Finite Group Databasebeta

← #25253631

Subgroups — #25253631

Order 11008.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146963C211yesmaximal, characteristic, complemented
2#19146269C211yesmaximal, characteristic
3#19136835C211yesmaximal, characteristic, complemented
4#19136777C211yesmaximal, characteristic, complemented
5#19136751C211yesmaximal, characteristic, complemented
6#19136706C211yesmaximal, characteristic, complemented
7#19136692C211yesmaximal, characteristic, complemented
8#19136634C211yesmaximal, characteristic, complemented
9#19136526C211yesmaximal, characteristic, complemented
10#19136525C211yesmaximal, characteristic, complemented
11#19136458C211yesmaximal, characteristic, complemented
12#19136423C211yesmaximal, characteristic, complemented
13#19136310C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2234C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583588—21no—
19#14583533—21no—
20C2×#13063270C2211yescharacteristic
21C2×#13063270C2211yescharacteristic, complemented
22C2×#13063269C2211yescharacteristic, complemented
23C2×#13063265C2211yescharacteristic, complemented
24C2×C16×D43C2211yescharacteristic, complemented
25#14583300C2211yescharacteristic, complemented
26#14583274C2211yescharacteristic
27#14583240—21no—
28#14583231—21no—
29#14583209—21no—
30#14583141C2211yescharacteristic, complemented
31#14583140C2211yescharacteristic, complemented
32#14583136C2211yescharacteristic
33#14583093—21no—
34#14583034—21no—
35#14583032—21no—
36#14582993C2211yescharacteristic, complemented
37#14582981C2211yescharacteristic
38C8×C22⋊D43C2211yescharacteristic
39#107×D43C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42#14582702C2211yescharacteristic, complemented
43#14582701C2211yescharacteristic
44#14582701C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic, complemented
46#14582699C2211yescharacteristic
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic, complemented
49#14582699C2211yescharacteristic, complemented
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51#14582674C2211yescharacteristic, complemented
52C43×#466C2211yescharacteristic
53C43×#427C2211yescharacteristic, complemented
54C43×#367C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×#357C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic, complemented
58C43×C22⋊C16C2211yescharacteristic, complemented
59C22×D172—21no—
60C2×D4×D43—21no—
61C2×D4×D43—41no—
62C2×Dic172C2311yescharacteristic
63C2×D344—22no—
64C2×D344—21no—
65C2×D344—41no—
66C2×D344C2311yescharacteristic
67C2×D344C2311yescharacteristic
68C2×#10621882—21no—
69C2×#10621882—21no—
70D8×D43—22no—
71D8×D43—41no—
72C2×C8×D43C2311yescharacteristic
73#13063321—21no—
74#13063318—41no—
75#13063317—41no—
76#13063316—21no—
77#13063307—41no—
78#13063305—21no—
79#13063304—21no—
80#13063300—21no—
81#13063298—41no—
82#13063295—41no—
83#13063293—41no—
84#13063290—21no—
85#13063287—21no—
86C4×C22⋊D43D411yescharacteristic
87#13063282—41no—
88C4⋊C4×D43—21no—
89#13063270—22no—
90#13063270—41no—
91#13063269—41no—
92#13063265—41no—
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C16×D43—41no—
96#13063259C2311yescharacteristic
97#13063258—21no—
98#13063256—21no—
99Dic43⋊C8D411yescharacteristic
100#13063250—21no—
101#13063248—21no—
102#13063248—21no—
103#13063245—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)D411yescharacteristic
106(C2×D43)⋊C8D411yescharacteristic
107C8×Dic43C2311yescharacteristic
108C2×D8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110#121×C43—21no—
111#117×C43—21no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#106×C43—21no—
118#102×C43—21no—
119C23×D43—41no—
120C23×D43—41no—
121C2×D4×C43—21no—
122C2×D4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C2×C22⋊D43—41no—
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43D811yescharacteristic
128D4×D43—42no—
129D4×D43—81no—
130D4×D43—84no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—41no—
134C2×D172—41no—
135C2×D172—42no—
136C2×D172—81no—
137C2×C4×D43—41no—
138C2×C4×D43—41no—
139C2×C4×D43C2×D411yescharacteristic
140C2×Dic86—21no—
141D8×C43—21no—
142D8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43C2×D411yescharacteristic
146C2×C8×C43C2411yescharacteristic
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C42×C43—41no—
