Finite Group Databasebeta

← #496×D43 #19145025

Subgroups — #496×D43 #19145025

Order 5504.

668 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 145 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×SD16×D43C212yesmaximal, complemented
2C2×D8×D43C212yesmaximal, complemented
3#127×D43C211yesmaximal, characteristic, complemented
4#124×D43C211yesmaximal, characteristic, complemented
5#14583289C211yesmaximal, characteristic, complemented
6#14583288C211yesmaximal, characteristic, complemented
7#14583287C212yesmaximal, complemented
8#14583286C211yesmaximal, characteristic, complemented
9#14583285C212yesmaximal, complemented
10#97×D43C211yesmaximal, characteristic, complemented
11C43×#496C211yesmaximal, characteristic, complemented
12C2×Q8×D43C2211yescharacteristic
13C2×D4×D43—22no—
14C2×D4×D43C2211yescharacteristic
15C2×D4×D43C2212yes—
16C2×#10621873C2212yescomplemented
17C2×#10621883C2212yescomplemented
18C2×#10621884C2212yescomplemented
19SD16×D43—28no—
20C2×D344C2212yescomplemented
21C2×#10621882C2212yescomplemented
22C2×#10621882C2212yescomplemented
23D8×D43—28no—
24C2×C8×D43C2212yes—
25#13063322C2211yescharacteristic, complemented
26#13063321—22no—
27#13063321C2212yescomplemented
28#13063314C2211yescharacteristic, complemented
29#13063313C2211yescharacteristic, complemented
30#13063312C2211yescharacteristic, complemented
31#13063311—22no—
32C22⋊C4×D43—22no—
33C42×D43C2211yescharacteristic
34#13063236C2211yescharacteristic, complemented
35#13063235C2212yescomplemented
36C2×SD16×C43C2212yescomplemented
37C2×D8×C43C2212yescomplemented
38#127×C43C2211yescharacteristic, complemented
39#124×C43C2211yescharacteristic, complemented
40#97×C43C2211yescharacteristic, complemented
41C23×D43—21no—
42C23×D43—22no—
43C2×Q8×C43C2311yescharacteristic
44C2×D4×C43—22no—
45C2×D4×C43C2311yescharacteristic
46C2×D4×C43C2312yes—
47C2×C22⋊D43—21no—
48C2×C22⋊D43—22no—
49C2×C22⋊D43—24no—
50Q8×D43—24no—
51D4×D43—24no—
52D4×D43—24no—
53D4×D43—24no—
54D4×D43—48no—
55C2×D172—22no—
56C2×D172C2311yescharacteristic
57C2×D172C2312yes—
58C2×C4×D43—21no—
59C2×C4×D43D412yes—
60C2×C4×D43C2311yescharacteristic
61C2×Dic86—21no—
62C2×Dic86C2311yescharacteristic
63SD16×C43—24no—
64D8×C43—24no—
65C2×C8×C43C2312yes—
66C22⋊C4×C43—22no—
67C42×C43C2311yescharacteristic
68C22⋊Dic43—22no—
69#10621884—24no—
70#10621883—24no—
71#10621882—24no—
72#10621882—24no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—22no—
75C4×Dic43D412yes—
76C4×Dic43C2311yescharacteristic
77C2×C43⋊C8C2312yes—
78D344—24no—
79#10621873—24no—
80C8×D43D418yescomplemented
81C23×C43—21no—
82C23×C43—22no—
83C22×D43—21no—
84C22×D43—22no—
85C22×D43—42no—
86C22×D43—44no—
87C22×D43—48no—
88C22×D43—44no—
89C22×D43C2×D411yescharacteristic
90Q8×C43—22no—
91D4×C43—22no—
92D4×C43—22no—
93D4×C43—22no—
94D4×C43—44no—
95C2×C4×C43—21no—
96C2×C4×C43C2×D412yes—
97C2×C4×C43C2411yescharacteristic
98C22⋊D43—48no—
99C22⋊D43—42no—
100C22⋊D43—44no—
101C2×Dic43—21no—
102C2×Dic43C2×D412yes—
103C2×Dic43C2×D411yescharacteristic
104D172—22no—
105D172—22no—
106D172—22no—
107D172—44no—
108C4×D43—24no—
109C4×D43—42no—
110C4×D43C2×D414yes—
111Dic86—22no—
112Dic86—42no—
113C8×C43C2×D414yescomplemented
114C43⋊C8C2×D414yescomplemented
115C22×C43—41no—
116C22×C43—42no—
117C22×C43—42no—
118C22×C43—44no—
119C22×C43C22×D411yescharacteristic
120C2×D43—41no—
121C2×D43—42no—
122C2×D43—42no—
123C2×D43—44no—
124C2×D43—88no—
125C2×D43—84no—
126C2×D43#12712yes—
127C2×D43AGL(1,ℤ/8)14yes—
128C4×C43—22no—
129C4×C43—41no—
130C4×C43C22×D412yes—
131Dic43—22no—
132Dic43—41no—
133Dic43#12712yes—
134C2×#496—431nomaximal, Sylow
135C2×C43—81no—
136C2×C43—82no—
137C2×C43C2×#12711yescharacteristic
138C2×C43C2×AGL(1,ℤ/8)12yes—
139D43—81no—
140D43—82no—
141D43#49614yesdirect product factor
