Finite Group Databasebeta

← #20252906

Subgroups — #20252906

Order 6016.

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

normal subgroups only

This group has 490 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×#13094055C211yesmaximal, characteristic, complemented
2#15689690C211yesmaximal, characteristic
3#15689601C211yesmaximal, characteristic, complemented
4#15689343C214yesmaximal, complemented
5#15689321C214yesmaximal, complemented
6#15689149C211yesmaximal, characteristic, complemented
7#15689128C211yesmaximal, characteristic, complemented
8#15689120C211yesmaximal, characteristic, complemented
9C22×SD16×C47C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11#13094055—24no—
12C2×#10625337C2212yescomplemented
13C2×#10625336C2212yescomplemented
14C2×#10625329C2211yescharacteristic
15#13094020C2212yes—
16#13094011C2212yes—
17#13093995—22no—
18#13093993—22no—
19Q8×Dic47—22no—
20Q8×Dic47C2214yescomplemented
21#13093983—22no—
22#13093983C2211yescharacteristic
23#13093983C2211yescharacteristic
24Dic47⋊C8C2214yescomplemented
25#13093949C2212yescomplemented
26#13093946C2212yescomplemented
27#13093945C2214yes—
28C22×Q8×C47C2211yescharacteristic
29C22×D4×C47C2211yescharacteristic
30C2×SD16×C47—24no—
31C2×SD16×C47C2214yes—
32C22×C8×C47C2211yescharacteristic
33C24×C47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47—22no—
36C2×Q8×C47D414yescomplemented
37C2×Q8×C47C2312yes—
38C2×D4×C47—22no—
39C2×D4×C47—21no—
40C2×D4×C47—22no—
41C2×D4×C47C2312yes—
42C22×C4×C47—21no—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—21no—
45C2×C22⋊D47—24no—
46#10625350—22no—
47#10625350—22no—
48C2×D188C2311yescharacteristic
49C2×C4×D47—21no—
50C2×Dic94C2311yescharacteristic
51SD16×C47—28no—
52C2×C8×C47—22no—
53C2×C8×C47C2312yes—
54C22⋊Dic47—21no—
55C22⋊Dic47—24no—
56C22⋊Dic47D412yes—
57#10625337—24no—
58#10625336—24no—
59C4⋊Dic47—24no—
60C4⋊Dic47D412yes—
61C4⋊Dic47C2312yes—
62C4×Dic47—21no—
63C4×Dic47—24no—
64C4×Dic47C2312yes—
65#10625329—22no—
66C2×C47⋊C8C2312yes—
67C23×C47—22no—
68C23×C47—42no—
69C23×C47—82no—
70C23×C47C2×D411yescharacteristic
71C22×D47—21no—
72Q8×C47—24no—
73Q8×C47—22no—
74Q8×C47C2×D414yes—
75D4×C47—22no—
76D4×C47—22no—
77D4×C47—42no—
78C2×C4×C47—24no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D412yes—
82C2×C4×C47#4112yes—
83C2×C4×C47C2411yescharacteristic
84C22⋊D47—42no—
85C22⋊D47—84no—
86C2×Dic47—22no—
87C2×Dic47—21no—
88C2×Dic47C2×D414yes—
89D188—21no—
90D188—21no—
91C4×D47—42no—
92Dic94—21no—
93Dic94—21no—
94C8×C47—22no—
95C47⋊C8—22no—
96C22×C47—22no—
97C22×C47—42no—
98C22×C47—44no—
99C22×C47—84no—
100C22×C47#12112yes—
101C22×C47C22×D411yescharacteristic
102C2×D47—41no—
103C2×D47—42no—
104C4×C47—24no—
105C4×C47#12112yes—
106C4×C47C22×D411yescharacteristic
107C4×C47C2×#4111yescharacteristic
108Dic47—24no—
109Dic47—41no—
110Dic47—42no—
111#3043—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47—82no—
114C2×C47C2×#12111yescharacteristic
115C2×C47#57712yes—
116D47—81no—
117C2×#137—471no—
118C22×SD16D4711yescharacteristic, complemented
119#535—471no—
120#519—471no—
121#464—474no—
122#460—474no—
123#424—471no—
124#418—471no—
125#416—471no—
126C47#304311yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C22×Q8C2×D4711yescharacteristic
129C22×D4C2×D4711yescharacteristic
130#137—944no—
131C2×Q16—472no—
132C2×SD16—24no—
133C2×SD16—472no—
134C2×SD16C2×D4714yes—
135C2×M16—471no—
136C22×C8C2×D4711yescharacteristic
137#127—472no—
138#124—472no—
139#121—942no—
140#120—942no—
141C4×Q8—474no—
142C4×Q8—942no—
143#117—471no—
144#117—471no—
145#117—942no—
146C4⋊C8—474no—
147#103—472no—
148#102—474no—
149#102—472no—
150C24—21no—
151#41—942no—
152#41—942no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—471no—
156C2×Q8C22⋊D4714yescomplemented
157C2×Q8C22×D4712yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4—471no—
162C2×D4—944no—
163C2×D4—941no—
164C2×D4C22×D4712yes—
165C22×C4—21no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168Q16—944no—
169SD16—28no—
170SD16—944no—
171M16—942no—
172C2×C8—22no—
173C2×C8—472no—
174C2×C8C22×D4712yes—
175C4⋊C4—472no—
176C4⋊C4—472no—
177C4⋊C4—944no—
178C22⋊C4—472no—
179C22⋊C4—944no—
180C22⋊C4—941no—
181C42—472no—
182C42—944no—
183C42—941no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—941no—
188C23D4×D4711yescharacteristic
189Q8—24no—
190Q8—22no—
191Q8—941no—
192Q8—941no—
193Q8C2×C22⋊D4714yes—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—941no—
198D4—941no—
199D4—3764no—
200D4—1882no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—474no—
204C2×C4—942no—
205C2×C4—941no—
206C2×C4—1882no—
207C2×C4D4×D4711yescharacteristic
208C2×C4#1062535212yes—
209C2×C4C2×C22⋊D4712yes—
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—942no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—1881no—
218C22—1882no—
219C22#1309399612yes—
220C22C2×D4×D4711yescharacteristic
221C4—24no—
222C4—944no—
223C4—1881no—
224C4—1882no—
225C4#1309399612yes—
226C4C22×C22⋊D4711yescharacteristic
227C4C2×#1062535211yescharacteristic
228C2—22no—
229C2—82no—
230C2—3761no—
231C2C2×#1309399611yescharacteristic
232C2#1568992912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC22×SD16×C47C2
socleC22×C47C22×D4
hypercenterC22×SD16D47
hypocenterC47#3043
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
3. #15689601C2semidirect
4. #15689343C2semidirect
5. #15689321C2semidirect
6. #15689149C2semidirect
7. #15689128C2semidirect
8. #15689120C2semidirect
9. C22×SD16×C47C2semidirect
12. C2×#10625337C22semidirect
13. C2×#10625336C22semidirect
20. Q8×Dic47C22semidirect
24. Dic47⋊C8C22semidirect
25. #13093949C22semidirect
26. #13093946C22semidirect
36. C2×Q8×C47D4semidirect
118. C22×SD16D47semidirect
126. C47#3043semidirect
156. C2×Q8C22⋊D47semidirect