Finite Group Databasebeta

← #20252613

Subgroups — #20252613

Order 6016.

994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×D4×D47C211yesmaximal, characteristic, complemented
2C2×#13094049C211yesmaximal, characteristic, complemented
3#15689630C211yesmaximal, characteristic, complemented
4#15689272C214yesmaximal, complemented
5#15689255C214yesmaximal, complemented
6#15689129C211yesmaximal, characteristic, complemented
7#15689128C211yesmaximal, characteristic, complemented
8#15689086C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
10C24×D47—21no—
11C22×D188C2211yescharacteristic
12C22×C22⋊D47—21no—
13C2×D4×D47—24no—
14C2×D4×D47—24no—
15C2×D4×D47—22no—
16C2×D4×D47C2214yes—
17C22×C4×D47C2211yescharacteristic
18#13094049—24no—
19C2×#10625336C2212yescomplemented
20C2×#10625334C2212yescomplemented
21C2×#10625329C2211yescharacteristic, complemented
22#13094005—21no—
23#13094000C2212yescomplemented
24#13093995C2212yescomplemented
25#13093992—21no—
26C4×C22⋊D47—22no—
27#13093983C2211yescharacteristic, complemented
28#13093946C2214yescomplemented
29#13093945C2214yescomplemented
30(C2×D47)⋊C8C2214yescomplemented
31C2×#41×C47C2211yescharacteristic, complemented
32C22×D4×C47C2211yescharacteristic
33AGL(1,ℤ/8)×C47—24no—
34C2×SD16×C47C2212yescomplemented
35C2×D8×C47C2212yescomplemented
36C2×M16×C47C2211yescharacteristic, complemented
37C24×C47—21no—
38C23×D47—28no—
39C23×D47—21no—
40C23×D47—24no—
41C23×D47—48no—
42C23×D47D411yescharacteristic
43#41×C47—22no—
44#41×C47—22no—
45C2×Q8×C47C2311yescharacteristic, complemented
46C2×D4×C47—21no—
47C2×D4×C47—21no—
48C2×D4×C47—22no—
49C2×D4×C47D414yescomplemented
50C2×D4×C47C2312yes—
51C2×D4×C47C2311yescharacteristic, complemented
52C22×C4×C47—21no—
53C22×C4×C47C2311yescharacteristic
54C2×C22⋊D47—28no—
55C2×C22⋊D47—22no—
56C2×C22⋊D47—24no—
57C22×Dic47D411yescharacteristic
58D4×D47—216no—
59D4×D47—28no—
60D4×D47—28no—
61C2×D188—21no—
62C2×D188—22no—
63C2×D188D414yescomplemented
64C2×D188C2312yes—
65C2×C4×D47—22no—
66C2×C4×D47—22no—
67C2×C4×D47D412yes—
68C2×C4×D47C2312yes—
69SD16×C47—24no—
70D8×C47—24no—
71M16×C47—22no—
72C2×C8×C47C2312yescomplemented
73C22⋊Dic47—21no—
74C22⋊Dic47—22no—
75#10625336—24no—
76#10625334—24no—
77(C2×D47)⋊C4—22no—
78C4⋊Dic47C2312yescomplemented
79Dic47⋊C4—22no—
80C4×Dic47—21no—
81#10625329—22no—
82C2×C47⋊C8C2312yescomplemented
83C23×C47—24no—
84C23×C47—22no—
85C23×C47—21no—
86C23×C47—44no—
87C23×C47C2×D411yescharacteristic
88C22×D47—22no—
89C22×D47—24no—
90C22×D47—216no—
91C22×D47—24no—
92C22×D47—22no—
93C22×D47—432no—
94C22×D47—48no—
95C22×D47—44no—
96C22×D47—48no—
97C22×D47C2×D412yes—
98Q8×C47—21no—
99Q8×C47—21no—
100D4×C47—24no—
101D4×C47—22no—
102D4×C47—21no—
103D4×C47—21no—
104D4×C47—42no—
105D4×C47C2×D414yes—
106C2×C4×C47—21no—
107C2×C4×C47—42no—
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D412yes—
110C2×C4×C47C2×D412yes—
111C2×C4×C47C2411yescharacteristic
112C22⋊D47—216no—
113C22⋊D47—44no—
114C2×Dic47—22no—
115C2×Dic47—22no—
116C2×Dic47C2×D412yes—
117D188—24no—
118D188—22no—
119D188C2×D414yes—
120C4×D47—24no—
121C4×D47—22no—
122C4×D47—22no—
123C8×C47—22no—
124C47⋊C8—22no—
125C22×C47—22no—
126C22×C47—24no—
127C22×C47—48no—
128C22×C47—44no—
129C22×C47—41no—
130C22×C47—42no—
131C22×C47#12012yes—
132C22×C47C22×D411yescharacteristic
133C2×D47—28no—
134C2×D47—22no—
135C2×D47—22no—
136C2×D47—24no—
137C2×D47—432no—
138C2×D47—48no—
139C2×D47—44no—
140C2×D47AGL(1,ℤ/8)14yescomplemented
141C4×C47—41no—
142C4×C47#12012yes—
143C4×C47C22×D411yescharacteristic
144C4×C47C22×D411yescharacteristic
145Dic47—22no—
146Dic47—42no—
147#3003—471nomaximal, Sylow
148C2×C47—22no—
149C2×C47—44no—
150C2×C47—81no—
151C2×C47C2×#12011yescharacteristic
152C2×C47C2×AGL(1,ℤ/8)12yes—
153D47—24no—
154D47—44no—
155C23×D4—471no—
156C2×AGL(1,ℤ/8)—471no—
157C2×AGL(1,ℤ/8)D4711yescharacteristic, complemented
158#525—471no—
159#450—474no—
160#447—474no—
161#418—471no—
162#418—471no—
163#407—471no—
