Finite Group Databasebeta

← #19145060

Subgroups — #19145060

Order 5504.

572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#13063354C212yesmaximal, complemented
2C2×#13063349C212yesmaximal, complemented
3#14583447C211yesmaximal, characteristic, complemented
4#124×D43C211yesmaximal, characteristic, complemented
5#14583294C211yesmaximal, characteristic, complemented
6#14583293C211yesmaximal, characteristic, complemented
7#14583286C211yesmaximal, characteristic, complemented
8#14583282C212yesmaximal, complemented
9#14583280C212yesmaximal, complemented
10#14582851C211yesmaximal, characteristic, complemented
11C43×#496C211yesmaximal, characteristic, complemented
12C2×#10621900C2212yes—
13C2×Q8×D43C2211yescharacteristic
14C2×D4×D43C2211yescharacteristic
15#13063354—28no—
16#13063349—28no—
17C2×Dic172C2212yescomplemented
18C2×#10621885C2212yescomplemented
19C2×#10621873C2212yes—
20C2×#10621883C2212yes—
21C2×#10621883C2212yescomplemented
22C2×#10621882C2212yes—
23C2×#10621872C2212yes—
24#13063325C2211yescharacteristic, complemented
25#13063314C2211yescharacteristic
26#13063313C2211yescharacteristic
27#13063312C2211yescharacteristic
28#13063312C2212yescomplemented
29#13063311—22no—
30#13063296—22no—
31D4×Dic43—22no—
32C22⋊C4×D43—22no—
33C42×D43C2211yescharacteristic
34#13063236C2211yescharacteristic, complemented
35C8×Dic43C2212yescomplemented
36C2×SD16×C43C2212yescomplemented
37C2×D8×C43C2212yes—
38#127×C43C2211yescharacteristic, complemented
39#124×C43C2211yescharacteristic
40#97×C43C2211yescharacteristic, complemented
41C23×D43—21no—
42C2×Q8×C43C2311yescharacteristic
43C2×D4×C43—22no—
44C2×D4×C43C2311yescharacteristic
45C2×D4×C43C2312yes—
46C2×C22⋊D43—21no—
47C2×C22⋊D43—22no—
48C22×Dic43—22no—
49Q8×D43—24no—
50#10621900—24no—
51#10621900—24no—
52D4×D43—24no—
53C2×D172C2311yescharacteristic
54C2×C4×D43—21no—
55C2×C4×D43D412yes—
56C2×C4×D43C2311yescharacteristic
57C2×Dic86—21no—
58C2×Dic86C2311yescharacteristic
59C2×Dic86C2312yes—
60SD16×C43—24no—
61D8×C43—24no—
62C2×C8×C43C2312yes—
63C22⋊C4×C43—22no—
64C42×C43C2311yescharacteristic
65C22⋊Dic43—22no—
66C22⋊Dic43—24no—
67#10621885—24no—
68#10621883—24no—
69#10621883—24no—
70#10621882—24no—
71(C2×D43)⋊C4—22no—
72(C2×D43)⋊C4—22no—
73C4⋊Dic43—22no—
74C4×Dic43D412yes—
75C4×Dic43C2311yescharacteristic
76C2×C43⋊C8C2312yes—
77Dic172—24no—
78#10621873—24no—
79#10621872D418yescomplemented
80C23×C43—21no—
81C23×C43—22no—
82C22×D43—21no—
83C22×D43—44no—
84C22×D43—42no—
85C22×D43C2×D411yescharacteristic
86Q8×C43—22no—
87D4×C43—22no—
88D4×C43—22no—
89D4×C43—22no—
90D4×C43—44no—
91C2×C4×C43—21no—
92C2×C4×C43C2×D412yes—
93C2×C4×C43C2411yescharacteristic
94C22⋊D43—44no—
95C22⋊D43—42no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—44no—
99C2×Dic43C2×D412yes—
100C2×Dic43C2×D411yescharacteristic
101D172—22no—
102C4×D43—42no—
103C4×D43—42no—
104C4×D43C2×D414yes—
105Dic86—22no—
106Dic86—22no—
107Dic86—22no—
108Dic86—42no—
109C8×C43C2×D414yes—
110C43⋊C8C2×D414yes—
111C22×C43—41no—
112C22×C43—42no—
113C22×C43—42no—
114C22×C43—44no—
115C22×C43C22×D411yescharacteristic
116C2×D43—22no—
117C2×D43—41no—
118C2×D43—42no—
119C2×D43—84no—
120C2×D43#12712yes—
121C4×C43—22no—
122C4×C43—41no—
123C4×C43C22×D412yes—
124Dic43—22no—
125Dic43—41no—
126Dic43—42no—
127Dic43#12712yes—
128#3153—431nomaximal, Sylow
129C2×C43—81no—
