Finite Group Databasebeta

← #19146393

Subgroups — #19146393

Order 5504.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583704C211yesmaximal, characteristic, complemented
2#14583703C212yesmaximal, complemented
3#14583700C211yesmaximal, characteristic, complemented
4#14583274C211yesmaximal, characteristic, complemented
5#14583170C211yesmaximal, characteristic, complemented
6#14583168C212yesmaximal, complemented
7#14583069C212yesmaximal, complemented
8#14583065C212yesmaximal, complemented
9#14583015C211yesmaximal, characteristic, complemented
10#14583014C211yesmaximal, characteristic, complemented
11C43×#472C211yesmaximal, characteristic, complemented
12#13063371C2212yescomplemented
13#13063370C2212yescomplemented
14#13063353—22no—
15#13063353C2212yescomplemented
16#13063353C2212yescomplemented
17#13063352—22no—
18#13063351C2212yescomplemented
19#13063349—22no—
20#13063349—22no—
21#13063347—21no—
22#13063347C2211yescharacteristic
23#13063346—22no—
24#13063345C2211yescharacteristic
25#13063344—21no—
26C2×D344—21no—
27C2×D344C2211yescharacteristic, complemented
28C2×#10621882C2212yescomplemented
29D8×D43—22no—
30D8×D43—21no—
31#13063333C2212yescomplemented
32#13063331C2211yescharacteristic, complemented
33#13063321C2212yescomplemented
34#13063260C2211yescharacteristic, complemented
35#13063252C2211yescharacteristic, complemented
36#13063251C2212yescomplemented
37#13063251C2211yescharacteristic, complemented
38#13063241C2212yescomplemented
39C8×Dic43C2211yescharacteristic, complemented
40AGL(1,ℤ/8)×C43C2212yescomplemented
41C2×D8×C43C2211yescharacteristic, complemented
42#131×C43C2211yescharacteristic, complemented
43#108×C43C2211yescharacteristic, complemented
44#100×C43C2212yescomplemented
45#41×C43C2311yescharacteristic
46C2×D4×C43C2312yes—
47C2×C22⋊D43—42no—
48C2×C22⋊D43—42no—
49#10621902—22no—
50#10621900—22no—
51#10621900—22no—
52D4×D43—22no—
53D4×D43—22no—
54D4×D43—22no—
55D4×D43—42no—
56#10621898—22no—
57#10621898C2311yescharacteristic
58#10621898C2312yes—
59C2×D172—22no—
60C2×D172C2312yes—
61SD16×C43—22no—
62D8×C43—22no—
63D8×C43—21no—
64D8×C43—21no—
65M16×C43—21no—
66M16×C43C2311yescharacteristic
67M16×C43C2312yes—
68C2×C8×C43—21no—
69C2×C8×C43C2311yescharacteristic
70#10621885D411yescharacteristic, complemented
71#10621884D411yescharacteristic, complemented
72#10621883—22no—
73#10621883D411yescharacteristic, complemented
74#10621882—22no—
75#10621882—22no—
76#10621882—22no—
77#10621882D411yescharacteristic, complemented
78C4×Dic43C2311yescharacteristic
79#10621877C2311yescharacteristic
80C2×C43⋊C8C2311yescharacteristic
81Dic172D411yescharacteristic, complemented
82D344—22no—
83D344—22no—
84D344—21no—
85D344—21no—
86D344D411yescharacteristic, complemented
87#10621873—22no—
88#10621873—22no—
89#10621873D412yescomplemented
90#10621872—21no—
91#10621872—22no—
92C8×D43—21no—
93C8×D43—22no—
94C23×C43—22no—
95C22×D43—22no—
96C22×D43—42no—
97C22×D43—42no—
98Q8×C43C2×D411yescharacteristic
99D4×C43—21no—
100D4×C43—22no—
101D4×C43—22no—
102D4×C43C2×D411yescharacteristic
103C2×C4×C43—21no—
104C2×C4×C43C2411yescharacteristic
105C22⋊D43—22no—
106C22⋊D43—21no—
107C22⋊D43—42no—
108C22⋊D43—42no—
109C22⋊D43—42no—
110C22⋊D43—84no—
111C2×Dic43—21no—
112C2×Dic43—42no—
113D172—22no—
114D172—22no—
115D172—42no—
116D172C2×D412yes—
117D172C2×D411yescharacteristic
118C4×D43—21no—
119C4×D43—22no—
120C4×D43—42no—
121Dic86C2×D411yescharacteristic
122Dic86C2×D412yes—
123C8×C43—22no—
124C8×C43—21no—
125C8×C43C2×D411yescharacteristic
126C8×C43C2×D411yescharacteristic
127C43⋊C8—21no—
128C43⋊C8C2×D411yescharacteristic
129C43⋊C8C2×D411yescharacteristic
130C22×C43—21no—
131C22×C43—42no—
132C22×C43—82no—
133C22×C43H(5,𝔽2)11yescharacteristic
134C2×D43—22no—
135C2×D43—21no—
136C2×D43—42no—
137C2×D43—82no—
138C2×D43—162no—
139C2×D43—162no—
140C4×C43—21no—
141C4×C43C22×D411yescharacteristic
142C4×C43C22×D411yescharacteristic
143Dic43—22no—
144Dic43—22no—
145Dic43—21no—
146#3292—431nomaximal, Sylow
147C2×C43—21no—
148C2×C43—41no—
149C2×C43—82no—
