Finite Group Databasebeta

← #20252909

Subgroups — #20252909

Order 6016.

490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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
2C22×#10625336C211yesmaximal, characteristic, complemented
3#15689692C211yesmaximal, characteristic
4#15689345C214yesmaximal, complemented
5#15689323C214yesmaximal, complemented
6#15689150C211yesmaximal, characteristic, complemented
7#15689127C211yesmaximal, characteristic, complemented
8#15689117C211yesmaximal, characteristic, complemented
9C47×#519C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C22×D188C2211yescharacteristic
12#13094055—24no—
13C2×#10625337C2212yescomplemented
14C2×#10625336—24no—
15C2×#10625336C2214yes—
16C2×#10625336C2212yescomplemented
17C2×#10625329C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094021C2212yes—
20#13094012C2212yes—
21#13093999—22no—
22#13093994—22no—
23C4⋊(C47⋊C8)C2214yescomplemented
24#13093947C2212yescomplemented
25#13093944C2214yes—
26#13093944C2212yescomplemented
27C22×Q8×C47C2211yescharacteristic
28C4×Q8×C47—22no—
29C4×Q8×C47C2214yescomplemented
30#117×C47—22no—
31#117×C47C2211yescharacteristic
32#117×C47C2211yescharacteristic
33C23×D47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47—22no—
36C2×Q8×C47D414yescomplemented
37C2×Q8×C47C2312yes—
38C22×C4×C47—21no—
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—21no—
41#10625350—22no—
42#10625350—22no—
43C2×D188—22no—
44C2×D188—22no—
45C2×D188—21no—
46C2×D188—24no—
47C2×D188C2312yes—
48C2×D188C2311yescharacteristic
49C2×C4×D47—21no—
50C2×Dic94C2311yescharacteristic
51C4⋊C4×C47—24no—
52C4⋊C4×C47D412yes—
53C4⋊C4×C47C2312yes—
54C22⋊C4×C47—21no—
55C22⋊C4×C47D412yes—
56C42×C47—24no—
57C42×C47—21no—
58C42×C47C2312yes—
59#10625337—24no—
60#10625336—28no—
61#10625336—24no—
62(C2×D47)⋊C4—24no—
63#10625329—22no—
64C2×C47⋊C8—22no—
65C2×C47⋊C8C2312yes—
66C2×C47⋊C8C2312yes—
67C23×C47C2×D411yescharacteristic
68C22×D47—22no—
69C22×D47—21no—
70C22×D47—42no—
71C22×D47—82no—
72Q8×C47—24no—
73Q8×C47—22no—
74Q8×C47C2×D414yes—
75C2×C4×C47—24no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×D414yes—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47#4112yes—
82C2×C4×C47C2411yescharacteristic
83C22⋊D47—42no—
84C2×Dic47—21no—
85D188—22no—
86D188—21no—
87D188—22no—
88D188—21no—
89D188—42no—
90D188—84no—
91C4×D47—42no—
92Dic94—21no—
93Dic94—21no—
94C47⋊C8—22no—
95C47⋊C8—22no—
96C22×C47—22no—
97C22×C47#12112yes—
98C22×C47C22×D411yescharacteristic
99C2×D47—41no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—44no—
103C2×D47—84no—
104C4×C47—24no—
105C4×C47—24no—
106C4×C47—42no—
107C4×C47#12112yes—
108C4×C47C22×D411yescharacteristic
109C4×C47C2×#4111yescharacteristic
110Dic47—41no—
111#3043—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47C2×#12111yescharacteristic
114C2×C47#57712yes—
115D47—81no—
116D47—82no—
117C2×#137—471no—
118C22×SD16—471no—
119#535—471no—
120#519D4711yescharacteristic, complemented
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×D4—471no—
130#137—944no—
131C2×Q16—472no—
132C2×SD16—474no—
133C2×SD16—472no—
134C2×SD16—944no—
135C2×M16—471no—
136C22×C8—471no—
137#127—472no—
138#124—472no—
139#121—942no—
140#120—942no—
141C4×Q8—22no—
142C4×Q8C2×D4714yescomplemented
143#117—22no—
144#117C2×D4711yescharacteristic
145#117C2×D4711yescharacteristic
146C4⋊C8—474no—
147#103—472no—
148#102—474no—
149#102—472no—
150C24—941no—
151#41—942no—
152#41—942no—
153C2×Q8—22no—
154C2×Q8—21no—
155C2×Q8—471no—
156C2×Q8D18814yescomplemented
157C2×Q8C22×D4712yes—
158C2×D4—472no—
159C2×D4—471no—
160C2×D4—941no—
161C2×D4—942no—
162C2×D4—942no—
163C2×D4—944no—
164C2×D4—941no—
165C22×C4—21no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168Q16—944no—
169SD16—948no—
170SD16—944no—
171M16—942no—
172C2×C8—472no—
173C2×C8—472no—
174C2×C8—942no—
175C4⋊C4—24no—
176C4⋊C4C22⋊D4712yes—
177C4⋊C4C22×D4712yes—
178C22⋊C4—21no—
179C22⋊C4—944no—
180C22⋊C4C22⋊D4712yes—
181C42—24no—
182C42—21no—
183C42C22×D4712yes—
184C23—942no—
185C23—941no—
186C23—3762no—
187C23—1882no—
188C23C2×C22⋊D4711yescharacteristic
189Q8—24no—
190Q8—22no—
191Q8—941no—
192Q8—941no—
193Q8C2×D18814yes—
194D4—942no—
195D4—941no—
196D4—942no—
197D4—941no—
198D4—3764no—
199D4—1882no—
200D4—1882no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—941no—
205C2×C4—1882no—
206C2×C4C2×D18812yes—
207C2×C4#1062535012yes—
208C2×C4C2×C22⋊D4714yes—
209C2×C4C2×C22⋊D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—942no—
212C8—942no—
213C22—22no—
214C22—3764no—
215C22—1881no—
216C22—1882no—
217C22—1882no—
218C22—1884no—
219C22#1309399812yes—
220C22C22×C22⋊D4711yescharacteristic
221C4—24no—
222C4—24no—
223C4—42no—
224C4—1881no—
225C4#1309399812yes—
226C4C22×D18811yescharacteristic
227C4C2×#1062535011yescharacteristic
228C2—22no—
229C2—3762no—
230C2—3761no—
231C2C2×#1309399811yescharacteristic
232C2#1568993112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#519C2
socleC22×C47C22×D4
hypercenter#519D47
hypocenterC47#3043
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
2. C22×#10625336C2semidirect
4. #15689345C2semidirect
5. #15689323C2semidirect
6. #15689150C2semidirect
7. #15689127C2semidirect
8. #15689117C2semidirect
9. C47×#519C2semidirect
13. C2×#10625337C22semidirect
16. C2×#10625336C22semidirect
23. C4⋊(C47⋊C8)C22semidirect
24. #13093947C22semidirect
26. #13093944C22semidirect
29. C4×Q8×C47C22semidirect
36. C2×Q8×C47D4semidirect
120. #519D47semidirect
126. C47#3043semidirect
142. C4×Q8C2×D47semidirect
156. C2×Q8D188semidirect