Finite Group Databasebeta

← #25253051

Subgroups — #25253051

Order 11008.

760 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
1C2×#14583335C211yesmaximal, characteristic, complemented
2C22×#13063266C211yesmaximal, characteristic, complemented
3#19146282C211yesmaximal, characteristic, complemented
4#19136859C211yesmaximal, characteristic, complemented
5#19136696C211yesmaximal, characteristic, complemented
6#19136689C211yesmaximal, characteristic, complemented
7#19136650C211yesmaximal, characteristic, complemented
8#19136627C211yesmaximal, characteristic, complemented
9#19136524C211yesmaximal, characteristic, complemented
10#19136516C211yesmaximal, characteristic, complemented
11#19136507C211yesmaximal, characteristic, complemented
12#19136506C211yesmaximal, characteristic, complemented
13#19136469C211yesmaximal, characteristic, complemented
14#19136421C211yesmaximal, characteristic, complemented
15D4×D8×C43C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic, complemented
17C22×D344C2211yescharacteristic, complemented
18#14583545—21no—
19#14583335—24no—
20C2×#13063269C2211yescharacteristic, complemented
21C2×#13063269C2211yescharacteristic, complemented
22C2×#13063269C2211yescharacteristic, complemented
23C2×#13063266—24no—
24C2×#13063266C2211yescharacteristic
25C2×#13063266C2211yescharacteristic
26C2×#13063266C2211yescharacteristic, complemented
27C2×#13063266C2211yescharacteristic, complemented
28C2×#13063266C2211yescharacteristic, complemented
29C2×#13063266C2211yescharacteristic, complemented
30C2×#13063265C2211yescharacteristic, complemented
31C22×C43⋊C16C2211yescharacteristic, complemented
32#14583283C2211yescharacteristic, complemented
33#14583140C2211yescharacteristic, complemented
34#14583135C2211yescharacteristic, complemented
35#14583115—21no—
36#14583052—21no—
37#14583046—21no—
38C4×D344C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40C4⋊(C43⋊C16)C2211yescharacteristic, complemented
41#14582702C2211yescharacteristic, complemented
42#14582700C2211yescharacteristic, complemented
43#14582700C2211yescharacteristic, complemented
44#14582700C2211yescharacteristic, complemented
45#14582699C2211yescharacteristic, complemented
46#14582699C2211yescharacteristic, complemented
47C22⋊(C43⋊C16)C2211yescharacteristic, complemented
48C22⋊(C43⋊C16)C2211yescharacteristic, complemented
49#14582675C2211yescharacteristic, complemented
50C22×D8×C43C2211yescharacteristic
51C22×D8×C43C2211yescharacteristic, complemented
52D42×C43—21no—
53C43×#493C2211yescharacteristic, complemented
54C43×#466C2211yescharacteristic
55C43×#466C2211yescharacteristic, complemented
56C43×#459—21no—
57C43×#447—21no—
58C43×#447—21no—
59C4×D8×C43C2211yescharacteristic, complemented
60C8×D4×C43C2211yescharacteristic
61C2×#10621898—21no—
62C22×D172—21no—
63#13063347—22no—
64#13063347—41no—
65C2×Dic172C2311yescharacteristic
66C2×#10621873—21no—
67C2×#10621873—21no—
68C2×D344—22no—
69C2×D344—21no—
70C2×D344—41no—
71C2×D344C2311yescharacteristic
72C2×D344C2311yescharacteristic
73#13063313—21no—
74#13063310—41no—
75#13063304—21no—
76#13063299—21no—
77#13063298—41no—
78#13063293—41no—
79C4×D172—21no—
80C22⋊C4×D43—41no—
81#13063269—22no—
82#13063269—22no—
83#13063269—41no—
84#13063266—22no—
85#13063266—22no—
86#13063266—22no—
87#13063266—22no—
88#13063266—41no—
89#13063266D414yescomplemented
90#13063265—22no—
91C2×C43⋊C16—22no—
92C2×C43⋊C16C2311yescharacteristic
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C2×C43⋊C16C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063250—21no—
98#13063247—21no—
99#13063247—21no—
100C22×D4×C43—21no—
101C22×D4×C43—21no—
102C22×D4×C43—41no—
