Finite Group Databasebeta

← #25253081

Subgroups — #25253081

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583339C211yesmaximal, characteristic, complemented
2C22×#13063269C211yesmaximal, characteristic, complemented
3D4×Dic172C211yesmaximal, characteristic, complemented
4#19136867C211yesmaximal, characteristic, complemented
5#19136706C211yesmaximal, characteristic, complemented
6#19136684C211yesmaximal, characteristic, complemented
7#19136654C211yesmaximal, characteristic, complemented
8#19136640C211yesmaximal, characteristic, complemented
9#19136535C211yesmaximal, characteristic, complemented
10#19136528C211yesmaximal, characteristic, complemented
11#19136524C211yesmaximal, characteristic, complemented
12#19136511C211yesmaximal, characteristic, complemented
13#19136459C211yesmaximal, characteristic, complemented
14#19136421C211yesmaximal, characteristic, complemented
15C43×#3280C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×Dic172C2211yescharacteristic, complemented
18D4×Dic86—21no—
19#14583339—24no—
20C2×#13063271C2211yescharacteristic, complemented
21C2×#13063271C2211yescharacteristic, complemented
22C2×#13063271C2211yescharacteristic, complemented
23C2×#13063269—24no—
24C2×#13063269C2211yescharacteristic
25C2×#13063269C2211yescharacteristic
26C2×#13063269C2211yescharacteristic
27C2×#13063269C2211yescharacteristic
28C2×#13063269C2211yescharacteristic
29C2×#13063269C2211yescharacteristic
30C2×#13063265C2211yescharacteristic, complemented
31C22×C43⋊C16C2211yescharacteristic
32#14583279C2211yescharacteristic, complemented
33#14583140C2211yescharacteristic
34#14583140C2211yescharacteristic, complemented
35#14583110—21no—
36#14583057—21no—
37#14583057—21no—
38C4×Dic172C2211yescharacteristic, complemented
39#14582724C2211yescharacteristic, complemented
40C4⋊(C43⋊C16)C2211yescharacteristic, complemented
41#14582703C2211yescharacteristic, complemented
42#14582702C2211yescharacteristic, complemented
43#14582702C2211yescharacteristic, complemented
44#14582702C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic
47C22⋊(C43⋊C16)C2211yescharacteristic
48C22⋊(C43⋊C16)C2211yescharacteristic, complemented
49#14582675C2211yescharacteristic, complemented
50C2×#135×C43C2211yescharacteristic
51C22×D8×C43C2211yescharacteristic
52C43×#546—21no—
53C43×#495C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#463—21no—
57C43×#450—21no—
58C43×#449—21no—
59C4×D8×C43C2211yescharacteristic
60C8×D4×C43C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86—21no—
63C2×Dic172—22no—
64C2×Dic172—22no—
65C2×Dic172—21no—
66C2×Dic172—21no—
67C2×Dic172—21no—
68C2×Dic172—41no—
69C2×Dic172—41no—
70C2×Dic172C2311yescharacteristic
71C2×Dic172C2311yescharacteristic
72C2×Dic172C2311yescharacteristic
73#13063325—21no—
74#13063324—41no—
75#13063304—21no—
76#13063304—21no—
77#13063302—41no—
78#13063302—41no—
79C4×Dic86—21no—
80D4×Dic43—41no—
81#13063271—22no—
82#13063271—22no—
83#13063271—41no—
84#13063269—22no—
85#13063269—22no—
86#13063269—22no—
87#13063269—22no—
88#13063269—41no—
89#13063269D414yescomplemented
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#13063250—21no—
99#13063250—21no—
100C2×#41×C43—21no—
101C22×D4×C43—21no—
102#135×C43—22no—
103#135×C43—41no—
104C2×Q16×C43C2311yescharacteristic
105C2×SD16×C43—21no—
106C2×SD16×C43—21no—
107C2×D8×C43—22no—
108C2×D8×C43—21no—
109C2×D8×C43—41no—
110C2×D8×C43C2311yescharacteristic
111C2×D8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#124×C43—21no—
115#123×C43—41no—
116C22⋊Q8×C43—21no—
117#121×C43—21no—
118#121×C43—41no—
119#120×C43—41no—
120C4×D4×C43—21no—
121C4×D4×C43D411yescharacteristic
122C2×C22⋊C4×C43—41no—
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
131C24×C43—41no—
132#41×C43—42no—
133#41×C43—81no—
134C2×Q8×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—42no—
141C2×D4×C43—81no—
142C2×D4×C43D811yescharacteristic
143C22×C4×C43—41no—
144C22×C4×C43—41no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×Dic43—41no—
148C22×Dic43—41no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—42no—
153C2×Dic86—42no—
154C2×Dic86—41no—
155C2×Dic86—41no—
156C2×Dic86—81no—
157C2×Dic86—81no—
158Q16×C43—21no—
