Finite Group Databasebeta

← #455×Dic43 #25102483

Subgroups — #455×Dic43 #25102483

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
1H(5,𝔽2)×Dic43C211yesmaximal, characteristic
2#137×Dic43C212yesmaximal, complemented
3#124×Dic43C211yesmaximal, characteristic, complemented
4#19134984C211yesmaximal, characteristic, complemented
5#19134966C212yesmaximal, complemented
6#19134830C212yesmaximal, complemented
7#19134807C211yesmaximal, characteristic, complemented
8#19134549C211yesmaximal, characteristic
9#104×Dic43C212yesmaximal, complemented
10#100×Dic43C211yesmaximal, characteristic, complemented
11C2×C43×#455C211yesmaximal, characteristic
12#14583382—22no—
13#14583382C2212yes—
14#14583374—22no—
15#14583374—22no—
16#14583374C2211yescharacteristic
17#41×Dic43—22no—
18#41×Dic43C2212yes—
19C2×Q8×Dic43C2211yescharacteristic, complemented
20C2×D4×Dic43—22no—
21C2×D4×Dic43—22no—
22C2×D4×Dic43C2211yescharacteristic
23#14583006—22no—
24#14583000—22no—
25Q16×Dic43—22no—
26SD16×Dic43—22no—
27#14582941C2212yescomplemented
28C2×#13063252C2212yes—
29#14582908C2212yescomplemented
30#14582900C2212yes—
31C2×#13063242C2211yescharacteristic
32M16×Dic43C2212yescomplemented
33#14582806C2211yescharacteristic, complemented
34#14582802C2211yescharacteristic
35#14582792—22no—
36#14582765C2211yescharacteristic, complemented
37C22⋊C4×Dic43—22no—
38C42×Dic43C2211yescharacteristic, complemented
39#14582667C2212yescomplemented
40#14582660C2212yescomplemented
41#14582659C2212yescomplemented
42C2×H(5,𝔽2)×C43C2211yescharacteristic
43C2×#137×C43C2212yes—
44C2×#124×C43C2211yescharacteristic
45C43×#455C418yescomplemented
46C2×#104×C43C2212yes—
47C2×#100×C43C2211yescharacteristic
48C23×Dic43—22no—
49C23×Dic43D412yes—
50C2×#10621877C2312yes—
51Q8×Dic43—22no—
52Q8×Dic43—22no—
53Q8×Dic43—22no—
54Q8×Dic43D412yes—
55Q8×Dic43D412yes—
56D4×Dic43—24no—
57D4×Dic43—24no—
58D4×Dic43—24no—
59D4×Dic43—24no—
60D4×Dic43—22no—
61D4×Dic43—22no—
62D4×Dic43—24no—
63D4×Dic43—22no—
64D4×Dic43—22no—
65D4×Dic43—22no—
66D4×Dic43—22no—
67D4×Dic43—22no—
68D4×Dic43D412yes—
69D4×Dic43D412yes—
70#13063284—24no—
71#13063284—22no—
72#13063284—22no—
73#13063284C2312yes—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—24no—
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43D412yes—
84C2×C4×Dic43—22no—
85C2×C4×Dic43—22no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063257—22no—
93#13063252—24no—
94#13063249—22no—
95#13063249—22no—
96#13063249—22no—
97#13063246—22no—
98#13063242—22no—
99#13063235—22no—
100C8×Dic43—22no—
101C43⋊#95—22no—
102C43⋊#95—22no—
103H(5,𝔽2)×C43—24no—
104H(5,𝔽2)×C43—22no—
105H(5,𝔽2)×C43C2×C414yes—
106C2×#41×C43—22no—
107C2×#41×C43C2312yes—
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43—22no—
110C22×D4×C43—22no—
111C22×D4×C43C2311yescharacteristic
112#137×C43—24no—
113#137×C43C2×C418yescomplemented
114C2×Q16×C43—22no—
115C2×SD16×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#100×C43C2×C414yescomplemented
123C24×C43—22no—
124C24×C43C2×D412yes—
125#41×C43—28no—
126#41×C43—28no—
127#41×C43—22no—
128#41×C43—22no—
129#41×C43C22×C414yes—
130#41×C43#4114yes—
131C2×Q8×C43—21no—
132C2×Q8×C43—22no—
133C2×Q8×C43—22no—
134C2×Q8×C43C22×C412yescomplemented
135C2×Q8×C43C2×D412yes—
136C2×D4×C43—24no—
137C2×D4×C43—28no—
138C2×D4×C43—28no—
139C2×D4×C43—28no—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43—28no—
143C2×D4×C43—22no—
144C2×D4×C43C22×C412yes—
145C2×D4×C43C2×D412yes—
146C2×D4×C43#4112yes—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—24no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—44no—
162C22×Dic43—84no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D412yes—