150C2×C43D4211yescharacteristic
151D43—42no—
152D43—41no—
153D43—82no—
154#576—432no—
155#576—431no—
156#576—431no—
157#493—431no—
158#472—431no—
159#472—432no—
160#472D4311yescharacteristic, complemented
161#453—432no—
162#453—432no—
163#443—431no—
164#443—431no—
165C43#329211yescharacteristic, complemented, Sylow
166H(5,𝔽2)—432no—
167H(5,𝔽2)—432no—
168AGL(1,ℤ/8)—432no—
169AGL(1,ℤ/8)—432no—
170AGL(1,ℤ/8)—432no—
171AGL(1,ℤ/8)—862no—
172AGL(1,ℤ/8)—862no—
173AGL(1,ℤ/8)—862no—
174AGL(1,ℤ/8)—862no—
175AGL(1,ℤ/8)C2×D4312yescomplemented
176#135—431no—
177#135—431no—
178#135—861no—
179#135—861no—
180#135—862no—
181C2×D8—432no—
182C2×D8—431no—
183C2×D8—861no—
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#108C2×D4311yescharacteristic, complemented
193#104—431no—
194#104—432no—
195#104—431no—
196#100—432no—
197#100C2×D4312yescomplemented
198C4×C8—431no—
199#41—432no—
200#41—431no—
201#41—862no—
202#41—862no—
203#41—862no—
204#41—862no—
205#41C22×D4311yescharacteristic
206C2×D4—432no—
207C2×D4—862no—
208C2×D4—862no—
209C2×D4—862no—
210C2×D4—862no—
211C2×D4—1722no—
212C2×D4—1722no—
213C2×D4—1722no—
214C2×D4C22×D4312yes—
215Q16—431no—
216Q16—431no—
217SD16—22no—
218SD16—431no—
219SD16—431no—
220SD16—432no—
221SD16—862no—
222SD16—862no—
223SD16—862no—
224D8—22no—
225D8—21no—
226D8—21no—
227D8—431no—
228D8—431no—
229D8—862no—
230D8—862no—
231D8—862no—
232D8—862no—
233D8—862no—
234D8—861no—
235D8—861no—
236M16—21no—
237M16—431no—
238M16—862no—
239M16—861no—
240M16C22×D4312yes—
241M16C22×D4311yescharacteristic
242C2×C8—21no—
243C2×C8—431no—
244C2×C8—862no—
245C2×C8—861no—
246C2×C8C22×D4311yescharacteristic
247C42—431no—
248C23—22no—
249C23—862no—
250C23—1722no—
251C23—1722no—
252Q8—431no—
253Q8—432no—
254Q8D4×D4311yescharacteristic
255D4—21no—
256D4—22no—
257D4—22no—
258D4—431no—
259D4—432no—
260D4—862no—
261D4—861no—
262D4—862no—
263D4—862no—
264D4—3444no—
265D4—1722no—
266D4—1722no—
267D4—1722no—
268D4—1722no—
269D4D4×D4311yescharacteristic
270C2×C4—21no—
271C2×C4—861no—
272C2×C4—862no—
273C2×C4—861no—
274C2×C4—1722no—
275C2×C4—1722no—
276C2×C4C23×D4311yescharacteristic
277C8—21no—
278C8—22no—
279C8—431no—
280C8—431no—
281C8—861no—
282C8D4×D4311yescharacteristic
283C8D4×D4311yescharacteristic
284C22—21no—
285C22—42no—
286C22—82no—
287C22—862no—
288C22—861no—
289C22—3442no—
290C22—1722no—
291C22—6882no—
292C22—6882no—
293C22#1306337111yescharacteristic
294C4—21no—
295C4—862no—
296C4—862no—
297C4—861no—
298C4C2×D4×D4311yescharacteristic
299C4C2×D4×D4311yescharacteristic
300C2—21no—
301C2—41no—
302C2—82no—
303C2—3442no—
304C2—1722no—
305C2—1721no—
306C2#1458353311yescharacteristic
subgroupG/H
centerC2#14583533
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#472C2
socleC2×C43D42
hypercenter#472D43
hypocenterC43#3292
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #14583704C2semidirect
2. #14583703C2semidirect
3. #14583700C2semidirect
4. #14583274C2semidirect
5. #14583170C2semidirect
6. #14583168C2semidirect
7. #14583069C2semidirect
8. #14583065C2semidirect
9. #14583015C2semidirect
10. #14583014C2semidirect
11. C43×#472C2semidirect
12. #13063371C22semidirect
13. #13063370C22semidirect
15. #13063353C22semidirect
16. #13063353C22semidirect
18. #13063351C22semidirect
27. C2×D344C22semidirect
28. C2×#10621882C22semidirect
31. #13063333C22semidirect
32. #13063331C22semidirect
33. #13063321C22semidirect
34. #13063260C22semidirect
35. #13063252C22semidirect
36. #13063251C22semidirect
37. #13063251C22semidirect
38. #13063241C22semidirect
39. C8×Dic43C22semidirect
40. AGL(1,ℤ/8)×C43C22semidirect
41. C2×D8×C43C22semidirect
42. #131×C43C22semidirect
43. #108×C43C22semidirect
44. #100×C43C22semidirect
70. #10621885D4semidirect
71. #10621884D4semidirect
73. #10621883D4semidirect
77. #10621882D4semidirect
81. Dic172D4semidirect
86. D344D4semidirect
89. #10621873D4semidirect
160. #472D43semidirect
165. C43#3292semidirect
175. AGL(1,ℤ/8)C2×D43semidirect
186. C2×D8C2×D43semidirect
189. #131C2×D43semidirect
192. #108C2×D43semidirect
197. #100C2×D43semidirect