Finite Group Databasebeta

← #20252900

Subgroups — #20252900

Order 6016.

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

normal subgroups only

This group has 494 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×#13094050C211yesmaximal, characteristic
2C22×#10625335C211yesmaximal, characteristic, complemented
3#15689699C211yesmaximal, characteristic, complemented
4#15689338C214yesmaximal, complemented
5#15689328C214yesmaximal, complemented
6#15689150C211yesmaximal, characteristic, complemented
7#15689131C211yesmaximal, characteristic, complemented
8#15689117C211yesmaximal, characteristic, complemented
9C47×#518C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C22×Dic94C2211yescharacteristic
12#13094050—24no—
13C2×#10625335—24no—
14C2×#10625335C2212yes—
15C2×#10625335C2214yes—
16C2×#10625334C2212yes—
17C2×#10625329C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094024C2212yescomplemented
20#13094012C2212yescomplemented
21#13094008—22no—
22#13094004—22no—
23C4⋊(C47⋊C8)C2214yescomplemented
24#13093947C2212yescomplemented
25#13093947C2214yescomplemented
26#13093944C2212yescomplemented
27C22×D4×C47C2211yescharacteristic
28C4×D4×C47—22no—
29C4×D4×C47C2214yes—
30#117×C47C2211yescharacteristic
31#117×C47C2211yescharacteristic
32C2×C22⋊C4×C47—22no—
33C24×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47—22no—
36C2×D4×C47D414yes—
37C2×D4×C47C2312yes—
38C22×C4×C47—24no—
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—21no—
41C22×Dic47—21no—
42#10625350—22no—
43#10625350—22no—
44C2×D188C2311yescharacteristic
45C2×C4×D47—21no—
46C2×Dic94—22no—
47C2×Dic94—22no—
48C2×Dic94—21no—
49C2×Dic94C2312yes—
50C2×Dic94C2311yescharacteristic
51C4⋊C4×C47D412yes—
52C4⋊C4×C47C2312yes—
53C22⋊C4×C47—21no—
54C22⋊C4×C47—24no—
55C22⋊C4×C47D412yes—
56C42×C47—21no—
57C42×C47C2312yes—
58#10625335—28no—
59#10625335—24no—
60#10625334—24no—
61(C2×D47)⋊C4—24no—
62C4⋊Dic47—24no—
63#10625329—22no—
64C2×C47⋊C8—22no—
65C2×C47⋊C8C2312yes—
66C2×C47⋊C8C2312yes—
67C23×C47—22no—
68C23×C47—24no—
69C23×C47—82no—
70C23×C47C2×D411yescharacteristic
71C22×D47—21no—
72D4×C47—24no—
73D4×C47—22no—
74D4×C47C2×D414yes—
75C2×C4×C47—22no—
76C2×C4×C47—84no—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×D414yes—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47#4112yes—
81C2×C4×C47C2411yescharacteristic
82C22⋊D47—42no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—42no—
86D188—21no—
87D188—21no—
88C4×D47—42no—
89Dic94—22no—
90Dic94—21no—
91Dic94—22no—
92Dic94—21no—
93Dic94—42no—
94C47⋊C8—22no—
95C47⋊C8—22no—
96C22×C47—22no—
97C22×C47—24no—
98C22×C47—44no—
99C22×C47—84no—
100C22×C47#12112yes—
101C22×C47C22×D411yescharacteristic
102C2×D47—41no—
103C2×D47—42no—
104C4×C47—24no—
105C4×C47—42no—
106C4×C47#12112yes—
107C4×C47C22×D411yescharacteristic
108C4×C47C2×#4111yescharacteristic
109Dic47—42no—
110Dic47—41no—
111#3042—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47—44no—
114C2×C47C2×#12111yescharacteristic
115C2×C47#57712yes—
116D47—81no—
117C2×AGL(1,ℤ/8)—471no—
118C22×SD16—471no—
119#536—471no—
120#518D4711yescharacteristic, complemented
121#463—474no—
122#461—474no—
123#424—471no—
124#419—471no—
125#416—471no—
126C47#304211yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C22×Q8—471no—
129C22×D4C2×D4711yescharacteristic
130AGL(1,ℤ/8)—944no—
131C2×SD16—474no—
132C2×SD16—472no—
133C2×SD16—944no—
134C2×D8—472no—
135C2×M16—471no—
136C22×C8—471no—
137C4⋊Q8—472no—
138#124—472no—
139#123—942no—
140C22⋊Q8—942no—
141C4×D4—22no—
142C4×D4C2×D4714yes—
143#117C2×D4711yescharacteristic
144#117C2×D4711yescharacteristic
145C2×C22⋊C4—22no—
146C4⋊C8—474no—
147#103—472no—
148#103—474no—
149#102—472no—
150C24—21no—
151#41—942no—
152#41—942no—
153C2×Q8—472no—
154C2×Q8—471no—
155C2×Q8—941no—
156C2×Q8—942no—
157C2×Q8—942no—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—471no—
161C2×D4—941no—
162C2×D4D18814yes—
163C2×D4C22×D4712yes—
164C22×C4—24no—
165C22×C4—941no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168SD16—948no—
169SD16—944no—
170D8—944no—
171M16—942no—
172C2×C8—472no—
173C2×C8—472no—
174C2×C8—942no—
175C4⋊C4—944no—
176C4⋊C4C22⋊D4712yes—
177C4⋊C4C22×D4712yes—
178C22⋊C4—21no—
179C22⋊C4—24no—
180C22⋊C4—944no—
181C22⋊C4C22⋊D4712yes—
182C42—21no—
183C42C22×D4712yes—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—941no—
188C23C2×C22⋊D4711yescharacteristic
189Q8—942no—
190Q8—941no—
191Q8—942no—
192Q8—941no—
193Q8—1882no—
194D4—24no—
195D4—22no—
196D4—941no—
197D4—941no—
198D4—1882no—
199D4C2×D18814yes—
200C2×C4—22no—
201C2×C4—84no—
202C2×C4—942no—
203C2×C4—941no—
204C2×C4—1882no—
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—24no—
215C22—44no—
216C22—84no—
217C22—1881no—
218C22—1882no—
219C22#1309399812yes—
220C22C22×C22⋊D4711yescharacteristic
221C4—24no—
222C4—42no—
223C4—1881no—
224C4—1882no—
225C4#1309399812yes—
226C4C22×D18811yescharacteristic
227C4C2×#1062535011yescharacteristic
228C2—22no—
229C2—44no—
230C2—3761no—
231C2C2×#1309399811yescharacteristic
232C2#1568993412yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#518C2
socleC22×C47C22×D4
hypercenter#518D47
hypocenterC47#3042
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C22×#10625335C2semidirect
3. #15689699C2semidirect
4. #15689338C2semidirect
5. #15689328C2semidirect
6. #15689150C2semidirect
7. #15689131C2semidirect
8. #15689117C2semidirect
9. C47×#518C2semidirect
19. #13094024C22semidirect
20. #13094012C22semidirect
23. C4⋊(C47⋊C8)C22semidirect
24. #13093947C22semidirect
25. #13093947C22semidirect
26. #13093944C22semidirect
120. #518D47semidirect
126. C47#3042semidirect