Finite Group Databasebeta

← #20252908

Subgroups — #20252908

Order 6016.

490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094057C211yesmaximal, characteristic, complemented
2C22×#10625335C211yesmaximal, characteristic, complemented
3#15689690C211yesmaximal, characteristic
4#15689600C211yesmaximal, characteristic, complemented
5#15689344C214yesmaximal, complemented
6#15689322C214yesmaximal, complemented
7#15689151C211yesmaximal, characteristic, complemented
8#15689117C211yesmaximal, characteristic, complemented
9C47×#418C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C22×Dic94C2211yescharacteristic
12#13094057—24no—
13C2×Dic188C2212yescomplemented
14C2×#10625325C2212yescomplemented
15C2×#10625335—24no—
16C2×#10625335C2214yes—
17C22×C47⋊C8C2211yescharacteristic
18#13094020C2212yes—
19#13094011C2212yes—
20#13093995—22no—
21#13093993—22no—
22C4×Dic94—22no—
23#13093989C2214yescomplemented
24#13093983C2211yescharacteristic
25#13093980—22no—
26Dic47⋊C8C2214yescomplemented
27#13093947C2212yescomplemented
28#13093944C2212yescomplemented
29C22×D4×C47C2211yescharacteristic
30C2×M16×C47C2211yescharacteristic
31#117×C47C2211yescharacteristic
32#102×C47C2214yes—
33C24×C47—21no—
34C2×D4×C47—22no—
35C2×D4×C47—21no—
36C2×D4×C47—22no—
37C2×D4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C2×C22⋊D47—21no—
40C2×C22⋊D47—24no—
41C22×Dic47—21no—
42#10625350—22no—
43#10625350—22no—
44C2×D188C2311yescharacteristic
45C2×C4×D47—21no—
46C2×Dic94—21no—
47C2×Dic94—22no—
48C2×Dic94D414yescomplemented
49C2×Dic94C2311yescharacteristic
50C2×Dic94C2312yes—
51M16×C47—22no—
52C2×C8×C47C2312yes—
53C4⋊C4×C47C2312yes—
54C22⋊C4×C47—21no—
55C42×C47—21no—
56C22⋊Dic47—24no—
57C22⋊Dic47D412yes—
58#10625335—28no—
59C4⋊Dic47D412yes—
60Dic47⋊C4—24no—
61C4×Dic47—24no—
62C4×Dic47C2312yes—
63C2×C47⋊C8—22no—
64C2×C47⋊C8C2312yes—
65Dic188—24no—
66#10625325—24no—
67C23×C47—22no—
68C23×C47—42no—
69C23×C47—82no—
70C23×C47C2×D411yescharacteristic
71C22×D47—21no—
72D4×C47—22no—
73D4×C47—22no—
74D4×C47—42no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D412yes—
78C2×C4×C47#4112yes—
79C2×C4×C47C2411yescharacteristic
80C22⋊D47—42no—
81C22⋊D47—84no—
82C2×Dic47—24no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47C2×D414yes—
86D188—21no—
87D188—21no—
88C4×D47—42no—
89Dic94—24no—
90Dic94—22no—
91Dic94—21no—
92Dic94—21no—
93Dic94C2×D414yes—
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—42no—
105C4×C47#12112yes—
106C4×C47C22×D411yescharacteristic
107C4×C47C2×#4111yescharacteristic
108Dic47—24no—
109Dic47—24no—
110Dic47—41no—
111#3043—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47—82no—
114C2×C47C2×#12111yescharacteristic
115C2×C47#57712yes—
116D47—81no—
117C2×#137—471no—
118C22×SD16—471no—
119#535—471no—
120#519—471no—
121#464—474no—
122#460—474no—
123#424—471no—
124#418D4711yescharacteristic, complemented
125#416—471no—
126C47#304311yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C22×Q8—471no—
129C22×D4C2×D4711yescharacteristic
130#137—944no—
131C2×Q16—472no—
132C2×SD16—474no—
133C2×SD16—472no—
134C2×SD16—944no—
135C2×M16C2×D4711yescharacteristic
136C22×C8—471no—
137#127—472no—
138#124—472no—
139#121—942no—
140#120—942no—
141C4×Q8—474no—
142C4×Q8—942no—
143#117—471no—
144#117—942no—
145#117C2×D4711yescharacteristic
146C4⋊C8—474no—
147#103—472no—
148#102—472no—
149#102C2×D4714yes—
150C24—21no—
151#41—942no—
152#41—942no—
153C2×Q8—474no—
154C2×Q8—472no—
155C2×Q8—471no—
156C2×Q8—942no—
157C2×Q8—941no—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4—21no—
161C2×D4—471no—
162C2×D4—944no—
163C2×D4—941no—
164C2×D4C22×D4712yes—
165C22×C4—941no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168Q16—944no—
169SD16—944no—
170SD16—948no—
171M16—22no—
172C2×C8—472no—
173C2×C8—942no—
174C2×C8C22×D4712yes—
175C4⋊C4—472no—
176C4⋊C4—944no—
177C4⋊C4C22×D4712yes—
178C22⋊C4—21no—
179C22⋊C4—472no—
180C22⋊C4—944no—
181C42—21no—
182C42—472no—
183C42—944no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—941no—
188C23D4×D4711yescharacteristic
189Q8—474no—
190Q8—944no—
191Q8—942no—
192Q8—941no—
193Q8—941no—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—941no—
198D4—941no—
199D4—3764no—
200D4—1882no—
201C2×C4—22no—
202C2×C4—474no—
203C2×C4—944no—
204C2×C4—942no—
205C2×C4—941no—
206C2×C4—1882no—
207C2×C4#1062535012yes—
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4712yes—
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—942no—
213C22—22no—
214C22—42no—
215C22—44no—
216C22—84no—
217C22—1881no—
218C22—1882no—
219C22#1309399712yes—
220C22C2×D4×D4711yescharacteristic
221C4—42no—
222C4—944no—
223C4—944no—
224C4—1881no—
225C4#1309399712yes—
226C4C2×D4×D4711yescharacteristic
227C4C2×#1062535011yescharacteristic
228C2—22no—
229C2—82no—
230C2—3761no—
231C2C2×#1309399711yescharacteristic
232C2#1568993312yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#418C2
socleC22×C47C22×D4
hypercenter#418D47
hypocenterC47#3043
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#13094057C2semidirect
2. C22×#10625335C2semidirect
4. #15689600C2semidirect
5. #15689344C2semidirect
6. #15689322C2semidirect
7. #15689151C2semidirect
8. #15689117C2semidirect
9. C47×#418C2semidirect
13. C2×Dic188C22semidirect
14. C2×#10625325C22semidirect
23. #13093989C22semidirect
26. Dic47⋊C8C22semidirect
27. #13093947C22semidirect
28. #13093944C22semidirect
48. C2×Dic94D4semidirect
124. #418D47semidirect
126. C47#3043semidirect