Finite Group Databasebeta

← C4×#14583072 #25102493

Subgroups — C4×#14583072 #25102493

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
1C2×#14583072C211yesmaximal, characteristic
2C4×#13063350C212yesmaximal, complemented
3C4×#13063314C211yesmaximal, characteristic, complemented
4#19134998C211yesmaximal, characteristic, complemented
5#19134971C212yesmaximal, complemented
6#19134828C212yesmaximal, complemented
7#19134810C211yesmaximal, characteristic, complemented
8#19134554C211yesmaximal, characteristic, complemented
9C4×#13063252C212yesmaximal, complemented
10C4×#13063244C211yesmaximal, characteristic, complemented
11C4×2−1+4×C43C211yesmaximal, characteristic, complemented
12C2×#13063350C2212yes—
13C2×#13063314C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583072C418yesdirect product factor
16#14583009—22no—
17#14582997—22no—
18C4×#10621884—22no—
19C4×#10621882—22no—
20#14582942C2212yes—
21C2×#13063252C2212yes—
22C2×#13063252C2212yes—
23#14582903C2212yes—
24#14582900C2212yes—
25C2×#13063244C2211yescharacteristic
26C2×#13063244C2211yescharacteristic
27C4×#10621877C2212yes—
28#14582806C2211yescharacteristic
29#14582800C2211yescharacteristic
30#14582789—22no—
31#14582764C2211yescharacteristic
32C4×(C2×D43)⋊C4—22no—
33C42×Dic43C2211yescharacteristic
34#14582668C2212yes—
35#14582658C2212yes—
36#14582658C2212yes—
37C2×2−1+4×C43C2211yescharacteristic
38C43×#520—22no—
39C43×#520—22no—
40C43×#520C2212yes—
41C43×#519—22no—
42C43×#519C2211yescharacteristic
43C4×#41×C43—22no—
44C4×#41×C43—22no—
45C4×#41×C43C2212yes—
46C2×C4×Q8×C43—22no—
47C2×C4×Q8×C43C2211yescharacteristic
48C22×D172C2311yescharacteristic
49C22×C4×D43—21no—
50#13063350—24no—
51#13063350C2×C418yescomplemented
52C2×#10621884—22no—
53C2×#10621882—22no—
54C2×#10621877C2312yes—
55C2×#10621877C2312yes—
56#13063314—22no—
57#13063314C2×C414yescomplemented
58C4×D172—22no—
59C4×D172—22no—
60C2×C4⋊Dic43C2311yescharacteristic
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—21no—
63C2×(C2×D43)⋊C4—22no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43C2311yescharacteristic
67C2×C4×Dic43C2311yescharacteristic
68#13063258—22no—
69#13063256—22no—
70#13063252—24no—
71#13063252C2×C418yescomplemented
72#13063249—22no—
73#13063246—22no—
74#13063245—22no—
75#13063245—22no—
76#13063244—22no—
77#13063244C2×C414yescomplemented
78#13063236—22no—
79C4×C43⋊C8—22no—
80C43⋊#95—22no—
81C43⋊#95—22no—
822−1+4×C43—24no—
832−1+4×C43—22no—
842−1+4×C43C2×C414yescomplemented
85C2×#41×C43—22no—
86C2×#41×C43—22no—
87C2×#41×C43C2312yes—
88C22×Q8×C43—22no—
89C22×Q8×C43C2311yescharacteristic
90C4×Q8×C43—22no—
91C4×Q8×C43—24no—
92C4×Q8×C43—22no—
93C4×Q8×C43—22no—
94C4×Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×Q8×C43—22no—
97C4×Q8×C43—22no—
98C4×Q8×C43D412yes—
99C4×Q8×C43D412yes—
100C4×D4×C43—22no—
101C4×D4×C43—24no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105C4×D4×C43—24no—
106C4×D4×C43—22no—
107C4×D4×C43D412yes—
108C4×D4×C43D412yes—
109#117×C43—24no—
110#117×C43—24no—
111#117×C43—22no—
112#117×C43—22no—
113#117×C43—22no—
114#117×C43C2312yes—
115C2×C4⋊C4×C43—24no—
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43D412yes—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—24no—
120C2×C42×C43—22no—
121C2×C42×C43D412yes—
122C2×C42×C43C2311yescharacteristic
123C23×D43—21no—
124#41×C43—28no—
125#41×C43—28no—
126#41×C43—28no—
127#41×C43—28no—
128#41×C43—22no—
129#41×C43—22no—
130#41×C43C22×C414yes—
131#41×C43#4114yes—
132C2×Q8×C43—22no—
133C2×Q8×C43—28no—
134C2×Q8×C43—28no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
137C2×Q8×C43C22×C412yes—
138C2×Q8×C43C2×D412yes—
139C2×Q8×C43#4112yes—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43C2×D412yes—
143C22×C4×C43—24no—
144C22×C4×C43—22no—
145C22×C4×C43—24no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C2×D172—21no—
