⋊C4—4324no—
398C2×C22⋊C4—433no—
399C2×C22⋊C4—433no—
400C2×C22⋊C4—433no—
401C2×C22⋊C4—8612no—
402C2×C22⋊C4C22×D4313yes—
403C2×C22⋊C4C22×D4313yes—
404C2×C42—433no—
405C2×C42—438no—
406C2×C42—433no—
407C2×C42—433no—
408C2×C42—433no—
409C2×C42—433no—
410C2×C42—433no—
411C2×C42—433no—
412C2×C42—433no—
413C2×C42—433no—
414C2×C42—433no—
415C2×C42—8612no—
416C2×C42—8612no—
417C2×C42—8612no—
418C2×C42C22×D4313yes—
419C2×C42C22×D4313yes—
420C2×C42C22×D4313yes—
421C2×C42C22×D4311yescharacteristic
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#95—433no—
432#95—433no—
433#95—433no—
434#95C22×D4313yes—
435#95C22×D4313yes—
436#95C22×D4313yes—
437#95C22×D4313yes—
438C24—431no—
439C24—434no—
440C24—431no—
441C24—866no—
442C24—866no—
443C24C23×D4311yescharacteristic
444C22×C4—26no—
445C22×C4—431no—
446C22×C4—4312no—
447C22×C4—433no—
448C22×C4—433no—
449C22×C4—433no—
450C22×C4—4312no—
451C22×C4—4312no—
452C22×C4—4312no—
453C22×C4—431no—
454C22×C4—433no—
455C22×C4—866no—
456C22×C4—866no—
457C22×C4—866no—
458C22×C4—866no—
459C22×C4—866no—
460C22×C4—866no—
461C22×C4—866no—
462C22×C4—866no—
463C22×C4—866no—
464C22×C4—866no—
465C22×C4—866no—
466C22×C4—866no—
467C22×C4—866no—
468C22×C4—17216no—
469C22×C4C23×D4311yescharacteristic
470C22×C4C23×D4313yes—
471C22×C4C23×D4313yes—
472C22×C4C23×D4313yes—
473C22×C4C23×D4313yes—
474C22×C4C23×D4311yescharacteristic
475C4⋊C4—26no—
476C4⋊C4—4312no—
477C4⋊C4—4312no—
478C4⋊C4—4312no—
479C4⋊C4—866no—
480C4⋊C4—866no—
481C4⋊C4—866no—
482C4⋊C4C2×C4×D43112yescomplemented
483C22⋊C4—26no—
484C22⋊C4—4312no—
485C22⋊C4—4312no—
486C22⋊C4—4312no—
487C22⋊C4—866no—
488C22⋊C4—866no—
489C22⋊C4—866no—
490C22⋊C4C2×C4×D43112yes—
491C42—26no—
492C42—26no—
493C42—26no—
494C42—4312no—
495C42—866no—
496C42—866no—
497C42—866no—
498C42—866no—
499C42—866no—
500C42—866no—
501C42—866no—
502C42—866no—
503C42—866no—
504C42C2×C4×D4314yescomplemented
505C23—23no—
506C23—23no—
507C23—432no—
508C23—436no—
509C23—436no—
510C23—432no—
511C23—8624no—
512C23—863no—
513C23—863no—
514C23—1724no—
515C23—17212no—
516C23C22×C4×D4312yes—
517C23C24×D4311yescharacteristic
518C2×C4—23no—
519C2×C4—23no—
520C2×C4—23no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—23no—
525C2×C4—23no—
526C2×C4—23no—
527C2×C4—23no—
528C2×C4—44no—
529C2×C4—436no—
530C2×C4—4316no—
531C2×C4—436no—
532C2×C4—436no—
533C2×C4—436no—
534C2×C4—8624no—
535C2×C4—8624no—
536C2×C4—8624no—
537C2×C4—863no—
538C2×C4—863no—
539C2×C4—863no—
540C2×C4—863no—
541C2×C4—863no—
542C2×C4—863no—
543C2×C4—863no—
544C2×C4—863no—
545C2×C4—863no—
546C2×C4—863no—
547C2×C4—1724no—
548C2×C4—1724no—
549C2×C4—17212no—
550C2×C4—1724no—
551C2×C4—1724no—
552C2×C4C22×C4×D4316yes—
553C2×C4C22×C4×D4316yes—
554C2×C4#41×D4316yes—
555C2×C4#41×D4316yes—