103C2×D8×C43—22no—
104C2×D8×C43—22no—
105C2×D8×C43—21no—
106C2×D8×C43—21no—
107C2×D8×C43—21no—
108C2×D8×C43—41no—
109C2×D8×C43—41no—
110C2×D8×C43C2311yescharacteristic
111C2×D8×C43C2311yescharacteristic
112C2×D8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#127×C43—21no—
116#121×C43—21no—
117#121×C43—21no—
118#121×C43—41no—
119#120×C43—41no—
120#120×C43—41no—
121C4×D4×C43—21no—
122C4×D4×C43D411yescharacteristic
123#107×C43C2311yescharacteristic
124C4⋊C8×C43D411yescharacteristic
125#102×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
128C22⋊C8×C43D411yescharacteristic
129C22⋊C8×C43D411yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C24×C43—41no—
132C24×C43—41no—
133C23×D43—41no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—41no—
138C2×D4×C43—41no—
139C2×D4×C43—41no—
140C2×D4×C43—41no—
141C2×D4×C43—41no—
142C2×D4×C43—41no—
143C2×D4×C43—42no—
144C2×D4×C43—42no—
145C2×D4×C43—81no—
146C2×D4×C43—81no—
147C2×D4×C43—84no—
148C2×D4×C43D811yescharacteristic
149C22×C4×C43—41no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154#10621898—42no—
155#10621898—81no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—41no—
159C2×D172—42no—
160C2×D172—81no—
161C2×C4×D43—41no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164D8×C43—21no—
165D8×C43—21no—
166D8×C43—21no—
167D8×C43—21no—
168D8×C43—21no—
169D8×C43—42no—
170D8×C43—42no—
171D8×C43—81no—
172D8×C43C2×D412yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43D811yescharacteristic
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43D811yescharacteristic
187C22⋊C4×C43D811yescharacteristic
188C42×C43C2×D411yescharacteristic
189C22⋊Dic43—41no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195Dic43⋊C4—41no—
196Dic172—21no—
197Dic172—21no—
198D344—21no—
199D344—21no—
200D344—21no—
201D344—42no—
202D344C2×D412yescomplemented
203#10621873—42no—
204#10621873—81no—
205C43⋊C16—21no—
206C43⋊C16—21no—
207C43⋊C16—21no—
208C43⋊C16C2×D412yescomplemented
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—82no—
213C23×C43—82no—
214C23×C43—82no—
215C23×C43—82no—
216C23×C43—161no—
217C23×C43—161no—
218C23×C43C2×D811yescharacteristic
219C23×C43C2×D811yescharacteristic
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—82no—
223C22×D43—82no—
224C22×D43—161no—
225D4×C43—22no—
226D4×C43—22no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—82no—
233D4×C43—82no—
234D4×C43—82no—
235D4×C43—82no—
236D4×C43—82no—
237D4×C43—161no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—82no—
244C2×C4×C43C2×D811yescharacteristic
245C2×C4×C43C2×D811yescharacteristic
246C2×C4×C43C2×D811yescharacteristic
247C2×C4×C43C2×D811yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C22⋊D43—82no—
250C22⋊D43—161no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253D172—22no—
254D172—41no—
255D172—41no—
256D172—41no—
257D172—82no—
258C4×D43—82no—
259C4×D43—161no—
260Dic86—41no—
261Dic86—41no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43C22×D411yescharacteristic
266C8×C43H(5,𝔽2)11yescharacteristic
267#33830—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—42no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—164no—
283C22×C43—164no—
284C22×C43#50912yescomplemented
285C22×C43C22×D811yescharacteristic
286C2×D43—42no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—164no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—81no—
298C4×C43D4211yescharacteristic
299C4×C43#57611yescharacteristic
300Dic43—81no—
301Dic43—81no—
302C2×#509—431no—
303C22×D16—431no—
304#3280—431no—
305D4×D8D4311yescharacteristic, complemented
306#2250—431no—
307#2218—431no—
308#2217—431no—
309#2210—431no—
310#2206—431no—
311#2187—431no—
