Finite Group Databasebeta

← C4×#14583079 #25102486

Subgroups — C4×#14583079 #25102486

Order 11008.

1442 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063370C211yesmaximal, characteristic
2C2×#14583079C211yesmaximal, characteristic
3C4×#13063358C212yesmaximal, complemented
4C4×#13063312C211yesmaximal, characteristic, complemented
5#19134981C211yesmaximal, characteristic, complemented
6#19134963C212yesmaximal, complemented
7#19134831C212yesmaximal, complemented
8#19134807C211yesmaximal, characteristic, complemented
9#19134551C211yesmaximal, characteristic
10C4×#13063251C212yesmaximal, complemented
11C4×#100×C43C211yesmaximal, characteristic, complemented
12C2×#13063370C2211yescharacteristic
13C2×#13063358C2212yes—
14C2×#13063312C2211yescharacteristic
15#14583380C2212yes—
16#14583378—22no—
17#14583374C2211yescharacteristic
18#14583372—22no—
19#14583371—22no—
20C4×#10621898C2212yes—
21C4×#10621900—22no—
22C2×C4×Dic86C2211yescharacteristic, complemented
23C2×C4×C22⋊D43—22no—
24C4×D4×D43—22no—
25#14583079C418yesdirect product factor
26#14583007—22no—
27#14583001—22no—
28C4×Dic172—22no—
29C4×#10621873—22no—
30#14582941C2212yescomplemented
31C2×#13063251C2212yes—
32C2×#13063251C2212yes—
33#14582909C2212yescomplemented
34#14582901C2212yes—
35#14582804C2211yescharacteristic, complemented
36#14582802C2211yescharacteristic
37#14582793—22no—
38#14582764C2211yescharacteristic, complemented
39C4×C22⋊Dic43—22no—
40C42×Dic43C2211yescharacteristic, complemented
41#14582660C2212yescomplemented
42#14582660C2212yescomplemented
43C2×C4×D4×C43C2211yescharacteristic
44C2×#100×C43C2211yescharacteristic
45C2×#100×C43C2211yescharacteristic
46C4×M16×C43C2212yescomplemented
47C43×#343C2212yescomplemented
48#13063370—22no—
49#13063370—24no—
50#13063370C2×C414yes—
51C2×#10621898C2312yes—
52C2×#10621900—22no—
53C22×Dic86C2311yescharacteristic
54C22×C22⋊D43—22no—
55C2×D4×D43—22no—
56C22×C4×D43—22no—
57#13063358—24no—
58#13063358C2×C418yescomplemented
59C2×Dic172—22no—
60C2×#10621873—22no—
61#13063312—22no—
62#13063312C2×C414yescomplemented
63C4×Dic86—22no—
64C4×Dic86—22no—
65C4×Dic86D412yes—
66C4×Dic86D412yes—
67#13063290—22no—
68C4×D172D412yes—
69C4×D172D412yes—
70D4×Dic43—22no—
71D4×Dic43—22no—
72#13063287—22no—
73C4×C22⋊D43—24no—
74C4×C22⋊D43—24no—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—24no—
77C4×C22⋊D43—22no—
78(C22⋊D43)⋊C4—24no—
79(C22⋊D43)⋊C4—24no—
80#13063284C2312yes—
81#13063283—22no—
82#13063282—22no—
83#13063281—24no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—22no—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—22no—
91C2×(C2×D43)⋊C4—22no—
92C22⋊C4×D43—24no—
93C2×C4×Dic43—22no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99C42×D43—22no—
100#13063259—22no—
101#13063257—22no—
102#13063251—24no—
103#13063251C2×C418yescomplemented
104#13063250—22no—
105#13063250—22no—
106#13063250—22no—
107#13063247—22no—
108C43⋊#95—22no—
109C43⋊#95—22no—
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43D412yes—
112C2×M16×C43C2312yes—
113C2×M16×C43C2312yes—
114C4×D4×C43—22no—
115C4×D4×C43—22no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43D412yes—
118C2×C42×C43C2311yescharacteristic
119#100×C43—22no—
