Finite Group Databasebeta

← #19146390

Subgroups — #19146390

Order 5504.

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

normal subgroups only

This group has 460 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#14583710C212yesmaximal, complemented
2#14583709C212yesmaximal, complemented
3#14583271C211yesmaximal, characteristic, complemented
4#14583161C212yesmaximal, complemented
5#14583160C212yesmaximal, complemented
6#14583083C212yesmaximal, complemented
7#14583066C211yesmaximal, characteristic, complemented
8#14583013C212yesmaximal, complemented
9C43×#453C211yesmaximal, characteristic, complemented
10#13063372C2212yes—
11#13063370C2211yescharacteristic, complemented
12#13063358C2212yescomplemented
13#13063355—22no—
14#13063355C2212yescomplemented
15#13063354—22no—
16#13063351—22no—
17#13063351C2212yes—
18#13063349—22no—
19#13063345—22no—
20#13063345C2212yes—
21#13063344—22no—
22C2×#10621883—22no—
23C2×#10621883C2212yescomplemented
24C2×#10621883C2212yescomplemented
25SD16×D43—22no—
26#13063333C2212yescomplemented
27#13063332C2212yescomplemented
28#13063325C2211yescharacteristic, complemented
29#13063260C2212yescomplemented
30#13063253C2212yescomplemented
31#13063243C2212yescomplemented
32#13063242C2211yescharacteristic, complemented
33C4×C43⋊C8C2211yescharacteristic, complemented
34H(5,𝔽2)×C43C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C43C2212yes—
36#127×C43C2211yescharacteristic
37#104×C43C2212yescomplemented
38#100×C43C2211yescharacteristic, complemented
39#41×C43—22no—
40#41×C43C2312yes—
41C2×D4×C43—22no—
42C2×D4×C43—41no—
43C2×D4×C43—41no—
44C2×D4×C43C2311yescharacteristic
45C2×D4×C43C2311yescharacteristic
46C2×C22⋊D43—41no—
47Q8×D43—22no—
48#10621900—22no—
49#10621900—22no—
50#10621900—42no—
51D4×D43—22no—
52#10621898—22no—
53#10621898C2312yes—
54C2×Dic86—22no—
55C2×Dic86C2312yes—
56SD16×C43—22no—
57D8×C43—22no—
58M16×C43C2312yes—
59C42×C43C2311yescharacteristic
60#10621885—22no—
61#10621885D412yescomplemented
62#10621884D412yescomplemented
63#10621883—22no—
64#10621883—22no—
65#10621883—22no—
66#10621883—22no—
67#10621883—22no—
68#10621883—22no—
69#10621883D412yescomplemented
70#10621882—22no—
71#10621882D412yescomplemented
72C4⋊Dic43—41no—
73#10621877—22no—
74#10621877C2312yes—
75C2×C43⋊C8—22no—
76C2×C43⋊C8C2312yes—
77Dic172—22no—
78#10621873—22no—
79#10621872—22no—
80C8×D43—22no—
81C23×C43—21no—
82C23×C43—21no—
83C23×C43—41no—
84C22×D43—41no—
85Q8×C43C2×D412yes—
86D4×C43—22no—
87D4×C43—22no—
88D4×C43—22no—
89D4×C43—42no—
90D4×C43—82no—
91D4×C43C2×D412yes—
92C2×C4×C43—21no—
93C2×C4×C43—22no—
94C2×C4×C43—41no—
95C2×C4×C43C2411yescharacteristic
96C22⋊D43—22no—
97C22⋊D43—42no—
98C22⋊D43—42no—
99C2×Dic43—22no—
100C2×Dic43—41no—
101C2×Dic43—42no—
102D172C2×D412yes—
103C4×D43—22no—
104C4×D43—42no—
105Dic86—22no—
106Dic86—22no—
107Dic86—42no—
108Dic86C2×D412yes—
109C8×C43—22no—
110C43⋊C8—22no—
111C43⋊C8C2×D412yes—
112C43⋊C8C2×D412yes—
113C22×C43—22no—
114C22×C43—41no—
115C22×C43—41no—
116C22×C43—81no—
117C22×C43—81no—
118C22×C43—161no—
119C22×C43H(5,𝔽2)11yescharacteristic
120C2×D43—22no—
121C2×D43—161no—
122C4×C43—22no—
123C4×C43—22no—
124C4×C43C22×D412yes—
125Dic43—22no—
126Dic43—42no—
127#3291—431nomaximal, Sylow
128C2×C43—21no—
129C2×C43—42no—
130C2×C43—81no—
131C2×C43—81no—
