Finite Group Databasebeta

← #25102538

Subgroups — #25102538

Order 11008.

1370 conjugacy classes of subgroups.

The subgroup lattice has 576 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#19137308C211yesmaximal, characteristic, complemented
4#19134999C211yesmaximal, characteristic, complemented
5#19134973C212yesmaximal, complemented
6#19134823C212yesmaximal, complemented
7#19134812C211yesmaximal, characteristic, complemented
8#19134554C211yesmaximal, characteristic, complemented
9#19134407C212yesmaximal, 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#14582774—22no—
37#14582769C2211yescharacteristic
38#14582745C2211yescharacteristic
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⋊Dic43—22no—
80C2×C4⋊Dic43D412yes—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—22no—
85C2×C4×Dic43—24no—
86C2×C4×Dic43—22no—
87C2×C4×Dic43D412yes—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063259—22no—
91#13063257—22no—
92#13063252—24no—
93#13063249—22no—
94#13063246—22no—
95#13063246—22no—
96#13063246—22no—
97#13063244—22no—
98#13063235—22no—
99C8×Dic43—22no—
100C43⋊#95—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
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—42no—
158C22×Dic43—82no—
159C22×Dic43C2×D412yes—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162SD16×C43—28no—
163D8×C43—28no—
164M16×C43—22no—
165M16×C43C22×C414yes—
166C2×C8×C43—22no—
167C22⋊C4×C43—28no—
168C42×C43—21no—
169C42×C43C22×C412yes—
170C22⋊Dic43—24no—
171C22⋊Dic43—22no—
172C22⋊Dic43—22no—
173C22⋊Dic43—22no—
174C22⋊Dic43—41no—
175C22⋊Dic43—41no—
176C22⋊Dic43—82no—
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⋊Dic43—82no—
186C4⋊Dic43C2×D412yes—
187C4⋊Dic43C2×D412yes—
188C4×Dic43—24no—
189C4×Dic43—24no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—22no—
196C4×Dic43C2×D412yes—
197C4×Dic43C2×D412yes—
198#10621877—22no—
199#10621877—22no—
200C2×C43⋊C8—22no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43C22×D411yescharacteristic
208Q8×C43—28no—
209Q8×C43—24no—
210Q8×C43—22no—
211Q8×C43—24no—
212Q8×C43C4×D414yes—
213D4×C43—28no—
214D4×C43—24no—
215D4×C43—24no—
216D4×C43—24no—
217D4×C43—22no—
218D4×C43—42no—
219D4×C43C4×D414yes—
220C2×C4×C43—216no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—22no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43C4×D414yes—
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C22×D412yes—
232C2×C4×C43C2×#4112yes—
233C2×C4×C43C2×#4111yescharacteristic
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—44no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—82no—
247C2×Dic43—84no—
248C2×Dic43—84no—
249C2×Dic43#12011yescharacteristic
250C2×Dic43#12011yescharacteristic
251C2×Dic43#12012yes—
252C8×C43—24no—
253C43⋊C8—42no—
254#21475—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—24no—
258C22×C43—44no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—82no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43C2×C4×D411yescharacteristic
266C22×C43C2×#12011yescharacteristic
267C22×C43#52511yescharacteristic
268C4×C43—24no—
269C4×C43—24no—
270C4×C43—42no—
271C4×C43C2×C4×D412yes—
272C4×C43#52512yes—
273Dic43—21no—
274Dic43—21no—
275Dic43—22no—
276Dic43—42no—
277Dic43—42no—
278Dic43—42no—
279Dic43—81no—
280Dic43—81no—
281C4×2−1+4—431no—
282C2×#454D4311yescharacteristic
283C4×AGL(1,ℤ/8)—432no—
284#2326—431no—
285#1888—431no—
286#1883—432no—
287#1859—432no—
288#1857—431no—
289#1793—431no—
290#1759—432no—
291C4×#101—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—44no—
295C2×C43—82no—
296C2×C43C4×#12011yescharacteristic
297C2×C43#302011yescharacteristic
298C2×C43#302111yescharacteristic
299C2×2−1+4C2×D4311yescharacteristic
300C2×AGL(1,ℤ/8)C2×D4312yes—
301C2×#124C2×D4311yescharacteristic
302#520—432no—
303#520—862no—
304#520—862no—
305#519—431no—
306#519—862no—
307C4×#41—432no—
308C4×#41—862no—
309C4×#41—862no—
310C2×C4×Q8—431no—
311C2×C4×Q8—862no—
312C2×C4×D4—431no—
313#454Dic4318yescomplemented
314#442—862no—
315#440—862no—
316C4×SD16—862no—
317C4×D8—862no—
318#428—432no—
319C2×#104—432no—
320C2×#104C2×D4312yes—
321#418—432no—
322#417—432no—
323C2×#101—431no—
324C2×#101C2×D4311yescharacteristic
325C4×M16—432no—
326#391—431no—
327#390—431no—
328#388—862no—
329#385—862no—
330#384—431no—
331#376—431no—
332#343—432no—
333#339—432no—
334#339—432no—
335C43#2147511yescharacteristic, complemented, Sylow
3362−1+4—24no—
3372−1+4—22no—
3382−1+4C2×Dic4314yescomplemented
339C2×#41—22no—
340C2×#41—22no—
341C2×#41C22×D4312yes—
342C22×Q8—22no—
343C22×Q8C22×D4311yescharacteristic