120#100×C43C2×C414yescomplemented
121#97×C43—22no—
122C4×C8×C43—22no—
123C24×C43C2×D412yes—
124C23×D43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—22no—
127C2×D4×C43C22×C412yes—
128C2×D4×C43#4112yes—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—44no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—24no—
137C2×C22⋊D43—28no—
138C2×C22⋊D43—28no—
139C2×C22⋊D43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147#10621900—28no—
148#10621900—28no—
149D4×D43—28no—
150D4×D43—28no—
151#10621898—22no—
152#10621898—22no—
153#10621898C22×C414yes—
154#10621898#4114yes—
155C2×D172C2×D412yes—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—24no—
159C2×C4×D43—22no—
160C2×C4×D43—84no—
161C2×Dic86—22no—
162C2×Dic86—22no—
163C2×Dic86—21no—
164C2×Dic86C22×C412yescomplemented
165C2×Dic86C2×D412yes—
166M16×C43—22no—
167M16×C43—22no—
168M16×C43—22no—
169M16×C43C22×C414yescomplemented
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C4⋊C4×C43—22no—
173C22⋊C4×C43—24no—
174C42×C43C2×D412yes—
175C42×C43C2×D412yes—
176C22⋊Dic43—24no—
177C22⋊Dic43—28no—
178C22⋊Dic43—22no—
179C22⋊Dic43—44no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43C2×D412yes—
185C4⋊Dic43C2×D412yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—42no—
190C4×Dic43—24no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—21no—
195C4×Dic43—22no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C4×Dic43—41no—
199C4×Dic43—41no—
200C4×Dic43C22×C412yescomplemented
201Dic172—28no—
202#10621873—28no—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43C4×D414yes—
208C23×C43C22×D411yescharacteristic
209C22×D43—22no—
210C22×D43—28no—
211C22×D43—82no—
212C22×D43—82no—
213D4×C43—24no—
214D4×C43—24no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—41no—
218C2×C4×C43—44no—
219C2×C4×C43—42no—
220C2×C4×C43—82no—
221C2×C4×C43#12012yes—
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43C23×C411yescharacteristic
225C2×C4×C43C22×D412yes—
226C2×C4×C43C2×#4112yes—
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—216no—
229C22⋊D43—24no—
230C22⋊D43—24no—
231C2×Dic43—28no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—42no—
245C2×Dic43—41no—
246C2×Dic43—82no—
247C2×Dic43—82no—
248D172—22no—
249D172C4×D414yes—
250C4×D43—24no—
251C4×D43—24no—
252C4×D43—44no—
253C4×D43—82no—
254C4×D43—84no—
255Dic86—22no—
256Dic86—24no—
257Dic86—42no—
258Dic86C4×D414yes—
259C8×C43—24no—
260C8×C43—42no—
261C4×#455—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—24no—
265C22×C43—44no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—82no—
269C22×C43C2×C4×D411yescharacteristic
270C22×C43C2×#12011yescharacteristic
271C22×C43#52511yescharacteristic
272C2×D43—24no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—88no—
276C4×C43—21no—
277C4×C43—22no—
278C4×C43—42no—
279C4×C43#45512yescomplemented
280C4×C43C2×C4×D412yes—
281C4×C43#52512yes—
282Dic43—24no—
283Dic43—42no—
284Dic43—42no—
285Dic43—42no—
286Dic43—42no—
287Dic43—42no—
288Dic43—81no—
289C4×H(5,𝔽2)—431no—
290C2×#455—431no—
291C4×#137—432no—
292C4×#124—431no—
293#1885—431no—
294#1882—432no—
295#1860—432no—
296#1856—431no—
297#1792—431no—
298C4×#104—432no—
299C4×#100D4311yescharacteristic, complemented