159Q16×C43—21no—
160SD16×C43—42no—
161SD16×C43—81no—
162D8×C43—21no—
163D8×C43—21no—
164D8×C43—21no—
165D8×C43—42no—
166D8×C43C2×D412yes—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43D811yescharacteristic
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43D811yescharacteristic
184C22⋊C4×C43D811yescharacteristic
185C42×C43C2×D411yescharacteristic
186C22⋊Dic43—41no—
187C22⋊Dic43—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—41no—
195Dic172—21no—
196Dic172—21no—
197Dic172—21no—
198Dic172—21no—
199Dic172—21no—
200Dic172—42no—
201Dic172—42no—
202Dic172—81no—
203Dic172C2×D412yes—
204C43⋊C16—21no—
205C43⋊C16—21no—
206C43⋊C16—21no—
207C43⋊C16C2×D412yes—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—82no—
211C23×C43—82no—
212C23×C43—161no—
213C23×C43C2×D811yescharacteristic
214C23×C43C2×D811yescharacteristic
215Q8×C43—41no—
216Q8×C43—41no—
217D4×C43—22no—
218D4×C43—22no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—82no—
223D4×C43—82no—
224D4×C43—161no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—82no—
232C2×C4×C43—161no—
233C2×C4×C43C2×D811yescharacteristic
234C2×C4×C43C2×D811yescharacteristic
235C2×C4×C43C2×D811yescharacteristic
236C2×C4×C43C2×D811yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—82no—
243C2×Dic43—82no—
244Dic86—22no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—82no—
251Dic86—82no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43C22×D411yescharacteristic
256C8×C43H(5,𝔽2)11yescharacteristic
257#33832—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—42no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—164no—
270C22×C43#51012yescomplemented
271C22×C43C22×D811yescharacteristic
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43D4211yescharacteristic
279C4×C43#57611yescharacteristic
280Dic43—42no—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284C2×#510—431no—
285C22×SD32—431no—
286D4×Q16—431no—
287#3280D4311yescharacteristic
288#2251—431no—
289#2220—431no—
290#2216—431no—
291#2211—431no—
292#2208—431no—
293#2189—431no—
294#2188—431no—
295#2187—431no—
296#2185—431no—
297#2175—431no—
298#2168—431no—
299C2×C43—22no—
300C2×C43—41no—
301C2×C43—82no—
302C2×C43—161no—
303C2×C43D4×D811yescharacteristic
304C2×C43C2×#51011yescharacteristic
305C2×C43#341611yescharacteristic
306C2×#135C2×D4311yescharacteristic
307C22×Q16—431no—
308C22×Q16—431no—
309C22×D8C2×D4311yescharacteristic
310D4×Q8—861no—
311#546—21no—
312#510—864no—
313C2×Q32—431no—
314C2×Q32—431no—
315C2×Q32—431no—
316C2×SD32—431no—
317C2×SD32—431no—
318C2×SD32—431no—
319C2×SD32—431no—
320C2×SD32—431no—
321C2×SD32—431no—
322C2×SD32—864no—
323C2×M32—431no—
324C22×C16—431no—
325#495C2×D4311yescharacteristic
326#494—431no—
327#467—431no—
328#467—431no—
329#467C2×D4311yescharacteristic
330#466C2×D4311yescharacteristic
331#463—21no—
332#462—861no—
333#451—861no—
334#451—861no—
335#450—21no—
336#449—21no—
337C4×Q16—431no—
338C4×D8C2×D4311yescharacteristic
339C8×D4C2×D4311yescharacteristic
340#366—431no—
341C4⋊C16—431no—
342#358—431no—
343#358—431no—
344#358—431no—
345#358—431no—
346#357—431no—
347#357—431no—
348C22⋊C16—431no—
349C22⋊C16—431no—
350#346—431no—
351C43#3383211yescharacteristic, complemented, Sylow
352C2×#41—21no—
353C22×Q8—861no—
354C22×Q8—861no—
355C22×D4—21no—
356#135—22no—
357#135—41no—
358C2×Q16—431no—
359C2×Q16—431no—
360C2×Q16—431no—
361C2×Q16—862no—
362C2×Q16—862no—
363C2×Q16—861no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—1721no—
367C2×Q16—1721no—
368C2×Q16C22×D4311yescharacteristic
369C2×SD16—21no—
370C2×SD16—21no—
371C2×D8—22no—
372C2×D8—21no—
373C2×D8—41no—
374C2×D8C22×D4311yescharacteristic
375C2×D8C22×D4311yescharacteristic
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378C4⋊Q8—861no—
379C4⋊Q8—1721no—
380#124—21no—
381#123—41no—
382C22⋊Q8—21no—
383C22⋊Q8—861no—
384C22⋊Q8—861no—
385C22⋊Q8—1721no—
386C22⋊Q8—1721no—
387#121—21no—
388#121—41no—
389#120—41no—
390C4×Q8—861no—
391C4×D4—21no—
392C4×D4—1721no—
393C4×D4C22⋊D4311yescharacteristic
394C2×C22⋊C4—41no—
395Q32—862no—
396Q32—862no—
397Q32—1721no—
398SD32—434no—
399SD32—862no—
400SD32—862no—
401SD32—862no—
402SD32—862no—
403SD32—1721no—
404M32—862no—