157C2×D172—22no—
158C2×D172—22no—
159C2×D172C22×C412yes—
160C2×C4×D43—44no—
161C2×C4×D43—41no—
162C2×C4×D43—41no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—24no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43C2×D412yes—
171C4⋊C4×C43C2×D412yes—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C42×C43—24no—
177C42×C43—24no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43—22no—
181C42×C43—22no—
182C42×C43—22no—
183C42×C43C2×D412yes—
184C42×C43C2×D412yes—
185#10621884—28no—
186#10621882—28no—
187(C2×D43)⋊C4—28no—
188(C2×D43)⋊C4—44no—
189(C2×D43)⋊C4—42no—
190C4⋊Dic43—22no—
191C4×Dic43—21no—
192C4×Dic43—22no—
193C4×Dic43—42no—
194C4×Dic43—42no—
195C4×Dic43C22×C412yes—
196#10621877—22no—
197#10621877—22no—
198#10621877—22no—
199#10621877C22×C414yes—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C23×C43—22no—
203C23×C43C22×D411yescharacteristic
204C22×D43—22no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—41no—
208C22×D43—41no—
209Q8×C43—28no—
210Q8×C43—24no—
211Q8×C43—22no—
212Q8×C43—24no—
213Q8×C43C4×D414yes—
214D4×C43—28no—
215D4×C43—24no—
216D4×C43—24no—
217D4×C43—22no—
218D4×C43C4×D414yes—
219C2×C4×C43—216no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—41no—
230C2×C4×C43—44no—
231C2×C4×C43—42no—
232C2×C4×C43—82no—
233C2×C4×C43—84no—
234C2×C4×C43C4×D414yes—
235C2×C4×C43#12012yes—
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43#12011yescharacteristic
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D412yes—
240C2×C4×C43C2×#4112yes—
241C2×C4×C43C2×#4111yescharacteristic
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—42no—
249C2×Dic43—41no—
250D172—24no—
251D172—42no—
252C4×D43—82no—
253C4×D43—82no—
254C43⋊C8—24no—
255C43⋊C8—42no—
256C4×#454—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—24no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43C2×C4×D411yescharacteristic
263C22×C43C2×#12011yescharacteristic
264C22×C43#52511yescharacteristic
265C2×D43—44no—
266C2×D43—42no—
267C2×D43—82no—
268C2×D43—81no—
269C2×D43—81no—
270C4×C43—21no—
271C4×C43—22no—
272C4×C43—24no—
273C4×C43—24no—
274C4×C43—42no—
275C4×C43—42no—
276C4×C43—42no—
277C4×C43#45412yescomplemented
278C4×C43C2×C4×D412yes—
279C4×C43#52512yes—
280Dic43—42no—
281Dic43—42no—
282Dic43—81no—
283C4×2−1+4D4311yescharacteristic, complemented
284C2×#454—431no—
285C4×AGL(1,ℤ/8)—432no—
286C4×#124—431no—
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—44no—
297C2×C43C4×#12011yescharacteristic
298C2×C43C2×#45411yescharacteristic
299C2×C43#301811yescharacteristic
300D43—82no—
301C2×2−1+4C2×D4311yescharacteristic
302C2×AGL(1,ℤ/8)—432no—
303C2×#124—431no—
304#520—22no—
305#520—22no—
306#520C2×D4312yes—
307#519—22no—
308#519C2×D4311yescharacteristic
309C4×#41—22no—
310C4×#41—22no—
311C4×#41C2×D4312yes—
312C2×C4×Q8—22no—
313C2×C4×Q8C2×D4311yescharacteristic
314C2×C4×D4—431no—
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#391—431no—
329#390—431no—
330#388—862no—
331#382—431no—
332C4×C22⋊C4—862no—
333C43—431no—
334#343—432no—
335#339—432no—
336#339—432no—
337C43C4×#45411yescharacteristic, complemented, Sylow
3382−1+4—24no—
3392−1+4—22no—
3402−1+4C4×D4314yescomplemented
341C2×#41—22no—
342C2×#41—22no—
343C2×#41C22×D4312yes—
344C22×Q8—22no—
345C22×Q8C22×D4311yescharacteristic
346C22×D4—431no—
347C23×C4—861no—
348AGL(1,ℤ/8)—438no—
349AGL(1,ℤ/8)—864no—
350C2×SD16—862no—
351C2×D8—862no—
352C2×M16—432no—
353C2×M16—432no—
354#124—434no—
355#124—862no—
356C4×Q8—22no—
357C4×Q8—24no—
358C4×Q8—22no—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8C22⋊D4312yes—
365C4×Q8C22⋊D4312yes—
366C4×D4—22no—
367C4×D4—24no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—24no—
372C4×D4—22no—
373C4×D4—862no—
374C4×D4—862no—
375C4×D4C22⋊D4312yes—
376C4×D4C22⋊D4312yes—
377#117—24no—
378#117—24no—
379#117—22no—