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—44no—
303C2×C43C4×#12011yescharacteristic
304C2×C43C2×#45511yescharacteristic
305C2×C43#301811yescharacteristic
306D43—44no—
307C2×H(5,𝔽2)—431no—
308C2×#137—432no—
309C2×#124—431no—
310#520—432no—
311#520—862no—
312#518—431no—
313#518—862no—
314#518—862no—
315C4×#41—432no—
316C4×#41—862no—
317C2×C4×Q8—431no—
318C2×C4×D4—862no—
319C2×C4×D4—862no—
320C2×C4×D4C2×D4311yescharacteristic
321#455—438no—
322#441—862no—
323#440—862no—
324C4×Q16—862no—
325C4×SD16—862no—
326#428—432no—
327C2×#104—432no—
328C2×#104—432no—
329#419—432no—
330#417—432no—
331C2×#100C2×D4311yescharacteristic
332C2×#100C2×D4311yescharacteristic
333C4×M16C2×D4312yescomplemented
334#391—431no—
335#390—431no—
336#388—862no—
337#382—431no—
338C4×C22⋊C4—862no—
339C43—431no—
340#343C2×D4312yescomplemented
341#339—432no—
342#339—432no—
343C43C4×#45511yescharacteristic, complemented, Sylow
344H(5,𝔽2)—434no—
345H(5,𝔽2)—864no—
346H(5,𝔽2)—862no—
347C2×#41—432no—
348C2×#41—862no—
349C22×Q8—431no—
350C22×D4—862no—
351C22×D4—862no—
352C22×D4C22×D4311yescharacteristic
353C23×C4—862no—
354C23×C4D17212yes—
355#137—438no—
356#137—864no—
357C2×Q16—862no—
358C2×SD16—862no—
359C2×M16C22×D4312yes—
360C2×M16C22×D4312yes—
361#124—434no—
362#124—862no—
363C4×Q8—432no—
364C4×Q8—432no—
365C4×Q8—862no—
366C4×Q8—862no—
367C4×Q8—862no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—432no—
371C4×D4—432no—
372C4×D4—864no—
373C4×D4—864no—
374C4×D4—862no—
375C4×D4—862no—
376C4×D4—862no—
377C4×D4—864no—
378C4×D4—864no—
379C4×D4—862no—
380C4×D4—864no—
381C4×D4—862no—
382#117—432no—
383#117—864no—
384#117—862no—
385#117—862no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4—862no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C22⋊C4—864no—
392C2×C22⋊C4—862no—
393C2×C22⋊C4—862no—
394C2×C22⋊C4—862no—
395C2×C22⋊C4—862no—
396C2×C22⋊C4D17212yes—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—862no—
400C2×C42—862no—
401C2×C42—861no—
402C2×C42—861no—
403C2×C42—861no—
404C2×C42C22×D4311yescharacteristic
405#107—862no—
406#106—862no—
407#104—438no—
408#104—864no—
409#103—862no—
410#103—862no—
411#103—862no—
412#102—862no—
413#100—22no—
414#100C4×D4314yescomplemented
415#97—22no—
416C4×C8—22no—
417#95—862no—
418#95—862no—
419C24—862no—
420C24C2×D17212yes—
421#41—434no—
422#41—434no—
423#41—868no—
424#41—868no—
425#41—862no—
426#41—862no—
427C2×Q8—432no—
428C2×Q8—432no—
429C2×Q8—861no—
430C2×Q8—862no—
431C2×Q8—862no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—432no—
435C2×D4—868no—
436C2×D4—868no—
437C2×D4—864no—
438C2×D4—868no—
439C2×D4—868no—
440C2×D4—862no—
441C2×D4C2×C4×D4312yes—
442C2×D4#1062189812yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—44no—
446C22×C4—864no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—861no—
457C22×C4—3444no—
458C22×C4C2×D17211yescharacteristic
459C22×C4C2×D17212yes—
460C22×C4C2×D17211yescharacteristic
461C22×C4C23×D4311yescharacteristic
462Q16—868no—
463SD16—868no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16C2×C4×D4314yescomplemented
468C2×C8—22no—
469C2×C8—22no—
470C4⋊C4—22no—
471C4⋊C4—432no—
472C4⋊C4—432no—
473C4⋊C4—864no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—1722no—
