Finite Group Databasebeta

← #20255184

Subgroups — #20255184

Order 6016.

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

normal subgroups only

This group has 476 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#15689927C212yesmaximal, complemented
2#15689926C212yesmaximal, complemented
3#15689499C211yesmaximal, characteristic, complemented
4#15689392C212yesmaximal, complemented
5#15689391C212yesmaximal, complemented
6#15689292C212yesmaximal, complemented
7#15689290C211yesmaximal, characteristic, complemented
8#15689237C212yesmaximal, complemented
9C47×#453C211yesmaximal, characteristic, complemented
10#13094070C2212yescomplemented
11#13094069C2211yescharacteristic, complemented
12#13094052C2212yescomplemented
13#13094051—22no—
14#13094050—22no—
15#13094050C2212yescomplemented
16#13094049—22no—
17#13094049C2212yescomplemented
18#13094048—22no—
19#13094045—22no—
20#13094044—22no—
21#13094044C2212yes—
22C2×#10625334—22no—
23C2×#10625334C2212yescomplemented
24C2×#10625334C2212yescomplemented
25D8×D47—22no—
26#13094032C2212yescomplemented
27#13094031C2212yescomplemented
28#13094021C2211yescharacteristic, complemented
29#13093959C2212yescomplemented
30#13093952C2212yescomplemented
31#13093941C2211yescharacteristic, complemented
32#13093940C2212yescomplemented
33C4×C47⋊C8C2211yescharacteristic, complemented
34H(5,𝔽2)×C47C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C47C2212yescomplemented
36#127×C47C2211yescharacteristic, complemented
37#104×C47C2212yescomplemented
38#100×C47C2211yescharacteristic, complemented
39#41×C47—22no—
40#41×C47C2312yes—
41C2×D4×C47—22no—
42C2×D4×C47—41no—
43C2×D4×C47—41no—
44C2×D4×C47C2311yescharacteristic
45C2×D4×C47C2311yescharacteristic
46C2×C22⋊D47—41no—
47#10625354—22no—
48#10625352—22no—
49D4×D47—22no—
50D4×D47—22no—
51D4×D47—42no—
52#10625350—22no—
53#10625350C2312yes—
54C2×D188—22no—
55C2×D188—41no—
56C2×D188C2312yes—
57SD16×C47—22no—
58D8×C47—22no—
59M16×C47C2312yes—
60C42×C47C2311yescharacteristic
61#10625337D412yescomplemented
62#10625336—22no—
63#10625336D412yescomplemented
64#10625335—22no—
65#10625335D412yescomplemented
66#10625334—22no—
67#10625334—22no—
68#10625334—22no—
69#10625334—22no—
70#10625334—22no—
71#10625334—22no—
72#10625334D412yescomplemented
73#10625329—22no—
74#10625329C2312yes—
75C2×C47⋊C8—22no—
76C2×C47⋊C8C2312yes—
77D376—22no—
78#10625325—22no—
79#10625324—22no—
80C8×D47—22no—
81C23×C47—21no—
82C23×C47—21no—
83C23×C47—41no—
84C22×D47—22no—
85C22×D47—41no—
86C22×D47—42no—
87Q8×C47C2×D412yes—
88D4×C47—22no—
89D4×C47—22no—
90D4×C47—22no—
91D4×C47—42no—
92D4×C47—82no—
93D4×C47C2×D412yes—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—41no—
97C2×C4×C47C2411yescharacteristic
98C22⋊D47—22no—
99C22⋊D47—42no—
100C22⋊D47—42no—
101C2×Dic47—41no—
102D188—22no—
103D188—22no—
104D188—42no—
105D188—82no—
106D188C2×D412yes—
107C4×D47—22no—
108C4×D47—42no—
109Dic94C2×D412yes—
110C8×C47—22no—
111C47⋊C8—22no—
112C47⋊C8C2×D412yes—
113C47⋊C8C2×D412yes—
114C22×C47—22no—
115C22×C47—41no—
116C22×C47—41no—
117C22×C47—81no—
118C22×C47—81no—
119C22×C47—161no—
120C22×C47H(5,𝔽2)11yescharacteristic
121C2×D47—22no—
122C2×D47—42no—
123C2×D47—82no—
124C2×D47—161no—
125C2×D47—162no—
126C4×C47—22no—
127C4×C47—22no—
128C4×C47C22×D412yes—
129Dic47—22no—
130#3292—471nomaximal, Sylow
131C2×C47—21no—
132C2×C47—42no—
133C2×C47—81no—
134C2×C47—81no—
135C2×C47D4211yescharacteristic
136D47—42no—
137D47—82no—
138#576—472no—
139#576—472no—
140#493—471no—
141#472—472no—
142#472—472no—
