Finite Group Databasebeta

← C4×#14583071 #25102491

Subgroups — C4×#14583071 #25102491

Order 11008.

1390 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063373C211yesmaximal, characteristic, complemented
2C2×#14583071C211yesmaximal, characteristic
3C4×#13063351C212yesmaximal, complemented
4#19134999C211yesmaximal, characteristic, complemented
5#19134974C212yesmaximal, complemented
6#19134827C212yesmaximal, complemented
7#19134809C211yesmaximal, characteristic, complemented
8#19134553C211yesmaximal, characteristic, complemented
9C4×#13063253C212yesmaximal, complemented
10C4×#13063244C211yesmaximal, characteristic, complemented
11C4×#124×C43C211yesmaximal, characteristic, complemented
12C2×#13063373C2211yescharacteristic
13C2×#13063351C2212yes—
14#14583381—22no—
15#14583380—22no—
16#14583380C2212yes—
17#14583377C2211yescharacteristic
18#14583375—22no—
19C4×#10621902—22no—
20C4×#10621898—22no—
21C4×#10621898C2212yes—
22C4×Q8×D43—22no—
23#14583071C418yesdirect product factor
24#14583009—22no—
25#14582999—22no—
26C4×#10621883—22no—
27C4×#10621882—22no—
28#14582939C2212yes—
29C2×#13063253C2212yes—
30C2×#13063253C2212yes—
31#14582904C2212yes—
32#14582898C2212yes—
33C2×#13063244C2211yescharacteristic
34C2×#13063244C2211yescharacteristic
35C4×#10621877C2212yes—
36#14582668C2212yes—
37#14582659C2212yes—
38#14582659C2212yes—
39C2×#124×C43C2211yescharacteristic
40C2×C4×Q8×C43C2211yescharacteristic
41C2×C4×D4×C43C2211yescharacteristic
42C43×#391C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#388—22no—
45C43×#382C2211yescharacteristic
46C4×C22⋊C4×C43—22no—
47C43×C43C2211yescharacteristic
48#13063373—22no—
49#13063373—24no—
50#13063373C2×C414yescomplemented
51C2×#10621902—22no—
52C2×#10621898—22no—
53C2×#10621898C2312yes—
54C2×Q8×D43—22no—
55#13063351—24no—
56#13063351C2×C418yescomplemented
57C2×#10621883—22no—
58C2×#10621882—22no—
59C2×#10621877C2312yes—
60C2×#10621877C2312yes—
61Q8×Dic43—22no—
62Q8×Dic43—22no—
63C4×Dic86—22no—
64C4×Dic86—22no—
65C4×Dic86D412yes—
66C4×Dic86D412yes—
67#13063290—24no—
68#13063290—22no—
69C4×D172—22no—
70C4×D172—22no—
71C4×D172D412yes—
72C4×D172D412yes—
73#13063287—24no—
74#13063287—22no—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—24no—
77C4×C22⋊D43—22no—
78#13063284—22no—
79#13063284C2312yes—
80#13063283—24no—
81#13063283—22no—
82#13063282—24no—
83#13063282—22no—
84C4⋊C4×D43—24no—
85C4⋊C4×D43—22no—
86C42×D43—24no—
87C42×D43—22no—
88#13063258—22no—
89#13063256—22no—
90#13063253—24no—
91#13063253C2×C418yescomplemented
92#13063248—22no—
93#13063246—22no—
94#13063246—22no—
95#13063245—22no—
96#13063244—22no—
97#13063244C2×C414yescomplemented
98#13063236—22no—
99C4×C43⋊C8—22no—
100C22×Q8×C43C2311yescharacteristic
101C22×D4×C43C2311yescharacteristic
102C23×C4×C43—21no—
103#124×C43—22no—
104#124×C43C2×C414yescomplemented
105C4×Q8×C43—22no—
106C4×Q8×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C2×C4⋊C4×C43D412yes—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—22no—
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43D412yes—
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#95×C43—22no—
