Finite Group Databasebeta

← #25253116

Subgroups — #25253116

Order 11008.

702 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583334C211yesmaximal, characteristic, complemented
2C2×#14583329C211yesmaximal, characteristic, complemented
3#19146282C211yesmaximal, characteristic, complemented
4#19136859C211yesmaximal, characteristic, complemented
5#19136706C211yesmaximal, characteristic, complemented
6#19136679C211yesmaximal, characteristic, complemented
7#19136657C211yesmaximal, characteristic, complemented
8#19136627C211yesmaximal, characteristic, complemented
9#19136535C211yesmaximal, characteristic, complemented
10#19136518C211yesmaximal, characteristic, complemented
11#19136516C211yesmaximal, characteristic, complemented
12#19136506C211yesmaximal, characteristic, complemented
13#19136457C211yesmaximal, characteristic, complemented
14#19136421C211yesmaximal, characteristic, complemented
15C43×#3287C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×D344C2211yescharacteristic
18#14583545—21no—
19#14583334—24no—
20#14583329—24no—
21C2×#13063271C2211yescharacteristic, complemented
22C2×#13063269C2211yescharacteristic, complemented
23C2×#13063269C2211yescharacteristic, complemented
24C2×#13063268C2211yescharacteristic
25C2×#13063268C2211yescharacteristic
26C2×#13063266C2211yescharacteristic
27C2×#13063266C2211yescharacteristic
28C2×#13063266C2211yescharacteristic
29C2×#13063266C2211yescharacteristic
30C2×#13063265C2211yescharacteristic
31C22×C43⋊C16C2211yescharacteristic, complemented
32#14583283C2211yescharacteristic
33#14583140C2211yescharacteristic
34#14583135C2211yescharacteristic
35#14583115—21no—
36#14583052—21no—
37#14583046—21no—
38C4×D344C2211yescharacteristic
39#14582724C2211yescharacteristic, complemented
40C4⋊(C43⋊C16)C2211yescharacteristic, complemented
41#14582703C2211yescharacteristic, complemented
42#14582702C2211yescharacteristic, complemented
43#14582700C2211yescharacteristic, complemented
44#14582700C2211yescharacteristic, complemented
45#14582699C2211yescharacteristic
46#14582699C2211yescharacteristic
47C22⋊(C43⋊C16)C2211yescharacteristic
48C22⋊(C43⋊C16)C2211yescharacteristic, complemented
49#14582675C2211yescharacteristic, complemented
50C2×#135×C43C2211yescharacteristic
51C2×#135×C43C2211yescharacteristic, complemented
52C43×#550—21no—
53C43×#493C2211yescharacteristic, complemented
54C43×#466C2211yescharacteristic
55C43×#466C2211yescharacteristic, complemented
56C43×#460—21no—
57C43×#449—21no—
58C43×#449—21no—
59C4×Q16×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#13063271—22no—
82#13063269—22no—
83#13063269—41no—
84#13063268—22no—
85#13063268D414yescomplemented
86#13063266—22no—
87#13063266—22no—
88#13063266—22no—
89#13063266—41no—
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—
100C2×#41×C43—21no—
101C2×#41×C43—21no—
102#135×C43—22no—
103#135×C43—22no—
104#135×C43—41no—
105#135×C43—41no—
106C2×Q16×C43C2311yescharacteristic
107C2×SD16×C43—21no—
108C2×SD16×C43—21no—
109C2×D8×C43—21no—
110C2×D8×C43C2311yescharacteristic
111C2×D8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#127×C43—21no—
115#127×C43—41no—
116#121×C43—21no—
117#121×C43—21no—
118#121×C43—41no—
119#121×C43—41no—
120C4×Q8×C43—21no—
121C4×D4×C43—41no—
122C4×D4×C43D411yescharacteristic
123#107×C43C2311yescharacteristic
124C4⋊C8×C43D411yescharacteristic
125#103×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
128C22⋊C8×C43D411yescharacteristic
129C22⋊C8×C43D411yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C23×D43—41no—
132#41×C43—42no—
133#41×C43—42no—
134#41×C43—81no—
135#41×C43—81no—
136C2×Q8×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—41no—
140C2×D4×C43—41no—
141C2×D4×C43—41no—
142C2×D4×C43—41no—
143C2×D4×C43—41no—
144C2×D4×C43—41no—
145C2×D4×C43D811yescharacteristic
146C22×C4×C43—41no—
147C22×C4×C43—41no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C2×C22⋊D43—41no—
151C2×C22⋊D43—41no—
152#10621898—42no—
153#10621898—81no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—41no—
157C2×D172—42no—
158C2×D172—81no—
159C2×C4×D43—41no—
160C2×C4×D43—41no—
161C2×Dic86—21no—
162Q16×C43—21no—
163Q16×C43C2×D412yes—
164SD16×C43—42no—
165SD16×C43—42no—
166D8×C43—21no—
167D8×C43—21no—
168D8×C43—21no—
169D8×C43—21no—
170D8×C43—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43D811yescharacteristic
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43D811yescharacteristic
185C22⋊C4×C43D811yescharacteristic
186C42×C43—41no—
187C42×C43C2×D411yescharacteristic
188C22⋊Dic43—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194Dic43⋊C4—41no—
195Dic172—21no—
196Dic172—21no—
197D344—21no—
198D344—21no—
199D344—21no—
200D344—42no—
201D344C2×D412yes—
202#10621873—42no—
203#10621873—81no—
204C43⋊C16—21no—
205C43⋊C16—21no—
206C43⋊C16—21no—
207C43⋊C16C2×D412yes—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C2×D811yescharacteristic
211C23×C43C2×D811yescharacteristic
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—82no—
215C22×D43—82no—
216C22×D43—161no—
217Q8×C43—22no—
218Q8×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—82no—
225D4×C43—82no—
226D4×C43—82no—
227D4×C43—161no—
228D4×C43—161no—
229D4×C43—161no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—82no—
237C2×C4×C43—82no—
238C2×C4×C43C2×D811yescharacteristic
239C2×C4×C43C2×D811yescharacteristic
240C2×C4×C43C2×D811yescharacteristic
241C2×C4×C43C2×D811yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C22⋊D43—82no—
244C22⋊D43—161no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247D172—22no—
248D172—41no—
249D172—41no—
250D172—41no—
251D172—82no—
252C4×D43—82no—
253C4×D43—161no—
254Dic86—41no—
255Dic86—41no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43C22×D411yescharacteristic