380#117—22no—
381#117—22no—
382#117C22×D4312yes—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4C22⋊D4312yes—
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—862no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—862no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42C22⋊D4312yes—
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—862no—
412#95—862no—
413C24—861no—
414#41—28no—
415#41—28no—
416#41—28no—
417#41—28no—
418#41—22no—
419#41—22no—
420#41C2×C4×D4314yes—
421#41#1062189814yes—
422C2×Q8—22no—
423C2×Q8—28no—
424C2×Q8—28no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8C2×C4×D4312yes—
428C2×Q8#1062189812yes—
429C2×Q8C2×C22⋊D4312yes—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—432no—
433C2×D4—862no—
434C2×D4—862no—
435C2×D4—861no—
436C2×D4C2×C22⋊D4312yes—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—1724no—
446C22×C4—1721no—
447C22×C4—1721no—
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—22no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—862no—
469C4⋊C4C2×C22⋊D4312yes—
470C4⋊C4C2×C22⋊D4312yes—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—868no—
476C22⋊C4—1724no—
477C22⋊C4—1722no—
478C42—24no—
479C42—24no—
480C42—22no—
481C42—22no—
482C42—22no—
483C42—22no—
484C42—22no—
485C42—432no—
486C42—861no—
487C42—862no—
488C42—1722no—
489C42—1722no—
490C42C2×C22⋊D4312yes—
491C42C2×C22⋊D4312yes—
492C23—22no—
493C23—862no—
494C23—1722no—
495C23—1722no—
496C23—1721no—
497C23—1721no—
498C23C22×C22⋊D4311yescharacteristic
499Q8—28no—
500Q8—24no—
501Q8—24no—
502Q8—22no—
503Q8C4×C22⋊D4314yes—
504D4—28no—
505D4—24no—
506D4—24no—
507D4—22no—
508D4—864no—
509D4—1722no—
510D4C4×C22⋊D4314yes—
511C2×C4—216no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—82no—
525C2×C4—84no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—3442no—
529C2×C4—3442no—
530C2×C4—1722no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4C4×C22⋊D4314yes—
537C2×C4#1306329411yescharacteristic
538C2×C4#1306329412yes—
539C2×C4#1306329411yescharacteristic
540C2×C4C22×C4×D4311yescharacteristic
541C2×C4C22×C22⋊D4312yes—
542C2×C4C2×#1062189812yes—
543C2×C4C2×#1062189811yescharacteristic
544C8—864no—
545C8—1722no—
546C22—21no—
547C22—21no—
548C22—24no—
549C22—42no—
550C22—42no—
551C22—3442no—
552C22—3441no—
553C22—3441no—
554C22—1724no—
555C22—1722no—
556C22C2×C4×C22⋊D4311yescharacteristic
557C22C2×#1306329411yescharacteristic
558C22#1458341011yescharacteristic
559C4—22no—
560C4—24no—
561C4—24no—
562C4—21no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—3441no—
567C4—1722no—
568C4—1722no—
569C4#1458307212yesdirect product factor
570C4C2×C4×C22⋊D4312yes—
571C4#1458341012yes—
572C2—21no—
573C2—21no—
574C2—44no—
575C2—3442no—
576C2C4×#1306329411yescharacteristic
577C2C2×#1458307211yescharacteristic
578C2#1914394411yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×2−1+4×C43C2
socleC22×C43C2×#120
prime radicalC2×#14583072C2
cosocleC22×C4×C43C24
hypercenterC4×2−1+4D43
hypocenterC43C4×#454
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. C4×#13063350C2semidirect
3. C4×#13063314C2semidirect
4. #19134998C2semidirect
5. #19134971C2semidirect
6. #19134828C2semidirect
7. #19134810C2semidirect
8. #19134554C2semidirect
9. C4×#13063252C2semidirect
10. C4×#13063244C2semidirect
11. C4×2−1+4×C43C2semidirect
15. #14583072C4direct (N × H)
51. #13063350C2×C4semidirect
57. #13063314C2×C4semidirect
71. #13063252C2×C4semidirect
77. #13063244C2×C4semidirect
84. 2−1+4×C43C2×C4semidirect
277. C4×C43#454semidirect
283. C4×2−1+4D43semidirect
337. C43C4×#454semidirect
340. 2−1+4C4×D43semidirect
569. C4#14583072direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145830722
C4×#130633502
C4×#130633142
#191349982
#191349712
#191348282
#191348102
#191345542
C4×#130632522
C4×#130632442
C4×2−1+4×C432
C4×#45443