Finite Group Databasebeta

← #25253634

Subgroups — #25253634

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#19146966C211yesmaximal, characteristic, complemented
2#19146269C211yesmaximal, characteristic
3#19136835C211yesmaximal, characteristic, complemented
4#19136788C211yesmaximal, characteristic, complemented
5#19136773C211yesmaximal, characteristic, complemented
6#19136751C211yesmaximal, characteristic, complemented
7#19136711C211yesmaximal, characteristic, complemented
8#19136633C211yesmaximal, characteristic, complemented
9#19136523C211yesmaximal, characteristic, complemented
10#19136522C211yesmaximal, characteristic, complemented
11#19136462C211yesmaximal, characteristic, complemented
12#19136420C211yesmaximal, characteristic, complemented
13#19136309C211yesmaximal, characteristic, complemented
14C2×#14582701C211yesmaximal, characteristic, complemented
15C43×#2217C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583591—21no—
19#14583533—21no—
20C2×#13063268C2211yescharacteristic
21C2×#13063268C2211yescharacteristic, complemented
22C2×#13063264C2211yescharacteristic, complemented
23#14583300C2211yescharacteristic, complemented
24#14583274C2211yescharacteristic
25#14583239—21no—
26#14583227—21no—
27#14583208—21no—
28#14583137C2211yescharacteristic, complemented
29#14583136C2211yescharacteristic
30#14583093—21no—
31#14583034—21no—
32#14583032—21no—
33Q16×Dic43C2211yescharacteristic, complemented
34#14582981C2211yescharacteristic
35C8×C22⋊D43C2211yescharacteristic
36#14582936C2211yescharacteristic, complemented
37C2×#13063259C2211yescharacteristic, complemented
38#14582724C2211yescharacteristic, complemented
39#14582724C2211yescharacteristic, complemented
40Dic43⋊C16C2211yescharacteristic, complemented
41#14582701C2211yescharacteristic
42#14582701C2211yescharacteristic
43#14582701C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic, complemented
46#14582700C2211yescharacteristic, complemented
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic, complemented
49C22⋊(C43⋊C16)C2211yescharacteristic, complemented
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51#14582674C2211yescharacteristic, complemented
52C2×SD32×C43C2211yescharacteristic, complemented
53C22×C16×C43C2211yescharacteristic, complemented
54C43×#467C2211yescharacteristic, complemented
55C43×#466C2211yescharacteristic
56C43×#367C2211yescharacteristic, complemented
57C43×#358C2211yescharacteristic, complemented
58C43×#357C2211yescharacteristic, complemented
59C22×D172—21no—
60C2×D4×D43—21no—
61C2×D4×D43—41no—
62C2×D344—22no—
63C2×D344—21no—
64C2×D344—41no—
65C2×D344C2311yescharacteristic
66C2×D344C2311yescharacteristic
67C2×#10621882—21no—
68C2×#10621882—21no—
69D8×D43—22no—
70D8×D43—41no—
71C2×C8×D43C2311yescharacteristic
72#13063321—21no—
73#13063320—41no—
74#13063316—21no—
75#13063316—41no—
76#13063309—41no—
77#13063301—21no—
78#13063300—21no—
79#13063298—41no—
80#13063295—41no—
81#13063293—41no—
82Q8×Dic43—21no—
83#13063287—21no—
84C4×C22⋊D43D411yescharacteristic
85#13063283—21no—
86#13063281—41no—
87C2×C4⋊Dic43—21no—
88#13063268—22no—
89#13063268—41no—
90#13063264—41no—
91C2×C43⋊C16C2311yescharacteristic
92C2×C43⋊C16C2311yescharacteristic
93#13063259—21no—
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063256—21no—
97#13063256—21no—
98Dic43⋊C8D411yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)D411yescharacteristic
104(C2×D43)⋊C8D411yescharacteristic
105C8×Dic43C2311yescharacteristic
106C2×Q16×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22⋊Q8×C43—21no—
110#121×C43—21no—
111SD32×C43—41no—
112C2×C16×C43—41no—
113C2×C16×C43C2311yescharacteristic
114C2×C16×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#103×C43—21no—
118#102×C43—21no—
119C23×D43—41no—
120C23×D43—41no—
121C2×Q8×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C2×C22⋊D43D811yescharacteristic
129C22×Dic43—41no—
130D4×D43—42no—
131D4×D43—81no—
132D4×D43—84no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—41no—
136C2×D172—41no—
137C2×D172—42no—
138C2×D172—81no—
139C2×C4×D43—41no—
140C2×C4×D43C2×D411yescharacteristic
141Q16×C43—21no—
142Q16×C43—21no—
143D8×C43—21no—
144D8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43C2×D411yescharacteristic
148C2×C8×C43C2411yescharacteristic
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C22⋊C4×C43—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)⋊C4—41no—
161(C2×D43)⋊C4D811yescharacteristic
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—41no—
165C4⋊Dic43—41no—
166C4⋊Dic43—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169Dic43⋊C4D811yescharacteristic
170C4×Dic43—41no—
171C4×Dic43—41no—
172C4×Dic43C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174C2×C43⋊C8C2×D411yescharacteristic
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
197Q8×C43—41no—
198Q8×C43—41no—
199D4×C43—41no—
200D4×C43—41no—
201D4×C43—82no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43C2×D811yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C22⋊D43—22no—
210C22⋊D43—82no—
211C22⋊D43—82no—
212C22⋊D43—161no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—82no—
216C2×Dic43C2×D811yescharacteristic
217C2×Dic43C2×D811yescharacteristic
