Finite Group Databasebeta

← #20253837

Subgroups — #20253837

Order 6016.

656 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094051C212yesmaximal, complemented
2C2×#13094048C212yesmaximal, complemented
3#15689672C211yesmaximal, characteristic, complemented
4#127×D47C211yesmaximal, characteristic, complemented
5#15689513C211yesmaximal, characteristic, complemented
6#15689512C211yesmaximal, characteristic, complemented
7#15689510C211yesmaximal, characteristic, complemented
8#15689498C212yesmaximal, complemented
9#15689494C212yesmaximal, complemented
10#15689075C211yesmaximal, characteristic, complemented
11C47×#496C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic
13C2×#10625352C2211yescharacteristic
14C2×D4×D47—22no—
15C2×D4×D47C2212yes—
16#13094051—28no—
17#13094048—28no—
18C2×#10625325C2212yescomplemented
19C2×#10625335C2212yescomplemented
20C2×#10625336C2212yescomplemented
21C2×D376C2212yescomplemented
22C2×#10625334C2212yescomplemented
23C2×#10625334C2212yescomplemented
24C2×#10625324C2212yes—
25#13094022C2211yescharacteristic, complemented
26#13094021C2211yescharacteristic
27#13094020—22no—
28#13094020C2212yes—
29#13094020C2211yescharacteristic, complemented
30#13094012C2211yescharacteristic, complemented
31#13093997—22no—
32(C22⋊D47)⋊C4—22no—
33C42×D47C2211yescharacteristic
34#13093935C2211yescharacteristic, complemented
35C8×Dic47C2212yescomplemented
36C2×SD16×C47C2212yescomplemented
37C2×D8×C47C2212yescomplemented
38#127×C47C2211yescharacteristic
39#124×C47C2211yescharacteristic, complemented
40#97×C47C2211yescharacteristic, complemented
41C23×D47—22no—
42C2×Q8×C47C2311yescharacteristic
43C2×D4×C47—22no—
44C2×D4×C47C2311yescharacteristic
45C2×D4×C47C2312yes—
46C2×C22⋊D47—21no—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—24no—
50C22×Dic47—21no—
51#10625354—24no—
52#10625352—24no—
53D4×D47—24no—
54D4×D47—24no—
55D4×D47—48no—
56C2×D188—21no—
57C2×D188—22no—
58C2×D188C2311yescharacteristic
59C2×D188C2312yes—
60C2×C4×D47—21no—
61C2×C4×D47D412yes—
62C2×C4×D47C2311yescharacteristic
63C2×Dic94C2311yescharacteristic
64SD16×C47—24no—
65D8×C47—24no—
66C2×C8×C47C2312yes—
67C22⋊C4×C47—22no—
68C42×C47C2311yescharacteristic
69#10625336—24no—
70#10625335—24no—
71#10625334—24no—
72#10625334—24no—
73(C2×D47)⋊C4—22no—
74Dic47⋊C4—22no—
75C4×Dic47D412yes—
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78D376—24no—
79#10625325—24no—
80#10625324D418yescomplemented
81C23×C47—21no—
82C23×C47—22no—
83C22×D47—21no—
84C22×D47—22no—
85C22×D47—48no—
86C22×D47—44no—
87C22×D47C2×D411yescharacteristic
88Q8×C47—22no—
89D4×C47—22no—
90D4×C47—22no—
91D4×C47—22no—
92D4×C47—44no—
93C2×C4×C47—21no—
94C2×C4×C47C2×D412yes—
95C2×C4×C47C2411yescharacteristic
96C22⋊D47—42no—
97C22⋊D47—44no—
98C22⋊D47—48no—
99C22⋊D47—44no—
100C2×Dic47—21no—
101C2×Dic47—42no—
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D412yes—
104D188—22no—
105D188—22no—
106D188—22no—
107D188—44no—
108D188—42no—
109C4×D47—24no—
110C4×D47—42no—
111C4×D47C2×D414yes—
112Dic94—22no—
113C8×C47C2×D414yescomplemented
114C47⋊C8C2×D414yescomplemented
115C22×C47—41no—
116C22×C47—42no—
117C22×C47—44no—
118C22×C47—42no—
119C22×C47C22×D411yescharacteristic
120C2×D47—22no—
121C2×D47—41no—
122C2×D47—42no—
123C2×D47—44no—
124C2×D47—42no—
125C2×D47—88no—
126C2×D47#12712yes—
127C4×C47—22no—
128C4×C47—41no—
129C4×C47C22×D412yes—
130Dic47—41no—
131Dic47#12712yes—
132Dic47AGL(1,ℤ/8)14yescomplemented
133#3151—471nomaximal, Sylow
134C2×C47—82no—
135C2×C47—81no—
136C2×C47C2×#12711yescharacteristic
137C2×C47C2×AGL(1,ℤ/8)12yes—
138D47—22no—
139D47—81no—
140D47—82no—
141C2×AGL(1,ℤ/8)—472no—