132C2×C43D4211yescharacteristic
133D43—42no—
134#577—432no—
135#577—432no—
136#492—431no—
137#471—432no—
138#471—432no—
139#456—432no—
140#453—431no—
141#453D4311yescharacteristic, complemented
142#443—432no—
143C43#329111yescharacteristic, complemented, Sylow
1442−1+4—432no—
145H(5,𝔽2)—431no—
146H(5,𝔽2)C2×D4311yescharacteristic, complemented
147#137—432no—
148#137—432no—
149#137—862no—
150#137—862no—
151AGL(1,ℤ/8)—432no—
152AGL(1,ℤ/8)—862no—
153AGL(1,ℤ/8)—862no—
154AGL(1,ℤ/8)C2×D4312yes—
155#135—432no—
156#135—862no—
157#135—862no—
158C2×SD16—432no—
159C2×SD16—432no—
160C2×SD16—862no—
161C2×SD16—862no—
162#131—432no—
163#131—432no—
164C4⋊Q8—431no—
165#127C2×D4311yescharacteristic
166#108—432no—
167#104—432no—
168#104C2×D4312yescomplemented
169#101—432no—
170#100—431no—
171#100C2×D4311yescharacteristic, complemented
172C4×C8—431no—
173#41—22no—
174#41—432no—
175#41—862no—
176#41—862no—
177#41—862no—
178#41—1722no—
179#41C22×D4312yes—
180C2×Q8—432no—
181C2×Q8—862no—
182C2×Q8—862no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—862no—
187C2×D4—1721no—
188C2×D4C22×D4311yescharacteristic
189C2×D4C22×D4311yescharacteristic
190Q16—432no—
191Q16—862no—
192Q16—862no—
193SD16—22no—
194SD16—432no—
195SD16—432no—
196SD16—862no—
197SD16—862no—
198SD16—862no—
199SD16—862no—
200SD16—862no—
201SD16—862no—
202SD16—862no—
203D8—22no—
204D8—432no—
205D8—862no—
206M16—432no—
207M16—862no—
208M16—862no—
209M16C22×D4312yes—
210C2×C8—432no—
211C2×C8—862no—
212C2×C8—862no—
213C4⋊C4—1721no—
214C42C22×D4311yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—1721no—
219Q8—432no—
220Q8—862no—
221Q8—862no—
222Q8—1722no—
223Q8D4×D4312yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—432no—
230D4—862no—
231D4—1722no—
232D4—1722no—
233D4D4×D4312yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—1722no—
240C2×C4—1721no—
241C2×C4—1722no—
242C2×C4C23×D4311yescharacteristic
243C8—22no—
244C8—432no—
245C8—432no—
246C8—862no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—862no—
254C22—6881no—
255C22#1306337011yescharacteristic
256C4—22no—
257C4—22no—
258C4—862no—
259C4—1722no—
260C4C2×D4×D4312yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—1722no—
266C2#1458353111yescharacteristic
subgroupG/H
centerC2#14583531
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#453C2
socleC2×C43D42
hypercenter#453D43
hypocenterC43#3291
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. #14583271C2semidirect
4. #14583161C2semidirect
5. #14583160C2semidirect
6. #14583083C2semidirect
7. #14583066C2semidirect
8. #14583013C2semidirect
9. C43×#453C2semidirect
11. #13063370C22semidirect
12. #13063358C22semidirect
14. #13063355C22semidirect
23. C2×#10621883C22semidirect
24. C2×#10621883C22semidirect
26. #13063333C22semidirect
27. #13063332C22semidirect
28. #13063325C22semidirect
29. #13063260C22semidirect
30. #13063253C22semidirect
31. #13063243C22semidirect
32. #13063242C22semidirect
33. C4×C43⋊C8C22semidirect
34. H(5,𝔽2)×C43C22semidirect
37. #104×C43C22semidirect
38. #100×C43C22semidirect
61. #10621885D4semidirect
62. #10621884D4semidirect
69. #10621883D4semidirect
71. #10621882D4semidirect
141. #453D43semidirect
143. C43#3291semidirect
146. H(5,𝔽2)C2×D43semidirect
168. #104C2×D43semidirect
171. #100C2×D43semidirect