556C22—26no—
557C22—41no—
558C22—43no—
559C22—434no—
560C22—4312no—
561C22—4312no—
562C22—866no—
563C22—17216no—
564C22—1721no—
565C22—1723no—
566C22C23×C4×D4311yescharacteristic
567C22C2×#41×D4313yes—
568C22C2×#41×D4313yes—
569C4—26no—
570C4—26no—
571C4—26no—
572C4—41no—
573C4—43no—
574C4—434no—
575C4—866no—
576C4—866no—
577C4—866no—
578C4—1721no—
579C4—1723no—
580C4#126×D4314yesdirect product factor
581C2—42no—
582C2—438no—
583C2—1722no—
584C2C4×#41×D4313yes—
585C2C2×#126×D4311yescharacteristic
586C2#529×D4313yes—
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC4×#126×C43C2
socle, cosocleC23×C43C25
prime radicalC24×D43C23
hypercenterC4×#126D43
hypocenterC43C2×C4×#126
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
2. #19137149C2semidirect
3. C4×#13063320C2semidirect
4. #126×Dic43C2semidirect
5. C4×#13063319C2semidirect
6. #19137145C2semidirect
7. C4×#13063318C2semidirect
8. #19137143C2semidirect
10. #387×D43C2semidirect
11. #383×D43C2semidirect
12. C4×C4⋊C4×D43C2semidirect
14. C43×D43C2semidirect
15. C4×#126×C43C2semidirect
20. #126×D43C4direct (N × H)
36. #14582786C22semidirect
37. #14582785C22semidirect
38. #14582784C22semidirect
39. #14582783C22semidirect
40. #14582782C22semidirect
41. #14582781C22semidirect
42. #14582780C22semidirect
43. #14582767C22semidirect
44. #14582766C22semidirect
45. #14582766C22semidirect
46. C4⋊C4×Dic43C22semidirect
47. C4⋊C4×Dic43C22semidirect
48. C4×Dic43⋊C4C22semidirect
49. C4×Dic43⋊C4C22semidirect
50. C4×C4⋊Dic43C22semidirect
51. #14582750C22semidirect
52. #14582750C22semidirect
64. C42×Dic43C22semidirect
65. C42×Dic43C22semidirect
66. C42×Dic43C22semidirect
69. C43×#387C22semidirect
70. C43×#383C22semidirect
71. C4×C4⋊C4×C43C22semidirect
73. C43×C43C22semidirect
85. #13063320C2×C4semidirect
86. #13063319C2×C4semidirect
87. #13063318C2×C4semidirect
95. C4⋊C4×D43C2×C4semidirect
117. C42×D43C2×C4semidirect
131. #126×C43C2×C4semidirect
182. C4⋊C4×C43C22×C4semidirect
188. C42×C43C22×C4semidirect
196. C4⋊Dic43C22×C4semidirect
199. Dic43⋊C4C22×C4semidirect
200. Dic43⋊C4C22×C4semidirect
210. C4×Dic43C22×C4semidirect
261. C4×D43#126direct (N × H)
281. C4×C43C2×#126semidirect
287. Dic43C2×#126semidirect
296. C4×#126D43direct (N × H)
308. D43C4×#126direct (N × H)
338. #387C2×D43semidirect
342. #383C2×D43semidirect
350. C4×C4⋊C4C2×D43semidirect
366. C43C2×D43semidirect
367. C43C2×C4×#126semidirect
383. #126C4×D43direct (N × H)
482. C4⋊C4C2×C4×D43semidirect
504. C42C2×C4×D43semidirect
580. C4#126×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#126×D432
#191371492
C4×#130633202
#126×Dic432
C4×#130633192
#191371452
C4×#130633182
#191371432
#388×D432
#387×D432
#383×D432
C4×C4⋊C4×D432
C4×C22⋊C4×D432
C43×D432
C4×#126×C432
C2×C4×#12643