130C2×C43—82no—
131C2×C43C2×#12711yescharacteristic
132C2×C43#57512yes—
133D43—22no—
134D43—81no—
135C2×#137—432no—
136C2×AGL(1,ℤ/8)—432no—
137#532—431no—
138C2×#124—431no—
139#497—431no—
140#497—431no—
141#496—431no—
142#496D4311yescharacteristic, complemented
143#495—432no—
144#495—432no—
145C4×M16—431no—
146C43#315311yescharacteristic, complemented, Sylow
147C2×#41—432no—
148C22×Q8—431no—
149C22×D4—431no—
150#137—868no—
151AGL(1,ℤ/8)—868no—
152C2×Q16—432no—
153C2×Q16—432no—
154C2×SD16—432no—
155C2×SD16—432no—
156C2×SD16—432no—
157C2×SD16C2×D4312yescomplemented
158C2×D8—432no—
159C2×D8C2×D4312yes—
160C2×M16—432no—
161C4⋊Q8—431no—
162#127C2×D4311yescharacteristic, complemented
163#124—431no—
164#124—431no—
165#124—432no—
166#124—431no—
167#124—862no—
168#124C2×D4311yescharacteristic
169#121—862no—
170C4×D4—862no—
171C2×C22⋊C4—862no—
172C2×C42—431no—
173#97—431no—
174#97C2×D4311yescharacteristic, complemented
175C4×C8—432no—
176C24—861no—
177#41—864no—
178#41—864no—
179C2×Q8—431no—
180C2×Q8—432no—
181C2×Q8—861no—
182C2×Q8—864no—
183C2×Q8C22×D4311yescharacteristic
184C2×D4—22no—
185C2×D4—431no—
186C2×D4—864no—
187C2×D4—861no—
188C2×D4—862no—
189C2×D4C22×D4311yescharacteristic
190C2×D4C22×D4312yes—
191C22×C4—431no—
192C22×C4—432no—
193C22×C4—861no—
194C22×C4—862no—
195Q16—864no—
196Q16—864no—
197SD16—24no—
198SD16—864no—
199SD16—864no—
200SD16—864no—
201D8—24no—
202D8—864no—
203M16—438no—
204C2×C8—432no—
205C2×C8C22×D4312yes—
206C4⋊C4—862no—
207C22⋊C4—22no—
208C22⋊C4—862no—
209C22⋊C4—862no—
210C22⋊C4—864no—
211C22⋊C4—862no—
212C42—432no—
213C42—431no—
214C42C22×D4311yescharacteristic
215C23—21no—
216C23—22no—
217C23—431no—
218C23—861no—
219C23—1722no—
220C23—1724no—
221Q8—22no—
222Q8—862no—
223Q8—862no—
224Q8—862no—
225Q8—1722no—
226D4—22no—
227D4—22no—
228D4—22no—
229D4—44no—
230D4—862no—
231D4—1722no—
232D4—1724no—
233C2×C4—21no—
234C2×C4—431no—
235C2×C4—434no—
236C2×C4—432no—
237C2×C4—861no—
238C2×C4—862no—
239C2×C4—1722no—
240C2×C4—1722no—
241C2×C4—1724no—
242C2×C4D4×D4312yes—
243C2×C4C23×D4311yescharacteristic
244C8—434no—
245C8D4×D4314yes—
246C22—42no—
247C22—41no—
248C22—44no—
249C22—42no—
250C22—432no—
251C22—862no—
252C22—3444no—
253C22—1721no—
254C22—1722no—
255C22C2×D4×D4311yescharacteristic
256C4—22no—
257C4—41no—
258C4—432no—
259C4—862no—
260C4—1722no—
261C4—1721no—
262C4C2×D4×D4312yes—
263C2—81no—
264C2—82no—
265C2—862no—
266C2—3441no—
267C2#127×D4311yescharacteristic
268C2#1458369512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#496C2
socleC22×C43C22×D4
hypercenter#496D43
hypocenterC43#3153
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#13063354C2semidirect
2. C2×#13063349C2semidirect
3. #14583447C2semidirect
4. #124×D43C2semidirect
5. #14583294C2semidirect
6. #14583293C2semidirect
7. #14583286C2semidirect
8. #14583282C2semidirect
9. #14583280C2semidirect
10. #14582851C2semidirect
11. C43×#496C2semidirect
17. C2×Dic172C22semidirect
18. C2×#10621885C22semidirect
21. C2×#10621883C22semidirect
24. #13063325C22semidirect
28. #13063312C22semidirect
34. #13063236C22semidirect
35. C8×Dic43C22semidirect
36. C2×SD16×C43C22semidirect
38. #127×C43C22semidirect
40. #97×C43C22semidirect
79. #10621872D4semidirect
142. #496D43semidirect
146. C43#3153semidirect
157. C2×SD16C2×D43semidirect
162. #127C2×D43semidirect
174. #97C2×D43semidirect