Finite Group Databasebeta

← #454×Dic43 #25102494

Subgroups — #454×Dic43 #25102494

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
12−1+4×Dic43C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×Dic43C212yesmaximal, complemented
3#124×Dic43C211yesmaximal, characteristic, complemented
4#19134999C211yesmaximal, characteristic, complemented
5#19134973C212yesmaximal, complemented
6#19134830C212yesmaximal, complemented
7#19134812C211yesmaximal, characteristic, complemented
8#19134554C211yesmaximal, characteristic, complemented
9#104×Dic43C212yesmaximal, complemented
10#101×Dic43C211yesmaximal, characteristic, complemented
11C2×C43×#454C211yesmaximal, characteristic
12#14583382—22no—
13#14583382—22no—
14#14583382C2212yes—
15#14583377—22no—
16#14583377C2211yescharacteristic
17#41×Dic43—22no—
18#41×Dic43—22no—
19#41×Dic43C2212yes—
20C2×Q8×Dic43—22no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23#14583011—22no—
24#14583000—22no—
25SD16×Dic43—22no—
26D8×Dic43—22no—
27#14582941C2212yes—
28C2×#13063252C2212yes—
29#14582904C2212yes—
30#14582900C2212yes—
31C2×#13063244C2211yescharacteristic
32M16×Dic43C2212yes—
33#14582806C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582792—22no—
36#14582765C2211yescharacteristic
37C22⋊C4×Dic43—22no—
38C42×Dic43C2211yescharacteristic
39#14582667C2212yes—
40#14582660C2212yes—
41#14582659C2212yes—
42C2×2−1+4×C43C2211yescharacteristic
43C2×AGL(1,ℤ/8)×C43C2212yes—
44C2×#124×C43C2211yescharacteristic
45C43×#454C418yescomplemented
46C2×#104×C43C2212yes—
47C2×#101×C43C2211yescharacteristic
48C23×Dic43—21no—
49C2×#10621877C2312yes—
50Q8×Dic43—22no—
51Q8×Dic43—24no—
52Q8×Dic43—22no—
53Q8×Dic43—22no—
54Q8×Dic43—22no—
55Q8×Dic43—22no—
56Q8×Dic43—22no—
57Q8×Dic43—22no—
58Q8×Dic43D412yes—
59Q8×Dic43D412yes—
60D4×Dic43—22no—
61D4×Dic43—24no—
62D4×Dic43—22no—
63D4×Dic43—22no—
64D4×Dic43—22no—
65D4×Dic43—24no—
66D4×Dic43—22no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43D412yes—
70D4×Dic43D412yes—
71#13063284—24no—
72#13063284—24no—
73#13063284—22no—
74#13063284—22no—
75#13063284—22no—
76#13063284C2312yes—
77C2×C4⋊Dic43—24no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43D412yes—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—22no—
84C2×C4×Dic43—24no—
85C2×C4×Dic43—22no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43D412yes—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063257—22no—
93#13063252—24no—
94#13063249—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—22no—
98#13063244—22no—
99#13063235—22no—
100C8×Dic43—22no—
101C43⋊#95—22no—
102C43⋊#95—22no—
1032−1+4×C43—24no—
1042−1+4×C43—22no—
1052−1+4×C43C2×C414yescomplemented
106C2×#41×C43—22no—
107C2×#41×C43—22no—
108C2×#41×C43C2312yes—
109C22×Q8×C43—22no—
110C22×Q8×C43C2311yescharacteristic
111C22×D4×C43C2311yescharacteristic
112AGL(1,ℤ/8)×C43—24no—
113AGL(1,ℤ/8)×C43C2×C418yescomplemented
114C2×SD16×C43—22no—
115C2×D8×C43—22no—
116C2×M16×C43C2312yes—
117#124×C43—22no—
118#124×C43C2×C414yescomplemented
119C2×C22⋊C4×C43—22no—
120C2×C42×C43C2311yescharacteristic
121#104×C43C2×C418yescomplemented
122#101×C43C2×C414yescomplemented
123C24×C43—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—21no—
142C2×D4×C43—22no—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43C22×C412yes—
146C2×D4×C43C2×D412yes—
147C22×C4×C43—24no—
148C22×C4×C43—22no—
149C22×C4×C43—21no—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—24no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—44no—
158C22×Dic43—41no—
159C22×Dic43—41no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D412yes—
162C22×Dic43C2×D411yescharacteristic
163SD16×C43—28no—
164D8×C43—28no—
165M16×C43—22no—
166M16×C43C22×C414yes—
167C2×C8×C43—22no—
168C22⋊C4×C43—28no—
169C42×C43—21no—
170C42×C43C22×C412yes—
171C22⋊Dic43—24no—
172C22⋊Dic43—22no—
173C22⋊Dic43—22no—
174C22⋊Dic43—22no—
175C22⋊Dic43—44no—
176C22⋊Dic43—42no—
177C4⋊Dic43—24no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43—22no—
182C4⋊Dic43—24no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43C2×D412yes—
186C4⋊Dic43C2×D412yes—
187C4×Dic43—24no—
188C4×Dic43—24no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43C2×D412yes—
198C4×Dic43C2×D412yes—
199#10621877—22no—
200#10621877—22no—
201C2×C43⋊C8—22no—
202C23×C43—22no—
203C23×C43—22no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43C22×D411yescharacteristic
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—24no—
218D4×C43—22no—
219D4×C43—42no—
220D4×C43C4×D414yes—
221C2×C4×C43—216no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—22no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C4×D414yes—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C22×D412yes—
233C2×C4×C43C2×#4112yes—
234C2×C4×C43C2×#4111yescharacteristic
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—44no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—41no—
247C2×Dic43—82no—
248C2×Dic43—82no—
249C2×Dic43—84no—
250C2×Dic43—82no—
251C2×Dic43#12011yescharacteristic
252C2×Dic43#12012yes—
253C2×Dic43#12011yescharacteristic
254C8×C43—24no—
255C43⋊C8—42no—
256C4×#454—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—24no—
260C22×C43—44no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—82no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43C2×C4×D411yescharacteristic
