Finite Group Databasebeta

← #20255182

Subgroups — #20255182

Order 6016.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689935C212yesmaximal, complemented
2#15689930C212yesmaximal, complemented
3#15689496C211yesmaximal, characteristic, complemented
4#15689387C212yesmaximal, complemented
5#15689386C212yesmaximal, complemented
6#15689307C212yesmaximal, complemented
7#15689292C212yesmaximal, complemented
8#15689241C211yesmaximal, characteristic, complemented
9C47×#443C211yesmaximal, characteristic, complemented
10#13094071C2212yes—
11#13094070C2212yescomplemented
12#13094057—22no—
13#13094057C2212yescomplemented
14#13094056—22no—
15#13094054C2212yescomplemented
16#13094052—22no—
17#13094052C2212yes—
18#13094049C2212yes—
19#13094048—22no—
20#13094046—22no—
21#13094046C2211yescharacteristic
22#13094045—22no—
23C2×#10625325—22no—
24C2×#10625325C2212yescomplemented
25C2×#10625325C2212yescomplemented
26SD16×D47—22no—
27#13094030C2212yescomplemented
28#13094024C2211yescharacteristic, complemented
29#13094021C2211yescharacteristic
30#13093960C2211yescharacteristic, complemented
31#13093952C2212yescomplemented
32#13093942C2212yescomplemented
33#13093940C2212yescomplemented
34#135×C47C2211yescharacteristic
35#131×C47C2212yescomplemented
36#108×C47C2211yescharacteristic, complemented
37#104×C47C2212yescomplemented
38C4×C8×C47C2211yescharacteristic, complemented
39#41×C47C2312yes—
40#10625354—22no—
41Q8×D47—22no—
42#10625352—22no—
43#10625352—42no—
44D4×D47—22no—
45D4×D47—42no—
46#10625350—22no—
47#10625350—22no—
48#10625350C2312yes—
49C2×D188—22no—
50C2×D188—41no—
51C2×D188C2312yes—
52C2×Dic94—22no—
53C2×Dic94C2312yes—
54Q16×C47D411yescharacteristic, complemented
55SD16×C47D412yescomplemented
56D8×C47D411yescharacteristic, complemented
57M16×C47—22no—
58M16×C47C2312yes—
59C2×C8×C47—22no—
60C2×C8×C47C2311yescharacteristic
61C2×C8×C47C2311yescharacteristic
62C42×C47C2311yescharacteristic
63#10625337—22no—
64#10625336—22no—
65#10625335—22no—
66#10625334—22no—
67C4⋊Dic47—41no—
68#10625329C2312yes—
69Dic188—22no—
70Dic188D411yescharacteristic, complemented
71D376—22no—
72D376D411yescharacteristic, complemented
73#10625325—22no—
74#10625325—22no—
75#10625325—22no—
76#10625325—22no—
77#10625325—22no—
78#10625325—22no—
79#10625325D412yescomplemented
80#10625324—22no—
81C8×D47—22no—
82C22×D47—22no—
83C22×D47—42no—
84Q8×C47C2×D412yes—
85D4×C47—22no—
86D4×C47C2×D412yes—
87C2×C4×C47—21no—
88C2×C4×C47—22no—
89C2×C4×C47C2411yescharacteristic
90C22⋊D47—22no—
91C22⋊D47—42no—
92C22⋊D47—42no—
93C2×Dic47—22no—
94C2×Dic47—42no—
95D188—22no—
96D188—22no—
97D188—42no—
98D188—82no—
99D188C2×D412yes—
100C4×D47—22no—
101C4×D47—42no—
102C4×D47—42no—
103Dic94—22no—
104Dic94—22no—
105Dic94—42no—
106Dic94C2×D412yes—
107C8×C47—22no—
108C8×C47C2×D411yescharacteristic
109C8×C47C2×D411yescharacteristic
110C8×C47C2×D411yescharacteristic
111C8×C47C2×D411yescharacteristic
112C47⋊C8—22no—
113C22×C47—22no—
114C22×C47H(5,𝔽2)11yescharacteristic
115C2×D47—22no—
116C2×D47—42no—
117C2×D47—82no—
118C2×D47—162no—
119C4×C47—22no—
120C4×C47—22no—
121C4×C47C22×D411yescharacteristic
122C4×C47C22×D411yescharacteristic
123Dic47—22no—
124Dic47—42no—
125#3291—471nomaximal, Sylow
126C2×C47—21no—
127C2×C47—42no—
128C2×C47D4211yescharacteristic
129D47—42no—
130D47—82no—
131#577—472no—
132#577—472no—
133#492—471no—
134#471—472no—
135#471—472no—
136#456—472no—
137#453—472no—
138#443—471no—
139#443D4711yescharacteristic, complemented