122#95×C43—22no—
123C24×C43—21no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43C22×C412yes—
127C2×Q8×C43#4112yes—
128C2×D4×C43—21no—
129C2×D4×C43—22no—
130C2×D4×C43—22no—
131C2×D4×C43C22×C412yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—44no—
136C22×C4×C43—41no—
137C22×C4×C43—41no—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C2×C22⋊D43—22no—
144#10621902—28no—
145#10621902—28no—
146Q8×D43—28no—
147Q8×D43—28no—
148#10621898—28no—
149#10621898—28no—
150#10621898—22no—
151#10621898—22no—
152#10621898C22×C414yes—
153#10621898#4114yes—
154C2×D172—22no—
155C2×D172C2×D412yes—
156C2×C4×D43—24no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—24no—
160C2×C4×D43—22no—
161C2×Dic86—22no—
162C2×Dic86C2×D412yes—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C22⋊C4×C43—28no—
167C22⋊C4×C43—44no—
168C22⋊C4×C43—42no—
169C42×C43—22no—
170C42×C43—22no—
171C42×C43—21no—
172C42×C43—22no—
173C42×C43—42no—
174C42×C43—42no—
175C42×C43C22×C412yes—
176C42×C43C2×D412yes—
177C42×C43C2×D412yes—
178C22⋊Dic43—22no—
179#10621883—28no—
180#10621882—28no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—22no—
183(C2×D43)⋊C4—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43C2×D412yes—
187C4⋊Dic43C2×D412yes—
188Dic43⋊C4—24no—
189Dic43⋊C4—22no—
190Dic43⋊C4—22no—
191C4×Dic43—24no—
192C4×Dic43—24no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—22no—
196#10621877—22no—
197#10621877—22no—
198#10621877—22no—
199#10621877C22×C414yes—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C23×C43—22no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43C22×D411yescharacteristic
208C22×D43—22no—
209Q8×C43—24no—
210Q8×C43—24no—
211D4×C43—24no—
212D4×C43—42no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—82no—
228C2×C4×C43—82no—
229C2×C4×C43C4×D414yes—
230C2×C4×C43#12012yes—
231C2×C4×C43#12011yescharacteristic
232C2×C4×C43#12011yescharacteristic
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43C22×D412yes—
235C2×C4×C43C2×#4112yes—
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—24no—
238C22⋊D43—24no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242D172—28no—
243D172—22no—
244D172C4×D414yes—
245C4×D43—216no—
246C4×D43—24no—
247C4×D43—24no—
248C4×D43—44no—
249C4×D43—82no—
250C4×D43—84no—
251Dic86—28no—
252Dic86—22no—
253Dic86C4×D414yes—
254C43⋊C8—24no—
255C43⋊C8—42no—
256C4×#454—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—44no—
260C22×C43—42no—
261C22×C43—82no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43C2×C4×D411yescharacteristic
265C22×C43C2×#12011yescharacteristic
266C22×C43#52511yescharacteristic
267C2×D43—24no—
268C2×D43—42no—
269C2×D43—42no—
270C4×C43—21no—
271C4×C43—22no—
272C4×C43—24no—
273C4×C43—42no—
274C4×C43—42no—
275C4×C43—42no—
276C4×C43—81no—
277C4×C43#45412yescomplemented
278C4×C43C2×C4×D412yes—
279C4×C43#52512yes—
280Dic43—24no—
281Dic43—42no—
282Dic43—42no—
283C4×2−1+4—431no—
284C2×#454—431no—
285C4×AGL(1,ℤ/8)—432no—
286C4×#124D4311yescharacteristic, complemented
287#1888—431no—
288#1883—432no—
289#1860—432no—
290#1857—431no—