268C22×C43C2×#12011yescharacteristic
269C22×C43#52511yescharacteristic
270C4×C43—24no—
271C4×C43—24no—
272C4×C43—42no—
273C4×C43C2×C4×D412yes—
274C4×C43#52512yes—
275Dic43—21no—
276Dic43—22no—
277Dic43—42no—
278Dic43—42no—
279Dic43—42no—
280Dic43—42no—
281Dic43—81no—
282Dic43#45412yesdirect product factor
283C4×2−1+4—431no—
284C2×#454D4311yescharacteristic
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×C43—82no—
298C2×C43C4×#12011yescharacteristic
299C2×C43C2×#45411yescharacteristic
300C2×C43#301811yescharacteristic
301C2×2−1+4C2×D4311yescharacteristic
302C2×AGL(1,ℤ/8)C2×D4312yes—
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—431no—
313C2×C4×Q8—862no—
314C2×C4×D4—431no—
315#454Dic4318yesdirect product factor
316#442—862no—
317#440—862no—
318C4×SD16—862no—
319C4×D8—862no—
320#428—432no—
321C2×#104—432no—
322C2×#104C2×D4312yes—
323#418—432no—
324#417—432no—
325C2×#101—431no—
326C2×#101C2×D4311yescharacteristic
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+4C2×Dic4314yescomplemented
341C2×#41—22no—
342C2×#41—22no—
343C2×#41C22×D4312yes—
344C22×Q8—22no—
345C22×Q8C22×D4311yescharacteristic
346C22×D4C22×D4311yescharacteristic
347C23×C4—861no—
348AGL(1,ℤ/8)—24no—
349AGL(1,ℤ/8)C2×Dic4318yescomplemented
350C2×SD16—22no—
351C2×D8—22no—
352C2×M16—432no—
353C2×M16C22×D4312yes—
354#124—22no—
355#124C2×Dic4314yescomplemented
356C4×Q8—432no—
357C4×Q8—432no—
358C4×Q8—862no—
359C4×Q8—862no—
360C4×Q8—862no—
361C4×Q8—862no—
362C4×Q8—862no—
363C4×Q8—864no—
364C4×Q8—862no—
365C4×Q8—862no—
366C4×D4—432no—
367C4×D4—432no—
368C4×D4—862no—
369C4×D4—862no—
370C4×D4—862no—
371C4×D4—862no—
372C4×D4—864no—
373C4×D4—862no—
374C4×D4—862no—
375C4×D4—864no—
376C4×D4—862no—
377#117—432no—
378#117—862no—
379#117—862no—
380#117—864no—
381#117—864no—
382#117—862no—
383C2×C4⋊C4—432no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—864no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—862no—
391C2×C42—431no—
392C2×C42—432no—
393C2×C42—431no—
394C2×C42—862no—
395C2×C42—864no—
396C2×C42—861no—
397C2×C42—861no—
398C2×C42C22×D4311yescharacteristic
399#107—862no—
400#106—862no—
401#104—864no—
402#104C2×Dic4318yescomplemented
403#103—862no—
404#102—862no—
405#102—862no—
406#102—862no—
407#101—862no—
408#101C2×Dic4314yescomplemented
409#97—862no—
410C4×C8—862no—
411#95—862no—
412#95—862no—
413C24—21no—
414#41—28no—
415#41—28no—
416#41—28no—
417#41—28no—
418#41—22no—
419#41—22no—
420#41#1062190014yes—
421#41C22×Dic4314yes—
422C2×Q8—22no—
423C2×Q8—28no—
424C2×Q8—28no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8D4×D4312yes—
428C2×Q8#1062190012yes—
429C2×Q8C22×Dic4312yes—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4D4×D4312yes—
436C2×D4C22×Dic4312yes—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—432no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—864no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4—1724no—
451C22×C4D4×D4312yes—
452C22×C4C23×D4311yescharacteristic
453SD16—28no—
454D8—28no—
455M16—22no—
456M16—862no—
457M16—862no—
458M16C22×Dic4314yes—
459C2×C8—22no—
460C2×C8—862no—
461C4⋊C4—432no—
462C4⋊C4—432no—
463C4⋊C4—864no—
464C4⋊C4—862no—
465C4⋊C4—862no—
466C4⋊C4—864no—
467C4⋊C4—862no—
468C4⋊C4—862no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C22⋊C4—28no—
472C22⋊C4—862no—
473C22⋊C4—862no—
474C22⋊C4—864no—
475C22⋊C4—862no—
476C22⋊C4—1722no—
477C22⋊C4—1724no—
478C42—21no—
479C42—432no—
480C42—432no—
481C42—862no—
482C42—862no—
483C42—862no—
484C42—862no—
485C42—864no—
486C42—864no—
487C42—862no—
488C42—862no—
489C42—1722no—
490C42—1722no—
491C42C22×Dic4312yes—
492C23—22no—
493C23—22no—
494C23—42no—
495C23—42no—
496C23—41no—
497C23—41no—
498C23C2×D4×D4311yescharacteristic
499Q8—28no—
500Q8—24no—
501Q8—22no—
502Q8—24no—
503Q8D4×Dic4314yes—
504D4—28no—
505D4—24no—
506D4—24no—
507D4—24no—
508D4—22no—
509D4—42no—
510D4D4×Dic4314yes—
511C2×C4—216no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—431no—
521C2×C4—431no—
522C2×C4—432no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—3442no—
529C2×C4—3442no—
530C2×C4—3442no—
531C2×C4—3444no—
532C2×C4—1724no—
533C2×C4—1721no—
534C2×C4—1722no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1722no—
539C2×C4D4×Dic4314yes—
540C2×C4C23×Dic4311yescharacteristic
541C2×C4C2×D4×D4312yes—
542C2×C4C2×#1062190012yes—
543C2×C4C2×#1062190011yescharacteristic
544C8—24no—
545C8—1722no—
546C22—21no—
547C22—21no—
548C22—24no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—82no—
554C22—81no—
555C22—81no—
556C22C2×D4×Dic4311yescharacteristic
557C22#120×D4311yescharacteristic
558C22#1458340511yescharacteristic
559C4—24no—
560C4—24no—
561C4—42no—
562C4—432no—
563C4—862no—
564C4—861no—
565C4—3441no—
566C4—1722no—
567C4—1722no—
568C4—1722no—
569C4—1722no—
570C4C2×D4×Dic4312yes—
571C4#1458340512yes—
572C2—21no—
573C2—21no—
574C2—44no—
575C2—82no—
576C2#120×Dic4311yescharacteristic
577C2#454×D4311yescharacteristic
578C2#1914394211yescharacteristic
subgroupG/H
centerC22#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#454C2
socleC22×C43C2×#120
cosocleC22×C4×C43C24
hypercenterC2×#454D43
hypocenterC43C4×#454
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#454

