Finite Group Databasebeta

← #20255183

Subgroups — #20255183

Order 6016.

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

normal subgroups only

This group has 460 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#15689934C212yesmaximal, complemented
2#15689933C212yesmaximal, complemented
3#15689495C211yesmaximal, characteristic, complemented
4#15689385C212yesmaximal, complemented
5#15689384C212yesmaximal, complemented
6#15689307C212yesmaximal, complemented
7#15689290C211yesmaximal, characteristic, complemented
8#15689237C212yesmaximal, complemented
9C47×#453C211yesmaximal, characteristic, complemented
10#13094071C2212yes—
11#13094069C2211yescharacteristic, complemented
12#13094057C2212yescomplemented
13#13094054—22no—
14#13094054C2212yescomplemented
15#13094053—22no—
16#13094050—22no—
17#13094050C2212yes—
18#13094048—22no—
19#13094044—22no—
20#13094044C2212yes—
21#13094043—22no—
22C2×#10625335—22no—
23C2×#10625335C2212yescomplemented
24C2×#10625335C2212yescomplemented
25SD16×D47—22no—
26#13094032C2212yescomplemented
27#13094031C2212yescomplemented
28#13094024C2211yescharacteristic, complemented
29#13093959C2212yescomplemented
30#13093952C2212yescomplemented
31#13093942C2212yescomplemented
32#13093941C2211yescharacteristic, complemented
33C4×C47⋊C8C2211yescharacteristic, complemented
34H(5,𝔽2)×C47C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C47C2212yes—
36#127×C47C2211yescharacteristic
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—
47Q8×D47—22no—
48#10625352—22no—
49#10625352—22no—
50#10625352—42no—
51D4×D47—22no—
52#10625350—22no—
53#10625350C2312yes—
54C2×Dic94—22no—
55C2×Dic94C2312yes—
56SD16×C47—22no—
57D8×C47—22no—
58M16×C47C2312yes—
59C42×C47C2311yescharacteristic
60#10625337—22no—
61#10625337D412yescomplemented
62#10625336D412yescomplemented
63#10625335—22no—
64#10625335—22no—
65#10625335—22no—
66#10625335—22no—
67#10625335—22no—
68#10625335—22no—
69#10625335D412yescomplemented
70#10625334—22no—
71#10625334D412yescomplemented
72C4⋊Dic47—41no—
73#10625329—22no—
74#10625329C2312yes—
75C2×C47⋊C8—22no—
76C2×C47⋊C8C2312yes—
77Dic188—22no—
78#10625325—22no—
79#10625324—22no—
80C8×D47—22no—
81C23×C47—21no—
82C23×C47—21no—
83C23×C47—41no—
84C22×D47—41no—
85Q8×C47C2×D412yes—
86D4×C47—22no—
87D4×C47—22no—
88D4×C47—22no—
89D4×C47—42no—
90D4×C47—82no—
91D4×C47C2×D412yes—
92C2×C4×C47—21no—
93C2×C4×C47—22no—
94C2×C4×C47—41no—
95C2×C4×C47C2411yescharacteristic
96C22⋊D47—22no—
97C22⋊D47—42no—
98C22⋊D47—42no—
99C2×Dic47—22no—
100C2×Dic47—41no—
101C2×Dic47—42no—
102D188C2×D412yes—
103C4×D47—22no—
104C4×D47—42no—
105Dic94—22no—
106Dic94—22no—
107Dic94—42no—
108Dic94C2×D412yes—
109C8×C47—22no—
110C47⋊C8—22no—
111C47⋊C8C2×D412yes—
112C47⋊C8C2×D412yes—
113C22×C47—22no—
114C22×C47—41no—
115C22×C47—41no—
116C22×C47—81no—
117C22×C47—81no—
118C22×C47—161no—
119C22×C47H(5,𝔽2)11yescharacteristic
120C2×D47—22no—
121C2×D47—161no—
122C4×C47—22no—
123C4×C47—22no—
124C4×C47C22×D412yes—
125Dic47—22no—
126Dic47—42no—
127#3291—471nomaximal, Sylow
128C2×C47—21no—
129C2×C47—42no—
130C2×C47—81no—
131C2×C47—81no—
132C2×C47D4211yescharacteristic
133D47—42no—
134#577—472no—
135#577—472no—
136#492—471no—
137#471—472no—
138#471—472no—