260C8×C43H(5,𝔽2)11yescharacteristic
261#33834—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43C22×D811yescharacteristic
275C2×D43—42no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—164no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—42no—
287C4×C43—81no—
288C4×C43D4211yescharacteristic
289C4×C43#57611yescharacteristic
290Dic43—81no—
291Dic43—81no—
292C2×#509—431no—
293C2×#508—431no—
294#3287D4311yescharacteristic, complemented
295#3280—431no—
296#2250—431no—
297#2220—431no—
298#2215—431no—
299#2211—431no—
300#2206—431no—
301#2189—431no—
302#2186—431no—
303#2186—431no—
304#2184—431no—
305#2175—431no—
306#2168—431no—
307C2×C43—41no—
308C2×C43—41no—
309C2×C43—161no—
310C2×C43—161no—
311C2×C43D4×D811yescharacteristic
312C2×C43#341411yescharacteristic
313C2×C43#341511yescharacteristic
314D43—82no—
315D43—161no—
316C2×#135—431no—
317C2×#135C2×D4311yescharacteristic
318C2×#135C2×D4311yescharacteristic, complemented
319C22×D8—431no—
320#550—21no—
321#546—861no—
322#509—864no—
323#508—864no—
324C2×Q32—431no—
325C2×SD32—431no—
326C2×SD32—431no—
327C2×SD32—431no—
328C2×SD32—431no—
329C2×D16—431no—
330C2×D16—431no—
331C2×D16—431no—
332C2×D16—431no—
333C2×M32—431no—
334C22×C16—431no—
335#495—431no—
336#493C2×D4311yescharacteristic, complemented
337#467—431no—
338#466—431no—
339#466C2×D4311yescharacteristic
340#466C2×D4311yescharacteristic, complemented
341#463—861no—
342#460—21no—
343#450—861no—
344#449—21no—
345#449—21no—
346#449—861no—
347C4×Q16C2×D4311yescharacteristic, complemented
348C4×D8—431no—
349C8×D4C2×D4311yescharacteristic
350#366—431no—
351C4⋊C16—431no—
352#358—431no—
353#358—431no—
354#357—431no—
355#357—431no—
356#357—431no—
357#357—431no—
358C22⋊C16—431no—
359C22⋊C16—431no—
360#346—431no—
361C43#3383411yescharacteristic, complemented, Sylow
362C2×#41—21no—
363C2×#41—21no—
364C2×#41—861no—
365C22×D4—861no—
366#135—22no—
367#135—22no—
368#135—41no—
369#135—41no—
370#135—862no—
371#135—1721no—
372C2×Q16—431no—
373C2×Q16C22×D4311yescharacteristic
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—861no—
377C2×SD16—861no—
378C2×D8—21no—
379C2×D8—431no—
380C2×D8—431no—
381C2×D8—862no—
382C2×D8—861no—
383C2×D8—1721no—
384C2×D8C22×D4311yescharacteristic
385C2×D8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387C22×C8C22×D4311yescharacteristic
388#127—21no—
389#127—41no—
390#124—861no—
391#123—1721no—
392C22⋊Q8—861no—
393#121—21no—
394#121—21no—
395#121—41no—
396#121—41no—
397#121—861no—
398#121—1721no—
399#120—1721no—
400C4×Q8—21no—
401C4×D4—41no—
402C4×D4—861no—
403C4×D4C22⋊D4311yescharacteristic
404C2×C22⋊C4—1721no—
405Q32—862no—
406SD32—434no—
407SD32—862no—
408SD32—862no—
409SD32—1721no—
410D16—862no—
411D16—862no—
412D16—862no—
413D16—1721no—
414M32—862no—
415C2×C16—431no—
416C2×C16—431no—
417C2×C16—431no—
418C2×C16—431no—
419C2×C16—862no—
420#107—431no—
421#107C22×D4311yescharacteristic
422C4⋊C8C22⋊D4311yescharacteristic
423#103—21no—
424#103—861no—
425#102—21no—
426#102—21no—
427#102—861no—
428#102—861no—
429C22⋊C8C22⋊D4311yescharacteristic
430C22⋊C8C22⋊D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432C24—1721no—
433#41—42no—
434#41—42no—
435#41—81no—
436#41—81no—
437#41—3441no—
438#41—1722no—
439C2×Q8—21no—
440C2×Q8—861no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—3441no—
452C2×D4—1722no—
453C2×D4—1721no—
454C2×D4—1721no—
455C2×D4—1721no—
456C2×D4#1062188211yescharacteristic
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—1721no—
460C22×C4—1721no—
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463Q16—21no—
464Q16—861no—
465Q16—861no—
466Q16D4×D4312yes—
467SD16—42no—
468SD16—42no—
469SD16—3441no—
470SD16—1722no—
471D8—21no—
472D8—21no—
473D8—21no—
474D8—21no—
475D8—81no—
476D8—432no—
477D8—861no—
478D8—861no—
479D8—861no—
480D8—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8C2×C22⋊D4311yescharacteristic
486C2×C8C2×C22⋊D4311yescharacteristic
487C2×C8C2×C22⋊D4311yescharacteristic
488C2×C8C23×D4311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4#1062188211yescharacteristic
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C22⋊C4#1062188211yescharacteristic
502C22⋊C4#1062188211yescharacteristic
503C42—41no—
504C42C2×C22⋊D4311yescharacteristic
505C16—432no—
506C16—861no—
507C16—861no—
508C16—861no—
509C23—41no—
510C23—41no—
511C23—3442no—
512C23—3442no—
513C23—1721no—
514C23—1721no—
515C23—6881no—
516C23C2×#1062188211yescharacteristic
517C23C2×#1062188211yescharacteristic
518Q8—22no—
519Q8—41no—
520Q8—1721no—
521Q8—1721no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—82no—
528D4—82no—
529D4—82no—
530D4—161no—
531D4—161no—
532D4—161no—
533D4—862no—
534D4—3442no—
535D4—3442no—
536D4—1721no—
537D4—1721no—
538D4—1721no—
539D4—6881no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—3442no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—6881no—
552C2×C4C2×#1062188211yescharacteristic
553C2×C4C2×#1062188211yescharacteristic
554C2×C4C2×#1062188211yescharacteristic
555C2×C4C2×#1062188211yescharacteristic
556C2×C4C22×C22⋊D4311yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8C2×D4×D4311yescharacteristic
561C8#1306337011yescharacteristic
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—1722no—
580C22—6884no—
581C22C22×#1062188211yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—81no—
588C4—3441no—
589C4—3441no—
590C4D4×C22⋊D4311yescharacteristic
591C4#1458370211yescharacteristic
592C2—41no—
593C2—41no—
594C2—161no—
595C2—161no—
596C2—3442no—
597C2—6881no—
598C2D4×#1062188211yescharacteristic
599C2#1914772911yescharacteristic
600C2#1914773411yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3287C2
socleC22×C43C22×D8
hypercenter#3287D43
hypocenterC43#33834
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3287

