Finite Group Databasebeta

← #453×Dic43 #25102472

Subgroups — #453×Dic43 #25102472

Order 11008.

1578 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(5,𝔽2)×Dic43C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×Dic43C212yesmaximal, complemented
3#127×Dic43C211yesmaximal, characteristic, complemented
4#19134994C211yesmaximal, characteristic, complemented
5#19134973C212yesmaximal, complemented
6#19134823C212yesmaximal, complemented
7#19134807C211yesmaximal, characteristic, complemented
8#19134549C211yesmaximal, characteristic, complemented
9#104×Dic43C212yesmaximal, complemented
10#100×Dic43C211yesmaximal, characteristic, complemented
11C2×C43×#453C211yesmaximal, characteristic
12#14583382—22no—
13#14583382C2212yes—
14#14583374—22no—
15#14583374—22no—
16#14583374C2211yescharacteristic
17#41×Dic43—22no—
18#41×Dic43C2212yes—
19C2×D4×Dic43—22no—
20C2×D4×Dic43—22no—
21C2×D4×Dic43—22no—
22C2×D4×Dic43C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic, complemented
24#14583011—22no—
25#14583000—22no—
26SD16×Dic43—22no—
27D8×Dic43—22no—
28#14582941C2212yescomplemented
29C2×#13063252C2212yes—
30#14582904C2212yescomplemented
31#14582900C2212yes—
32C2×#13063242C2211yescharacteristic
33M16×Dic43C2212yescomplemented
34#14582802—22no—
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic, complemented
37#14582769C2211yescharacteristic, complemented
38C42×Dic43C2211yescharacteristic, complemented
39#14582667C2212yescomplemented
40#14582660C2212yescomplemented
41#14582659C2212yescomplemented
42C2×H(5,𝔽2)×C43C2211yescharacteristic
43C2×AGL(1,ℤ/8)×C43C2212yes—
44C2×#127×C43C2211yescharacteristic
45C43×#453C418yescomplemented
46C2×#104×C43C2212yes—
47C2×#100×C43C2211yescharacteristic
48C23×Dic43—22no—
49C23×Dic43—21no—
50C23×Dic43D412yes—
51C2×#10621877C2312yes—
52Q8×Dic43—22no—
53Q8×Dic43D412yescomplemented
54Q8×Dic43D412yescomplemented
55D4×Dic43—24no—
56D4×Dic43—24no—
57D4×Dic43—24no—
58D4×Dic43—24no—
59D4×Dic43—22no—
60D4×Dic43—22no—
61D4×Dic43—24no—
62D4×Dic43—22no—
63D4×Dic43—22no—
64D4×Dic43—22no—
65D4×Dic43—22no—
66D4×Dic43—22no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—48no—
70D4×Dic43D412yescomplemented
71D4×Dic43D412yescomplemented
72#13063284—24no—
73#13063284—22no—
74#13063284—22no—
75#13063284C2312yes—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—24no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—22no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43D412yes—
88C2×C4×Dic43—22no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—22no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063259—22no—
95#13063257—22no—
96#13063252—24no—
97#13063249—22no—
98#13063246—22no—
99#13063246—22no—
100#13063246—22no—
101#13063242—22no—
102#13063235—22no—
103C8×Dic43—22no—
104H(5,𝔽2)×C43—24no—
105H(5,𝔽2)×C43—22no—
106H(5,𝔽2)×C43C2×C414yescomplemented
107C2×#41×C43—22no—
108C2×#41×C43C2312yes—
109C22×D4×C43—22no—
110C22×D4×C43—22no—
111C22×D4×C43—22no—
112C22×D4×C43C2311yescharacteristic
113C22×D4×C43C2311yescharacteristic
114AGL(1,ℤ/8)×C43—24no—
115AGL(1,ℤ/8)×C43C2×C418yescomplemented
116C2×SD16×C43—22no—
117C2×D8×C43—22no—
118C2×M16×C43C2312yes—
119#127×C43—22no—
120#127×C43C2×C414yescomplemented
121C2×C42×C43C2311yescharacteristic
122#104×C43C2×C418yescomplemented
123#100×C43C2×C414yescomplemented
124C24×C43—22no—
125C24×C43—21no—
126C24×C43C2×D412yes—
127#41×C43—28no—
128#41×C43—28no—
129#41×C43—22no—
130#41×C43—22no—
131#41×C43C22×C414yes—
132#41×C43#4114yes—
133C2×Q8×C43C2×D412yes—
134C2×D4×C43—24no—
135C2×D4×C43—28no—
136C2×D4×C43—28no—
137C2×D4×C43—28no—
138C2×D4×C43—22no—
139C2×D4×C43—22no—
140C2×D4×C43—21no—
141C2×D4×C43—28no—
142C2×D4×C43—28no—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43—44no—
147C2×D4×C43—44no—
148C2×D4×C43C22×C412yes—
149C2×D4×C43C22×C412yescomplemented
150C2×D4×C43C2×D412yes—
151C2×D4×C43#4112yes—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—21no—
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—24no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—44no—
166C22×Dic43—44no—
167C22×Dic43—41no—
168C22×Dic43—41no—