165C22×Dic43C2×D411yescharacteristic
166Q16×C43—28no—
167SD16×C43—28no—
168M16×C43—22no—
169M16×C43C22×C414yescomplemented
170C2×C8×C43—22no—
171C22⋊C4×C43—28no—
172C42×C43—21no—
173C42×C43C22×C412yescomplemented
174C22⋊Dic43—24no—
175C22⋊Dic43—24no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C22⋊Dic43—24no—
179C22⋊Dic43—22no—
180C22⋊Dic43—44no—
181C4⋊Dic43—24no—
182C4⋊Dic43—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—42no—
187C4⋊Dic43C2×D412yes—
188C4⋊Dic43C2×D412yes—
189C4×Dic43—24no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198C4×Dic43C2×D412yes—
199C4×Dic43C2×D412yes—
200#10621877—22no—
201#10621877—22no—
202C2×C43⋊C8—22no—
203C23×C43—28no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—82no—
210C23×C43—82no—
211C23×C43C4×D414yes—
212C23×C43C22×D411yescharacteristic
213Q8×C43—22no—
214Q8×C43—24no—
215Q8×C43—42no—
216Q8×C43C4×D414yes—
217D4×C43—216no—
218D4×C43—24no—
219D4×C43—24no—
220D4×C43—24no—
221D4×C43—22no—
222D4×C43—24no—
223D4×C43C4×D414yes—
224C2×C4×C43—28no—
225C2×C4×C43—22no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D412yes—
236C2×C4×C43C2×#4112yes—
237C2×C4×C43C2×#4111yescharacteristic
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—44no—
247C2×Dic43—44no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—41no—
251C2×Dic43—82no—
252C2×Dic43—82no—
253C2×Dic43—82no—
254C2×Dic43—84no—
255C2×Dic43—82no—
256C2×Dic43#12012yes—
257C2×Dic43#12011yescharacteristic
258C2×Dic43#12011yescharacteristic
259C8×C43—24no—
260C43⋊C8—42no—
261C4×#455—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—24no—
265C22×C43—24no—
266C22×C43—44no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—82no—
272C22×C43—88no—
273C22×C43C2×C4×D411yescharacteristic
274C22×C43C2×#12011yescharacteristic
275C22×C43#52511yescharacteristic
276C4×C43—24no—
277C4×C43—42no—
278C4×C43—42no—
279C4×C43C2×C4×D412yes—
280C4×C43#52512yes—
281Dic43—21no—
282Dic43—22no—
283Dic43—42no—
284Dic43—42no—
285Dic43—42no—
286Dic43—42no—
287Dic43—81no—
288Dic43#45512yesdirect product factor
289C4×H(5,𝔽2)—431no—
290C2×#455D4311yescharacteristic
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×#100—431no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—44no—
303C2×C43—44no—
304C2×C43C4×#12011yescharacteristic
305C2×C43C2×#45511yescharacteristic
306C2×C43#301811yescharacteristic
307C2×H(5,𝔽2)C2×D4311yescharacteristic
308C2×#137C2×D4312yes—
309C2×#124C2×D4311yescharacteristic
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—431no—
319C2×C4×D4—862no—
320C2×C4×D4—862no—
321#455Dic4318yesdirect product factor
322#441—862no—
323#440—862no—
324C4×Q16—862no—
325C4×SD16—862no—
326#428—432no—
327C2×#104—432no—
328C2×#104C2×D4312yes—
329#419—432no—
330#417—432no—
331C2×#100—431no—
332C2×#100C2×D4311yescharacteristic
333C4×M16—432no—
334#391—431no—
335#390—431no—
336#388—862no—
337#382—431no—
338C4×C22⋊C4—862no—
339C43—431no—
340#343—432no—
341#339—432no—
342#339—432no—
343C43C4×#45511yescharacteristic, complemented, Sylow
344H(5,𝔽2)—24no—
345H(5,𝔽2)—22no—
346H(5,𝔽2)C2×Dic4314yes—
347C2×#41—22no—
348C2×#41C22×D4312yes—
349C22×Q8C22×D4311yescharacteristic
350C22×D4—22no—
351C22×D4—22no—
352C22×D4C22×D4311yescharacteristic
353C23×C4—432no—
354C23×C4—862no—
355#137—24no—
356#137C2×Dic4318yescomplemented
357C2×Q16—22no—
358C2×SD16—22no—
359C2×M16—432no—
360C2×M16C22×D4312yes—
361#124—22no—
362#124C2×Dic4314yescomplemented
363C4×Q8—432no—
364C4×Q8—432no—
365C4×Q8—862no—
366C4×Q8—862no—
367C4×Q8—862no—
368C4×D4—432no—
369C4×D4—432no—
370C4×D4—862no—
371C4×D4—862no—
372C4×D4—862no—
373C4×D4—862no—
374C4×D4—862no—
375C4×D4—864no—
