Finite Group Databasebeta

← #19146392

Subgroups — #19146392

Order 5504.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583702C212yesmaximal, complemented
2#14583701C211yesmaximal, characteristic, complemented
3#14583274C211yesmaximal, characteristic, complemented
4#14583169C211yesmaximal, characteristic, complemented
5#14583167C212yesmaximal, complemented
6#14583166C211yesmaximal, characteristic, complemented
7#14583067C212yesmaximal, complemented
8#14583065C212yesmaximal, complemented
9#14583016C211yesmaximal, characteristic, complemented
10#14583014C211yesmaximal, characteristic, complemented
11C43×#576C211yesmaximal, characteristic, complemented
12#13063371C2212yescomplemented
13#13063352—22no—
14#13063351—22no—
15#13063351C2212yescomplemented
16#13063350—22no—
17#13063350C2212yescomplemented
18#13063350C2212yescomplemented
19#13063348—21no—
20#13063345—22no—
21#13063345C2211yescharacteristic
22C2×D344C2211yescharacteristic, complemented
23C2×#10621882—22no—
24C2×#10621882C2212yescomplemented
25D8×D43—21no—
26#13063332C2212yescomplemented
27#13063331C2211yescharacteristic, complemented
28#13063321C2212yescomplemented
29#13063261C2211yescharacteristic, complemented
30#13063260C2211yescharacteristic, complemented
31#13063252C2212yescomplemented
32#13063252C2211yescharacteristic, complemented
33#13063251C2211yescharacteristic, complemented
34#13063242C2212yescomplemented
35#13063241C2212yescomplemented
36C8×Dic43C2211yescharacteristic, complemented
37H(5,𝔽2)×C43C2212yescomplemented
38AGL(1,ℤ/8)×C43—22no—
39AGL(1,ℤ/8)×C43C2212yescomplemented
40#135×C43—21no—
41#135×C43C2211yescharacteristic
42C2×D8×C43—21no—
43C2×D8×C43C2211yescharacteristic, complemented
44#131×C43C2211yescharacteristic, complemented
45#41×C43—22no—
46#41×C43—22no—
47#41×C43C2311yescharacteristic
48#41×C43C2312yes—
49C2×D4×C43—22no—
50C2×D4×C43—22no—
51C2×D4×C43—42no—
52C2×D4×C43C2312yes—
53C2×C22⋊D43—42no—
54#10621902—22no—
55D4×D43—22no—
56D4×D43—42no—
57#10621898—22no—
58#10621898C2311yescharacteristic
59C2×D172—22no—
60C2×D172C2312yes—
61Q16×C43D411yescharacteristic, complemented
62SD16×C43—22no—
63SD16×C43D412yescomplemented
64D8×C43—22no—
65D8×C43—21no—
66D8×C43—21no—
67D8×C43D411yescharacteristic, complemented
68M16×C43—21no—
69M16×C43C2311yescharacteristic
70C2×C8×C43—21no—
71C2×C8×C43C2311yescharacteristic
72#10621885D411yescharacteristic, complemented
73#10621884—22no—
74#10621884—22no—
75#10621884D411yescharacteristic, complemented
76#10621883—22no—
77#10621883D411yescharacteristic, complemented
78#10621882—22no—
79#10621882—22no—
80#10621882—22no—
81#10621882—22no—
82#10621882—22no—
83#10621882D411yescharacteristic, complemented
84C4×Dic43C2311yescharacteristic
85#10621877—22no—
86#10621877C2312yes—
87#10621877C2311yescharacteristic
88C2×C43⋊C8—22no—
89C2×C43⋊C8C2311yescharacteristic
90D344—21no—
91D344—21no—
92#10621872—21no—
93C8×D43—21no—
94C23×C43—22no—
95C23×C43—42no—
96C22×D43—22no—
97C22×D43—42no—
98Q8×C43C2×D411yescharacteristic
99Q8×C43C2×D412yes—
100D4×C43—22no—
101D4×C43—21no—
102D4×C43—22no—
103D4×C43—22no—
104D4×C43—42no—
105D4×C43—42no—
106D4×C43C2×D411yescharacteristic
107D4×C43C2×D412yes—
108C2×C4×C43—22no—
109C2×C4×C43—21no—
110C2×C4×C43—42no—
111C2×C4×C43C2411yescharacteristic
112C22⋊D43—21no—
113C22⋊D43—42no—
114C22⋊D43—84no—
115C2×Dic43—21no—
116D172—22no—
117D172—22no—
118D172—42no—
119D172C2×D411yescharacteristic
120C4×D43—21no—
121C4×D43—42no—
122Dic86C2×D411yescharacteristic
123C8×C43—21no—
124C8×C43C2×D411yescharacteristic
125C8×C43C2×D411yescharacteristic
126C43⋊C8—21no—
127C43⋊C8—22no—
128C43⋊C8C2×D411yescharacteristic
129C43⋊C8C2×D411yescharacteristic
130C22×C43—22no—
131C22×C43—21no—
132C22×C43—42no—
133C22×C43—82no—
134C22×C43—162no—
135C22×C43H(5,𝔽2)11yescharacteristic
136C2×D43—21no—
137C2×D43—42no—
138C2×D43—82no—
139C2×D43—162no—
140C4×C43—22no—
141C4×C43—21no—
142C4×C43C22×D411yescharacteristic
143C4×C43C22×D411yescharacteristic
144Dic43—22no—
145Dic43—21no—
146#3292—431nomaximal, Sylow
147C2×C43—21no—
148C2×C43—42no—
149C2×C43—41no—
150C2×C43—82no—
151C2×C43D4211yescharacteristic
152D43—41no—
153D43—82no—
154#576—432no—
155#576—431no—