218C2×Dic43C2×D811yescharacteristic
219D172—22no—
220D172—41no—
221D172—41no—
222D172—41no—
223D172—82no—
224D172—82no—
225C4×D43—21no—
226C4×D43—21no—
227C4×D43—82no—
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—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43#50912yes—
240C22×C43C22×D811yescharacteristic
241C2×D43—21no—
242C2×D43—21no—
243C2×D43—21no—
244C2×D43—42no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—81no—
250C2×D43—164no—
251C2×D43—164no—
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#2234—431no—
267#2232—431no—
268#2228—431no—
269#2220—431no—
270#2217D4311yescharacteristic, complemented
271#2207—431no—
272#2187—431no—
273#2187—431no—
274#2175—431no—
275#2168—431no—
276#2140—431no—
277C2×#357—431no—
278C2×C43—22no—
279C2×C43—161no—
280C2×C43#329411yescharacteristic
281C2×C43C2×#50911yescharacteristic
282C2×C43#341611yescharacteristic
283D43—41no—
284D43—82no—
285D43—161no—
286C22×D8—431no—
287C22×D8—431no—
288#552—861no—
289D42—861no—
290C2×SD32—431no—
291C2×SD32—431no—
292C2×SD32C2×D4311yescharacteristic, complemented
293C2×M32—431no—
294C22×C16C2×D4311yescharacteristic, complemented
295#499—431no—
296#493—431no—
297#485—861no—
298#483—861no—
299#479—861no—
300#467—431no—
301#467C2×D4311yescharacteristic, complemented
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#427—431no—
311C2×#107—431no—
312#367C2×D4311yescharacteristic, complemented
313#366—431no—
314#366—431no—
315C4⋊C16—431no—
316#358C2×D4311yescharacteristic, complemented
317#357—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322#357—431no—
323#357—431no—
324#357—431no—
325#357C2×D4311yescharacteristic, complemented
326C22⋊C16—431no—
327C22⋊C16—431no—
328#346—431no—
329C43#3387711yescharacteristic, complemented, Sylow
330C22×D4—861no—
331C22×D4—861no—
332C22×D4—1721no—
333C2×Q16C22×D4311yescharacteristic
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—21no—
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—861no—
362#117—1721no—
363C2×C4⋊C4—861no—
364SD32—41no—
365SD32—862no—
366SD32—1721no—
367M32—1721no—
368C2×C16—41no—
369C2×C16—431no—
370C2×C16—431no—
371C2×C16C22×D4311yescharacteristic
372C2×C16C22×D4311yescharacteristic
373#107—431no—
374#107—431no—
375#107—861no—
376#107C22×D4311yescharacteristic
377#107C22×D4311yescharacteristic
378#106—861no—
379#106—861no—
380C4⋊C8—431no—
381#103—21no—
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—21no—
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—21no—
413Q16—21no—
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—41no—
434C4⋊C4—431no—
435C4⋊C4—861no—
436C4⋊C4—861no—
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—431no—
451C42—1721no—
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—41no—
469Q8—41no—
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#1306337011yescharacteristic
504C22—21no—
505C22—21no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—861no—
510C22—861no—
511C22—861no—
512C22—3441no—
513C22—3441no—
514C22—3441no—
515C22—3441no—
516C22—3441no—
517C22—1722no—
518C22—6884no—
519C22—6884no—
520C22#1458333612yes—
521C22C2×D8×D4311yescharacteristic
522C4—21no—
523C4—81no—
524C4—81no—
525C4—81no—
526C4—861no—
527C4—861no—
528C4—861no—
529C4—3441no—
530C4—3441no—
531C4#1458353811yescharacteristic
532C4#1458370611yescharacteristic
533C2—22no—
534C2—161no—
535C2—3442no—
536C2—1721no—
537C2—6881no—
538C2#1914640311yescharacteristic
539C2C2×#1458333611yescharacteristic
540C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2217C2
socleC22×C43C22×D8
prime radical#19146269C2
hypercenter#2217D43
hypocenterC43#33877
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #19146966C2semidirect
3. #19136835C2semidirect
4. #19136788C2semidirect
5. #19136773C2semidirect
6. #19136751C2semidirect
7. #19136711C2semidirect
8. #19136633C2semidirect
9. #19136523C2semidirect
10. #19136522C2semidirect
11. #19136462C2semidirect
12. #19136420C2semidirect
13. #19136309C2semidirect
14. C2×#14582701C2semidirect
15. C43×#2217C2semidirect
21. C2×#13063268C22semidirect
22. C2×#13063264C22semidirect
23. #14583300C22semidirect
28. #14583137C22semidirect
33. Q16×Dic43C22semidirect
36. #14582936C22semidirect
37. C2×#13063259C22semidirect
38. #14582724C22semidirect
39. #14582724C22semidirect
40. Dic43⋊C16C22semidirect
43. #14582701C22semidirect
44. #14582701C22semidirect
45. #14582700C22semidirect
46. #14582700C22semidirect
48. #14582699C22semidirect
49. C22⋊(C43⋊C16)C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. #14582674C22semidirect
52. C2×SD32×C43C22semidirect
53. C22×C16×C43C22semidirect
54. C43×#467C22semidirect
56. C43×#367C22semidirect
57. C43×#358C22semidirect
58. C43×#357C22semidirect
270. #2217D43semidirect
292. C2×SD32C2×D43semidirect
294. C22×C16C2×D43semidirect
301. #467C2×D43semidirect
312. #367C2×D43semidirect
316. #358C2×D43semidirect
325. #357C2×D43semidirect
329. C43#33877semidirect

Maximal subgroups

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

subgroupindex
#191469662
#191462692
#191368352
#191367882
#191367732
#191367512
#191367112
#191366332
#191365232
#191365222
#191364622
#191364202
#191363092
C2×#145827012
C43×#22172
#3387743