Complements

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

NH ≅ G/Ntype
1. 2−1+4×Dic43C2semidirect
2. AGL(1,ℤ/8)×Dic43C2semidirect
3. #124×Dic43C2semidirect
4. #19134999C2semidirect
5. #19134973C2semidirect
6. #19134830C2semidirect
7. #19134812C2semidirect
8. #19134554C2semidirect
9. #104×Dic43C2semidirect
10. #101×Dic43C2semidirect
45. C43×#454C4semidirect
105. 2−1+4×C43C2×C4semidirect
113. AGL(1,ℤ/8)×C43C2×C4semidirect
118. #124×C43C2×C4semidirect
121. #104×C43C2×C4semidirect
122. #101×C43C2×C4semidirect
282. Dic43#454direct (N × H)
315. #454Dic43direct (N × H)
337. C43C4×#454semidirect
340. 2−1+4C2×Dic43semidirect
349. AGL(1,ℤ/8)C2×Dic43semidirect
355. #124C2×Dic43semidirect
402. #104C2×Dic43semidirect
408. #101C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
2−1+4×Dic432
AGL(1,ℤ/8)×Dic432
#124×Dic432
#191349992
#191349732
#191348302
#191348122
#191345542
#104×Dic432
#101×Dic432
C2×C43×#4542
C4×#45443