405C2×C16—431no—
406C2×C16—431no—
407C2×C16—431no—
408C2×C16—431no—
409C2×C16—862no—
410#107—431no—
411#107C22×D4311yescharacteristic
412C4⋊C8C22⋊D4311yescharacteristic
413#103—21no—
414#103—861no—
415#103—861no—
416#103—861no—
417#102—21no—
418#102—21no—
419C22⋊C8C22⋊D4311yescharacteristic
420C22⋊C8C22⋊D4311yescharacteristic
421C4×C8C22×D4311yescharacteristic
422C24—41no—
423#41—42no—
424#41—81no—
425C2×Q8—21no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—3441no—
430C2×Q8—3441no—
431C2×Q8—1722no—
432C2×Q8—1722no—
433C2×Q8—1721no—
434C2×Q8—1721no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—42no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—81no—
442C2×D4#1062188211yescharacteristic
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4C2×C22⋊D4311yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449Q16—21no—
450Q16—21no—
451Q16—432no—
452Q16—861no—
453Q16—861no—
454Q16—861no—
455Q16—861no—
456Q16—861no—
457Q16—3441no—
458Q16—1722no—
459Q16—1722no—
460SD16—42no—
461SD16—81no—
462D8—21no—
463D8—21no—
464D8—21no—
465D8—42no—
466D8D4×D4312yes—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×C22⋊D4311yescharacteristic
472C2×C8C2×C22⋊D4311yescharacteristic
473C2×C8C2×C22⋊D4311yescharacteristic
474C2×C8C23×D4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4#1062188211yescharacteristic
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C22⋊C4#1062188211yescharacteristic
492C22⋊C4#1062188211yescharacteristic
493C42—1721no—
494C42C2×C22⋊D4311yescharacteristic
495C16—432no—
496C16—861no—
497C16—861no—
498C16—861no—
499C23—41no—
500C23—41no—
501C23—82no—
502C23—82no—
503C23—161no—
504C23C2×#1062188211yescharacteristic
505C23C2×#1062188211yescharacteristic
506Q8—41no—
507Q8—41no—
508Q8—862no—
509Q8—3442no—
510Q8—3442no—
511Q8—1721no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—82no—
522D4—82no—
523D4—161no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—82no—
531C2×C4—161no—
532C2×C4—3442no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4C2×#1062188211yescharacteristic
539C2×C4C2×#1062188211yescharacteristic
540C2×C4C2×#1062188211yescharacteristic
541C2×C4C2×#1062188211yescharacteristic
542C2×C4C22×C22⋊D4311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8C2×D4×D4311yescharacteristic
547C8#1306337011yescharacteristic
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—164no—
560C22#1458333912yescomplemented
561C22C22×#1062188211yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—81no—
567C4—81no—
568C4—3441no—
569C4—3441no—
570C4—3441no—
571C4—1722no—
572C4D4×C22⋊D4311yescharacteristic
573C4#1458370211yescharacteristic
574C2—22no—
575C2—41no—
576C2—82no—
577C2—161no—
578C2D4×#1062188211yescharacteristic
579C2C2×#1458333911yescharacteristic
580C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
Fitting, prime radicalC43×#3280C2
socleC22×C43C22×D8
hypercenter#3280D43
hypocenterC43#33832
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. C2×#14583339C2semidirect
2. C22×#13063269C2semidirect
3. D4×Dic172C2semidirect
4. #19136867C2semidirect
5. #19136706C2semidirect
6. #19136684C2semidirect
7. #19136654C2semidirect
8. #19136640C2semidirect
9. #19136535C2semidirect
10. #19136528C2semidirect
11. #19136524C2semidirect
12. #19136511C2semidirect
13. #19136459C2semidirect
14. #19136421C2semidirect
17. C22×Dic172C22semidirect
20. C2×#13063271C22semidirect
21. C2×#13063271C22semidirect
22. C2×#13063271C22semidirect
30. C2×#13063265C22semidirect
32. #14583279C22semidirect
34. #14583140C22semidirect
38. C4×Dic172C22semidirect
39. #14582724C22semidirect
40. C4⋊(C43⋊C16)C22semidirect
41. #14582703C22semidirect
42. #14582702C22semidirect
43. #14582702C22semidirect
44. #14582702C22semidirect
48. C22⋊(C43⋊C16)C22semidirect
49. #14582675C22semidirect
89. #13063269D4semidirect
270. C22×C43#510semidirect
351. C43#33832semidirect
560. C22#14583339semidirect

Maximal subgroups

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

subgroupindex
C2×#145833392
C22×#130632692
D4×Dic1722
#191368672
#191367062
#191366842
#191366542
#191366402
#191365352
#191365282
#191365242
#191365112
#191364592
#191364212
C43×#32802
#3383243