Finite Group Databasebeta

← #19146380

Subgroups — #19146380

Order 5504.

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

normal subgroups only

This group has 454 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#14583712C211yesmaximal, characteristic, complemented
2#14583705C212yesmaximal, complemented
3#14583700C211yesmaximal, characteristic, complemented
4#14583171C211yesmaximal, characteristic, complemented
5#14583166C211yesmaximal, characteristic, complemented
6#14583159C212yesmaximal, complemented
7#14583076C212yesmaximal, complemented
8#14583071C212yesmaximal, complemented
9#14583017C211yesmaximal, characteristic, complemented
10#14583017C211yesmaximal, characteristic, complemented
11C43×#495C211yesmaximal, characteristic, complemented
12#13063373C2212yescomplemented
13#13063370C2212yes—
14#13063357—22no—
15#13063356C2212yes—
16#13063356C2212yescomplemented
17#13063354—22no—
18#13063352—22no—
19#13063351C2212yes—
20#13063351C2212yescomplemented
21#13063349—22no—
22#13063348—21no—
23#13063347C2211yescharacteristic
24#13063347C2211yescharacteristic
25#13063346—22no—
26#13063344—21no—
27Q16×D43—21no—
28SD16×D43—22no—
29D8×D43—21no—
30#13063331C2211yescharacteristic
31#13063331C2212yescomplemented
32#13063331C2211yescharacteristic, complemented
33#13063261C2211yescharacteristic, complemented
34#13063261C2211yescharacteristic, complemented
35#13063253C2211yescharacteristic
36#13063253C2211yescharacteristic, complemented
37#13063253C2212yescomplemented
38#13063244C2212yescomplemented
39#13063242C2212yescomplemented
40C2×Q16×C43C2211yescharacteristic, complemented
41C2×SD16×C43C2212yescomplemented
42C2×D8×C43C2211yescharacteristic
43#124×C43C2212yescomplemented
44C4×C8×C43C2211yescharacteristic, complemented
45C2×Q8×C43C2312yes—
46C2×D4×C43C2312yes—
47C2×C22⋊D43—42no—
48#10621902—22no—
49#10621902—22no—
50Q8×D43—22no—
51Q8×D43—22no—
52#10621900—22no—
53#10621900—22no—
54D4×D43—22no—
55D4×D43—22no—
56#10621898—42no—
57#10621898C2311yescharacteristic
58#10621898C2312yes—
59#10621898C2311yescharacteristic
60Q16×C43—21no—
61Q16×C43—21no—
62SD16×C43—22no—
63SD16×C43—22no—
64D8×C43—21no—
65D8×C43—21no—
66C2×C8×C43C2311yescharacteristic
67C2×C8×C43C2311yescharacteristic
68C22⋊C4×C43—42no—
69C42×C43C2311yescharacteristic
70#10621885—22no—
71#10621885—22no—
72#10621884—22no—
73#10621884—22no—
74#10621883—22no—
75#10621883—22no—
76#10621882—22no—
77#10621882—22no—
78#10621877C2311yescharacteristic
79#10621877C2312yes—
80#10621877C2311yescharacteristic
81Dic172D411yescharacteristic
82Dic172D411yescharacteristic
83D344D411yescharacteristic
84D344D411yescharacteristic
85#10621873D411yescharacteristic
86#10621873D411yescharacteristic
87#10621873D412yes—
88#10621872—21no—
89#10621872—22no—
90#10621872—21no—
91C8×D43—21no—
92C8×D43—22no—
93C8×D43—21no—
94C23×C43—22no—
95C22×D43—42no—
96Q8×C43—22no—
97Q8×C43—22no—
98D4×C43—22no—
99D4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43—22no—
102C2×C4×C43C2411yescharacteristic
103C22⋊D43—21no—
104C22⋊D43—22no—
105C22⋊D43—21no—
106C22⋊D43—42no—
107C22⋊D43—42no—
108C2×Dic43—42no—
109D172—42no—
110D172C2×D411yescharacteristic
111D172C2×D412yes—
112D172C2×D411yescharacteristic
113C4×D43—21no—
114C4×D43—22no—
115C4×D43—21no—
116C4×D43—42no—
117C4×D43—42no—
118Dic86—42no—
119Dic86C2×D411yescharacteristic
120Dic86C2×D412yes—
121Dic86C2×D411yescharacteristic
122C8×C43C2×D411yescharacteristic
123C8×C43C2×D411yescharacteristic
124C8×C43C2×D411yescharacteristic
125C8×C43C2×D411yescharacteristic
126C43⋊C8—21no—
127C43⋊C8—22no—
128C43⋊C8—21no—
129C22×C43—42no—
130C22×C43—82no—
131C22×C43H(5,𝔽2)11yescharacteristic
132C2×D43—21no—
133C2×D43—22no—
134C2×D43—21no—
135C2×D43—162no—
136C4×C43—41no—
137C4×C43—42no—
138C4×C43C22×D411yescharacteristic
139C4×C43C22×D411yescharacteristic
140Dic43—21no—
