Finite Group Databasebeta

← #496×D47 #20253818

Subgroups — #496×D47 #20253818

Order 6016.

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×D47C212yesmaximal, complemented
2C2×D8×D47C212yesmaximal, complemented
3#127×D47C211yesmaximal, characteristic, complemented
4#124×D47C211yesmaximal, characteristic, complemented
5#15689513C211yesmaximal, characteristic, complemented
6#15689512C211yesmaximal, characteristic, complemented
7#15689511C212yesmaximal, complemented
8#15689510C211yesmaximal, characteristic, complemented
9#15689509C212yesmaximal, complemented
10#97×D47C211yesmaximal, characteristic, complemented
11C47×#496C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2211yescharacteristic
13C2×D4×D47—22no—
14C2×D4×D47C2211yescharacteristic
15C2×D4×D47C2212yes—
16C2×#10625325C2212yescomplemented
17C2×#10625335C2212yescomplemented
18C2×#10625336C2212yescomplemented
19SD16×D47—28no—
20C2×D376C2212yescomplemented
21C2×#10625334C2212yescomplemented
22C2×#10625334C2212yescomplemented
23D8×D47—28no—
24C2×C8×D47C2212yes—
25#13094021C2211yescharacteristic, complemented
26#13094020—22no—
27#13094020C2212yescomplemented
28#13094013C2211yescharacteristic, complemented
29#13094012C2211yescharacteristic, complemented
30#13094011C2211yescharacteristic, complemented
31#13094010—22no—
32C22⋊C4×D47—22no—
33C42×D47C2211yescharacteristic
34#13093935C2211yescharacteristic, complemented
35#13093934C2212yescomplemented
36C2×SD16×C47C2212yescomplemented
37C2×D8×C47C2212yescomplemented
38#127×C47C2211yescharacteristic, complemented
39#124×C47C2211yescharacteristic, complemented
40#97×C47C2211yescharacteristic, complemented
41C23×D47—21no—
42C23×D47—22no—
43C2×Q8×C47C2311yescharacteristic
44C2×D4×C47—22no—
45C2×D4×C47C2311yescharacteristic
46C2×D4×C47C2312yes—
47C2×C22⋊D47—21no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—24no—
50Q8×D47—24no—
51D4×D47—24no—
52D4×D47—24no—
53D4×D47—24no—
54D4×D47—48no—
55C2×D188—22no—
56C2×D188C2311yescharacteristic
57C2×D188C2312yes—
58C2×C4×D47—21no—
59C2×C4×D47D412yes—
60C2×C4×D47C2311yescharacteristic
61C2×Dic94—21no—
62C2×Dic94C2311yescharacteristic
63SD16×C47—24no—
64D8×C47—24no—
65C2×C8×C47C2312yes—
66C22⋊C4×C47—22no—
67C42×C47C2311yescharacteristic
68C22⋊Dic47—22no—
69#10625336—24no—
70#10625335—24no—
71#10625334—24no—
72#10625334—24no—
73(C2×D47)⋊C4—22no—
74(C2×D47)⋊C4—22no—
75C4×Dic47D412yes—
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78D376—24no—
79#10625325—24no—
80C8×D47D418yescomplemented
81C23×C47—21no—
82C23×C47—22no—
83C22×D47—21no—
84C22×D47—22no—
85C22×D47—42no—
86C22×D47—44no—
87C22×D47—48no—
88C22×D47—44no—
89C22×D47C2×D411yescharacteristic
90Q8×C47—22no—
91D4×C47—22no—
92D4×C47—22no—
93D4×C47—22no—
94D4×C47—44no—
95C2×C4×C47—21no—
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2411yescharacteristic
98C22⋊D47—48no—
99C22⋊D47—42no—
100C22⋊D47—44no—
101C2×Dic47—21no—
102C2×Dic47C2×D412yes—
103C2×Dic47C2×D411yescharacteristic
104D188—22no—
105D188—22no—
106D188—22no—
107D188—44no—
108C4×D47—24no—
109C4×D47—42no—
110C4×D47C2×D414yes—
111Dic94—22no—
112Dic94—42no—
113C8×C47C2×D414yescomplemented
114C47⋊C8C2×D414yescomplemented
115C22×C47—41no—
116C22×C47—42no—
117C22×C47—44no—
118C22×C47—42no—
119C22×C47C22×D411yescharacteristic
120C2×D47—42no—
121C2×D47—41no—
122C2×D47—44no—
123C2×D47—42no—
124C2×D47—88no—
125C2×D47—84no—
126C2×D47#12712yes—
127C2×D47AGL(1,ℤ/8)14yes—
128C4×C47—22no—
129C4×C47—41no—
130C4×C47C22×D412yes—
131Dic47—22no—
132Dic47—41no—
133Dic47#12712yes—
134C2×#496—471nomaximal, Sylow
135C2×C47—82no—
136C2×C47—81no—
137C2×C47C2×#12711yescharacteristic
138C2×C47C2×AGL(1,ℤ/8)12yes—
139D47—82no—
140D47—81no—
141D47#49614yesdirect product factor
142C22×SD16—472no—
143C22×D8—472no—