478C22⋊C4—24no—
479C22⋊C4—864no—
480C22⋊C4—864no—
481C22⋊C4—868no—
482C22⋊C4—862no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C22⋊C4—1724no—
486C42—432no—
487C42—864no—
488C42—862no—
489C42—862no—
490C42—862no—
491C42—861no—
492C42—862no—
493C42—1722no—
494C42—1722no—
495C42—1721no—
496C42—1721no—
497C42D4×D4312yes—
498C42D4×D4312yes—
499C23—22no—
500C23—22no—
501C23—42no—
502C23—42no—
503C23—868no—
504C23—862no—
505C23—3442no—
506C23—3442no—
507C23C4×D17214yes—
508C23C22×D17211yescharacteristic
509Q8—434no—
510Q8—862no—
511Q8—864no—
512Q8—1722no—
513D4—24no—
514D4—24no—
515D4—434no—
516D4—8616no—
517D4—864no—
518D4—864no—
519D4—862no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—868no—
527C2×C4—862no—
528C2×C4—864no—
529C2×C4—864no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—3442no—
536C2×C4—3444no—
537C2×C4—3442no—
538C2×C4—3442no—
539C2×C4—1722no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1724no—
548C2×C4#1306329512yes—
549C2×C4#1306329511yescharacteristic
550C2×C4#1306329511yescharacteristic
551C2×C4C22×C4×D4311yescharacteristic
552C2×C4C2×D4×D4312yes—
553C2×C4#41×D4312yes—
554C2×C4C2×#1062189811yescharacteristic
555C8—24no—
556C8—42no—
557C22—21no—
558C22—21no—
559C22—24no—
560C22—44no—
561C22—42no—
562C22—42no—
563C22—82no—
564C22—864no—
565C22—3448no—
566C22—1722no—
567C22—1722no—
568C22C2×C4×D17211yescharacteristic
569C22C2×#1306329511yescharacteristic
570C22#1458341111yescharacteristic
571C4—22no—
572C4—21no—
573C4—42no—
574C4—864no—
575C4—3441no—
576C4—1722no—
577C4—1722no—
578C4—1722no—
579C4—1722no—
580C4—1722no—
581C4#1458307912yesdirect product factor
582C4C4×D4×D4312yes—
583C4#1458340812yes—
584C2—21no—
585C2—21no—
586C2—44no—
587C2—1724no—
588C2C4×#1306329511yescharacteristic
589C2C2×#1458307911yescharacteristic
590C2#1914394811yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#100×C43C2
socleC22×C43C2×#120
prime radicalC2×#13063370C22
cosocleC22×C4×C43C24
hypercenterC4×#100D43
hypocenterC43C4×#455
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
3. C4×#13063358C2semidirect
4. C4×#13063312C2semidirect
5. #19134981C2semidirect
6. #19134963C2semidirect
7. #19134831C2semidirect
8. #19134807C2semidirect
10. C4×#13063251C2semidirect
11. C4×#100×C43C2semidirect
22. C2×C4×Dic86C22semidirect
25. #14583079C4direct (N × H)
30. #14582941C22semidirect
33. #14582909C22semidirect
35. #14582804C22semidirect
38. #14582764C22semidirect
40. C42×Dic43C22semidirect
41. #14582660C22semidirect
42. #14582660C22semidirect
46. C4×M16×C43C22semidirect
47. C43×#343C22semidirect
58. #13063358C2×C4semidirect
62. #13063312C2×C4semidirect
103. #13063251C2×C4semidirect
120. #100×C43C2×C4semidirect
164. C2×Dic86C22×C4semidirect
169. M16×C43C22×C4semidirect
200. C4×Dic43C22×C4semidirect
279. C4×C43#455semidirect
299. C4×#100D43semidirect
333. C4×M16C2×D43semidirect
340. #343C2×D43semidirect
343. C43C4×#455semidirect
414. #100C4×D43semidirect
467. M16C2×C4×D43semidirect
581. C4#14583079direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130633702
C2×#145830792
C4×#130633582
C4×#130633122
#191349812
#191349632
#191348312
#191348072
#191345512
C4×#130632512
C4×#100×C432
C4×#45543