142C2×AGL(1,ℤ/8)—472no—
143#532—471no—
144C2×#127—471no—
145#496—471no—
146#496—471no—
147#496—471no—
148#496D4711yescharacteristic, complemented
149#493—472no—
150#492—472no—
151C4×M16—471no—
152C47#315111yescharacteristic, complemented, Sylow
153C2×#41—471no—
154C2×#41—471no—
155C22×D4—472no—
156C22×D4—942no—
157AGL(1,ℤ/8)—948no—
158AGL(1,ℤ/8)—948no—
159C2×SD16—472no—
160C2×SD16—472no—
161C2×SD16—472no—
162C2×SD16C2×D4712yescomplemented
163C2×D8—472no—
164C2×D8—472no—
165C2×D8—472no—
166C2×D8C2×D4712yescomplemented
167C2×M16—472no—
168C4⋊Q8—471no—
169#127—472no—
170#127—471no—
171#127—471no—
172#127—942no—
173#127C2×D4711yescharacteristic
174#124—471no—
175#124C2×D4711yescharacteristic, complemented
176#121—942no—
177C4×D4—942no—
178C2×C42—471no—
179#97—471no—
180#97C2×D4711yescharacteristic, complemented
181C4×C8—472no—
182C24—942no—
183#41—944no—
184#41—944no—
185C2×Q8—471no—
186C2×Q8C22×D4711yescharacteristic
187C2×D4—22no—
188C2×D4—471no—
189C2×D4—472no—
190C2×D4—941no—
191C2×D4—944no—
192C2×D4—944no—
193C2×D4—942no—
194C2×D4—944no—
195C2×D4—942no—
196C2×D4—941no—
197C2×D4—942no—
198C2×D4—1888no—
199C2×D4C22×D4711yescharacteristic
200C2×D4C22×D4712yes—
201C22×C4—471no—
202C22×C4—472no—
203C22×C4—941no—
204C22×C4—941no—
205SD16—24no—
206SD16—944no—
207SD16—944no—
208SD16—944no—
209D8—24no—
210D8—944no—
211D8—944no—
212D8—944no—
213M16—478no—
214C2×C8—472no—
215C2×C8C22×D4712yes—
216C4⋊C4—942no—
217C22⋊C4—22no—
218C22⋊C4—942no—
219C42—472no—
220C42—471no—
221C42C22×D4711yescharacteristic
222C23—21no—
223C23—22no—
224C23—471no—
225C23—941no—
226C23—942no—
227C23—1884no—
228C23—1888no—
229Q8—22no—
230Q8—942no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—44no—
235D4—942no—
236D4—942no—
237D4—942no—
238D4—1884no—
239D4—1882no—
240D4—1884no—
241D4—1884no—
242D4—1888no—
243D4—1882no—
244C2×C4—21no—
245C2×C4—472no—
246C2×C4—471no—
247C2×C4—474no—
248C2×C4—944no—
249C2×C4—941no—
250C2×C4—1882no—
251C2×C4—1882no—
252C2×C4D4×D4712yes—
253C2×C4C23×D4711yescharacteristic
254C8—474no—
255C8D4×D4714yescomplemented
256C22—44no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—472no—
261C22—942no—
262C22—3768no—
263C22—1884no—
264C22—1882no—
265C22—1881no—
266C22—1882no—
267C22C2×D4×D4711yescharacteristic
268C4—22no—
269C4—41no—
270C4—474no—
271C4—472no—
272C4—1881no—
273C4C2×D4×D4712yes—
274C2—82no—
275C2—81no—
276C2—942no—
277C2—3762no—
278C2—3761no—
279C2#127×D4711yescharacteristic
280C2AGL(1,ℤ/8)×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#496C2
socleC22×C47C22×D4
hypercenter#496D47
hypocenterC47#3151
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×#13094051C2semidirect
2. C2×#13094048C2semidirect
3. #15689672C2semidirect
4. #127×D47C2semidirect
5. #15689513C2semidirect
6. #15689512C2semidirect
7. #15689510C2semidirect
8. #15689498C2semidirect
9. #15689494C2semidirect
10. #15689075C2semidirect
11. C47×#496C2semidirect
18. C2×#10625325C22semidirect
19. C2×#10625335C22semidirect
20. C2×#10625336C22semidirect
21. C2×D376C22semidirect
22. C2×#10625334C22semidirect
23. C2×#10625334C22semidirect
25. #13094022C22semidirect
29. #13094020C22semidirect
30. #13094012C22semidirect
34. #13093935C22semidirect
35. C8×Dic47C22semidirect
36. C2×SD16×C47C22semidirect
37. C2×D8×C47C22semidirect
39. #124×C47C22semidirect
40. #97×C47C22semidirect
80. #10625324D4semidirect
113. C8×C47C2×D4semidirect
114. C47⋊C8C2×D4semidirect
132. Dic47AGL(1,ℤ/8)semidirect
148. #496D47semidirect
152. C47#3151semidirect
162. C2×SD16C2×D47semidirect
166. C2×D8C2×D47semidirect
175. #124C2×D47semidirect
180. #97C2×D47semidirect
255. C8D4×D47semidirect