164C47#300311yescharacteristic, complemented, Sylow
165C25—941no—
166C2×#41C2×D4711yescharacteristic, complemented
167C22×D4—474no—
168C22×D4—471no—
169C22×D4—942no—
170C22×D4—941no—
171C22×D4—944no—
172C22×D4—944no—
173C22×D4C2×D4711yescharacteristic
174C23×C4—471no—
175AGL(1,ℤ/8)—24no—
176AGL(1,ℤ/8)—944no—
177C2×SD16—472no—
178C2×SD16C2×D4712yescomplemented
179C2×D8—472no—
180C2×D8C2×D4712yescomplemented
181C2×M16—471no—
182C2×M16C2×D4711yescharacteristic, complemented
183#123—941no—
184C22⋊Q8—472no—
185#121—472no—
186#120—941no—
187C4×D4—942no—
188#117—471no—
189#102—474no—
190#102—474no—
191C22⋊C8—474no—
192C24—21no—
193C24—471no—
194C24—944no—
195C24—948no—
196C24—941no—
197C24—1888no—
198#41—22no—
199#41—22no—
200C2×Q8C22×D4711yescharacteristic, complemented
201C2×D4—21no—
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—474no—
205C2×D4—472no—
206C2×D4—944no—
207C2×D4—948no—
208C2×D4—9416no—
209C2×D4—948no—
210C2×D4—948no—
211C2×D4—942no—
212C2×D4—941no—
213C2×D4—942no—
214C2×D4C22⋊D4714yescomplemented
215C2×D4C22×D4712yes—
216C2×D4C22×D4711yescharacteristic, complemented
217C22×C4—21no—
218C22×C4—471no—
219C22×C4—472no—
220C22×C4—472no—
221C22×C4—942no—
222C22×C4—942no—
223C22×C4C22×D4711yescharacteristic
224SD16—24no—
225SD16—944no—
226D8—24no—
227D8—944no—
228M16—22no—
229M16—942no—
230C2×C8—472no—
231C2×C8C22×D4712yescomplemented
232C4⋊C4—472no—
233C4⋊C4—942no—
234C22⋊C4—942no—
235C22⋊C4—942no—
236C22⋊C4—941no—
237C42—941no—
238C23—24no—
239C23—22no—
240C23—21no—
241C23—44no—
242C23—472no—
243C23—944no—
244C23—9416no—
245C23—942no—
246C23—944no—
247C23—942no—
248C23—1884no—
249C23—1888no—
250C23—18832no—
251C23—1888no—
252C23D4×D4711yescharacteristic
253Q8—21no—
254Q8—21no—
255D4—24no—
256D4—22no—
257D4—21no—
258D4—21no—
259D4—42no—
260D4—474no—
261D4—9416no—
262D4—944no—
263D4—942no—
264D4—1884no—
265D4C2×C22⋊D4714yes—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—472no—
269C2×C4—942no—
270C2×C4—944no—
271C2×C4—942no—
272C2×C4—942no—
273C2×C4—942no—
274C2×C4D4×D4711yescharacteristic
275C2×C4D4×D4712yes—
276C2×C4C2×C22⋊D4712yes—
277C2×C4C23×D4711yescharacteristic
278C8—22no—
279C8—942no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—41no—
285C22—42no—
286C22—474no—
287C22—948no—
288C22—942no—
289C22—942no—
290C22—944no—
291C22—1888no—
292C22—18832no—
293C22—1884no—
294C22#1309399212yes—
295C22C2×D4×D4711yescharacteristic
296C4—41no—
297C4—942no—
298C4—1882no—
299C4#1309399212yes—
300C4C2×D4×D4711yescharacteristic
301C4C22×C22⋊D4711yescharacteristic
302C2—22no—
303C2—44no—
304C2—81no—
305C2—944no—
306C2—1884no—
307C2C2×#1309399211yescharacteristic
308C2AGL(1,ℤ/8)×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC22×C47C22×D4
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47#3003
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×D4×D47C2semidirect
2. C2×#13094049C2semidirect
3. #15689630C2semidirect
4. #15689272C2semidirect
5. #15689255C2semidirect
6. #15689129C2semidirect
7. #15689128C2semidirect
8. #15689086C2semidirect
9. C2×AGL(1,ℤ/8)×C47C2semidirect
19. C2×#10625336C22semidirect
20. C2×#10625334C22semidirect
21. C2×#10625329C22semidirect
23. #13094000C22semidirect
24. #13093995C22semidirect
27. #13093983C22semidirect
28. #13093946C22semidirect
29. #13093945C22semidirect
30. (C2×D47)⋊C8C22semidirect
31. C2×#41×C47C22semidirect
34. C2×SD16×C47C22semidirect
35. C2×D8×C47C22semidirect
36. C2×M16×C47C22semidirect
45. C2×Q8×C47C23semidirect
49. C2×D4×C47D4semidirect
51. C2×D4×C47C23semidirect
63. C2×D188D4semidirect
72. C2×C8×C47C23semidirect
78. C4⋊Dic47C23semidirect
82. C2×C47⋊C8C23semidirect
140. C2×D47AGL(1,ℤ/8)semidirect
157. C2×AGL(1,ℤ/8)D47semidirect
164. C47#3003semidirect
166. C2×#41C2×D47semidirect
178. C2×SD16C2×D47semidirect
180. C2×D8C2×D47semidirect
182. C2×M16C2×D47semidirect
200. C2×Q8C22×D47semidirect
214. C2×D4C22⋊D47semidirect
216. C2×D4C22×D47semidirect
231. C2×C8C22×D47semidirect