Finite Group Databasebeta

← #25253100

Subgroups — #25253100

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583333C211yesmaximal, characteristic, complemented
2#19146311C211yesmaximal, characteristic, complemented
3#19146274C211yesmaximal, characteristic, complemented
4#19136863C211yesmaximal, characteristic, complemented
5#19136700C211yesmaximal, characteristic, complemented
6#19136691C211yesmaximal, characteristic, complemented
7#19136652C211yesmaximal, characteristic, complemented
8#19136638C211yesmaximal, characteristic, complemented
9#19136535C211yesmaximal, characteristic, complemented
10#19136532C211yesmaximal, characteristic, complemented
11#19136522C211yesmaximal, characteristic, complemented
12#19136518C211yesmaximal, characteristic, complemented
13#19136471C211yesmaximal, characteristic, complemented
14#19136420C211yesmaximal, characteristic, complemented
15C2×C43×#508C211yesmaximal, characteristic, complemented
16C2×#13063344C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583548—21no—
19#14583537—21no—
20#14583333—24no—
21C2×#13063271C2211yescharacteristic, complemented
22C2×#13063270C2211yescharacteristic
23C2×#13063269C2211yescharacteristic
24C2×#13063268C2211yescharacteristic
25C2×#13063266C2211yescharacteristic
26C2×#13063264C2211yescharacteristic
27#14583284C2211yescharacteristic
28#14583277C2211yescharacteristic, complemented
29#14583140C2211yescharacteristic, complemented
30#14583137C2211yescharacteristic
31#14583137C2211yescharacteristic
32#14583135C2211yescharacteristic
33#14583116—21no—
34#14583102—21no—
35#14583061—21no—
36#14583058—21no—
37#14583048—21no—
38#14583044—21no—
39D8×Dic43C2211yescharacteristic
40D8×Dic43C2211yescharacteristic, complemented
41C8×C22⋊D43C2211yescharacteristic
42#14582727C2211yescharacteristic, complemented
43Dic43⋊C16C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582703C2211yescharacteristic, complemented
46#14582703C2211yescharacteristic, complemented
47#14582701C2211yescharacteristic
48#14582700C2211yescharacteristic
49#14582700C2211yescharacteristic, complemented
50C22⋊(C43⋊C16)C2211yescharacteristic, complemented
51(C2×D43)⋊C16C2211yescharacteristic
52#14582674C2211yescharacteristic, complemented
53C2×#135×C43C2211yescharacteristic
54C2×#135×C43C2211yescharacteristic, complemented
55C43×#508—24no—
56C2×Q32×C43C2211yescharacteristic, complemented
57C2×SD32×C43C2211yescharacteristic
58C2×SD32×C43C2211yescharacteristic, complemented
59C2×D16×C43C2211yescharacteristic
60C22×C16×C43C2211yescharacteristic, complemented
61C2×#10621900—21no—
62C2×D4×D43—21no—
63#13063344—22no—
64#13063344—41no—
65C2×Dic172C2311yescharacteristic
66C2×#10621885—21no—
67C2×#10621883—21no—
68C2×#10621884—21no—
69C2×D344C2311yescharacteristic
70C2×#10621882—21no—
71D8×D43—22no—
72D8×D43—41no—
73C2×C8×D43C2311yescharacteristic
74#13063323—21no—
75#13063314—21no—
76#13063308—41no—
77#13063308—41no—
78#13063306—41no—
79#13063304—21no—
80#13063301—21no—
81#13063301—21no—
82#13063299—21no—
83#13063297—41no—
84#13063297—41no—
85#13063293—41no—
86D4×Dic43—21no—
87D4×Dic43—21no—
88C4×C22⋊D43D411yescharacteristic
89C2×Dic43⋊C4—41no—
90C2×(C2×D43)⋊C4—41no—
91#13063271—41no—
92#13063270—22no—
93#13063269—22no—
94#13063268—41no—
95#13063266—22no—
96#13063264—22no—
97C2×C43⋊C16C2311yescharacteristic
98C2×C43⋊C16C2311yescharacteristic
99#13063259C2311yescharacteristic