169C22×Dic43—84no—
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D412yes—
172C22×Dic43C2×D411yescharacteristic
173SD16×C43—28no—
174D8×C43—28no—
175M16×C43—22no—
176M16×C43C22×C414yescomplemented
177C2×C8×C43—22no—
178C42×C43—21no—
179C42×C43C22×C412yescomplemented
180C22⋊Dic43—24no—
181C22⋊Dic43—24no—
182C22⋊Dic43—22no—
183C22⋊Dic43—22no—
184C22⋊Dic43—24no—
185C22⋊Dic43—22no—
186C22⋊Dic43—44no—
187C22⋊Dic43—44no—
188C22⋊Dic43—42no—
189C4⋊Dic43—24no—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43—44no—
195C4⋊Dic43C2×D412yes—
196C4⋊Dic43C2×D412yes—
197C4×Dic43—24no—
198C4×Dic43—24no—
199C4×Dic43—22no—
200C4×Dic43—22no—
201C4×Dic43—22no—
202C4×Dic43—22no—
203C4×Dic43—42no—
204C4×Dic43C2×D412yes—
205C4×Dic43C2×D412yes—
206#10621877—22no—
207#10621877—22no—
208C2×C43⋊C8—22no—
209C23×C43—28no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—42no—
215C23×C43—42no—
216C23×C43—42no—
217C23×C43—42no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—82no—
221C23×C43—82no—
222C23×C43C4×D414yes—
223C23×C43C22×D411yescharacteristic
224Q8×C43—22no—
225Q8×C43C4×D414yescomplemented
226D4×C43—216no—
227D4×C43—24no—
228D4×C43—24no—
229D4×C43—24no—
230D4×C43—24no—
231D4×C43—22no—
232D4×C43—24no—
233D4×C43—416no—
234D4×C43—42no—
235D4×C43C4×D414yescomplemented
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—28no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—24no—
242C2×C4×C43—24no—
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D412yes—
245C2×C4×C43C2×#4112yes—
246C2×C4×C43C2×#4111yescharacteristic
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—44no—
256C2×Dic43—44no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—41no—
260C2×Dic43—82no—
261C2×Dic43—82no—
262C2×Dic43—82no—
263C2×Dic43—82no—
264C2×Dic43—84no—
265C2×Dic43—82no—
266C2×Dic43—82no—
267C2×Dic43#12012yes—
268C2×Dic43#12011yescharacteristic
269C2×Dic43#12011yescharacteristic
270C8×C43—24no—
271C43⋊C8—42no—
272C4×#453—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—24no—
276C22×C43—24no—
277C22×C43—44no—
278C22×C43—44no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—82no—
285C22×C43—82no—
286C22×C43—88no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43C2×C4×D411yescharacteristic
290C22×C43C2×#12011yescharacteristic
291C22×C43#52511yescharacteristic
292C4×C43—24no—
293C4×C43—24no—
294C4×C43C2×C4×D412yes—
295C4×C43#52512yes—
296Dic43—21no—
297Dic43—22no—
298Dic43—42no—
299Dic43—42no—
300Dic43—42no—
301Dic43—42no—
302Dic43—81no—
303Dic43#45312yesdirect product factor
304C4×H(5,𝔽2)—431no—
305C2×#453D4311yescharacteristic
306C4×AGL(1,ℤ/8)—432no—
307C4×#127—431no—
308#1887—431no—
309#1883—432no—
310#1859—432no—
311#1856—431no—
312#1792—431no—
313C4×#104—432no—
314C4×#100—431no—
315C2×C43—21no—
316C2×C43—21no—
317C2×C43—44no—
318C2×C43—44no—
319C2×C43—82no—
320C2×C43C4×#12011yescharacteristic
321C2×C43C2×#45311yescharacteristic
322C2×C43#301811yescharacteristic
323C2×H(5,𝔽2)C2×D4311yescharacteristic
324C2×AGL(1,ℤ/8)C2×D4312yes—
325C2×#127C2×D4311yescharacteristic
326#520—432no—
327#520—862no—
328#518—431no—
329#518—862no—
330#518—862no—
331C4×#41—432no—
332C4×#41—862no—
333C2×C4×D4—431no—
334C2×C4×D4—431no—
335C2×C4×D4—862no—
336C2×C4×D4—862no—
337C2×C4×D4—862no—
338#453Dic4318yesdirect product factor
339#442—862no—
340#440—862no—
341C4×SD16—862no—
342C4×D8—862no—
343#428—432no—
344C2×#104—432no—
345C2×#104C2×D4312yes—
346#418—432no—
347#417—432no—
348C2×#100—431no—
349C2×#100C2×D4311yescharacteristic
350C4×M16—432no—
351#390—431no—
352#390—431no—
353#390—862no—
354#384—431no—
355C43—431no—
356#343—432no—
357#339—432no—
358#339—432no—
359C43C4×#45311yescharacteristic, complemented, Sylow
360H(5,𝔽2)—24no—
361H(5,𝔽2)—22no—
362H(5,𝔽2)C2×Dic4314yescomplemented
363C2×#41—22no—
364C2×#41C22×D4312yes—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4C22×D4311yescharacteristic
369C22×D4C22×D4311yescharacteristic
370C23×C4—432no—
371C23×C4—861no—
372C23×C4—862no—
373AGL(1,ℤ/8)—24no—
374AGL(1,ℤ/8)C2×Dic4318yescomplemented
375C2×SD16—22no—
376C2×D8—22no—
377C2×M16—432no—
378C2×M16C22×D4312yes—
379#127—22no—
