Finite Group Databasebeta

← #20255178

Subgroups — #20255178

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#15689932C212yesmaximal, complemented
2#15689931C212yesmaximal, complemented
3#15689497C211yesmaximal, characteristic, complemented
4#15689389C212yesmaximal, complemented
5#15689388C212yesmaximal, complemented
6#15689305C211yesmaximal, characteristic, complemented
7#15689292C212yesmaximal, complemented
8#15689237C212yesmaximal, complemented
9C47×#456C211yesmaximal, characteristic, complemented
10#13094072C2211yescharacteristic
11#13094070C2212yescomplemented
12#13094056—22no—
13#13094055—22no—
14#13094055C2212yescomplemented
15#13094052C2212yes—
16#13094051—22no—
17#13094049—22no—
18#13094049C2212yes—
19#13094047—22no—
20#13094044—22no—
21#13094044C2212yes—
22C2×#10625336—22no—
23C2×#10625336C2212yescomplemented
24C2×#10625336C2212yescomplemented
25SD16×D47—22no—
26#13094032C2212yescomplemented
27#13094031C2212yescomplemented
28#13094021C2211yescharacteristic
29#13093959C2212yescomplemented
30#13093952C2212yescomplemented
31#13093943C2211yescharacteristic, complemented
32#13093940C2212yescomplemented
33C4×C47⋊C8C2211yescharacteristic, complemented
342−1+4×C47C2211yescharacteristic
35#137×C47C2212yescomplemented
36C4⋊Q8×C47C2211yescharacteristic, complemented
37#104×C47C2212yescomplemented
38#101×C47C2211yescharacteristic, complemented
39#41×C47—22no—
40#41×C47—41no—
41#41×C47C2312yes—
42C2×Q8×C47—22no—
43C2×Q8×C47C2311yescharacteristic
44C2×Q8×C47C2311yescharacteristic
45#10625354—22no—
46#10625354—22no—
47Q8×D47—22no—
48D4×D47—22no—
49D4×D47—42no—
50#10625350—22no—
51#10625350—41no—
52#10625350C2312yes—
53C2×D188—22no—
54C2×D188—41no—
55C2×D188C2312yes—
56Q16×C47—22no—
57SD16×C47—22no—
58M16×C47C2312yes—
59C4⋊C4×C47—41no—
60C42×C47C2311yescharacteristic
61#10625337—22no—
62#10625337D412yescomplemented
63#10625336—22no—
64#10625336—22no—
65#10625336—22no—
66#10625336—22no—
67#10625336—22no—
68#10625336—22no—
69#10625336D412yescomplemented
70#10625335D412yescomplemented
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—
81C22×D47—22no—
82C22×D47—42no—
83Q8×C47—22no—
84Q8×C47—22no—
85Q8×C47—41no—
86Q8×C47C2×D412yes—
87D4×C47—22no—
88D4×C47—41no—
89D4×C47C2×D412yes—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—42no—
95C2×C4×C47C2411yescharacteristic
96C22⋊D47—22no—
97C22⋊D47—42no—
98D188—22no—
99D188—22no—
100D188—42no—
101D188—41no—
102D188—82no—
103D188C2×D412yes—
104C4×D47—22no—
105C4×D47—42no—
106C4×D47—42no—
107Dic94—41no—
108Dic94C2×D412yes—
109C8×C47—22no—
110C47⋊C8—22no—
111C47⋊C8C2×D412yes—
112C47⋊C8C2×D412yes—
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×C47—41no—
122C4×C47—41no—
123C4×C47C22×D412yes—
124Dic47—22no—
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—471no—
137#456D4711yescharacteristic, complemented
138#453—472no—
139#443—472no—
140C47#329111yescharacteristic, complemented, Sylow
1412−1+4—471no—
1422−1+4C2×D4711yescharacteristic
143H(5,𝔽2)—472no—
144#137—472no—
