Finite Group Databasebeta

← #19146356

Subgroups — #19146356

Order 5504.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583710C211yesmaximal, characteristic, complemented
2#14583709C211yesmaximal, characteristic, complemented
3#14583703C211yesmaximal, characteristic, complemented
4#14583702C211yesmaximal, characteristic, complemented
5#14583286C211yesmaximal, characteristic, complemented
6#14583168C211yesmaximal, characteristic, complemented
7#14583167C211yesmaximal, characteristic, complemented
8#14583161C211yesmaximal, characteristic, complemented
9#14583160C211yesmaximal, characteristic, complemented
10#14583078C211yesmaximal, characteristic, complemented
11#14583073C211yesmaximal, characteristic, complemented
12#14583066C211yesmaximal, characteristic, complemented
13#14583018C211yesmaximal, characteristic, complemented
14#14583018C211yesmaximal, characteristic, complemented
15C43×#453C211yesmaximal, characteristic, complemented
16#13063372C2211yescharacteristic, complemented
17#13063371C2211yescharacteristic
18#13063370C2211yescharacteristic, complemented
19#13063358C2211yescharacteristic, complemented
20#13063355—21no—
21#13063355C2211yescharacteristic, complemented
22#13063354—21no—
23#13063353C2211yescharacteristic, complemented
24#13063352—21no—
25#13063351—21no—
26#13063351—21no—
27#13063351C2211yescharacteristic
28#13063351C2211yescharacteristic, complemented
29#13063350—21no—
30#13063350C2211yescharacteristic, complemented
31#13063349—21no—
32#13063349—21no—
33#13063346—21no—
34#13063345—21no—
35#13063345—21no—
36#13063345C2211yescharacteristic
37#13063345C2211yescharacteristic
38#13063344—21no—
39C2×#10621883—21no—
40C2×#10621883C2211yescharacteristic, complemented
41C2×#10621883C2211yescharacteristic, complemented
42SD16×D43—21no—
43C2×#10621882—21no—
44C2×#10621882C2211yescharacteristic, complemented
45C2×#10621882C2211yescharacteristic, complemented
46D8×D43—21no—
47#13063333C2211yescharacteristic, complemented
48#13063333C2211yescharacteristic, complemented
49#13063332C2211yescharacteristic, complemented
50#13063332C2211yescharacteristic, complemented
51#13063313C2211yescharacteristic, complemented
52#13063260C2211yescharacteristic, complemented
53#13063260C2211yescharacteristic, complemented
54#13063253C2211yescharacteristic, complemented
55#13063253C2211yescharacteristic, complemented
56#13063243C2211yescharacteristic, complemented
57#13063242C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic, complemented
59#13063236C2211yescharacteristic, complemented
60H(5,𝔽2)×C43C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C43C2211yescharacteristic
62AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
63#127×C43C2211yescharacteristic, complemented
64#104×C43C2211yescharacteristic, complemented
65#104×C43C2211yescharacteristic, complemented
66#100×C43C2211yescharacteristic, complemented
67#41×C43—21no—
68#41×C43—21no—
69#41×C43C2311yescharacteristic
70#41×C43C2311yescharacteristic
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43C2311yescharacteristic
76C2×D4×C43C2311yescharacteristic
77C2×C22⋊D43—41no—
78#10621902—21no—
79Q8×D43—21no—
80#10621900—21no—
81#10621900—21no—
82#10621900—21no—
83#10621900—41no—
84D4×D43—21no—
85D4×D43—21no—
86D4×D43—21no—
87D4×D43—41no—
88#10621898—21no—
89#10621898—21no—
90#10621898C2311yescharacteristic
91#10621898C2311yescharacteristic
92C2×D172—21no—
93C2×D172C2311yescharacteristic
94C2×Dic86—21no—
95C2×Dic86C2311yescharacteristic
96SD16×C43—21no—
97SD16×C43—21no—
98D8×C43—21no—
99D8×C43—21no—
100M16×C43C2311yescharacteristic
101M16×C43C2311yescharacteristic
102C42×C43C2311yescharacteristic
103#10621885—21no—
104#10621885D411yescharacteristic, complemented
105#10621885D411yescharacteristic, complemented
106#10621884—21no—
107#10621884D411yescharacteristic, complemented
108#10621884D411yescharacteristic, complemented
109#10621883—21no—
110#10621883—21no—
111#10621883—21no—
112#10621883—21no—
113#10621883—21no—
114#10621883—21no—
115#10621883—21no—
