Finite Group Databasebeta

← #19146361

Subgroups — #19146361

Order 5504.

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

normal subgroups only

This group has 464 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#14583705C212yesmaximal, complemented
2#14583700C212yesmaximal, complemented
3#14583166C212yesmaximal, complemented
4#14583159C212yesmaximal, complemented
5#14583076C211yesmaximal, characteristic, complemented
6#14583071C211yesmaximal, characteristic, complemented
7#14583066C212yesmaximal, complemented
8#14583022C212yesmaximal, complemented
9C43×#496C211yesmaximal, characteristic, complemented
10#13063373C2211yescharacteristic, complemented
11#13063370C2211yescharacteristic
12#13063370C2212yescomplemented
13#13063356C2212yescomplemented
14#13063354—22no—
15#13063352—22no—
16#13063351C2212yes—
17#13063351C2212yescomplemented
18#13063351C2212yescomplemented
19#13063349—22no—
20#13063349—22no—
21#13063347C2212yes—
22#13063346—22no—
23#13063344—22no—
24SD16×D43—22no—
25D8×D43—22no—
26#13063331C2212yescomplemented
27#13063331C2212yescomplemented
28#13063261C2212yescomplemented
29#13063253C2212yescomplemented
30#13063253C2212yescomplemented
31#13063244C2211yescharacteristic, complemented
32#13063242C2212yescomplemented
33#13063242C2211yescharacteristic, complemented
34C2×SD16×C43C2212yescomplemented
35C2×D8×C43C2212yescomplemented
36#127×C43C2211yescharacteristic, complemented
37#124×C43C2211yescharacteristic, complemented
38#97×C43C2211yescharacteristic, complemented
39C2×Q8×C43C2311yescharacteristic
40C2×D4×C43—41no—
41C2×D4×C43C2311yescharacteristic
42C2×D4×C43C2312yes—
43C2×C22⋊D43—41no—
44C2×C22⋊D43—42no—
45#10621902—22no—
46Q8×D43—22no—
47#10621900—22no—
48#10621900—22no—
49#10621900—22no—
50D4×D43—22no—
51D4×D43—22no—
52D4×D43—22no—
53#10621898—41no—
54#10621898C2312yes—
55#10621898C2312yes—
56SD16×C43—22no—
57SD16×C43—22no—
58D8×C43—22no—
59D8×C43—22no—
60C2×C8×C43C2312yes—
61C22⋊C4×C43—41no—
62C42×C43C2311yescharacteristic
63#10621885—22no—
64#10621884—22no—
65#10621883—22no—
66#10621883—22no—
67#10621883—22no—
68#10621882—22no—
69#10621882—22no—
70#10621882—22no—
71#10621877C2312yes—
72#10621877C2312yes—
73Dic172D412yescomplemented
74D344D412yescomplemented
75#10621873D412yescomplemented
76#10621873D412yescomplemented
77#10621872—22no—
78#10621872—22no—
79C8×D43—22no—
80C8×D43—22no—
81C23×C43—21no—
82C23×C43—22no—
83C22×D43—41no—
84C22×D43—42no—
85Q8×C43—22no—
86D4×C43—22no—
87D4×C43—22no—
88D4×C43—22no—
89D4×C43—82no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43C2411yescharacteristic
93C22⋊D43—22no—
94C22⋊D43—22no—
95C22⋊D43—42no—
96C22⋊D43—42no—
97C22⋊D43—42no—
98C2×Dic43—42no—
99C2×Dic43—41no—
100D172—41no—
101D172C2×D412yes—
102D172C2×D412yes—
103C4×D43—22no—
104C4×D43—22no—
105C4×D43—42no—
106Dic86—41no—
107Dic86C2×D412yes—
108Dic86C2×D412yes—
109C8×C43C2×D412yes—
110C8×C43C2×D412yes—
111C43⋊C8—22no—
112C43⋊C8—22no—
113C22×C43—41no—
114C22×C43—42no—
115C22×C43—81no—
116C22×C43—82no—
117C22×C43H(5,𝔽2)11yescharacteristic
118C2×D43—22no—
119C2×D43—22no—
120C2×D43—162no—
121C2×D43—161no—
122C4×C43—41no—
123C4×C43—41no—
124C4×C43C22×D412yes—
125Dic43—22no—
126Dic43—22no—
127#3288—431nomaximal, Sylow
128C2×C43—21no—
129C2×C43—81no—
130C2×C43—82no—
131C2×C43D4211yescharacteristic
132D43—42no—
133D43—42no—
134#577—432no—
135#576—432no—
136#496D4311yescharacteristic, complemented
137#472—432no—
138#471—432no—