376C4×D4—862no—
377C4×D4—864no—
378C4×D4—864no—
379C4×D4—864no—
380C4×D4—864no—
381C4×D4—862no—
382#117—432no—
383#117—862no—
384#117—862no—
385#117—864no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—862no—
389C2×C4⋊C4—862no—
390C2×C4⋊C4—861no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—432no—
393C2×C22⋊C4—864no—
394C2×C22⋊C4—862no—
395C2×C22⋊C4—862no—
396C2×C22⋊C4—862no—
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—864no—
408#104C2×Dic4318yescomplemented
409#103—862no—
410#103—862no—
411#103—862no—
412#102—862no—
413#100—862no—
414#100C2×Dic4314yescomplemented
415#97—862no—
416C4×C8—862no—
417#95—862no—
418#95—862no—
419C24—22no—
420C24D4×D4312yes—
421#41—28no—
422#41—28no—
423#41—22no—
424#41—22no—
425#41#1062190014yes—
426#41C22×Dic4314yes—
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8D4×D4312yes—
431C2×Q8C22×Dic4312yescomplemented
432C2×D4—24no—
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—22no—
437C2×D4—28no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4D4×D4312yes—
441C2×D4#1062190012yes—
442C2×D4C22×Dic4312yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—432no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—864no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—3444no—
460C22×C4—1724no—
461C22×C4C23×D4311yescharacteristic
462Q16—28no—
463SD16—28no—
464M16—22no—
465M16—862no—
466M16—862no—
467M16C22×Dic4314yescomplemented
468C2×C8—22no—
469C2×C8—862no—
470C4⋊C4—432no—
471C4⋊C4—432no—
472C4⋊C4—862no—
473C4⋊C4—862no—
474C4⋊C4—864no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—1722no—
478C22⋊C4—28no—
479C22⋊C4—864no—
480C22⋊C4—862no—
481C22⋊C4—862no—
482C22⋊C4—864no—
483C22⋊C4—864no—
484C22⋊C4—862no—
485C22⋊C4—1724no—
486C42—21no—
487C42—432no—
488C42—432no—
489C42—862no—
490C42—862no—
491C42—864no—
492C42—862no—
493C42—862no—
494C42—1721no—
495C42—1721no—
496C42—1722no—
497C42—1722no—
498C42C22×Dic4312yescomplemented
499C23—28no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—42no—
504C23—42no—
505C23—82no—
506C23—82no—
507C23D4×Dic4314yes—
508C23C2×D4×D4311yescharacteristic
509Q8—22no—
510Q8—24no—
511Q8—42no—
512Q8D4×Dic4314yes—
513D4—216no—
514D4—24no—
515D4—24no—
516D4—24no—
517D4—22no—
518D4—24no—
519D4D4×Dic4314yes—
520C2×C4—28no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—431no—
531C2×C4—432no—
532C2×C4—431no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—862no—
538C2×C4—3442no—
539C2×C4—3442no—
540C2×C4—3442no—
541C2×C4—3444no—
542C2×C4—3442no—
543C2×C4—1724no—
544C2×C4—1724no—
545C2×C4—1721no—
546C2×C4—1722no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1722no—
551C2×C4C23×Dic4311yescharacteristic
552C2×C4C2×D4×D4312yes—
553C2×C4C2×#1062190012yes—
554C2×C4C2×#1062190011yescharacteristic
555C8—24no—
556C8—1722no—
557C22—21no—
558C22—21no—
559C22—24no—
560C22—24no—
561C22—44no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—82no—
567C22—88no—
568C22C2×D4×Dic4311yescharacteristic
569C22#120×D4311yescharacteristic
570C22#1458340511yescharacteristic
571C4—24no—
572C4—42no—
573C4—42no—
574C4—432no—
575C4—862no—
576C4—861no—
577C4—3441no—
578C4—1722no—
579C4—1722no—
580C4—1722no—
581C4—1722no—
582C4C2×D4×Dic4312yes—
583C4#1458340512yes—
584C2—21no—
585C2—21no—
586C2—44no—
587C2—44no—
588C2#120×Dic4311yescharacteristic
589C2#455×D4311yescharacteristic
590C2#1914394511yescharacteristic
subgroupG/H
centerC22#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#455C2
socleC22×C43C2×#120
prime radicalC2×H(5,𝔽2)×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#455D43
hypocenterC43C4×#455
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#455

