Finite Group Databasebeta

← #20252903

Subgroups — #20252903

Order 6016.

494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 494 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×#13094049C211yesmaximal, characteristic
2C22×#10625325C211yesmaximal, characteristic, complemented
3#15689694C211yesmaximal, characteristic, complemented
4#15689597C211yesmaximal, characteristic, complemented
5#15689337C214yesmaximal, complemented
6#15689327C214yesmaximal, complemented
7#15689149C211yesmaximal, characteristic, complemented
8#15689131C211yesmaximal, characteristic, complemented
9C47×#416C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12#13094049—24no—
13C2×#10625325—24no—
14C2×#10625325C2214yes—
15C2×#10625336C2212yes—
16C2×#10625334C2212yes—
17C2×#10625329C2211yescharacteristic
18#13094022C2212yescomplemented
19#13094011C2212yescomplemented
20#13094005—22no—
21#13094003—22no—
22C4×D188—22no—
23#13093986C2214yes—
24#13093983C2211yescharacteristic
25C22⋊C4×D47—22no—
26Dic47⋊C8C2214yescomplemented
27#13093947C2214yescomplemented
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
41C22×Dic47—21no—
42C2×D188—21no—
43C2×D188—22no—
44C2×D188D414yes—
45C2×D188C2312yes—
46C2×C4×D47—24no—
47C2×Dic94—22no—
48C2×Dic94—22no—
49C2×Dic94—21no—
50C2×Dic94C2312yes—
51C2×C8×C47—22no—
52C2×C8×C47C2312yes—
53C4⋊C4×C47C2312yes—
54C22⋊C4×C47—21no—
55C42×C47—21no—
56C22⋊Dic47—24no—
57C22⋊Dic47D412yes—
58#10625336—24no—
59#10625334—24no—
60(C2×D47)⋊C4—24no—
61C4⋊Dic47D412yes—
62Dic47⋊C4—24no—
63C4×Dic47C2312yes—
64#10625329—22no—
65C2×C47⋊C8C2312yes—
66#10625325—28no—
67C23×C47—21no—
68C23×C47C2×D411yescharacteristic
69C22×D47—22no—
70C22×D47—24no—
71C22×D47—82no—
72Q8×C47—21no—
73Q8×C47—21no—
74D4×C47—21no—
75D4×C47—21no—
76D4×C47—42no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47—42no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D412yes—
82C2×C4×C47#4112yes—
83C2×C4×C47C2411yescharacteristic
84C2×Dic47—22no—
85C2×Dic47—42no—
86C2×Dic47C2×D414yes—
87D188—24no—
88D188—22no—
89D188C2×D414yes—
90C4×D47—84no—
91Dic94—22no—
92Dic94—22no—
93Dic94—42no—
94C8×C47—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—41no—
105C4×C47—42no—
106C4×C47#12112yes—
107C4×C47C22×D411yescharacteristic
108C4×C47C2×#4111yescharacteristic
109Dic47—24no—
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#536—471no—
120#518—471no—
121#463—474no—
122#461—474no—
123#424—471no—
124#419—471no—
125#416D4711yescharacteristic, complemented
126C47#304211yescharacteristic, complemented, Sylow
127C2×#41C2×D4711yescharacteristic
128C22×Q8—471no—
129C22×D4—471no—
130AGL(1,ℤ/8)—944no—
131C2×SD16—472no—
132C2×SD16—474no—
133C2×SD16—944no—
134C2×D8—472no—
135C2×M16—471no—
136C22×C8C2×D4711yescharacteristic
137C4⋊Q8—472no—
138#124—472no—
139#123—942no—
140C22⋊Q8—942no—
141C4×D4—474no—
142C4×D4—942no—
143#117—471no—
144#117C2×D4711yescharacteristic
145C2×C22⋊C4—942no—
146C4⋊C8—474no—
147#103—474no—
148#103C2×D4712yescomplemented
149#102C2×D4712yescomplemented
150C24—941no—
151#41—22no—
152#41—22no—
153C2×Q8—472no—
154C2×Q8—941no—
155C2×Q8—942no—
156C2×Q8—942no—
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—944no—
166C22×C4—941no—
167C22×C4C22×D4711yescharacteristic
168SD16—948no—
169SD16—944no—
170D8—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—
181C22⋊C4—944no—
182C42—21no—
183C42—472no—
184C23—21no—
185C23—944no—
186C23—942no—
187C23—3762no—
188C23D4×D4711yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—942no—
192Q8—942no—
193Q8—1882no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—474no—
198D4—944no—
199D4—942no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—474no—
204C2×C4—942no—
205C2×C4—3764no—
206C2×C4—1882no—
207C2×C4#1062535012yes—
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4712yes—
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—942no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—944no—
217C22—3764no—
218C22—1884no—
219C22#1309399712yes—
220C22C2×D4×D4711yescharacteristic
221C4—41no—
222C4—42no—
223C4—944no—
224C4—1882no—
225C4#1309399712yes—
226C4C2×D4×D4711yescharacteristic
227C4C2×#1062535011yescharacteristic
228C2—22no—
229C2—81no—
230C2—1884no—
231C2C2×#1309399711yescharacteristic
232C2#1568993012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#416C2
socleC22×C47C22×D4
hypercenter#416D47
hypocenterC47#3042
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
2. C22×#10625325C2semidirect
3. #15689694C2semidirect
4. #15689597C2semidirect
5. #15689337C2semidirect
6. #15689327C2semidirect
7. #15689149C2semidirect
8. #15689131C2semidirect
9. C47×#416C2semidirect
18. #13094022C22semidirect
19. #13094011C22semidirect
26. Dic47⋊C8C22semidirect
27. #13093947C22semidirect
31. #103×C47C22semidirect
32. #102×C47C22semidirect
125. #416D47semidirect
126. C47#3042semidirect
148. #103C2×D47semidirect
149. #102C2×D47semidirect