Finite Group Databasebeta

← #20252911

Subgroups — #20252911

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
1C22×#10625336C211yesmaximal, characteristic, complemented
2#15689687C211yesmaximal, characteristic
3#15689601C211yesmaximal, characteristic, complemented
4#15689347C214yesmaximal, complemented
5#15689321C214yesmaximal, complemented
6#15689151C211yesmaximal, characteristic, complemented
7#15689129C211yesmaximal, characteristic, complemented
8#15689119C211yesmaximal, characteristic, complemented
9C2×#137×C47C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C2×#10625336—24no—
12C2×#10625336C2214yes—
13C22×C47⋊C8C2211yescharacteristic
14#13094020C2212yes—
15#13094013C2212yes—
16#13093998—22no—
17#13093992—22no—
18Q8×Dic47—22no—
19Q8×Dic47C2214yescomplemented
20#13093983—22no—
21#13093983C2211yescharacteristic
22#13093983C2211yescharacteristic
23Dic47⋊C8C2214yescomplemented
24#13093948C2212yescomplemented
25#13093946C2214yes—
26#13093945C2212yescomplemented
27C2×#41×C47C2211yescharacteristic
28C22×Q8×C47C2211yescharacteristic
29#137×C47—24no—
30C2×Q16×C47C2212yescomplemented
31C2×SD16×C47C2212yescomplemented
32C2×M16×C47C2211yescharacteristic
33C23×D47—21no—
34#41×C47—22no—
35#41×C47—22no—
36C2×Q8×C47—21no—
37C2×Q8×C47—22no—
38C2×Q8×C47D414yescomplemented
39C2×Q8×C47C2311yescharacteristic
40C2×Q8×C47C2312yes—
41C2×D4×C47—21no—
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—24no—
47C2×D188—22no—
48C2×D188—22no—
49C2×D188—21no—
50C2×D188C2312yes—
51Q16×C47—24no—
52SD16×C47—24no—
53M16×C47—22no—
54C2×C8×C47C2312yes—
55C22⋊Dic47—21no—
56C22⋊Dic47D412yes—
57#10625336—28no—
58(C2×D47)⋊C4—24no—
59C4⋊Dic47—24no—
60C4⋊Dic47D412yes—
61C4⋊Dic47C2312yes—
62C4×Dic47—21no—
63C4×Dic47—24no—
64C4×Dic47C2312yes—
65C2×C47⋊C8—22no—
66C2×C47⋊C8C2312yes—
67C23×C47—21no—
68C23×C47C2×D411yescharacteristic
69C22×D47—22no—
70C22×D47—42no—
71C22×D47—82no—
72Q8×C47—24no—
73Q8×C47—22no—
74Q8×C47—21no—
75Q8×C47—21no—
76Q8×C47C2×D414yes—
77D4×C47—21no—
78D4×C47—21no—
79D4×C47—42no—
80C2×C4×C47—24no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—42no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D412yes—
86C2×C4×C47#4112yes—
87C2×C4×C47C2411yescharacteristic
88C22⋊D47—84no—
89C2×Dic47—22no—
90C2×Dic47C2×D414yes—
91D188—22no—
92D188—22no—
93D188—42no—
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—24no—
105C4×C47—41no—
106C4×C47#12112yes—
107C4×C47C22×D411yescharacteristic
108C4×C47C2×#4111yescharacteristic
109Dic47—24no—
110Dic47—42no—
111#3043—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47—81no—
114C2×C47C2×#12111yescharacteristic
115C2×C47#57712yes—
116D47—82no—
117C2×#137D4711yescharacteristic, complemented
118C22×SD16—471no—
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×#41C2×D4711yescharacteristic
128C22×Q8C2×D4711yescharacteristic
129C22×D4—471no—
130#137—24no—
131C2×Q16C2×D4712yescomplemented
132C2×SD16—474no—
133C2×SD16—944no—
134C2×SD16C2×D4712yescomplemented
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—471no—
145#117—942no—
146C4⋊C8—474no—
147#103—472no—
148#102—472no—
149#102—474no—
150C24—941no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8C22⋊D4714yescomplemented
156C2×Q8C22×D4711yescharacteristic
157C2×Q8C22×D4712yes—
158C2×D4—21no—
159C2×D4—472no—
160C2×D4—944no—
161C2×D4—941no—
162C2×D4—942no—
163C2×D4—942no—
164C2×D4C22×D4711yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C22×D4711yescharacteristic
168Q16—24no—
169SD16—24no—
170SD16—948no—
171M16—22no—
172C2×C8—472no—
173C2×C8—942no—
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—21no—
185C23—942no—
186C23—3762no—
187C23—1882no—
188C23D4×D4711yescharacteristic
189Q8—24no—
190Q8—22no—
191Q8—21no—
192Q8—21no—
193Q8C2×C22⋊D4714yes—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—942no—
198D4—942no—
199D4—3764no—
200D4—1882no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—474no—
206C2×C4—942no—
207C2×C4D4×D4711yescharacteristic
208C2×C4#1062535212yes—
209C2×C4C2×C22⋊D4712yes—
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—942no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—3764no—
217C22—1882no—
218C22—1884no—
219C22#1309399612yes—
220C22C2×D4×D4711yescharacteristic
221C4—24no—
222C4—41no—
223C4—944no—
224C4—1882no—
225C4#1309399612yes—
226C4C22×C22⋊D4711yescharacteristic
227C4C2×#1062535211yescharacteristic
228C2—22no—
229C2—81no—
230C2—3762no—
231C2C2×#1309399611yescharacteristic
232C2#1568993212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#137×C47C2
socleC22×C47C22×D4
hypercenterC2×#137D47
hypocenterC47#3043
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#10625336C2semidirect
3. #15689601C2semidirect
4. #15689347C2semidirect
5. #15689321C2semidirect
6. #15689151C2semidirect
7. #15689129C2semidirect
8. #15689119C2semidirect
9. C2×#137×C47C2semidirect
19. Q8×Dic47C22semidirect
23. Dic47⋊C8C22semidirect
24. #13093948C22semidirect
26. #13093945C22semidirect
30. C2×Q16×C47C22semidirect
31. C2×SD16×C47C22semidirect
38. C2×Q8×C47D4semidirect
117. C2×#137D47semidirect
126. C47#3043semidirect
131. C2×Q16C2×D47semidirect
134. C2×SD16C2×D47semidirect
155. C2×Q8C22⋊D47semidirect