Complements

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

NH ≅ G/Ntype
2. #137×Dic43C2semidirect
3. #124×Dic43C2semidirect
4. #19134984C2semidirect
5. #19134966C2semidirect
6. #19134830C2semidirect
7. #19134807C2semidirect
9. #104×Dic43C2semidirect
10. #100×Dic43C2semidirect
19. C2×Q8×Dic43C22semidirect
27. #14582941C22semidirect
29. #14582908C22semidirect
32. M16×Dic43C22semidirect
33. #14582806C22semidirect
36. #14582765C22semidirect
38. C42×Dic43C22semidirect
39. #14582667C22semidirect
40. #14582660C22semidirect
41. #14582659C22semidirect
45. C43×#455C4semidirect
113. #137×C43C2×C4semidirect
118. #124×C43C2×C4semidirect
121. #104×C43C2×C4semidirect
122. #100×C43C2×C4semidirect
134. C2×Q8×C43C22×C4semidirect
169. M16×C43C22×C4semidirect
173. C42×C43C22×C4semidirect
288. Dic43#455direct (N × H)
321. #455Dic43direct (N × H)
343. C43C4×#455semidirect
356. #137C2×Dic43semidirect
362. #124C2×Dic43semidirect
408. #104C2×Dic43semidirect
414. #100C2×Dic43semidirect
431. C2×Q8C22×Dic43semidirect
467. M16C22×Dic43semidirect
498. C42C22×Dic43semidirect

Maximal subgroups

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

subgroupindex
H(5,𝔽2)×Dic432
#137×Dic432
#124×Dic432
#191349842
#191349662
#191348302
#191348072
#191345492
#104×Dic432
#100×Dic432
C2×C43×#4552
C4×#45543