Finite Group Databasebeta

← #20252912

Subgroups — #20252912

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×#13094054C211yesmaximal, characteristic, complemented
2C22×#10625325C211yesmaximal, characteristic, complemented
3#15689687C211yesmaximal, characteristic
4#15689600C211yesmaximal, characteristic, complemented
5#15689348C214yesmaximal, complemented
6#15689322C214yesmaximal, complemented
7#15689149C211yesmaximal, characteristic, complemented
8#15689127C211yesmaximal, characteristic, complemented
9C47×#416C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12#13094054—24no—
13C2×#10625337C2212yescomplemented
14C2×#10625325—24no—
15C2×#10625325C2214yes—
16C2×#10625335C2212yescomplemented
17C2×#10625329C2211yescharacteristic
18#13094020C2212yes—
19#13094013C2212yes—
20#13093998—22no—
21#13093992—22no—
22C4×Dic94—22no—
23#13093989C2214yescomplemented
24#13093983C2211yescharacteristic
25#13093980—22no—
26Dic47⋊C8C2214yescomplemented
27#13093944C2214yes—
28C2×#41×C47C2211yescharacteristic
29C22×C8×C47C2211yescharacteristic
30#117×C47C2211yescharacteristic
31#103×C47C2212yescomplemented
32#102×C47C2212yescomplemented
33C23×D47—21no—
34#41×C47—22no—
35#41×C47—22no—
36C2×Q8×C47C2311yescharacteristic
37C2×D4×C47—21no—
38C2×D4×C47C2311yescharacteristic
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—24no—
42C22×Dic47—21no—
43C2×D188—22no—
44C2×D188—22no—
45C2×D188—21no—
46C2×D188C2312yes—
47C2×Dic94—21no—
48C2×Dic94—22no—
49C2×Dic94D414yescomplemented
50C2×Dic94C2312yes—
51C2×C8×C47—22no—
52C2×C8×C47C2312yes—
53C4⋊C4×C47C2312yes—
54C22⋊C4×C47—21no—
55C42×C47—21no—
56C22⋊Dic47D412yes—
57#10625337—24no—
58#10625335—24no—
59(C2×D47)⋊C4—24no—
60C4⋊Dic47D412yes—
61Dic47⋊C4—24no—
62C4×Dic47—24no—
63C4×Dic47C2312yes—
64#10625329—22no—
65C2×C47⋊C8C2312yes—
66#10625325—28no—
67C23×C47—21no—
68C23×C47C2×D411yescharacteristic
69C22×D47—22no—
70C22×D47—42no—
71C22×D47—82no—
72Q8×C47—21no—
73Q8×C47—21no—
74D4×C47—21no—
75D4×C47—21no—
76D4×C47—42no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—42no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D412yes—
82C2×C4×C47#4112yes—
83C2×C4×C47C2411yescharacteristic
84C22⋊D47—84no—
85C2×Dic47—24no—
86C2×Dic47—22no—
87C2×Dic47C2×D414yes—
88D188—22no—
89D188—22no—
90D188—42no—
91Dic94—24no—
92Dic94—22no—
93Dic94C2×D414yes—
94C8×C47—22no—
95C47⋊C8—22no—
96C22×C47—22no—
97C22×C47—41no—
98C22×C47—42no—
99C22×C47#12112yes—
100C22×C47C22×D411yescharacteristic
101C2×D47—42no—
102C2×D47—44no—
103C2×D47—84no—
104C4×C47—41no—
105C4×C47—42no—
106C4×C47#12112yes—
107C4×C47C22×D411yescharacteristic
108C4×C47C2×#4111yescharacteristic
109Dic47—24no—
110Dic47—24no—
111#3043—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47—81no—
114C2×C47C2×#12111yescharacteristic
115C2×C47#57712yes—
116D47—82no—
117C2×#137—471no—
118C22×SD16—471no—
119#535—471no—
120#519—471no—
121#464—474no—
122#460—474no—
123#424—471no—
124#418—471no—
125#416D4711yescharacteristic, complemented
126C47#304311yescharacteristic, complemented, Sylow
127C2×#41C2×D4711yescharacteristic
128C22×Q8—471no—
129C22×D4—471no—
130#137—944no—
131C2×Q16—472no—
132C2×SD16—472no—
133C2×SD16—474no—
134C2×SD16—944no—
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—942no—
145#117C2×D4711yescharacteristic
146C4⋊C8—474no—
147#103C2×D4712yescomplemented
148#102—474no—
149#102C2×D4712yescomplemented
150C24—941no—
151#41—22no—
152#41—22no—
153C2×Q8—474no—
154C2×Q8—472no—
155C2×Q8—942no—
156C2×Q8—941no—
157C2×Q8C22×D4711yescharacteristic
158C2×D4—21no—
159C2×D4—472no—
160C2×D4—944no—
161C2×D4—942no—
162C2×D4—942no—
163C2×D4—941no—
164C2×D4C22×D4711yescharacteristic
165C22×C4—21no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168Q16—944no—
169SD16—948no—
170SD16—944no—
171M16—942no—
172C2×C8—22no—
173C2×C8—472no—
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—21no—
185C23—942no—
186C23—3762no—
187C23—1882no—
188C23D4×D4711yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—474no—
192Q8—944no—
193Q8—942no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—942no—
198D4—942no—
199D4—3764no—
200D4—1882no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—474no—
205C2×C4—944no—
206C2×C4—942no—
207C2×C4#1062535012yes—
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4712yes—
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—942no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—3764no—
217C22—1882no—
218C22—1884no—
219C22#1309399712yes—
220C22C2×D4×D4711yescharacteristic
221C4—41no—
222C4—42no—
223C4—944no—
224C4—944no—
225C4#1309399712yes—
226C4C2×D4×D4711yescharacteristic
227C4C2×#1062535011yescharacteristic
228C2—22no—
229C2—81no—
230C2—3762no—
231C2C2×#1309399711yescharacteristic
232C2#1568993012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#416C2
socleC22×C47C22×D4
hypercenter#416D47
hypocenterC47#3043
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#13094054C2semidirect
2. C22×#10625325C2semidirect
4. #15689600C2semidirect
5. #15689348C2semidirect
6. #15689322C2semidirect
7. #15689149C2semidirect
8. #15689127C2semidirect
9. C47×#416C2semidirect
13. C2×#10625337C22semidirect
16. C2×#10625335C22semidirect
23. #13093989C22semidirect
26. Dic47⋊C8C22semidirect
31. #103×C47C22semidirect
32. #102×C47C22semidirect
49. C2×Dic94D4semidirect
125. #416D47semidirect
126. C47#3043semidirect
147. #103C2×D47semidirect
149. #102C2×D47semidirect