116#10621883D411yescharacteristic, complemented
117#10621883D411yescharacteristic, complemented
118#10621882—21no—
119#10621882—21no—
120#10621882—21no—
121#10621882—21no—
122#10621882—21no—
123#10621882—21no—
124#10621882—21no—
125#10621882D411yescharacteristic, complemented
126#10621882D411yescharacteristic, complemented
127(C2×D43)⋊C4—41no—
128#10621877—21no—
129#10621877—21no—
130#10621877C2311yescharacteristic
131#10621877C2311yescharacteristic
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8C2311yescharacteristic
135C2×C43⋊C8C2311yescharacteristic
136Dic172—21no—
137D344—21no—
138#10621873—21no—
139#10621873—21no—
140#10621872—21no—
141#10621872—21no—
142C8×D43—21no—
143C8×D43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—41no—
147C22×D43—21no—
148C22×D43—41no—
149C22×D43—41no—
150Q8×C43C2×D411yescharacteristic
151Q8×C43C2×D411yescharacteristic
152D4×C43—21no—
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—21no—
156D4×C43—21no—
157D4×C43—21no—
158D4×C43—41no—
159D4×C43—41no—
160D4×C43—82no—
161D4×C43C2×D411yescharacteristic
162D4×C43C2×D411yescharacteristic
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—41no—
167C2×C4×C43C2411yescharacteristic
168C22⋊D43—21no—
169C22⋊D43—21no—
170C22⋊D43—41no—
171C22⋊D43—41no—
172C22⋊D43—41no—
173C22⋊D43—41no—
174C2×Dic43—21no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177D172—21no—
178D172—21no—
179D172—41no—
180D172C2×D411yescharacteristic
181D172C2×D411yescharacteristic
182C4×D43—21no—
183C4×D43—21no—
184C4×D43—41no—
185C4×D43—41no—
186Dic86—21no—
187Dic86—21no—
188Dic86—41no—
189Dic86C2×D411yescharacteristic
190Dic86C2×D411yescharacteristic
191C8×C43—21no—
192C8×C43—21no—
193C43⋊C8—21no—
194C43⋊C8—21no—
195C43⋊C8C2×D411yescharacteristic
196C43⋊C8C2×D411yescharacteristic
197C43⋊C8C2×D411yescharacteristic
198C43⋊C8C2×D411yescharacteristic
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—81no—
204C22×C43—81no—
205C22×C43—161no—
206C22×C43H(5,𝔽2)11yescharacteristic
207C2×D43—21no—
208C2×D43—21no—
209C2×D43—41no—
210C2×D43—81no—
211C2×D43—161no—
212C2×D43—161no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—41no—
216C4×C43C22×D411yescharacteristic
217C4×C43C22×D411yescharacteristic
218Dic43—21no—
219Dic43—21no—
220Dic43—41no—
221#3288—431nomaximal, Sylow
222C2×C43—21no—
223C2×C43—41no—
224C2×C43—41no—
225C2×C43—81no—
226C2×C43—81no—
227C2×C43D4211yescharacteristic
228D43—41no—
229D43—41no—
230D43—81no—
231#577—431no—
232#577—431no—
233#576—431no—
234#576—431no—
235#496—431no—
236#472—431no—
237#472—431no—
238#471—431no—
239#471—431no—
240#455—431no—
241#454—431no—
242#453—431no—
243#453D4311yescharacteristic, complemented
244#444—431no—
245#444—431no—
246C43#328811yescharacteristic, complemented, Sylow
2472−1+4—431no—
248H(5,𝔽2)—431no—
249H(5,𝔽2)—431no—
250H(5,𝔽2)C2×D4311yescharacteristic, complemented
251#137—431no—
252#137—431no—
253#137—861no—
254#137—861no—
255AGL(1,ℤ/8)—431no—
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—431no—
258AGL(1,ℤ/8)—431no—
259AGL(1,ℤ/8)—861no—
260AGL(1,ℤ/8)—861no—
261AGL(1,ℤ/8)—861no—
262AGL(1,ℤ/8)—861no—
263AGL(1,ℤ/8)—861no—
264AGL(1,ℤ/8)—861no—
265AGL(1,ℤ/8)C2×D4311yescharacteristic
266AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
267#135—431no—
268#135—431no—
269#135—861no—
270#135—861no—
271#135—861no—
272#135—861no—
273C2×SD16—431no—
274C2×SD16—431no—
275C2×SD16—861no—
276C2×SD16—861no—
277C2×D8—431no—
278C2×D8—431no—
279C2×D8—861no—
280C2×D8—861no—
281#131—431no—
282#131—431no—
283#131—431no—
284#131—431no—
285#127C2×D4311yescharacteristic, complemented
286#124—431no—
287#108—431no—
288#108—431no—
289#104—431no—
290#104—431no—
291#104C2×D4311yescharacteristic, complemented
292#104C2×D4311yescharacteristic, complemented
293#101—431no—
294#100—431no—
295#100—431no—
296#100C2×D4311yescharacteristic, complemented
297#97—431no—
298#41—21no—
299#41—21no—
300#41—431no—
301#41—431no—
302#41—861no—
303#41—861no—
304#41—861no—
305#41—861no—
306#41—861no—
307#41—861no—
308#41—1721no—
309#41C22×D4311yescharacteristic
