Finite Group Databasebeta

← #20252896

Subgroups — #20252896

Order 6016.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 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
1C2×#13094049C211yesmaximal, characteristic
2C22×#10625336C211yesmaximal, characteristic, complemented
3#15689597C211yesmaximal, characteristic, complemented
4#15689335C214yesmaximal, complemented
5#15689325C214yesmaximal, complemented
6#15689150C211yesmaximal, characteristic, complemented
7#15689132C211yesmaximal, characteristic, complemented
8#15689119C211yesmaximal, characteristic, complemented
9C47×#536C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11#13094049—24no—
12C2×#10625336—24no—
13C2×#10625336C2212yes—
14C2×#10625336C2214yes—
15C2×#10625334C2212yes—
16C2×#10625329C2211yescharacteristic
17C22×C47⋊C8C2211yescharacteristic
18C4×D188C2214yes—
19#13093986—22no—
20#13093983C2211yescharacteristic
21C22⋊C4×D47—22no—
22C4⋊(C47⋊C8)C2214yescomplemented
23#13093948C2212yescomplemented
24#13093948C2214yescomplemented
25#13093945C2212yescomplemented
26C2×#41×C47C2211yescharacteristic
27C22×Q8×C47C2211yescharacteristic
28C4⋊Q8×C47C2212yescomplemented
29#124×C47C2212yescomplemented
30#123×C47—22no—
31C22⋊Q8×C47—22no—
32#117×C47C2211yescharacteristic
33C23×D47—21no—
34#41×C47—22no—
35#41×C47—22no—
36C2×Q8×C47—21no—
37C2×Q8×C47—22no—
38C2×Q8×C47—22no—
39C2×Q8×C47C2312yes—
40C2×Q8×C47C2311yescharacteristic
41C2×D4×C47—21no—
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C2×D188—21no—
47C2×D188—22no—
48C2×D188D414yes—
49C2×D188C2312yes—
50C2×C4×D47—24no—
51C4⋊C4×C47—24no—
52C4⋊C4×C47D412yes—
53C22⋊C4×C47—24no—
54C22⋊C4×C47D412yes—
55C42×C47C2312yes—
56C22⋊Dic47—21no—
57#10625336—28no—
58#10625336—24no—
59#10625334—24no—
60(C2×D47)⋊C4—24no—
61C4⋊Dic47C2312yes—
62C4×Dic47—21no—
63#10625329—22no—
64C2×C47⋊C8—22no—
65C2×C47⋊C8C2312yes—
66C2×C47⋊C8C2312yes—
67C23×C47—21no—
68C23×C47C2×D411yescharacteristic
69C22×D47—22no—
70C22×D47—24no—
71C22×D47—82no—
72Q8×C47—22no—
73Q8×C47—21no—
74Q8×C47—22no—
75Q8×C47—21no—
76Q8×C47—42no—
77D4×C47—21no—
78D4×C47—21no—
79D4×C47—42no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—42no—
83C2×C4×C47—42no—
84C2×C4×C47C2×D412yes—
85C2×C4×C47C2×D414yes—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47#4112yes—
88C2×C4×C47C2411yescharacteristic
89C2×Dic47—22no—
90D188—24no—
91D188—22no—
92D188C2×D414yes—
93C4×D47—84no—
94C47⋊C8—22no—
95C47⋊C8—22no—
96C22×C47—22no—
97C22×C47—41no—
98C22×C47—42no—
99C22×C47#12112yes—
100C22×C47C22×D411yescharacteristic
101C2×D47—24no—
102C2×D47—44no—
103C2×D47—84no—
104C4×C47—24no—
105C4×C47—41no—
106C4×C47—42no—
107C4×C47#12112yes—
108C4×C47C22×D411yescharacteristic
109C4×C47C2×#4111yescharacteristic
110Dic47—42no—
111#3042—471nomaximal, Sylow
112C2×C47—22no—
113C2×C47—81no—
114C2×C47C2×#12111yescharacteristic
115C2×C47#57712yes—
116D47—44no—
117C2×AGL(1,ℤ/8)—471no—
118C22×SD16—471no—
119#536D4711yescharacteristic, complemented
120#518—471no—
121#463—474no—
122#461—474no—
123#424—471no—
124#419—471no—
125#416—471no—
126C47#304211yescharacteristic, complemented, Sylow
127C2×#41C2×D4711yescharacteristic
128C22×Q8C2×D4711yescharacteristic
129C22×D4—471no—
130AGL(1,ℤ/8)—944no—
131C2×SD16—474no—
132C2×SD16—472no—
133C2×SD16—944no—
134C2×D8—472no—
135C2×M16—471no—
136C22×C8—471no—
137C4⋊Q8C2×D4712yescomplemented
138#124C2×D4712yescomplemented
139#123—22no—
140C22⋊Q8—22no—
141C4×D4—474no—
142C4×D4—942no—
143#117—471no—
144#117C2×D4711yescharacteristic
145C2×C22⋊C4—942no—
146C4⋊C8—474no—
147#103—472no—
148#103—474no—
149#102—472no—
150C24—941no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8C22×D4712yes—
157C2×Q8C22×D4711yescharacteristic
158C2×D4—21no—
159C2×D4—474no—
160C2×D4—472no—
161C2×D4—942no—
162C2×D4—941no—
163C2×D4C22×D4711yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—944no—
167C22×C4C22×D4711yescharacteristic
168SD16—948no—
169SD16—944no—
170D8—944no—
171M16—942no—
172C2×C8—472no—
173C2×C8—472no—
174C2×C8—942no—
175C4⋊C4—24no—
176C4⋊C4—472no—
177C4⋊C4C22⋊D4712yes—
178C22⋊C4—24no—
179C22⋊C4—941no—
180C22⋊C4—944no—
181C22⋊C4C22⋊D4712yes—
182C42—941no—
183C42C22×D4712yes—
184C23—21no—
185C23—944no—
186C23—942no—
187C23—3762no—
188C23C2×C22⋊D4711yescharacteristic
189Q8—22no—
190Q8—21no—
191Q8—22no—
192Q8—21no—
193Q8—42no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—474no—
198D4—944no—
199D4—942no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—942no—
205C2×C4—3764no—
206C2×C4D4×D4712yes—
207C2×C4#1062535212yes—
208C2×C4C2×C22⋊D4714yes—
209C2×C4C2×C22⋊D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—942no—
212C8—942no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—944no—
217C22—3764no—
218C22—1884no—
219C22#1309399512yes—
220C22C22×C22⋊D4711yescharacteristic
221C4—24no—
222C4—41no—
223C4—42no—
224C4—1882no—
225C4#1309399512yes—
226C4C2×D4×D4711yescharacteristic
227C4C2×#1062535211yescharacteristic
228C2—22no—
229C2—81no—
230C2—1884no—
231C2C2×#1309399511yescharacteristic
232C2#1568993112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#536C2
socleC22×C47C22×D4
hypercenter#536D47
hypocenterC47#3042
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C22×#10625336C2semidirect
3. #15689597C2semidirect
4. #15689335C2semidirect
5. #15689325C2semidirect
6. #15689150C2semidirect
7. #15689132C2semidirect
8. #15689119C2semidirect
9. C47×#536C2semidirect
22. C4⋊(C47⋊C8)C22semidirect
23. #13093948C22semidirect
24. #13093948C22semidirect
25. #13093945C22semidirect
28. C4⋊Q8×C47C22semidirect
29. #124×C47C22semidirect
119. #536D47semidirect
126. C47#3042semidirect
137. C4⋊Q8C2×D47semidirect
138. #124C2×D47semidirect