291#1793—431no—
292C4×#104—432no—
293C4×#101—431no—
294C2×C43—21no—
295C2×C43—21no—
296C2×C43—82no—
297C2×C43C4×#12011yescharacteristic
298C2×C43C2×#45411yescharacteristic
299C2×C43#301811yescharacteristic
300D43—44no—
301C2×2−1+4—431no—
302C2×AGL(1,ℤ/8)—432no—
303C2×#124C2×D4311yescharacteristic
304#520—432no—
305#520—862no—
306#520—862no—
307#519—431no—
308#519—862no—
309C4×#41—432no—
310C4×#41—862no—
311C4×#41—862no—
312C2×C4×Q8—862no—
313C2×C4×Q8C2×D4311yescharacteristic
314C2×C4×D4C2×D4311yescharacteristic
315#454—438no—
316#442—862no—
317#440—862no—
318C4×SD16—862no—
319C4×D8—862no—
320#428—432no—
321C2×#104—432no—
322C2×#104—432no—
323#418—432no—
324#417—432no—
325C2×#101—431no—
326C2×#101—431no—
327C4×M16—432no—
328#391C2×D4311yescharacteristic
329#390C2×D4311yescharacteristic
330#388—22no—
331#382C2×D4311yescharacteristic
332C4×C22⋊C4—22no—
333C43C2×D4311yescharacteristic
334#343—432no—
335#339—432no—
336#339—432no—
337C43C4×#45411yescharacteristic, complemented, Sylow
3382−1+4—434no—
3392−1+4—864no—
3402−1+4—862no—
341C2×#41—432no—
342C2×#41—862no—
343C2×#41—862no—
344C22×Q8—862no—
345C22×Q8C22×D4311yescharacteristic
346C22×D4C22×D4311yescharacteristic
347C23×C4—21no—
348AGL(1,ℤ/8)—438no—
349AGL(1,ℤ/8)—864no—
350C2×SD16—862no—
351C2×D8—862no—
352C2×M16—432no—
353C2×M16—432no—
354#124—22no—
355#124C4×D4314yescomplemented
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—432no—
359C4×Q8—432no—
360C4×Q8—862no—
361C4×Q8—862no—
362C4×Q8—862no—
363C4×Q8—864no—
364C4×Q8—862no—
365C4×Q8—862no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—432no—
369C4×D4—432no—
370C4×D4—862no—
371C4×D4—862no—
372C4×D4—862no—
373C4×D4—864no—
374C4×D4—862no—
375C4×D4—862no—
376C4×D4—864no—
377#117—432no—
378#117—864no—
379#117—862no—
380#117—864no—
381#117—862no—
382#117—862no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4—864no—
385C2×C4⋊C4C22⋊D4312yes—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—22no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—22no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—864no—
394C2×C42—862no—
395C2×C42C22⋊D4312yes—
396C2×C42C22×D4311yescharacteristic
397C2×C42C22×D4311yescharacteristic
398C2×C42C22×D4311yescharacteristic
399#107—862no—
400#106—862no—
401#104—438no—
402#104—864no—
403#103—862no—
404#102—862no—
405#102—862no—
406#102—862no—
407#101—434no—
408#101—862no—
409#97—862no—
410C4×C8—862no—
411#95—22no—
412#95—22no—
413C24—21no—
414#41—434no—
415#41—434no—
416#41—868no—
417#41—868no—
418#41—868no—
419#41—868no—
420#41—862no—
421#41—862no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—432no—
425C2×Q8—862no—
426C2×Q8—868no—
427C2×Q8—868no—
428C2×Q8C2×C4×D4312yes—
429C2×Q8#1062189812yes—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—432no—
434C2×D4—862no—
435C2×D4—862no—
436C2×D4C2×C4×D4312yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—44no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—864no—
444C22×C4—864no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4C2×C22⋊D4312yes—
449C22×C4C2×C22⋊D4311yescharacteristic