344C22×D4C22×D4311yescharacteristic
345C23×C4—861no—
346AGL(1,ℤ/8)—24no—
347AGL(1,ℤ/8)C2×Dic4318yescomplemented
348C2×SD16—22no—
349C2×D8—22no—
350C2×M16—432no—
351C2×M16C22×D4312yes—
352#124—22no—
353#124C2×Dic4314yescomplemented
354C4×Q8—432no—
355C4×Q8—432no—
356C4×Q8—862no—
357C4×Q8—862no—
358C4×Q8—862no—
359C4×Q8—862no—
360C4×Q8—862no—
361C4×Q8—864no—
362C4×Q8—862no—
363C4×Q8—862no—
364C4×D4—432no—
365C4×D4—432no—
366C4×D4—862no—
367C4×D4—862no—
368C4×D4—862no—
369C4×D4—862no—
370C4×D4—864no—
371C4×D4—862no—
372C4×D4—862no—
373C4×D4—864no—
374C4×D4—862no—
375#117—432no—
376#117—862no—
377#117—862no—
378#117—864no—
379#117—864no—
380#117—862no—
381C2×C4⋊C4—432no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—864no—
386C2×C4⋊C4—862no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4—861no—
390C2×C42—431no—
391C2×C42—432no—
392C2×C42—431no—
393C2×C42—862no—
394C2×C42—864no—
395C2×C42C22×D4311yescharacteristic
396#107—862no—
397#106—862no—
398#104—864no—
399#104C2×Dic4318yescomplemented
400#103—862no—
401#102—862no—
402#102—862no—
403#102—862no—
404#101—862no—
405#101C2×Dic4314yescomplemented
406#97—862no—
407C4×C8—862no—
408#95—861no—
409#95—861no—
410#95—862no—
411C24—21no—
412#41—28no—
413#41—28no—
414#41—28no—
415#41—28no—
416#41—22no—
417#41—22no—
418#41#1062190014yes—
419#41C22×Dic4314yes—
420C2×Q8—22no—
421C2×Q8—28no—
422C2×Q8—28no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8D4×D4312yes—
426C2×Q8#1062190012yes—
427C2×Q8C22×Dic4312yes—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4D4×D4312yes—
434C2×D4C22×Dic4312yes—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—432no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—864no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—3442no—
447C22×C4—1722no—
448C22×C4D4×D4312yes—
449C22×C4C23×D4311yescharacteristic
450SD16—28no—
451D8—28no—
452M16—22no—
453M16—862no—
454M16—862no—
455M16C22×Dic4314yes—
456C2×C8—22no—
457C2×C8—862no—
458C4⋊C4—432no—
459C4⋊C4—432no—
460C4⋊C4—864no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4—864no—
464C4⋊C4—862no—
465C4⋊C4—862no—
466C4⋊C4—862no—
467C4⋊C4—862no—
468C4⋊C4—3442no—
469C22⋊C4—28no—
470C22⋊C4—862no—
471C22⋊C4—862no—
472C22⋊C4—864no—
473C22⋊C4—862no—
474C22⋊C4—3442no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—21no—
478C42—432no—
479C42—432no—
480C42—862no—
481C42—862no—
482C42—862no—
483C42—862no—
484C42—864no—
485C42—864no—
486C42—862no—
487C42—862no—
488C42C22×Dic4312yes—
489C23—22no—
490C23—22no—
491C23—42no—
492C23—42no—
493C23—41no—
494C23—41no—
495C23C2×D4×D4311yescharacteristic
496Q8—28no—
497Q8—24no—
498Q8—22no—
499Q8—24no—
500Q8D4×Dic4314yes—
501D4—28no—
502D4—24no—
503D4—24no—
504D4—24no—
505D4—22no—
506D4—42no—
507D4D4×Dic4314yes—
508C2×C4—216no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—431no—
518C2×C4—431no—
519C2×C4—432no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—862no—
523C2×C4—3444no—
524C2×C4—3442no—
525C2×C4—3444no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1724no—
529C2×C4—1721no—
530C2×C4—1722no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1722no—
535C2×C4D4×Dic4314yes—
536C2×C4C23×Dic4311yescharacteristic
537C2×C4C2×D4×D4312yes—
538C2×C4C2×#1062190012yes—
539C2×C4C2×#1062190011yescharacteristic
540C8—24no—
541C8—1722no—
542C22—21no—
543C22—21no—
544C22—24no—
545C22—44no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—82no—
550C22—81no—
551C22—81no—
552C22C2×D4×Dic4311yescharacteristic
553C22#120×D4311yescharacteristic
554C22#1458340511yescharacteristic
555C4—24no—
556C4—24no—
557C4—42no—
558C4—861no—
559C4—861no—
560C4—862no—
561C4—3441no—
562C4—3441no—
563C4—1722no—
564C4—1722no—
565C4—1722no—
566C4C2×D4×Dic4312yes—
567C4#1458340512yes—
568C2—21no—
569C2—21no—
570C2—44no—
571C2—82no—
572C2#120×Dic4311yescharacteristic
573C2#1914395611yescharacteristic
574C2#1914396511yescharacteristic
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
hypocenterC43#21475
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. #19137308C2semidirect
4. #19134999C2semidirect
5. #19134973C2semidirect
6. #19134823C2semidirect
7. #19134812C2semidirect
8. #19134554C2semidirect
9. #19134407C2semidirect
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
313. #454Dic43semidirect
335. C43#21475semidirect
338. 2−1+4C2×Dic43semidirect
347. AGL(1,ℤ/8)C2×Dic43semidirect
353. #124C2×Dic43semidirect
399. #104C2×Dic43semidirect
405. #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
#191373082
#191349992
#191349732
#191348232
#191348122
#191345542
#191344072
#101×Dic432
C2×C43×#4542
#2147543