143#453—471no—
144#453—472no—
145#453D4711yescharacteristic, complemented
146#443—472no—
147C47#329211yescharacteristic, complemented, Sylow
148H(5,𝔽2)—472no—
149H(5,𝔽2)—471no—
150H(5,𝔽2)C2×D4711yescharacteristic, complemented
151AGL(1,ℤ/8)—472no—
152AGL(1,ℤ/8)—472no—
153AGL(1,ℤ/8)—472no—
154AGL(1,ℤ/8)—942no—
155AGL(1,ℤ/8)—942no—
156AGL(1,ℤ/8)—942no—
157AGL(1,ℤ/8)—942no—
158AGL(1,ℤ/8)C2×D4712yescomplemented
159#135—472no—
160#135—942no—
161#135—942no—
162C2×D8—472no—
163C2×D8—472no—
164C2×D8—942no—
165C2×D8—942no—
166#131—472no—
167#131—472no—
168#127—471no—
169#127C2×D4711yescharacteristic, complemented
170#108—472no—
171#104—472no—
172#104C2×D4712yescomplemented
173#100—471no—
174#100—472no—
175#100C2×D4711yescharacteristic, complemented
176C4×C8—471no—
177#41—22no—
178#41—472no—
179#41—942no—
180#41—942no—
181#41—942no—
182#41C22×D4712yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—472no—
187C2×D4—942no—
188C2×D4—942no—
189C2×D4—942no—
190C2×D4—1881no—
191C2×D4—1882no—
192C2×D4—1881no—
193C2×D4C22×D4711yescharacteristic
194C2×D4C22×D4711yescharacteristic
195Q16—472no—
196SD16—22no—
197SD16—472no—
198SD16—472no—
199SD16—942no—
200SD16—942no—
201SD16—942no—
202D8—22no—
203D8—472no—
204D8—942no—
205D8—942no—
206D8—942no—
207D8—942no—
208D8—942no—
209D8—942no—
210D8—942no—
211M16—472no—
212M16—942no—
213M16—942no—
214M16C22×D4712yes—
215C2×C8—472no—
216C2×C8—942no—
217C2×C8—942no—
218C42C22×D4711yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—942no—
223C23—1882no—
224C23—1881no—
225Q8—472no—
226Q8D4×D4712yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—472no—
233D4—942no—
234D4—942no—
235D4—942no—
236D4—3762no—
237D4—1882no—
238D4—1882no—
239D4—1882no—
240D4D4×D4712yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—942no—
245C2×C4—1882no—
246C2×C4—1881no—
247C2×C4C23×D4711yescharacteristic
248C8—22no—
249C8—472no—
250C8—472no—
251C8—942no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—942no—
259C22—3762no—
260C22—1882no—
261C22—7522no—
262C22—7521no—
263C22#1309406911yescharacteristic
264C4—22no—
265C4—22no—
266C4—942no—
267C4C2×D4×D4712yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—3762no—
273C2—1882no—
274C2#1568975511yescharacteristic
subgroupG/H
centerC2#15689755
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#453C2
socleC2×C47D42
hypercenter#453D47
hypocenterC47#3292
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #15689927C2semidirect
2. #15689926C2semidirect
3. #15689499C2semidirect
4. #15689392C2semidirect
5. #15689391C2semidirect
6. #15689292C2semidirect
7. #15689290C2semidirect
8. #15689237C2semidirect
9. C47×#453C2semidirect
10. #13094070C22semidirect
11. #13094069C22semidirect
12. #13094052C22semidirect
15. #13094050C22semidirect
17. #13094049C22semidirect
23. C2×#10625334C22semidirect
24. C2×#10625334C22semidirect
26. #13094032C22semidirect
27. #13094031C22semidirect
28. #13094021C22semidirect
29. #13093959C22semidirect
30. #13093952C22semidirect
31. #13093941C22semidirect
32. #13093940C22semidirect
33. C4×C47⋊C8C22semidirect
34. H(5,𝔽2)×C47C22semidirect
35. AGL(1,ℤ/8)×C47C22semidirect
36. #127×C47C22semidirect
37. #104×C47C22semidirect
38. #100×C47C22semidirect
61. #10625337D4semidirect
63. #10625336D4semidirect
65. #10625335D4semidirect
72. #10625334D4semidirect
145. #453D47semidirect
147. C47#3292semidirect
150. H(5,𝔽2)C2×D47semidirect
158. AGL(1,ℤ/8)C2×D47semidirect
169. #127C2×D47semidirect
172. #104C2×D47semidirect
175. #100C2×D47semidirect