139#455—431no—
140#454—431no—
141#453—432no—
142#444—432no—
143C43#328811yescharacteristic, complemented, Sylow
1442−1+4—431no—
145H(5,𝔽2)—431no—
146H(5,𝔽2)—432no—
147#137—432no—
148#137—862no—
149AGL(1,ℤ/8)—432no—
150AGL(1,ℤ/8)—432no—
151AGL(1,ℤ/8)—432no—
152AGL(1,ℤ/8)—862no—
153AGL(1,ℤ/8)—862no—
154AGL(1,ℤ/8)—862no—
155#135—432no—
156#135—862no—
157#135—862no—
158C2×SD16—862no—
159C2×SD16C2×D4312yescomplemented
160C2×D8—862no—
161C2×D8C2×D4312yescomplemented
162#131—432no—
163#131—432no—
164#127C2×D4311yescharacteristic, complemented
165#124C2×D4311yescharacteristic, complemented
166#108—432no—
167#104—432no—
168#104—432no—
169#101—431no—
170#100—432no—
171#100—431no—
172#97C2×D4311yescharacteristic, complemented
173#41—432no—
174#41—432no—
175#41—862no—
176#41—862no—
177#41—862no—
178#41—862no—
179#41—1721no—
180C2×Q8—862no—
181C2×Q8C22×D4311yescharacteristic
182C2×D4—41no—
183C2×D4—862no—
184C2×D4—862no—
185C2×D4—862no—
186C2×D4—1721no—
187C2×D4—1722no—
188C2×D4C22×D4311yescharacteristic
189C2×D4C22×D4312yes—
190Q16—432no—
191Q16—862no—
192SD16—22no—
193SD16—22no—
194SD16—432no—
195SD16—432no—
196SD16—862no—
197SD16—862no—
198SD16—862no—
199SD16—862no—
200D8—22no—
201D8—22no—
202D8—432no—
203D8—862no—
204D8—862no—
205D8—862no—
206M16—432no—
207M16—432no—
208M16—862no—
209M16—862no—
210C2×C8—862no—
211C2×C8—862no—
212C2×C8C22×D4312yes—
213C22⋊C4—41no—
214C42C22×D4311yescharacteristic
215C23—21no—
216C23—22no—
217C23—1722no—
218C23—1721no—
219Q8—22no—
220Q8—432no—
221Q8—432no—
222Q8—1721no—
223D4—22no—
224D4—22no—
225D4—22no—
226D4—82no—
227D4—432no—
228D4—432no—
229D4—862no—
230D4—862no—
231D4—1721no—
232D4—1722no—
233D4—1722no—
234D4—1722no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—862no—
238C2×C4—862no—
239C2×C4—1722no—
240C2×C4—1721no—
241C2×C4—1722no—
242C2×C4C23×D4311yescharacteristic
243C8—862no—
244C8—862no—
245C8D4×D4312yes—
246C8D4×D4312yes—
247C22—41no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—862no—
252C22—862no—
253C22—6881no—
254C22—6882no—
255C22#1306337011yescharacteristic
256C4—41no—
257C4—41no—
258C4—862no—
259C4—862no—
260C4C2×D4×D4312yes—
261C2—21no—
262C2—82no—
263C2—81no—
264C2—1722no—
265C2—1722no—
266C2#1458353411yescharacteristic
subgroupG/H
centerC2#14583534
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#496C2
socleC2×C43D42
hypercenter#496D43
hypocenterC43#3288
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14583705C2semidirect
2. #14583700C2semidirect
3. #14583166C2semidirect
4. #14583159C2semidirect
5. #14583076C2semidirect
6. #14583071C2semidirect
7. #14583066C2semidirect
8. #14583022C2semidirect
9. C43×#496C2semidirect
10. #13063373C22semidirect
12. #13063370C22semidirect
13. #13063356C22semidirect
17. #13063351C22semidirect
18. #13063351C22semidirect
26. #13063331C22semidirect
27. #13063331C22semidirect
28. #13063261C22semidirect
29. #13063253C22semidirect
30. #13063253C22semidirect
31. #13063244C22semidirect
32. #13063242C22semidirect
33. #13063242C22semidirect
34. C2×SD16×C43C22semidirect
35. C2×D8×C43C22semidirect
36. #127×C43C22semidirect
37. #124×C43C22semidirect
38. #97×C43C22semidirect
73. Dic172D4semidirect
74. D344D4semidirect
75. #10621873D4semidirect
76. #10621873D4semidirect
136. #496D43semidirect
143. C43#3288semidirect
159. C2×SD16C2×D43semidirect
161. C2×D8C2×D43semidirect
164. #127C2×D43semidirect
165. #124C2×D43semidirect
172. #97C2×D43semidirect