312#2186—431no—
313#2184—431no—
314#2184—431no—
315#2177—431no—
316#2168—431no—
317C2×C43—22no—
318C2×C43—41no—
319C2×C43—82no—
320C2×C43—161no—
321C2×C43—161no—
322C2×C43D4×D811yescharacteristic
323C2×C43C2×#50911yescharacteristic
324C2×C43#341511yescharacteristic
325D43—82no—
326D43—161no—
327C2×#135—431no—
328C22×D8—431no—
329C22×D8C2×D4311yescharacteristic
330C22×D8C2×D4311yescharacteristic, complemented
331#546—861no—
332D42—21no—
333#509—864no—
334C2×SD32—431no—
335C2×SD32—431no—
336C2×SD32—431no—
337C2×D16—431no—
338C2×D16—431no—
339C2×D16—431no—
340C2×D16—431no—
341C2×D16—431no—
342C2×D16—431no—
343C2×D16—864no—
344C2×M32—431no—
345C22×C16—431no—
346#495—431no—
347#493C2×D4311yescharacteristic, complemented
348#467—431no—
349#466—431no—
350#466C2×D4311yescharacteristic
351#466C2×D4311yescharacteristic, complemented
352#463—861no—
353#459—21no—
354#450—861no—
355#449—861no—
356#447—21no—
357#447—21no—
358C4×D8—431no—
359C4×D8C2×D4311yescharacteristic, complemented
360C8×D4C2×D4311yescharacteristic
361#367—431no—
362C4⋊C16—431no—
363#358—431no—
364#357—431no—
365#357—431no—
366#357—431no—
367#357—431no—
368#357—431no—
369C22⋊C16—431no—
370C22⋊C16—431no—
371#346—431no—
372C43#3383011yescharacteristic, complemented, Sylow
373C2×#41—861no—
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—41no—
377C22×D4—861no—
378#135—862no—
379#135—1721no—
380C2×Q16—431no—
381C2×SD16—861no—
382C2×SD16—861no—
383C2×D8—22no—
384C2×D8—22no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—41no—
389C2×D8—41no—
390C2×D8—431no—
391C2×D8—431no—
392C2×D8—862no—
393C2×D8—861no—
394C2×D8—1721no—
395C2×D8C22×D4311yescharacteristic
396C2×D8C22×D4311yescharacteristic
397C2×D8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400#127—21no—
401#124—861no—
402#123—1721no—
403C22⋊Q8—861no—
404#121—21no—
405#121—21no—
406#121—41no—
407#121—861no—
408#121—1721no—
409#120—41no—
410#120—41no—
411#120—1721no—
412C4×D4—21no—
413C4×D4—861no—
414C4×D4C22⋊D4311yescharacteristic
415C2×C22⋊C4—1721no—
416SD32—862no—
417SD32—862no—
418SD32—1721no—
419D16—434no—
420D16—862no—
421D16—862no—
422D16—862no—
423D16—862no—
424D16—1721no—
425M32—862no—
426C2×C16—431no—
427C2×C16—431no—
428C2×C16—431no—
429C2×C16—431no—
430C2×C16—862no—
431#107—431no—
432#107C22×D4311yescharacteristic
433C4⋊C8C22⋊D4311yescharacteristic
434#103—861no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—861no—
439#102—861no—
440C22⋊C8C22⋊D4311yescharacteristic
441C22⋊C8C22⋊D4311yescharacteristic
442C4×C8C22×D4311yescharacteristic
443C24—41no—
444C24—41no—
445C24—1721no—
446#41—3441no—
447#41—1722no—
448C2×Q8—861no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4—84no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—3441no—
466C2×D4—1722no—
467C2×D4—1721no—
468C2×D4—1721no—
469C2×D4—1721no—
470C2×D4#1062188211yescharacteristic
471C22×C4—41no—
472C22×C4—1721no—
473C22×C4—1721no—
474C22×C4C2×C22⋊D4311yescharacteristic
475C22×C4C2×C22⋊D4311yescharacteristic
476Q16—861no—
477Q16—861no—
478SD16—3441no—
479SD16—1722no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—21no—
485D8—42no—
486D8—42no—
487D8—81no—
488D8—432no—
489D8—861no—
490D8—861no—
491D8—861no—
492D8—1722no—
493D8D4×D4312yes—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8C2×C22⋊D4311yescharacteristic
499C2×C8C2×C22⋊D4311yescharacteristic
500C2×C8C2×C22⋊D4311yescharacteristic
501C2×C8C23×D4311yescharacteristic
502C4⋊C4—21no—
503C4⋊C4—861no—
504C4⋊C4—1721no—
505C4⋊C4#1062188211yescharacteristic
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C22⋊C4—1721no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C22⋊C4#1062188211yescharacteristic