144C2×#127—471no—
145C2×#124—471no—
146#496—472no—
147#496—472no—
148#496—471no—
149#496—471no—
150#496—471no—
151#496D4711yescharacteristic, direct product factor
152C2×#97—471no—
153C47C2×#49611yescharacteristic, complemented, Sylow
154C22×Q8—471no—
155C22×D4—471no—
156C22×D4—472no—
157C22×D4—942no—
158C2×SD16—472no—
159C2×SD16—472no—
160C2×SD16—472no—
161C2×SD16—948no—
162C2×SD16C2×D4712yescomplemented
163C2×D8—472no—
164C2×D8—472no—
165C2×D8—472no—
166C2×D8—948no—
167C2×D8C2×D4712yescomplemented
168C22×C8—472no—
169#127—472no—
170#127—471no—
171#127—942no—
172#127C2×D4711yescharacteristic, complemented
173#124—471no—
174#124—471no—
175#124—471no—
176#124—942no—
177#124C2×D4711yescharacteristic, complemented
178C2×C22⋊C4—942no—
179C2×C42—471no—
180#97—472no—
181#97—471no—
182#97C2×D4711yescharacteristic, complemented
183C24—941no—
184C24—942no—
185C2×Q8—471no—
186C2×Q8—941no—
187C2×Q8—944no—
188C2×Q8C22×D4711yescharacteristic
189C2×D4—22no—
190C2×D4—471no—
191C2×D4—472no—
192C2×D4—944no—
193C2×D4—944no—
194C2×D4—944no—
195C2×D4—941no—
196C2×D4—944no—
197C2×D4—942no—
198C2×D4—942no—
199C2×D4—1888no—
200C2×D4C22×D4711yescharacteristic
201C2×D4C22×D4712yes—
202C22×C4—471no—
203C22×C4—472no—
204C22×C4—941no—
205SD16—24no—
206SD16—944no—
207SD16—944no—
208SD16—944no—
209D8—24no—
210D8—944no—
211D8—944no—
212D8—944no—
213C2×C8—472no—
214C2×C8—478no—
215C2×C8C22×D4712yes—
216C22⋊C4—22no—
217C22⋊C4—942no—
218C22⋊C4—942no—
219C22⋊C4—942no—
220C42—472no—
221C42—471no—
222C42C22×D4711yescharacteristic
223C23—21no—
224C23—22no—
225C23—471no—
226C23—941no—
227C23—942no—
228C23—1882no—
229C23—1884no—
230C23—1888no—
231C23—1884no—
232Q8—22no—
233Q8—942no—
234Q8—1882no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—44no—
239D4—942no—
240D4—942no—
241D4—942no—
242D4—1884no—
243D4—1882no—
244D4—1884no—
245D4—1888no—
246C2×C4—21no—
247C2×C4—471no—
248C2×C4—474no—
249C2×C4—472no—
250C2×C4—944no—
251C2×C4—941no—
252C2×C4—1882no—
253C2×C4D4×D4712yes—
254C2×C4C23×D4711yescharacteristic
255C8—474no—
256C8D4×D4714yescomplemented
257C22—44no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—474no—
262C22—472no—
263C22—3768no—
264C22—3764no—
265C22—1884no—
266C22—1882no—
267C22—1881no—
268C22—1882no—
269C22C2×D4×D4711yescharacteristic
270C4—22no—
271C4—41no—
272C4—472no—
273C4—942no—
274C4—1881no—
275C4C2×D4×D4712yes—
276C2—82no—
277C2—81no—
278C2—474no—
279C2—3762no—
280C2—3761no—
281C2#127×D4711yescharacteristic
282C2AGL(1,ℤ/8)×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#496C2
socleC22×C47C22×D4
hypercenter#496D47
hypocenterC47C2×#496
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D47C2semidirect
2. C2×D8×D47C2semidirect
3. #127×D47C2semidirect
4. #124×D47C2semidirect
5. #15689513C2semidirect
6. #15689512C2semidirect
7. #15689511C2semidirect
8. #15689510C2semidirect
9. #15689509C2semidirect
10. #97×D47C2semidirect
11. C47×#496C2semidirect
16. C2×#10625325C22semidirect
17. C2×#10625335C22semidirect
18. C2×#10625336C22semidirect
20. C2×D376C22semidirect
21. C2×#10625334C22semidirect
22. C2×#10625334C22semidirect
25. #13094021C22semidirect
27. #13094020C22semidirect
28. #13094013C22semidirect
29. #13094012C22semidirect
30. #13094011C22semidirect
34. #13093935C22semidirect
35. #13093934C22semidirect
36. C2×SD16×C47C22semidirect
37. C2×D8×C47C22semidirect
38. #127×C47C22semidirect
39. #124×C47C22semidirect
40. #97×C47C22semidirect
80. C8×D47D4semidirect
113. C8×C47C2×D4semidirect
114. C47⋊C8C2×D4semidirect
141. D47#496direct (N × H)
151. #496D47direct (N × H)
153. C47C2×#496semidirect
162. C2×SD16C2×D47semidirect
167. C2×D8C2×D47semidirect
172. #127C2×D47semidirect
177. #124C2×D47semidirect
182. #97C2×D47semidirect
256. C8D4×D47semidirect