153C22⋊Dic43—41no—
154C22⋊Dic43D811yescharacteristic
155#10621882—42no—
156#10621882—81no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4D811yescharacteristic
161C4⋊Dic43—21no—
162C4⋊Dic43—41no—
163C4⋊Dic43—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4D811yescharacteristic
169C4×Dic43—41no—
170C4×Dic43C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173Dic172—21no—
174Dic172—21no—
175D344—21no—
176D344—21no—
177D344—21no—
178D344—42no—
179D344#4112yes—
180C8×D43—21no—
181C8×D43—21no—
182C16×C43—21no—
183C16×C43—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C23×C43C2×D811yescharacteristic
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—82no—
191C22×D43—82no—
192C22×D43—82no—
193C22×D43—82no—
194C22×D43—161no—
195C22×D43—161no—
196C22×D43C2×D811yescharacteristic
197D4×C43—41no—
198D4×C43—41no—
199D4×C43—82no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43C2×D811yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C22⋊D43—22no—
208C22⋊D43—82no—
209C22⋊D43—82no—
210C22⋊D43—161no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43C2×D811yescharacteristic
214C2×Dic43C2×D811yescharacteristic
215C2×Dic43C2×D811yescharacteristic
216D172—22no—
217D172—41no—
218D172—41no—
219D172—41no—
220D172—82no—
221D172—82no—
222C4×D43—21no—
223C4×D43—21no—
224C4×D43—82no—
225C4×D43—82no—
226Dic86—41no—
227Dic86—41no—
228C8×C43—21no—
229C8×C43C2×#4111yescharacteristic
230C8×C43H(5,𝔽2)11yescharacteristic
231C43⋊C8—21no—
232C43⋊C8—21no—
233#33877—431nomaximal, Sylow
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43C22×D811yescharacteristic
241C2×D43—21no—
242C2×D43—21no—
243C2×D43—42no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—164no—
250C2×D43—164no—
251C2×D43#50912yes—
252C4×C43—21no—
253C4×C43—81no—
254C4×C43—81no—
255C4×C43—81no—
256C4×C43#54611yescharacteristic
257C4×C43#57711yescharacteristic
258Dic43—21no—
259Dic43—21no—
260Dic43—21no—
261Dic43—81no—
262Dic43—81no—
263#3336—431no—
264D4×D8—431no—
265#2244—431no—
266#2234D4311yescharacteristic, complemented
267#2232—431no—
268#2228—431no—
269#2220—431no—
270#2217—431no—
271#2207—431no—
272#2187—431no—
273#2187—431no—
274#2175—431no—
275#2168—431no—
276#2140—431no—
277C2×#357—431no—
278C2×C43—41no—
279C2×C43—161no—
280C2×C43#329411yescharacteristic
281C2×C43C2×#50911yescharacteristic
282C2×C43#341611yescharacteristic
283D43—22no—
284D43—82no—
285D43—161no—
286C22×D8—431no—
287C22×D8—431no—
288#552—861no—
289D42—861no—
290C2×SD32—431no—
291C2×SD32—431no—
292C2×SD32—431no—
293C2×M32—431no—
294C22×C16—431no—
295#499—431no—
296#493—431no—
297#485—861no—
298#483—861no—
299#479—861no—
300#467—431no—
301#467—431no—
302#466—431no—
303#466C2×D4311yescharacteristic
304#459—861no—
305#447—861no—
306#447—861no—
307C4×Q16—431no—
308C4×D8—431no—
309C8×D4—431no—
310#427C2×D4311yescharacteristic, complemented
311C2×#107—431no—
312#367C2×D4311yescharacteristic, complemented
313#366—431no—
314#366C2×D4311yescharacteristic, complemented
315C4⋊C16—431no—
316#358—431no—
317#357—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322#357—431no—
323#357—431no—
324#357C2×D4311yescharacteristic, complemented
325#357C2×D4311yescharacteristic, complemented
326C22⋊C16—431no—
327C22⋊C16C2×D4311yescharacteristic, complemented
328#346—431no—
329C43#3387711yescharacteristic, complemented, Sylow
330C22×D4—861no—
331C22×D4—861no—
332C22×D4—1721no—
333C2×Q16—431no—
334C2×D8—431no—
335C2×D8—431no—
336C2×D8—862no—
337C2×D8—861no—
338C2×D8—861no—
339C2×D8—862no—
340C2×D8—861no—
341C2×D8—1721no—
342C2×D8—1721no—
343C2×D8C22×D4311yescharacteristic
344C22×C8—431no—
345C22×C8C22×D4311yescharacteristic
346#127—861no—
347#126—1721no—
348#125—861no—
349#125—1721no—
350#123—1721no—
351C22⋊Q8—861no—
352C22⋊Q8—861no—
353#121—21no—
354#121—861no—
355#121—1721no—
356#120—1721no—
357#120—1721no—
358C4×Q8—861no—
359C4×D4—431no—
360C4×D4—861no—
361#117—21no—
362#117—1721no—
363C2×C4⋊C4—861no—
364SD32—862no—
365SD32—1721no—
366SD32—1721no—
367M32—1721no—
368C2×C16—431no—
369C2×C16—431no—
370C2×C16—1721no—
371C2×C16C22×D4311yescharacteristic
372C2×C16C22×D4311yescharacteristic
373#107—431no—
374#107—861no—
375#107C22×D4311yescharacteristic
376#107C22×D4311yescharacteristic
377#107C22×D4311yescharacteristic
378#106—21no—
379#106—861no—