145#137—942no—
146#137—942no—
147#137C2×D4712yescomplemented
148AGL(1,ℤ/8)—472no—
149AGL(1,ℤ/8)—472no—
150AGL(1,ℤ/8)—942no—
151AGL(1,ℤ/8)—942no—
152#135—472no—
153#135—942no—
154#135—942no—
155C2×SD16—472no—
156C2×SD16—472no—
157C2×SD16—942no—
158C2×SD16—942no—
159#131—472no—
160#131—472no—
161C4⋊Q8C2×D4711yescharacteristic, complemented
162#127—471no—
163#108—472no—
164#104—472no—
165#104C2×D4712yescomplemented
166#101—471no—
167#101C2×D4711yescharacteristic, complemented
168#100—472no—
169C4×C8—471no—
170#41—22no—
171#41—41no—
172#41—472no—
173#41—942no—
174#41—942no—
175#41—942no—
176#41—1881no—
177#41C22×D4712yes—
178C2×Q8—22no—
179C2×Q8—942no—
180C2×Q8C22×D4711yescharacteristic
181C2×Q8C22×D4711yescharacteristic
182C2×D4—472no—
183C2×D4—942no—
184C2×D4—942no—
185C2×D4—1881no—
186C2×D4—1882no—
187Q16—22no—
188Q16—472no—
189Q16—942no—
190SD16—22no—
191SD16—472no—
192SD16—472no—
193SD16—942no—
194SD16—942no—
195SD16—942no—
196SD16—942no—
197SD16—942no—
198SD16—942no—
199SD16—942no—
200D8—472no—
201D8—942no—
202D8—942no—
203M16—472no—
204M16—942no—
205M16—942no—
206M16C22×D4712yes—
207C2×C8—472no—
208C2×C8—942no—
209C2×C8—942no—
210C4⋊C4—41no—
211C42C22×D4711yescharacteristic
212C23—942no—
213C23—1882no—
214Q8—22no—
215Q8—22no—
216Q8—41no—
217Q8—472no—
218Q8—1881no—
219Q8D4×D4712yes—
220D4—22no—
221D4—41no—
222D4—472no—
223D4—942no—
224D4—942no—
225D4—942no—
226D4—3762no—
227D4—1882no—
228D4—1881no—
229D4—1882no—
230D4D4×D4712yes—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—942no—
237C2×C4—1882no—
238C2×C4—1882no—
239C2×C4C23×D4711yescharacteristic
240C8—22no—
241C8—472no—
242C8—472no—
243C8—942no—
244C22—22no—
245C22—942no—
246C22—3762no—
247C22—1882no—
248C22—7522no—
249C22#1309406911yescharacteristic
250C4—22no—
251C4—22no—
252C4—41no—
253C4—41no—
254C4—942no—
255C4C2×D4×D4712yes—
256C2—21no—
257C2—42no—
258C2—3762no—
259C2—1882no—
260C2#1568975511yescharacteristic
subgroupG/H
centerC2#15689755
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#456C2
socleC2×C47D42
hypercenter#456D47
hypocenterC47#3291
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #15689932C2semidirect
2. #15689931C2semidirect
3. #15689497C2semidirect
4. #15689389C2semidirect
5. #15689388C2semidirect
6. #15689305C2semidirect
7. #15689292C2semidirect
8. #15689237C2semidirect
9. C47×#456C2semidirect
11. #13094070C22semidirect
14. #13094055C22semidirect
23. C2×#10625336C22semidirect
24. C2×#10625336C22semidirect
26. #13094032C22semidirect
27. #13094031C22semidirect
29. #13093959C22semidirect
30. #13093952C22semidirect
31. #13093943C22semidirect
32. #13093940C22semidirect
33. C4×C47⋊C8C22semidirect
35. #137×C47C22semidirect
36. C4⋊Q8×C47C22semidirect
37. #104×C47C22semidirect
38. #101×C47C22semidirect
62. #10625337D4semidirect
69. #10625336D4semidirect
70. #10625335D4semidirect
72. #10625334D4semidirect
137. #456D47semidirect
140. C47#3291semidirect
147. #137C2×D47semidirect
161. C4⋊Q8C2×D47semidirect
165. #104C2×D47semidirect
167. #101C2×D47semidirect