310#41C22×D4311yescharacteristic
311C2×Q8—431no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—431no—
319C2×D4—861no—
320C2×D4—861no—
321C2×D4—861no—
322C2×D4—861no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4C22×D4311yescharacteristic
326C2×D4C22×D4311yescharacteristic
327Q16—431no—
328Q16—431no—
329Q16—861no—
330Q16—861no—
331SD16—21no—
332SD16—21no—
333SD16—431no—
334SD16—431no—
335SD16—431no—
336SD16—431no—
337SD16—861no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16—861no—
346SD16—861no—
347D8—21no—
348D8—21no—
349D8—431no—
350D8—431no—
351D8—861no—
352D8—861no—
353D8—861no—
354D8—861no—
355D8—861no—
356D8—861no—
357D8—861no—
358D8—861no—
359M16—431no—
360M16—431no—
361M16—861no—
362M16—861no—
363M16—861no—
364M16—861no—
365M16C22×D4311yescharacteristic
366M16C22×D4311yescharacteristic
367C2×C8—431no—
368C2×C8—431no—
369C2×C8—861no—
370C2×C8—861no—
371C2×C8—861no—
372C2×C8—861no—
373C22⋊C4—1721no—
374C42C22×D4311yescharacteristic
375C23—21no—
376C23—21no—
377C23—41no—
378C23—861no—
379C23—1721no—
380C23—1721no—
381Q8—431no—
382Q8—431no—
383Q8—861no—
384Q8—861no—
385Q8—1721no—
386Q8D4×D4311yescharacteristic
387Q8D4×D4311yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—41no—
395D4—41no—
396D4—82no—
397D4—431no—
398D4—431no—
399D4—861no—
400D4—861no—
401D4—861no—
402D4—861no—
403D4—1721no—
404D4—1721no—
405D4—1721no—
406D4—1721no—
407D4—1721no—
408D4D4×D4311yescharacteristic
409D4D4×D4311yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—861no—
415C2×C4—861no—
416C2×C4—861no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4C23×D4311yescharacteristic
422C8—21no—
423C8—21no—
424C8—431no—
425C8—431no—
426C8—431no—
427C8—431no—
428C8—861no—
429C8—861no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—81no—
435C22—81no—
436C22—161no—
437C22—861no—
438C22—861no—
439C22—3441no—
440C22—1721no—
441C22—6881no—
442C22—6881no—
443C22#1306337011yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—861no—
448C4—861no—
449C4—1721no—
450C4C2×D4×D4311yescharacteristic
451C4C2×D4×D4311yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2—81no—
457C2—3441no—
458C2—1721no—
459C2—1721no—
460C2#1458353111yescharacteristic
subgroupG/H
centerC2#14583531
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#453C2
socleC2×C43D42
hypercenter#453D43
hypocenterC43#3288
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14583710C2semidirect
2. #14583709C2semidirect
3. #14583703C2semidirect
4. #14583702C2semidirect
5. #14583286C2semidirect
6. #14583168C2semidirect
7. #14583167C2semidirect
8. #14583161C2semidirect
9. #14583160C2semidirect
10. #14583078C2semidirect
11. #14583073C2semidirect
12. #14583066C2semidirect
13. #14583018C2semidirect
14. #14583018C2semidirect
15. C43×#453C2semidirect
16. #13063372C22semidirect
18. #13063370C22semidirect
19. #13063358C22semidirect
21. #13063355C22semidirect
23. #13063353C22semidirect
28. #13063351C22semidirect
30. #13063350C22semidirect
40. C2×#10621883C22semidirect
41. C2×#10621883C22semidirect
44. C2×#10621882C22semidirect
45. C2×#10621882C22semidirect
47. #13063333C22semidirect
48. #13063333C22semidirect
49. #13063332C22semidirect
50. #13063332C22semidirect
51. #13063313C22semidirect
52. #13063260C22semidirect
53. #13063260C22semidirect
54. #13063253C22semidirect
55. #13063253C22semidirect
56. #13063243C22semidirect
57. #13063242C22semidirect
58. #13063241C22semidirect
59. #13063236C22semidirect
60. H(5,𝔽2)×C43C22semidirect
62. AGL(1,ℤ/8)×C43C22semidirect
63. #127×C43C22semidirect
64. #104×C43C22semidirect
65. #104×C43C22semidirect
66. #100×C43C22semidirect
104. #10621885D4semidirect
105. #10621885D4semidirect
107. #10621884D4semidirect
108. #10621884D4semidirect
116. #10621883D4semidirect
117. #10621883D4semidirect
125. #10621882D4semidirect
126. #10621882D4semidirect
243. #453D43semidirect
246. C43#3288semidirect
250. H(5,𝔽2)C2×D43semidirect
266. AGL(1,ℤ/8)C2×D43semidirect
285. #127C2×D43semidirect
291. #104C2×D43semidirect
292. #104C2×D43semidirect
296. #100C2×D43semidirect