100#13063259C2311yescharacteristic
101Dic43⋊C8D411yescharacteristic
102#13063250—21no—
103#13063249—21no—
104#13063249—21no—
105#13063247—21no—
106#13063246—21no—
107#13063246—21no—
108C22⋊(C43⋊C8)D411yescharacteristic
109(C2×D43)⋊C8D411yescharacteristic
110C8×Dic43C2311yescharacteristic
111C2×#41×C43—21no—
112C2×#41×C43—21no—
113#135×C43—22no—
114#135×C43—22no—
115#135×C43—41no—
116#135×C43—41no—
117C2×Q16×C43C2311yescharacteristic
118C2×Q16×C43C2311yescharacteristic
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×D8×C43C2311yescharacteristic
122C2×D8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124Q32×C43—22no—
125SD32×C43—22no—
126SD32×C43—22no—
127D16×C43D414yescomplemented
128C2×C16×C43—22no—
129C2×C16×C43C2311yescharacteristic
130C2×C16×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×Q8×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—41no—
141C2×D4×C43—41no—
142C22×C4×C43—41no—
143C22×C4×C43—41no—
144C22×C4×C43C2×D411yescharacteristic
145C2×C22⋊D43—41no—
146C2×C22⋊D43—41no—
147C2×C22⋊D43—41no—
148C2×C22⋊D43D811yescharacteristic
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152#10621900—42no—
153#10621900—81no—
154D4×D43—42no—
155D4×D43—81no—
156C2×D172—21no—
157C2×C4×D43C2×D411yescharacteristic
158C2×Dic86—21no—
159Q16×C43—21no—
160Q16×C43—21no—
161Q16×C43—21no—
162Q16×C43—21no—
163SD16×C43—42no—
164SD16×C43—42no—
165D8×C43—21no—
166D8×C43—21no—
167D8×C43C2×D412yes—
168D8×C43C2×D412yes—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2411yescharacteristic
173C22⋊Dic43—41no—
174C22⋊Dic43—41no—
175C22⋊Dic43—41no—
176C22⋊Dic43D811yescharacteristic
177#10621885—81no—
178#10621884—81no—
179#10621883—42no—
180#10621882—42no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4D811yescharacteristic
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4D811yescharacteristic
195C4×Dic43C2×D411yescharacteristic
196C2×C43⋊C8C2×D411yescharacteristic
197C2×C43⋊C8C2×D411yescharacteristic
198Dic172—21no—
199Dic172—21no—
200D344—21no—
201D344—21no—
202C8×D43—21no—
203C8×D43—21no—
204C16×C43—21no—
205C16×C43C2×D412yes—
206C43⋊C16—21no—
207C43⋊C16—21no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C2×D811yescharacteristic
211C22×D43—41no—
212C22×D43—82no—
213C22×D43—82no—
214C22×D43—161no—
215C22×D43C2×D811yescharacteristic
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220D4×C43—22no—
221D4×C43—22no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—82no—
225D4×C43—82no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—82no—
231C2×C4×C43—82no—
232C2×C4×C43C2×D811yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C22⋊D43—41no—
235C22⋊D43—82no—
236C22⋊D43—82no—
237C22⋊D43—161no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—82no—
242C2×Dic43—82no—
243C2×Dic43—161no—
244C2×Dic43C2×D811yescharacteristic
245C2×Dic43C2×D811yescharacteristic
246C2×Dic43C2×D811yescharacteristic
247D172—41no—
248D172—41no—
249C4×D43—21no—
250C4×D43—21no—
251Dic86—41no—
252Dic86—41no—
253C8×C43—21no—
254C8×C43C22×D411yescharacteristic
255C8×C43H(5,𝔽2)11yescharacteristic
256C43⋊C8—21no—
257C43⋊C8—21no—
258#33833—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43C22×D811yescharacteristic
269C2×D43—21no—
270C2×D43—21no—
271C2×D43—21no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—164no—
276C4×C43—21no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43D4211yescharacteristic