380#127C2×Dic4314yescomplemented
381C4×Q8—432no—
382C4×Q8—432no—
383C4×Q8—862no—
384C4×D4—432no—
385C4×D4—432no—
386C4×D4—862no—
387C4×D4—862no—
388C4×D4—862no—
389C4×D4—862no—
390C4×D4—862no—
391C4×D4—862no—
392C4×D4—862no—
393C4×D4—864no—
394C4×D4—862no—
395C4×D4—864no—
396C4×D4—864no—
397C4×D4—864no—
398C4×D4—864no—
399C4×D4—862no—
400C4×D4—1728no—
401#117—432no—
402#117—862no—
403#117—862no—
404#117—864no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—862no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4—862no—
410C2×C22⋊C4—432no—
411C2×C22⋊C4—864no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—862no—
416C2×C22⋊C4—862no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—862no—
420C2×C42—861no—
421C2×C42—862no—
422C2×C42—861no—
423C2×C42C22×D4311yescharacteristic
424#107—862no—
425#106—862no—
426#104—864no—
427#104C2×Dic4318yescomplemented
428#103—862no—
429#102—862no—
430#102—862no—
431#102—862no—
432#100—862no—
433#100C2×Dic4314yescomplemented
434#97—862no—
435C4×C8—862no—
436C24—22no—
437C24—21no—
438C24D4×D4312yes—
439#41—28no—
440#41—28no—
441#41—22no—
442#41—22no—
443#41#1062190014yes—
444#41C22×Dic4314yes—
445C2×Q8D4×D4312yes—
446C2×D4—24no—
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—28no—
450C2×D4—22no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4D4×D4312yes—
461C2×D4#1062190012yes—
462C2×D4C22×Dic4312yes—
463C2×D4C22×Dic4312yescomplemented
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—432no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—864no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—3444no—
480C22×C4—1721no—
481C22×C4—1721no—
482C22×C4—1724no—
483C22×C4—1724no—
484C22×C4C23×D4311yescharacteristic
485SD16—28no—
486D8—28no—
487M16—22no—
488M16—862no—
489M16—862no—
490M16C22×Dic4314yescomplemented
491C2×C8—22no—
492C2×C8—862no—
493C4⋊C4—432no—
494C4⋊C4—432no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—864no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—1724no—
501C22⋊C4—864no—
502C22⋊C4—862no—
503C22⋊C4—862no—
504C22⋊C4—864no—
505C22⋊C4—864no—
506C22⋊C4—862no—
507C22⋊C4—1722no—
508C22⋊C4—1724no—
509C22⋊C4—1724no—
510C42—21no—
511C42—432no—
512C42—432no—
513C42—862no—
514C42—862no—
515C42—864no—
516C42—864no—
517C42—862no—
518C42—862no—
519C42—1722no—
520C42C22×Dic4312yescomplemented
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—41no—
531C23—41no—
532C23—82no—
533C23—82no—
534C23D4×Dic4314yes—
535C23C2×D4×D4311yescharacteristic
536Q8—22no—
537Q8D4×Dic4314yescomplemented
538D4—216no—
539D4—24no—
540D4—24no—
541D4—24no—
542D4—24no—
543D4—22no—
544D4—24no—
545D4—416no—
546D4—42no—
547D4D4×Dic4314yescomplemented
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—28no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—431no—
556C2×C4—432no—
557C2×C4—431no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—3442no—
564C2×C4—3442no—
565C2×C4—3442no—
566C2×C4—3442no—
567C2×C4—3442no—
568C2×C4—3444no—
569C2×C4—3442no—
570C2×C4—1724no—
571C2×C4—1724no—
572C2×C4—1721no—
573C2×C4—1722no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1722no—
578C2×C4C23×Dic4311yescharacteristic
579C2×C4C2×D4×D4312yes—
580C2×C4C2×#1062190012yes—
581C2×C4C2×#1062190011yescharacteristic
582C8—24no—
583C8—1722no—
584C22—21no—
585C22—21no—
586C22—24no—
587C22—24no—
588C22—44no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—82no—
596C22—82no—
597C22—88no—
598C22—81no—
599C22—81no—
600C22C2×D4×Dic4311yescharacteristic
601C22#120×D4311yescharacteristic
602C22#1458340511yescharacteristic
603C4—24no—
604C4—24no—
605C4—432no—
606C4—862no—
607C4—861no—
608C4—3441no—
609C4—1722no—
610C4—1722no—
611C4—1722no—
612C4—1722no—
613C4C2×D4×Dic4312yes—
614C4#1458340512yes—
615C2—21no—
616C2—21no—
617C2—44no—
618C2—44no—
619C2—82no—
620C2#120×Dic4311yescharacteristic
621C2#453×D4311yescharacteristic
622C2#1914394011yescharacteristic
subgroupG/H
centerC22#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#453C2
socleC22×C43C2×#120
cosocleC22×C4×C43C24
hypercenterC2×#453D43
hypocenterC43C4×#453
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#453