142C22×SD16—432no—
143C22×D8—432no—
144C2×#127—431no—
145C2×#124—431no—
146#496—432no—
147#496—432no—
148#496—431no—
149#496—431no—
150#496—431no—
151#496D4311yescharacteristic, direct product factor
152C2×#97—431no—
153C43C2×#49611yescharacteristic, complemented, Sylow
154C22×Q8—431no—
155C22×D4—431no—
156C22×D4—432no—
157C22×D4—862no—
158C2×SD16—432no—
159C2×SD16—432no—
160C2×SD16—432no—
161C2×SD16—868no—
162C2×SD16C2×D4312yescomplemented
163C2×D8—432no—
164C2×D8—432no—
165C2×D8—432no—
166C2×D8—868no—
167C2×D8C2×D4312yescomplemented
168C22×C8—432no—
169#127—432no—
170#127—431no—
171#127—862no—
172#127C2×D4311yescharacteristic, complemented
173#124—431no—
174#124—431no—
175#124—431no—
176#124—862no—
177#124C2×D4311yescharacteristic, complemented
178C2×C22⋊C4—862no—
179C2×C42—431no—
180#97—432no—
181#97—431no—
182#97C2×D4311yescharacteristic, complemented
183C24—861no—
184C24—862no—
185C2×Q8—431no—
186C2×Q8—861no—
187C2×Q8—864no—
188C2×Q8C22×D4311yescharacteristic
189C2×D4—22no—
190C2×D4—431no—
191C2×D4—432no—
192C2×D4—864no—
193C2×D4—864no—
194C2×D4—864no—
195C2×D4—861no—
196C2×D4—864no—
197C2×D4—862no—
198C2×D4—862no—
199C2×D4—1728no—
200C2×D4C22×D4311yescharacteristic
201C2×D4C22×D4312yes—
202C22×C4—431no—
203C22×C4—432no—
204C22×C4—861no—
205SD16—24no—
206SD16—864no—
207SD16—864no—
208SD16—864no—
209D8—24no—
210D8—864no—
211D8—864no—
212D8—864no—
213C2×C8—432no—
214C2×C8—438no—
215C2×C8C22×D4312yes—
216C22⋊C4—22no—
217C22⋊C4—862no—
218C22⋊C4—862no—
219C22⋊C4—862no—
220C42—432no—
221C42—431no—
222C42C22×D4311yescharacteristic
223C23—21no—
224C23—22no—
225C23—431no—
226C23—861no—
227C23—862no—
228C23—1722no—
229C23—1724no—
230C23—1728no—
231C23—1724no—
232Q8—22no—
233Q8—862no—
234Q8—1722no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—44no—
239D4—862no—
240D4—862no—
241D4—862no—
242D4—1724no—
243D4—1722no—
244D4—1724no—
245D4—1728no—
246C2×C4—21no—
247C2×C4—431no—
248C2×C4—434no—
249C2×C4—432no—
250C2×C4—864no—
251C2×C4—861no—
252C2×C4—1722no—
253C2×C4D4×D4312yes—
254C2×C4C23×D4311yescharacteristic
255C8—434no—
256C8D4×D4314yescomplemented
257C22—44no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—434no—
262C22—432no—
263C22—3448no—
264C22—3444no—
265C22—1724no—
266C22—1722no—
267C22—1721no—
268C22—1722no—
269C22C2×D4×D4311yescharacteristic
270C4—22no—
271C4—41no—
272C4—432no—
273C4—862no—
274C4—1721no—
275C4C2×D4×D4312yes—
276C2—82no—
277C2—81no—
278C2—434no—
279C2—3442no—
280C2—3441no—
281C2#127×D4311yescharacteristic
282C2AGL(1,ℤ/8)×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#496C2
socleC22×C43C22×D4
hypercenter#496D43
hypocenterC43C2×#496
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×SD16×D43C2semidirect
2. C2×D8×D43C2semidirect
3. #127×D43C2semidirect
4. #124×D43C2semidirect
5. #14583289C2semidirect
6. #14583288C2semidirect
7. #14583287C2semidirect
8. #14583286C2semidirect
9. #14583285C2semidirect
10. #97×D43C2semidirect
11. C43×#496C2semidirect
16. C2×#10621873C22semidirect
17. C2×#10621883C22semidirect
18. C2×#10621884C22semidirect
20. C2×D344C22semidirect
21. C2×#10621882C22semidirect
22. C2×#10621882C22semidirect
25. #13063322C22semidirect
27. #13063321C22semidirect
28. #13063314C22semidirect
29. #13063313C22semidirect
30. #13063312C22semidirect
34. #13063236C22semidirect
35. #13063235C22semidirect
36. C2×SD16×C43C22semidirect
37. C2×D8×C43C22semidirect
38. #127×C43C22semidirect
39. #124×C43C22semidirect
40. #97×C43C22semidirect
80. C8×D43D4semidirect
113. C8×C43C2×D4semidirect
114. C43⋊C8C2×D4semidirect
141. D43#496direct (N × H)
151. #496D43direct (N × H)
153. C43C2×#496semidirect
162. C2×SD16C2×D43semidirect
167. C2×D8C2×D43semidirect
172. #127C2×D43semidirect
177. #124C2×D43semidirect
182. #97C2×D43semidirect
256. C8D4×D43semidirect