380C4⋊C8—431no—
381#103—861no—
382#103—861no—
383#103—861no—
384#102—21no—
385#102—861no—
386#102—861no—
387C22⋊C8—431no—
388C22⋊C8—431no—
389C4×C8—431no—
390C24—1721no—
391C24—1721no—
392C2×Q8—861no—
393C2×D4—21no—
394C2×D4—41no—
395C2×D4—431no—
396C2×D4—861no—
397C2×D4—861no—
398C2×D4—3441no—
399C2×D4—3441no—
400C2×D4—3444no—
401C2×D4—1722no—
402C2×D4—1721no—
403C2×D4—1721no—
404C2×D4—1721no—
405C2×D4—1721no—
406C2×D4—1722no—
407C2×D4—1721no—
408C22×C4—431no—
409C22×C4—1721no—
410C22×C4—1721no—
411C22×C4D4×D4311yescharacteristic
412Q16—861no—
413Q16—861no—
414D8—21no—
415D8—21no—
416D8—432no—
417D8—861no—
418D8—861no—
419D8—861no—
420D8—3441no—
421D8—1722no—
422D8—1722no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—431no—
426C2×C8—431no—
427C2×C8—861no—
428C2×C8—861no—
429C2×C8D4×D4311yescharacteristic
430C2×C8C23×D4311yescharacteristic
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—431no—
435C4⋊C4—861no—
436C4⋊C4—1721no—
437C4⋊C4—1721no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4—1721no—
441C4⋊C4—1721no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—431no—
445C22⋊C4—431no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C22⋊C4—1721no—
450C42—41no—
451C42—431no—
452C42—1721no—
453C16—21no—
454C16—21no—
455C16—861no—
456C16—861no—
457C23—41no—
458C23—431no—
459C23—3442no—
460C23—3442no—
461C23—3442no—
462C23—3442no—
463C23—1721no—
464C23—1721no—
465C23—6881no—
466C23—6881no—
467C23D8×D4311yescharacteristic
468Q8—1721no—
469Q8—1721no—
470D4—41no—
471D4—41no—
472D4—82no—
473D4—862no—
474D4—862no—
475D4—3442no—
476D4—3442no—
477D4—3442no—
478D4—3442no—
479D4—1721no—
480D4—1721no—
481D4—1721no—
482D4—6881no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—431no—
489C2×C4—431no—
490C2×C4—431no—
491C2×C4—861no—
492C2×C4—861no—
493C2×C4—3442no—
494C2×C4—3442no—
495C2×C4—1721no—
496C2×C4—1721no—
497C2×C4D8×D4311yescharacteristic
498C2×C4C2×D4×D4311yescharacteristic
499C8—21no—
500C8—861no—
501C8—861no—
502C8#41×D4311yescharacteristic
503C8#1306337111yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—432no—
511C22—861no—
512C22—861no—
513C22—3441no—
514C22—3441no—
515C22—3441no—
516C22—3441no—
517C22—3441no—
518C22—1722no—
519C22—6884no—
520C22—6884no—
521C22C2×D8×D4311yescharacteristic
522C4—21no—
523C4—81no—
524C4—81no—
525C4—81no—
526C4—861no—
527C4—861no—
528C4—861no—
529C4—3441no—
530C4—3441no—
531C4#1458354111yescharacteristic
532C4#1458370811yescharacteristic
533C2—41no—
534C2—161no—
535C2—862no—
536C2—3442no—
537C2—6881no—
538C2#1914640611yescharacteristic
539C2#509×D4311yescharacteristic
540C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2234C2
socleC22×C43C22×D8
prime radical#19146269C2
hypercenter#2234D43
hypocenterC43#33877
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
1. #19146963C2semidirect
3. #19136835C2semidirect
4. #19136777C2semidirect
5. #19136751C2semidirect
6. #19136706C2semidirect
7. #19136692C2semidirect
8. #19136634C2semidirect
9. #19136526C2semidirect
10. #19136525C2semidirect
11. #19136458C2semidirect
12. #19136423C2semidirect
13. #19136310C2semidirect
14. #357×D43C2semidirect
15. C43×#2234C2semidirect
21. C2×#13063270C22semidirect
22. C2×#13063269C22semidirect
23. C2×#13063265C22semidirect
24. C2×C16×D43C22semidirect
25. #14583300C22semidirect
30. #14583141C22semidirect
31. #14583140C22semidirect
36. #14582993C22semidirect
39. #107×D43C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. #14582702C22semidirect
44. #14582701C22semidirect
45. #14582700C22semidirect
48. #14582699C22semidirect
49. #14582699C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. #14582674C22semidirect
53. C43×#427C22semidirect
54. C43×#367C22semidirect
55. C43×#366C22semidirect
56. C43×#357C22semidirect
57. C43×#357C22semidirect
58. C43×C22⋊C16C22semidirect
266. #2234D43semidirect
310. #427C2×D43semidirect
312. #367C2×D43semidirect
314. #366C2×D43semidirect
324. #357C2×D43semidirect
325. #357C2×D43semidirect
327. C22⋊C16C2×D43semidirect
329. C43#33877semidirect

Maximal subgroups

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

subgroupindex
#191469632
#191462692
#191368352
#191367772
#191367512
#191367062
#191366922
#191366342
#191365262
#191365252
#191364582
#191364232
#191363102
#357×D432
C43×#22342
#3387743