139#456—472no—
140#453—471no—
141#453D4711yescharacteristic, complemented
142#443—472no—
143C47#329111yescharacteristic, complemented, Sylow
1442−1+4—472no—
145H(5,𝔽2)—471no—
146H(5,𝔽2)C2×D4711yescharacteristic, complemented
147#137—472no—
148#137—472no—
149#137—942no—
150#137—942no—
151AGL(1,ℤ/8)—472no—
152AGL(1,ℤ/8)—942no—
153AGL(1,ℤ/8)—942no—
154AGL(1,ℤ/8)C2×D4712yes—
155#135—472no—
156#135—942no—
157#135—942no—
158C2×SD16—472no—
159C2×SD16—472no—
160C2×SD16—942no—
161C2×SD16—942no—
162#131—472no—
163#131—472no—
164C4⋊Q8—471no—
165#127C2×D4711yescharacteristic
166#108—472no—
167#104—472no—
168#104C2×D4712yescomplemented
169#101—472no—
170#100—471no—
171#100C2×D4711yescharacteristic, complemented
172C4×C8—471no—
173#41—22no—
174#41—472no—
175#41—942no—
176#41—942no—
177#41—942no—
178#41—1882no—
179#41C22×D4712yes—
180C2×Q8—472no—
181C2×Q8—942no—
182C2×Q8—942no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—942no—
187C2×D4—1881no—
188C2×D4C22×D4711yescharacteristic
189C2×D4C22×D4711yescharacteristic
190Q16—472no—
191Q16—942no—
192Q16—942no—
193SD16—22no—
194SD16—472no—
195SD16—472no—
196SD16—942no—
197SD16—942no—
198SD16—942no—
199SD16—942no—
200SD16—942no—
201SD16—942no—
202SD16—942no—
203D8—22no—
204D8—472no—
205D8—942no—
206M16—472no—
207M16—942no—
208M16—942no—
209M16C22×D4712yes—
210C2×C8—472no—
211C2×C8—942no—
212C2×C8—942no—
213C4⋊C4—1881no—
214C42C22×D4711yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—1881no—
219Q8—472no—
220Q8—942no—
221Q8—942no—
222Q8—1882no—
223Q8D4×D4712yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—472no—
230D4—942no—
231D4—1882no—
232D4—1882no—
233D4D4×D4712yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—1882no—
240C2×C4—1881no—
241C2×C4—1882no—
242C2×C4C23×D4711yescharacteristic
243C8—22no—
244C8—472no—
245C8—472no—
246C8—942no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—942no—
254C22—7521no—
255C22#1309406911yescharacteristic
256C4—22no—
257C4—22no—
258C4—942no—
259C4—1882no—
260C4C2×D4×D4712yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—1882no—
266C2#1568975511yescharacteristic
subgroupG/H
centerC2#15689755
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#453C2
socleC2×C47D42
hypercenter#453D47
hypocenterC47#3291
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. #15689934C2semidirect
2. #15689933C2semidirect
3. #15689495C2semidirect
4. #15689385C2semidirect
5. #15689384C2semidirect
6. #15689307C2semidirect
7. #15689290C2semidirect
8. #15689237C2semidirect
9. C47×#453C2semidirect
11. #13094069C22semidirect
12. #13094057C22semidirect
14. #13094054C22semidirect
23. C2×#10625335C22semidirect
24. C2×#10625335C22semidirect
26. #13094032C22semidirect
27. #13094031C22semidirect
28. #13094024C22semidirect
29. #13093959C22semidirect
30. #13093952C22semidirect
31. #13093942C22semidirect
32. #13093941C22semidirect
33. C4×C47⋊C8C22semidirect
34. H(5,𝔽2)×C47C22semidirect
37. #104×C47C22semidirect
38. #100×C47C22semidirect
61. #10625337D4semidirect
62. #10625336D4semidirect
69. #10625335D4semidirect
71. #10625334D4semidirect
141. #453D47semidirect
143. C47#3291semidirect
146. H(5,𝔽2)C2×D47semidirect
168. #104C2×D47semidirect
171. #100C2×D47semidirect