140C47#329111yescharacteristic, complemented, Sylow
1412−1+4—472no—
142H(5,𝔽2)—472no—
143#137—472no—
144#137—472no—
145#137—942no—
146#137—942no—
147AGL(1,ℤ/8)—472no—
148AGL(1,ℤ/8)—472no—
149AGL(1,ℤ/8)—942no—
150AGL(1,ℤ/8)—942no—
151#135—471no—
152#135—942no—
153#135—942no—
154#135C2×D4711yescharacteristic
155C2×SD16—472no—
156C2×SD16—472no—
157C2×SD16—942no—
158C2×SD16—942no—
159#131—472no—
160#131C2×D4712yescomplemented
161C4⋊Q8—471no—
162#127—471no—
163#108—471no—
164#108C2×D4711yescharacteristic, complemented
165#104—472no—
166#104C2×D4712yescomplemented
167#101—472no—
168#100—472no—
169C4×C8C2×D4711yescharacteristic, complemented
170#41—472no—
171#41—942no—
172#41—942no—
173#41—942no—
174#41—942no—
175#41—1882no—
176#41C22×D4712yes—
177C2×Q8—472no—
178C2×Q8—942no—
179C2×Q8—942no—
180C2×D4—472no—
181C2×D4—942no—
182C2×D4—942no—
183C2×D4—1881no—
184C2×D4—1882no—
185Q16—471no—
186Q16—942no—
187Q16—942no—
188Q16D18811yescharacteristic, complemented
189SD16—472no—
190SD16—942no—
191SD16—942no—
192SD16—942no—
193SD16—942no—
194SD16—942no—
195SD16—942no—
196SD16—942no—
197SD16—942no—
198SD16D18812yescomplemented
199D8—471no—
200D8—942no—
201D8—942no—
202D8D18811yescharacteristic, complemented
203M16—22no—
204M16—472no—
205M16—942no—
206M16C22×D4712yes—
207C2×C8—22no—
208C2×C8—942no—
209C2×C8C22×D4711yescharacteristic
210C2×C8C22×D4711yescharacteristic
211C4⋊C4—1881no—
212C42C22×D4711yescharacteristic
213C23—942no—
214C23—1882no—
215Q8—472no—
216Q8—942no—
217Q8—942no—
218Q8—1882no—
219Q8C2×D18812yes—
220D4—22no—
221D4—472no—
222D4—942no—
223D4—942no—
224D4—942no—
225D4—3762no—
226D4—1882no—
227D4—1882no—
228D4—1882no—
229D4C2×D18812yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—1882no—
235C2×C4—1882no—
236C2×C4—1882no—
237C2×C4C23×D4711yescharacteristic
238C8—22no—
239C8—942no—
240C8C2×D18811yescharacteristic
241C8C2×D18811yescharacteristic
242C8D4×D4711yescharacteristic
243C8D4×D4711yescharacteristic
244C22—22no—
245C22—942no—
246C22—3762no—
247C22—1882no—
248C22—7522no—
249C22#1309407011yescharacteristic
250C4—22no—
251C4—22no—
252C4—942no—
253C4—1882no—
254C4C2×D4×D4711yescharacteristic
255C4C22×D18811yescharacteristic
256C2—21no—
257C2—42no—
258C2—3762no—
259C2—1882no—
260C2D4×D18811yescharacteristic
subgroupG/H
centerC2D4×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#443C2
socleC2×C47D42
hypercenter#443D47
hypocenterC47#3291
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #15689935C2semidirect
2. #15689930C2semidirect
3. #15689496C2semidirect
4. #15689387C2semidirect
5. #15689386C2semidirect
6. #15689307C2semidirect
7. #15689292C2semidirect
8. #15689241C2semidirect
9. C47×#443C2semidirect
11. #13094070C22semidirect
13. #13094057C22semidirect
15. #13094054C22semidirect
24. C2×#10625325C22semidirect
25. C2×#10625325C22semidirect
27. #13094030C22semidirect
28. #13094024C22semidirect
30. #13093960C22semidirect
31. #13093952C22semidirect
32. #13093942C22semidirect
33. #13093940C22semidirect
35. #131×C47C22semidirect
36. #108×C47C22semidirect
37. #104×C47C22semidirect
38. C4×C8×C47C22semidirect
54. Q16×C47D4semidirect
55. SD16×C47D4semidirect
56. D8×C47D4semidirect
70. Dic188D4semidirect
72. D376D4semidirect
79. #10625325D4semidirect
139. #443D47semidirect
140. C47#3291semidirect
160. #131C2×D47semidirect
164. #108C2×D47semidirect
166. #104C2×D47semidirect
169. C4×C8C2×D47semidirect
188. Q16D188semidirect
198. SD16D188semidirect
202. D8D188semidirect