Complements

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

NH ≅ G/Ntype
1. H(5,𝔽2)×Dic43C2semidirect
2. AGL(1,ℤ/8)×Dic43C2semidirect
3. #127×Dic43C2semidirect
4. #19134994C2semidirect
5. #19134973C2semidirect
6. #19134823C2semidirect
7. #19134807C2semidirect
8. #19134549C2semidirect
9. #104×Dic43C2semidirect
10. #100×Dic43C2semidirect
23. C2×D4×Dic43C22semidirect
28. #14582941C22semidirect
30. #14582904C22semidirect
33. M16×Dic43C22semidirect
36. #14582802C22semidirect
37. #14582769C22semidirect
38. C42×Dic43C22semidirect
39. #14582667C22semidirect
40. #14582660C22semidirect
41. #14582659C22semidirect
45. C43×#453C4semidirect
53. Q8×Dic43D4semidirect
54. Q8×Dic43D4semidirect
70. D4×Dic43D4semidirect
71. D4×Dic43D4semidirect
106. H(5,𝔽2)×C43C2×C4semidirect
115. AGL(1,ℤ/8)×C43C2×C4semidirect
120. #127×C43C2×C4semidirect
122. #104×C43C2×C4semidirect
123. #100×C43C2×C4semidirect
149. C2×D4×C43C22×C4semidirect
176. M16×C43C22×C4semidirect
179. C42×C43C22×C4semidirect
225. Q8×C43C4×D4semidirect
235. D4×C43C4×D4semidirect
303. Dic43#453direct (N × H)
338. #453Dic43direct (N × H)
359. C43C4×#453semidirect
362. H(5,𝔽2)C2×Dic43semidirect
374. AGL(1,ℤ/8)C2×Dic43semidirect
380. #127C2×Dic43semidirect
427. #104C2×Dic43semidirect
433. #100C2×Dic43semidirect
463. C2×D4C22×Dic43semidirect
490. M16C22×Dic43semidirect
520. C42C22×Dic43semidirect
537. Q8D4×Dic43semidirect
547. D4D4×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
AGL(1,ℤ/8)×Dic432
#127×Dic432
#191349942
#191349732
#191348232
#191348072
#191345492
#104×Dic432
#100×Dic432
C2×C43×#4532
C4×#45343