450C22×C4C2×C22⋊D4312yes—
451C22×C4C2×C22⋊D4311yescharacteristic
452C22×C4C23×D4311yescharacteristic
453SD16—868no—
454D8—868no—
455M16—434no—
456M16—862no—
457M16—862no—
458M16—862no—
459C2×C8—862no—
460C2×C8—862no—
461C4⋊C4—24no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—432no—
465C4⋊C4—432no—
466C4⋊C4—864no—
467C4⋊C4—862no—
468C4⋊C4—862no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C22⋊C4—28no—
472C22⋊C4—44no—
473C22⋊C4—42no—
474C22⋊C4—864no—
475C22⋊C4—862no—
476C22⋊C4—862no—
477C22⋊C4—862no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—22no—
482C42—42no—
483C42—42no—
484C42—864no—
485C42—864no—
486C42—862no—
487C42—862no—
488C42—862no—
489C42C2×C4×D4312yes—
490C42D4×D4312yes—
491C42D4×D4312yes—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—41no—
496C23—41no—
497C23—862no—
498C23C22×C22⋊D4311yescharacteristic
499Q8—24no—
500Q8—24no—
501Q8—434no—
502Q8—868no—
503Q8—862no—
504D4—24no—
505D4—42no—
506D4—434no—
507D4—868no—
508D4—864no—
509D4—864no—
510D4—862no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—8616no—
528C2×C4—862no—
529C2×C4—864no—
530C2×C4—864no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—3442no—
534C2×C4—3444no—
535C2×C4—1724no—
536C2×C4C4×C22⋊D4314yes—
537C2×C4#1306329311yescharacteristic
538C2×C4#1306329312yes—
539C2×C4#1306329311yescharacteristic
540C2×C4C22×C4×D4311yescharacteristic
541C2×C4C2×D4×D4312yes—
542C2×C4#41×D4312yes—
543C2×C4C2×#1062189811yescharacteristic
544C8—864no—
545C8—1722no—
546C22—21no—
547C22—21no—
548C22—44no—
549C22—42no—
550C22—82no—
551C22—81no—
552C22—81no—
553C22—864no—
554C22—1722no—
555C22—1722no—
556C22C2×C4×C22⋊D4311yescharacteristic
557C22C2×#1306329311yescharacteristic
558C22#1458340611yescharacteristic
559C4—22no—
560C4—24no—
561C4—21no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—81no—
566C4—864no—
567C4—1722no—
568C4—1722no—
569C4#1458307112yesdirect product factor
570C4C4×D4×D4312yes—
571C4#1458340812yes—
572C2—21no—
573C2—21no—
574C2—82no—
575C2—1724no—
576C2C4×#1306329311yescharacteristic
577C2C2×#1458307111yescharacteristic
578C2#1914394311yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#124×C43C2
socleC22×C43C2×#120
prime radicalC2×#14583071C2
cosocleC22×C4×C43C24
hypercenterC4×#124D43
hypocenterC43C4×#454
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. C4×#13063373C2semidirect
3. C4×#13063351C2semidirect
4. #19134999C2semidirect
5. #19134974C2semidirect
6. #19134827C2semidirect
7. #19134809C2semidirect
8. #19134553C2semidirect
9. C4×#13063253C2semidirect
10. C4×#13063244C2semidirect
11. C4×#124×C43C2semidirect
23. #14583071C4direct (N × H)
50. #13063373C2×C4semidirect
56. #13063351C2×C4semidirect
91. #13063253C2×C4semidirect
97. #13063244C2×C4semidirect
104. #124×C43C2×C4semidirect
277. C4×C43#454semidirect
286. C4×#124D43semidirect
337. C43C4×#454semidirect
355. #124C4×D43semidirect
569. C4#14583071direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130633732
C2×#145830712
C4×#130633512
#191349992
#191349742
#191348272
#191348092
#191345532
C4×#130632532
C4×#130632442
C4×#124×C432
C4×#45443