280C4×C43#57611yescharacteristic
281Dic43—21no—
282Dic43—21no—
283Dic43—21no—
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287C2×#509—431no—
288C2×#508D4311yescharacteristic, complemented
289#3283—431no—
290#3280—431no—
291#2251—431no—
292#2219—431no—
293#2217—431no—
294#2210—431no—
295#2208—431no—
296#2189—431no—
297#2189—431no—
298#2187—431no—
299#2186—431no—
300#2177—431no—
301#2168—431no—
302C2×C43—41no—
303C2×C43—82no—
304C2×C43—82no—
305C2×C43D4×D811yescharacteristic
306C2×C43#341411yescharacteristic
307C2×C43#341611yescharacteristic
308D43—41no—
309D43—161no—
310C2×#135—431no—
311C2×#135C2×D4311yescharacteristic
312C2×#135C2×D4311yescharacteristic, complemented
313C22×D8—431no—
314#547—861no—
315#546—861no—
316#509—864no—
317#508—24no—
318C2×Q32—431no—
319C2×Q32C2×D4311yescharacteristic, complemented
320C2×SD32—431no—
321C2×SD32—431no—
322C2×SD32—431no—
323C2×SD32C2×D4311yescharacteristic
324C2×SD32C2×D4311yescharacteristic, complemented
325C2×D16—431no—
326C2×D16C2×D4311yescharacteristic
327C2×M32—431no—
328C22×C16C2×D4311yescharacteristic, complemented
329#495—431no—
330#494—431no—
331#467—431no—
332#467—431no—
333#467—431no—
334#466—431no—
335#463—861no—
336#461—861no—
337#452—861no—
338#452—861no—
339#450—861no—
340#449—861no—
341C4×D8—431no—
342C4×D8—431no—
343C8×D4—431no—
344#367—431no—
345C4⋊C16—431no—
346#358—431no—
347#358—431no—
348#358—431no—
349#357—431no—
350#357—431no—
351#357—431no—
352C22⋊C16—431no—
353C22⋊C16—431no—
354#346—431no—
355C43#3383311yescharacteristic, complemented, Sylow
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—861no—
359C22×D4—861no—
360#135—22no—
361#135—22no—
362#135—41no—
363#135—41no—
364#135—862no—
365#135—1721no—
366C2×Q16—431no—
367C2×Q16—861no—
368C2×Q16C22×D4311yescharacteristic
369C2×Q16C22×D4311yescharacteristic
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×D8—431no—
375C2×D8—861no—
376C2×D8—862no—
377C2×D8—1721no—
378C2×D8C22×D4311yescharacteristic
379C2×D8C22×D4311yescharacteristic
380C22×C8—431no—
381C22×C8C22×D4311yescharacteristic
382C4⋊Q8—861no—
383#124—861no—
384#123—1721no—
385#123—1721no—
386#123—1721no—
387C22⋊Q8—861no—
388C22⋊Q8—861no—
389C22⋊Q8—861no—
390#121—861no—
391#121—1721no—
392#121—1721no—
393#120—1721no—
394C4×D4—431no—
395C4×D4—861no—
396C4×D4—861no—
397C2×C4⋊C4—1721no—
398C2×C22⋊C4—1721no—
399Q32—22no—
400Q32—1721no—
401SD32—22no—
402SD32—22no—
403SD32—862no—
404SD32—862no—
405SD32—1721no—
406D16—862no—
407D16C22⋊D4314yescomplemented
408M32—862no—
409C2×C16—22no—
410C2×C16—431no—
411C2×C16—431no—
412C2×C16C22×D4311yescharacteristic
413C2×C16C22×D4311yescharacteristic
414#107—431no—
415#107—431no—
416C4⋊C8—431no—
417#103—861no—
418#103—861no—
419#103—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423C22⋊C8—431no—
424C22⋊C8—431no—
425C4×C8—431no—
426C24—1721no—
427#41—42no—
428#41—42no—
429#41—81no—
430#41—81no—
431#41—3441no—
432#41—1722no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—861no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—431no—
441C2×D4—861no—
442C2×D4—3441no—
443C2×D4—1721no—
444C2×D4—1722no—
445C2×D4—1721no—
446C2×D4—1721no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—431no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4D4×D4311yescharacteristic
454Q16—21no—
455Q16—21no—
456Q16—21no—
457Q16—21no—
458Q16—861no—
459Q16—861no—
460Q16—3441no—