Complements

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

NH ≅ G/Ntype
1. C2×#14583334C2semidirect
2. C2×#14583329C2semidirect
3. #19146282C2semidirect
4. #19136859C2semidirect
5. #19136706C2semidirect
6. #19136679C2semidirect
7. #19136657C2semidirect
8. #19136627C2semidirect
9. #19136535C2semidirect
10. #19136518C2semidirect
11. #19136516C2semidirect
12. #19136506C2semidirect
13. #19136457C2semidirect
14. #19136421C2semidirect
15. C43×#3287C2semidirect
21. C2×#13063271C22semidirect
22. C2×#13063269C22semidirect
23. C2×#13063269C22semidirect
31. C22×C43⋊C16C22semidirect
39. #14582724C22semidirect
40. C4⋊(C43⋊C16)C22semidirect
41. #14582703C22semidirect
42. #14582702C22semidirect
43. #14582700C22semidirect
44. #14582700C22semidirect
48. C22⋊(C43⋊C16)C22semidirect
49. #14582675C22semidirect
51. C2×#135×C43C22semidirect
53. C43×#493C22semidirect
55. C43×#466C22semidirect
59. C4×Q16×C43C22semidirect
85. #13063268D4semidirect
294. #3287D43semidirect
318. C2×#135C2×D43semidirect
336. #493C2×D43semidirect
340. #466C2×D43semidirect
347. C4×Q16C2×D43semidirect
361. C43#33834semidirect

Maximal subgroups

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

subgroupindex
C2×#145833342
C2×#145833292
#191462822
#191368592
#191367062
#191366792
#191366572
#191366272
#191365352
#191365182
#191365162
#191365062
#191364572
#191364212
C43×#32872
#3383443