141Dic43—22no—
142Dic43—21no—
143#3290—431nomaximal, Sylow
144C2×C43—21no—
145C2×C43—82no—
146C2×C43D4211yescharacteristic
147D43—41no—
148D43—42no—
149D43—41no—
150#578—431no—
151#577—432no—
152#576—431no—
153#495D4311yescharacteristic, complemented
154#473—431no—
155#472—431no—
156#471—432no—
157#455—432no—
158#454—432no—
159#443—431no—
160#443—431no—
161C43#329011yescharacteristic, complemented, Sylow
1622−1+4—432no—
163H(5,𝔽2)—432no—
164#137—432no—
165#137—432no—
166#137—862no—
167#137—862no—
168AGL(1,ℤ/8)—432no—
169AGL(1,ℤ/8)—432no—
170AGL(1,ℤ/8)—862no—
171AGL(1,ℤ/8)—862no—
172#135—431no—
173#135—431no—
174#135—861no—
175#135—861no—
176#135—862no—
177C2×Q16—861no—
178C2×Q16C2×D4311yescharacteristic, complemented
179C2×SD16—862no—
180C2×SD16C2×D4312yescomplemented
181C2×D8—861no—
182C2×D8C2×D4311yescharacteristic
183#131—431no—
184#131—432no—
185#131—431no—
186#124C2×D4312yescomplemented
187#108—431no—
188#108—431no—
189#104—431no—
190#104—431no—
191#104—432no—
192#101—432no—
193#100—432no—
194C4×C8C2×D4311yescharacteristic, complemented
195#41—431no—
196#41—432no—
197#41—431no—
198#41—862no—
199#41—862no—
200#41—862no—
201#41—862no—
202#41—1722no—
203C2×Q8—862no—
204C2×Q8—862no—
205C2×Q8C22×D4312yes—
206C2×D4—862no—
207C2×D4—862no—
208C2×D4—1722no—
209C2×D4C22×D4312yes—
210Q16—21no—
211Q16—21no—
212Q16—431no—
213Q16—431no—
214Q16—862no—
215Q16—862no—
216SD16—22no—
217SD16—22no—
218SD16—431no—
219SD16—431no—
220SD16—432no—
221SD16—862no—
222SD16—862no—
223SD16—862no—
224SD16—862no—
225D8—21no—
226D8—21no—
227D8—431no—
228D8—431no—
229D8—862no—
230D8—862no—
231M16—431no—
232M16—432no—
233M16—431no—
234M16—861no—
235M16—862no—
236M16—861no—
237C2×C8—861no—
238C2×C8—862no—
239C2×C8—861no—
240C2×C8C22×D4311yescharacteristic
241C2×C8C22×D4311yescharacteristic
242C22⋊C4—42no—
243C42C22×D4311yescharacteristic
244C23—22no—
245C23—1722no—
246Q8—22no—
247Q8—22no—
248Q8—431no—
249Q8—432no—
250Q8—431no—
251Q8—1722no—
252D4—22no—
253D4—22no—
254D4—431no—
255D4—432no—
256D4—431no—
257D4—861no—
258D4—862no—
259D4—861no—
260D4—1722no—
261D4—1722no—
262D4—1722no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—861no—
266C2×C4—862no—
267C2×C4—861no—
268C2×C4—1722no—
269C2×C4—1722no—
270C2×C4—1722no—
271C2×C4C23×D4311yescharacteristic
272C8—861no—
273C8—862no—
274C8—861no—
275C8D4×D4311yescharacteristic
276C8D4×D4311yescharacteristic
277C8D4×D4311yescharacteristic
278C8D4×D4311yescharacteristic
279C22—42no—
280C22—82no—
281C22—861no—
282C22—862no—
283C22—861no—
284C22—6882no—
285C22#1306337011yescharacteristic
286C4—41no—
287C4—42no—
288C4—861no—
289C4—862no—
290C4—861no—
291C4C2×D4×D4311yescharacteristic
292C4C2×D4×D4311yescharacteristic
293C2—21no—
294C2—82no—
295C2—1721no—
296C2—1722no—
297C2—1721no—
298C2#1458353411yescharacteristic
subgroupG/H
centerC2#14583534
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#495C2
socleC2×C43D42
hypercenter#495D43
hypocenterC43#3290
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #14583712C2semidirect
2. #14583705C2semidirect
3. #14583700C2semidirect
4. #14583171C2semidirect
5. #14583166C2semidirect
6. #14583159C2semidirect
7. #14583076C2semidirect
8. #14583071C2semidirect
9. #14583017C2semidirect
10. #14583017C2semidirect
11. C43×#495C2semidirect
12. #13063373C22semidirect
16. #13063356C22semidirect
20. #13063351C22semidirect
31. #13063331C22semidirect
32. #13063331C22semidirect
33. #13063261C22semidirect
34. #13063261C22semidirect
36. #13063253C22semidirect
37. #13063253C22semidirect
38. #13063244C22semidirect
39. #13063242C22semidirect
40. C2×Q16×C43C22semidirect
41. C2×SD16×C43C22semidirect
43. #124×C43C22semidirect
44. C4×C8×C43C22semidirect
153. #495D43semidirect
161. C43#3290semidirect
178. C2×Q16C2×D43semidirect
180. C2×SD16C2×D43semidirect
186. #124C2×D43semidirect
194. C4×C8C2×D43semidirect