Finite Group Databasebeta

← #19146377

Subgroups — #19146377

Order 5504.

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

normal subgroups only

This group has 454 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#14583713C211yesmaximal, characteristic, complemented
2#14583710C212yesmaximal, complemented
3#14583282C211yesmaximal, characteristic, complemented
4#14583174C211yesmaximal, characteristic, complemented
5#14583166C211yesmaximal, characteristic, complemented
6#14583160C212yesmaximal, complemented
7#14583077C212yesmaximal, complemented
8#14583070C212yesmaximal, complemented
9#14583016C211yesmaximal, characteristic, complemented
10#14583014C211yesmaximal, characteristic, complemented
11C43×#576C211yesmaximal, characteristic, complemented
12#13063372C2212yescomplemented
13#13063355—22no—
14#13063355C2212yes—
15#13063355C2212yescomplemented
16#13063354—22no—
17#13063351—22no—
18#13063351C2212yescomplemented
19#13063345—22no—
20#13063345C2211yescharacteristic
21#13063344—21no—
22C2×Dic172C2211yescharacteristic, complemented
23Q16×D43—21no—
24C2×#10621883—22no—
25C2×#10621883C2212yescomplemented
26#13063332C2212yescomplemented
27#13063331C2211yescharacteristic, complemented
28#13063312C2212yescomplemented
29#13063261C2211yescharacteristic, complemented
30#13063260C2211yescharacteristic, complemented
31#13063252C2211yescharacteristic
32#13063252C2212yescomplemented
33#13063251C2211yescharacteristic, complemented
34#13063243C2212yescomplemented
35#13063242C2212yescomplemented
36C8×Dic43C2211yescharacteristic, complemented
37H(5,𝔽2)×C43C2212yes—
38AGL(1,ℤ/8)×C43—22no—
39AGL(1,ℤ/8)×C43C2212yes—
40#135×C43—21no—
41#135×C43C2211yescharacteristic
42C2×D8×C43—21no—
43C2×D8×C43C2211yescharacteristic
44#131×C43C2211yescharacteristic
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—
53Q8×D43—22no—
54#10621900—22no—
55#10621900—42no—
56#10621898—22no—
57#10621898C2311yescharacteristic
58C2×Dic86—22no—
59C2×Dic86C2312yes—
60Q16×C43D411yescharacteristic
61SD16×C43—22no—
62SD16×C43D412yes—
63D8×C43—22no—
64D8×C43—21no—
65D8×C43—21no—
66D8×C43D411yescharacteristic
67M16×C43—21no—
68M16×C43C2311yescharacteristic
69C2×C8×C43—21no—
70C2×C8×C43C2311yescharacteristic
71C22⋊Dic43—42no—
72#10621885—22no—
73#10621885—22no—
74#10621885D411yescharacteristic
75#10621884D411yescharacteristic
76#10621883—22no—
77#10621883—22no—
78#10621883—22no—
79#10621883—22no—
80#10621883—22no—
81#10621883D411yescharacteristic
82#10621882—22no—
83#10621882D411yescharacteristic
84C4×Dic43C2311yescharacteristic
85#10621877—22no—
86#10621877C2311yescharacteristic
87#10621877C2312yes—
88C2×C43⋊C8—22no—
89C2×C43⋊C8C2311yescharacteristic
90Dic172—21no—
91Dic172—21no—
92#10621872—21no—
93C8×D43—21no—
94C23×C43—22no—
95C23×C43—42no—
96Q8×C43C2×D411yescharacteristic
97Q8×C43C2×D412yes—
98D4×C43—22no—
99D4×C43—21no—
100D4×C43—22no—
101D4×C43—22no—
102D4×C43—42no—
103D4×C43—42no—
104D4×C43C2×D411yescharacteristic
105D4×C43C2×D412yes—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43—42no—
109C2×C4×C43C2411yescharacteristic
110C22⋊D43—21no—
111C22⋊D43—42no—
112C2×Dic43—21no—
113C2×Dic43—22no—
114C2×Dic43—42no—
115D172C2×D411yescharacteristic
116C4×D43—21no—
117C4×D43—42no—
118Dic86—22no—
119Dic86—22no—
120Dic86—42no—
121Dic86C2×D411yescharacteristic
122C8×C43—21no—
123C8×C43C2×D411yescharacteristic
124C8×C43C2×D411yescharacteristic
125C43⋊C8—21no—
126C43⋊C8—22no—
127C43⋊C8C2×D411yescharacteristic
128C43⋊C8C2×D411yescharacteristic
129C22×C43—21no—
130C22×C43—22no—
131C22×C43—42no—
132C22×C43—82no—
133C22×C43—162no—
134C22×C43H(5,𝔽2)11yescharacteristic
135C2×D43—21no—
136C4×C43—22no—