156#576D4311yescharacteristic, complemented
157#493—431no—
158#472—432no—
159#472—431no—
160#472—431no—
161#453—432no—
162#453—432no—
163#443—431no—
164#443—431no—
165C43#329211yescharacteristic, complemented, Sylow
166H(5,𝔽2)—432no—
167H(5,𝔽2)C2×D4312yescomplemented
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—432no—
170AGL(1,ℤ/8)—432no—
171AGL(1,ℤ/8)—432no—
172AGL(1,ℤ/8)—862no—
173AGL(1,ℤ/8)—862no—
174AGL(1,ℤ/8)—862no—
175AGL(1,ℤ/8)C2×D4312yescomplemented
176#135—21no—
177#135—431no—
178#135—862no—
179#135—861no—
180#135C2×D4311yescharacteristic
181C2×D8—21no—
182C2×D8—432no—
183C2×D8—431no—
184C2×D8—862no—
185C2×D8—861no—
186C2×D8C2×D4311yescharacteristic, complemented
187#131—432no—
188#131—431no—
189#131C2×D4311yescharacteristic, complemented
190#127—432no—
191#108—431no—
192#108—431no—
193#104—431no—
194#104—432no—
195#104—431no—
196#100—432no—
197#100—432no—
198C4×C8—431no—
199#41—22no—
200#41—22no—
201#41—431no—
202#41—862no—
203#41—862no—
204#41C22×D4311yescharacteristic
205#41C22×D4312yes—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4—432no—
210C2×D4—862no—
211C2×D4—862no—
212C2×D4—1722no—
213C2×D4—1722no—
214C2×D4C22×D4312yes—
215Q16—431no—
216Q16C22⋊D4311yescharacteristic, complemented
217SD16—22no—
218SD16—431no—
219SD16—431no—
220SD16—862no—
221SD16—862no—
222SD16—862no—
223SD16C22⋊D4312yescomplemented
224D8—22no—
225D8—21no—
226D8—21no—
227D8—431no—
228D8—862no—
229D8—862no—
230D8—862no—
231D8—862no—
232D8—862no—
233D8—861no—
234D8—861no—
235D8C22⋊D4311yescharacteristic, complemented
236M16—21no—
237M16—432no—
238M16—431no—
239M16—862no—
240M16—861no—
241M16C22×D4311yescharacteristic
242C2×C8—21no—
243C2×C8—431no—
244C2×C8—862no—
245C2×C8—861no—
246C2×C8C22×D4311yescharacteristic
247C42—431no—
248C23—22no—
249C23—42no—
250C23—862no—
251C23—1722no—
252Q8—431no—
253Q8D4×D4311yescharacteristic
254Q8C2×C22⋊D4312yes—
255D4—21no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—431no—
262D4—861no—
263D4—862no—
264D4—862no—
265D4—3444no—
266D4—1722no—
267D4—1722no—
268D4D4×D4311yescharacteristic
269D4C2×C22⋊D4312yes—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—861no—
274C2×C4—861no—
275C2×C4—1722no—
276C2×C4C23×D4311yescharacteristic
277C8—21no—
278C8—431no—
279C8—431no—
280C8—862no—
281C8—861no—
282C8C2×C22⋊D4311yescharacteristic
283C8C2×C22⋊D4311yescharacteristic
284C22—21no—
285C22—22no—
286C22—42no—
287C22—82no—
288C22—162no—
289C22—861no—
290C22—3442no—
291C22—1722no—
292C22—6882no—
293C22#1306337011yescharacteristic
294C4—21no—
295C4—22no—
296C4—862no—
297C4—861no—
298C4C2×D4×D4311yescharacteristic
299C4C22×C22⋊D4311yescharacteristic
300C2—21no—
301C2—41no—
302C2—42no—
303C2—82no—
304C2—3442no—
305C2—1721no—
306C2D4×C22⋊D4311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#576C2
socleC2×C43D42
hypercenter#576D43
hypocenterC43#3292
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #14583702C2semidirect
2. #14583701C2semidirect
3. #14583274C2semidirect
4. #14583169C2semidirect
5. #14583167C2semidirect
6. #14583166C2semidirect
7. #14583067C2semidirect
8. #14583065C2semidirect
9. #14583016C2semidirect
10. #14583014C2semidirect
11. C43×#576C2semidirect
12. #13063371C22semidirect
15. #13063351C22semidirect
17. #13063350C22semidirect
18. #13063350C22semidirect
22. C2×D344C22semidirect
24. C2×#10621882C22semidirect
26. #13063332C22semidirect
27. #13063331C22semidirect
28. #13063321C22semidirect
29. #13063261C22semidirect
30. #13063260C22semidirect
31. #13063252C22semidirect
32. #13063252C22semidirect
33. #13063251C22semidirect
34. #13063242C22semidirect
35. #13063241C22semidirect
36. C8×Dic43C22semidirect
37. H(5,𝔽2)×C43C22semidirect
39. AGL(1,ℤ/8)×C43C22semidirect
43. C2×D8×C43C22semidirect
44. #131×C43C22semidirect
61. Q16×C43D4semidirect
63. SD16×C43D4semidirect
67. D8×C43D4semidirect
72. #10621885D4semidirect
75. #10621884D4semidirect
77. #10621883D4semidirect
83. #10621882D4semidirect
156. #576D43semidirect
165. C43#3292semidirect
167. H(5,𝔽2)C2×D43semidirect
175. AGL(1,ℤ/8)C2×D43semidirect
186. C2×D8C2×D43semidirect
189. #131C2×D43semidirect
216. Q16C22⋊D43semidirect
223. SD16C22⋊D43semidirect
235. D8C22⋊D43semidirect