461SD16—42no—
462SD16—42no—
463SD16—3441no—
464SD16—1722no—
465D8—21no—
466D8—21no—
467D8—861no—
468D8—861no—
469D8—1722no—
470D8C2×C22⋊D4312yes—
471D8C2×C22⋊D4312yes—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8D4×D4311yescharacteristic
479C2×C8C23×D4311yescharacteristic
480C4⋊C4—431no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C22⋊C4—431no—
489C22⋊C4—431no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C22⋊C4—1721no—
495C22⋊C4—1721no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C42—431no—
499C16—21no—
500C16—861no—
501C16—861no—
502C16C2×C22⋊D4312yes—
503C23—41no—
504C23—41no—
505C23—431no—
506C23—3442no—
507C23—3442no—
508C23—1721no—
509C23—6881no—
510C23D8×D4311yescharacteristic
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—1721no—
516Q8—1721no—
517D4—22no—
518D4—22no—
519D4—41no—
520D4—41no—
521D4—82no—
522D4—82no—
523D4—3442no—
524D4—3442no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528D4—6881no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—431no—
536C2×C4—431no—
537C2×C4—431no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—3442no—
541C2×C4—3442no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—6881no—
546C2×C4D8×D4311yescharacteristic
547C2×C4C2×D4×D4311yescharacteristic
548C8—21no—
549C8—861no—
550C8—861no—
551C8C22×C22⋊D4311yescharacteristic
552C8#1306337011yescharacteristic
553C22—21no—
554C22—21no—
555C22—21no—
556C22—42no—
557C22—42no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—861no—
563C22—861no—
564C22—861no—
565C22—3441no—
566C22—3441no—
567C22—3441no—
568C22—6884no—
569C22C2×D8×D4311yescharacteristic
570C4—21no—
571C4—81no—
572C4—81no—
573C4—861no—
574C4—861no—
575C4—861no—
576C4—3441no—
577C4—3441no—
578C4—3441no—
579C4D4×C22⋊D4311yescharacteristic
580C4#1458370011yescharacteristic
581C2—41no—
582C2—82no—
583C2—82no—
584C2—1721no—
585C2—6881no—
586C2D8×C22⋊D4311yescharacteristic
587C2#1914772811yescharacteristic
588C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#508C2
socleC22×C43C22×D8
hypercenterC2×#508D43
hypocenterC43#33833
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#14583333C2semidirect
2. #19146311C2semidirect
3. #19146274C2semidirect
4. #19136863C2semidirect
5. #19136700C2semidirect
6. #19136691C2semidirect
7. #19136652C2semidirect
8. #19136638C2semidirect
9. #19136535C2semidirect
10. #19136532C2semidirect
11. #19136522C2semidirect
12. #19136518C2semidirect
13. #19136471C2semidirect
14. #19136420C2semidirect
15. C2×C43×#508C2semidirect
21. C2×#13063271C22semidirect
28. #14583277C22semidirect
29. #14583140C22semidirect
40. D8×Dic43C22semidirect
42. #14582727C22semidirect
43. Dic43⋊C16C22semidirect
44. #14582704C22semidirect
45. #14582703C22semidirect
46. #14582703C22semidirect
49. #14582700C22semidirect
50. C22⋊(C43⋊C16)C22semidirect
52. #14582674C22semidirect
54. C2×#135×C43C22semidirect
56. C2×Q32×C43C22semidirect
58. C2×SD32×C43C22semidirect
60. C22×C16×C43C22semidirect
127. D16×C43D4semidirect
288. C2×#508D43semidirect
312. C2×#135C2×D43semidirect
319. C2×Q32C2×D43semidirect
324. C2×SD32C2×D43semidirect
328. C22×C16C2×D43semidirect
355. C43#33833semidirect
407. D16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833332
#191463112
#191462742
#191368632
#191367002
#191366912
#191366522
#191366382
#191365352
#191365322
#191365222
#191365182
#191364712
#191364202
C2×C43×#5082
#3383343