515C22⋊C4#1062188211yescharacteristic
516C42C2×C22⋊D4311yescharacteristic
517C16—432no—
518C16—861no—
519C16—861no—
520C16—861no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—82no—
525C23—82no—
526C23—82no—
527C23—82no—
528C23—161no—
529C23—161no—
530C23—3442no—
531C23—3442no—
532C23—1721no—
533C23—1721no—
534C23—6881no—
535C23C2×#1062188211yescharacteristic
536C23C2×#1062188211yescharacteristic
537Q8—1721no—
538Q8—1721no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—82no—
547D4—82no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4—161no—
552D4—862no—
553D4—3442no—
554D4—3442no—
555D4—1721no—
556D4—1721no—
557D4—1721no—
558D4—6881no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—82no—
565C2×C4—3442no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—6881no—
569C2×C4C2×#1062188211yescharacteristic
570C2×C4C2×#1062188211yescharacteristic
571C2×C4C2×#1062188211yescharacteristic
572C2×C4C2×#1062188211yescharacteristic
573C2×C4C22×C22⋊D4311yescharacteristic
574C8—21no—
575C8—21no—
576C8—21no—
577C8C2×D4×D4311yescharacteristic
578C8#1306337011yescharacteristic
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—164no—
594C22—164no—
595C22—3441no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—3441no—
600C22—1722no—
601C22—6884no—
602C22#1458333512yescomplemented
603C22C22×#1062188211yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—81no—
609C4—3441no—
610C4—3441no—
611C4D4×C22⋊D4311yescharacteristic
612C4#1458370211yescharacteristic
613C2—22no—
614C2—41no—
615C2—82no—
616C2—161no—
617C2—161no—
618C2—3442no—
619C2—6881no—
620C2D4×#1062188211yescharacteristic
621C2C2×#1458333511yescharacteristic
622C2#1914773411yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingD4×D8×C43C2
socleC22×C43C22×D8
hypercenterD4×D8D43
hypocenterC43#33830
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583335C2semidirect
2. C22×#13063266C2semidirect
3. #19146282C2semidirect
4. #19136859C2semidirect
5. #19136696C2semidirect
6. #19136689C2semidirect
7. #19136650C2semidirect
8. #19136627C2semidirect
9. #19136524C2semidirect
10. #19136516C2semidirect
11. #19136507C2semidirect
12. #19136506C2semidirect
13. #19136469C2semidirect
14. #19136421C2semidirect
15. D4×D8×C43C2semidirect
16. C2×#13063347C22semidirect
17. C22×D344C22semidirect
20. C2×#13063269C22semidirect
21. C2×#13063269C22semidirect
22. C2×#13063269C22semidirect
26. C2×#13063266C22semidirect
27. C2×#13063266C22semidirect
28. C2×#13063266C22semidirect
29. C2×#13063266C22semidirect
30. C2×#13063265C22semidirect
31. C22×C43⋊C16C22semidirect
32. #14583283C22semidirect
33. #14583140C22semidirect
34. #14583135C22semidirect
38. C4×D344C22semidirect
39. #14582726C22semidirect
40. C4⋊(C43⋊C16)C22semidirect
41. #14582702C22semidirect
42. #14582700C22semidirect
43. #14582700C22semidirect
44. #14582700C22semidirect
45. #14582699C22semidirect
46. #14582699C22semidirect
47. C22⋊(C43⋊C16)C22semidirect
48. C22⋊(C43⋊C16)C22semidirect
49. #14582675C22semidirect
51. C22×D8×C43C22semidirect
53. C43×#493C22semidirect
55. C43×#466C22semidirect
59. C4×D8×C43C22semidirect
89. #13063266D4semidirect
202. D344C2×D4semidirect
208. C43⋊C16C2×D4semidirect
284. C22×C43#509semidirect
305. D4×D8D43semidirect
330. C22×D8C2×D43semidirect
347. #493C2×D43semidirect
351. #466C2×D43semidirect
359. C4×D8C2×D43semidirect
372. C43#33830semidirect
602. C22#14583335semidirect

Maximal subgroups

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

subgroupindex
C2×#145833352
C22×#130632662
#191462822
#191368592
#191366962
#191366892
#191366502
#191366272
#191365242
#191365162
#191365072
#191365062
#191364692
#191364212
D4×D8×C432
#3383043