137C4×C43—21no—
138C4×C43C22×D411yescharacteristic
139C4×C43C22×D411yescharacteristic
140Dic43—21no—
141Dic43—41no—
142Dic43—42no—
143#3290—431nomaximal, Sylow
144C2×C43—21no—
145C2×C43—42no—
146C2×C43—41no—
147C2×C43—82no—
148C2×C43D4211yescharacteristic
149D43—41no—
150#578—431no—
151#577—432no—
152#576D4311yescharacteristic, complemented
153#495—431no—
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)C2×D4312yes—
164#137—432no—
165#137—432no—
166#137—862no—
167#137—862no—
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—432no—
170AGL(1,ℤ/8)—862no—
171AGL(1,ℤ/8)C2×D4312yes—
172#135—21no—
173#135—431no—
174#135—862no—
175#135—861no—
176#135C2×D4311yescharacteristic
177C2×Q16—431no—
178C2×Q16—861no—
179C2×SD16—432no—
180C2×SD16—862no—
181C2×D8—21no—
182C2×D8C2×D4311yescharacteristic
183#131—432no—
184#131—431no—
185#131C2×D4311yescharacteristic
186#124—432no—
187#108—431no—
188#108—431no—
189#104—431no—
190#104—432no—
191#104—431no—
192#101—432no—
193#100—432no—
194C4×C8—431no—
195#41—22no—
196#41—22no—
197#41—431no—
198#41—862no—
199#41—862no—
200#41—1722no—
201#41C22×D4311yescharacteristic
202#41C22×D4312yes—
203C2×Q8—432no—
204C2×Q8—862no—
205C2×Q8—862no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4C22×D4312yes—
210Q16—431no—
211Q16—862no—
212Q16—862no—
213Q16—861no—
214Q16—861no—
215Q16C22⋊D4311yescharacteristic
216SD16—22no—
217SD16—431no—
218SD16—431no—
219SD16—862no—
220SD16—862no—
221SD16—862no—
222SD16—862no—
223SD16—862no—
224SD16C22⋊D4312yes—
225D8—22no—
226D8—21no—
227D8—21no—
228D8—431no—
229D8—862no—
230D8C22⋊D4311yescharacteristic
231M16—21no—
232M16—431no—
233M16—432no—
234M16—862no—
235M16—861no—
236M16C22×D4311yescharacteristic
237C2×C8—21no—
238C2×C8—431no—
239C2×C8—862no—
240C2×C8—861no—
241C2×C8C22×D4311yescharacteristic
242C22⋊C4—1722no—
243C42—431no—
244C23—22no—
245C23—42no—
246Q8—431no—
247Q8—862no—
248Q8—862no—
249Q8—1722no—
250Q8D4×D4311yescharacteristic
251Q8C2×C22⋊D4312yes—
252D4—21no—
253D4—22no—
254D4—22no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—431no—
259D4—861no—
260D4—1722no—
261D4D4×D4311yescharacteristic
262D4C2×C22⋊D4312yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—862no—
269C2×C4—1722no—
270C2×C4—1722no—
271C2×C4C23×D4311yescharacteristic
272C8—21no—
273C8—431no—
274C8—431no—
275C8—862no—
276C8—861no—
277C8C2×C22⋊D4311yescharacteristic
278C8C2×C22⋊D4311yescharacteristic
279C22—22no—
280C22—21no—
281C22—42no—
282C22—82no—
283C22—162no—
284C22—861no—
285C22#1306337011yescharacteristic
286C4—21no—
287C4—22no—
288C4—861no—
289C4—1721no—
290C4—1722no—
291C4C2×D4×D4311yescharacteristic
292C4C22×C22⋊D4311yescharacteristic
293C2—21no—
294C2—41no—
295C2—42no—
296C2—82no—
297C2—1721no—
298C2D4×C22⋊D4311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#576C2
socleC2×C43D42
hypercenter#576D43
hypocenterC43#3290
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. #14583713C2semidirect
2. #14583710C2semidirect
3. #14583282C2semidirect
4. #14583174C2semidirect
5. #14583166C2semidirect
6. #14583160C2semidirect
7. #14583077C2semidirect
8. #14583070C2semidirect
9. #14583016C2semidirect
10. #14583014C2semidirect
11. C43×#576C2semidirect
12. #13063372C22semidirect
15. #13063355C22semidirect
18. #13063351C22semidirect
22. C2×Dic172C22semidirect
25. C2×#10621883C22semidirect
26. #13063332C22semidirect
27. #13063331C22semidirect
28. #13063312C22semidirect
29. #13063261C22semidirect
30. #13063260C22semidirect
32. #13063252C22semidirect
33. #13063251C22semidirect
34. #13063243C22semidirect
35. #13063242C22semidirect
36. C8×Dic43C22semidirect
152. #576D43semidirect
161. C43#3290semidirect