Finite Group Databasebeta

← #20252885

Subgroups — #20252885

Order 6016.

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

normal subgroups only

This group has 500 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×#13094055C211yesmaximal, characteristic, complemented
2C2×#13094052C211yesmaximal, characteristic
3C2×#13094013C211yesmaximal, characteristic, complemented
4#15689591C211yesmaximal, characteristic, complemented
5#15689348C214yesmaximal, complemented
6#15689341C214yesmaximal, complemented
7#15689146C211yesmaximal, characteristic, complemented
8#15689127C211yesmaximal, characteristic, complemented
9C47×#419C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C22×D188C2211yescharacteristic
12#13094055—24no—
13#13094052—24no—
14C2×#10625337C2212yescomplemented
15C2×#10625325C2212yes—
16C2×#10625336C2212yescomplemented
17C2×D376C2212yes—
18C2×#10625329C2211yescharacteristic
19#13094013—21no—
20#13094013—21no—
21#13094013C2214yes—
22#13093989C2212yescomplemented
23#13093986C2212yescomplemented
24(C22⋊D47)⋊C4—22no—
25#13093981—21no—
26C2×(C2×D47)⋊C4—22no—
27C2×C4×Dic47C2211yescharacteristic
28C42×D47—21no—
29Dic47⋊C8C2214yescomplemented
30#13093944C2214yes—
31C22×Q8×C47C2211yescharacteristic
32C2×M16×C47C2211yescharacteristic
33#117×C47C2211yescharacteristic
34#103×C47C2214yescomplemented
35C23×D47—21no—
36C2×Q8×C47—21no—
37C2×Q8×C47—22no—
38C2×Q8×C47—22no—
39C2×Q8×C47C2312yes—
40C22×C4×C47—21no—
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—21no—
43C22×Dic47D412yes—
44#10625350—22no—
45#10625350D414yes—
46C2×D188—22no—
47C2×D188—22no—
48C2×D188—21no—
49C2×D188C2312yes—
50C2×D188C2311yescharacteristic
51C2×C4×D47—21no—
52C2×C4×D47—22no—
53C2×Dic94C2311yescharacteristic
54M16×C47—22no—
55C2×C8×C47C2312yes—
56C4⋊C4×C47C2312yes—
57C22⋊C4×C47—21no—
58C42×C47—21no—
59#10625337—24no—
60#10625336—24no—
61(C2×D47)⋊C4—24no—
62(C2×D47)⋊C4—24no—
63(C2×D47)⋊C4—22no—
64Dic47⋊C4—22no—
65C4×Dic47—22no—
66C4×Dic47D411yescharacteristic
67C4×Dic47D411yescharacteristic
68C4×Dic47C2312yes—
69#10625329—22no—
70C2×C47⋊C8C2312yes—
71D376—24no—
72#10625325—24no—
73C23×C47C2×D411yescharacteristic
74C22×D47—21no—
75C22×D47—22no—
76C22×D47—44no—
77C22×D47—42no—
78Q8×C47—22no—
79Q8×C47—22no—
80Q8×C47—42no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—42no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D412yes—
86C2×C4×C47#4112yes—
87C2×C4×C47C2411yescharacteristic
88C22⋊D47—24no—
89C2×Dic47—21no—
90C2×Dic47—42no—
91C2×Dic47C2×D412yes—
92C2×Dic47C2×D412yes—
93D188—22no—
94D188—21no—
95D188—22no—
96D188—42no—
97D188C2×D412yes—
98C4×D47—24no—
99C4×D47—44no—
100Dic94—21no—
101Dic94C2×D412yes—
102C8×C47—22no—
103C47⋊C8—22no—
104C22×C47—22no—
105C22×C47#12112yes—
106C22×C47C22×D411yescharacteristic
107C2×D47—22no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—44no—
111C2×D47—84no—
112C4×C47—42no—
113C4×C47—42no—
114C4×C47#12112yes—
115C4×C47C22×D411yescharacteristic
116C4×C47C2×#4111yescharacteristic
117Dic47—22no—
118Dic47—22no—
119Dic47—22no—
120#3040—471nomaximal, Sylow
121C2×C47—22no—
122C2×C47C2×#12111yescharacteristic
123C2×C47#57512yes—
124D47—42no—
125D47—82no—
126C2×#137—471no—
127C2×AGL(1,ℤ/8)—471no—
128C2×#124—471no—
129C4×#41—471no—
130#464—474no—
131#463—474no—
132#423—471no—
133#419D4711yescharacteristic, complemented
134#418—471no—
135C47#304011yescharacteristic, complemented, Sylow
136C2×#41—471no—
137C22×Q8C2×D4711yescharacteristic
138C22×D4—471no—
139#137—944no—
140AGL(1,ℤ/8)—944no—
141C2×Q16—472no—
142C2×SD16—472no—
143C2×SD16—472no—
144C2×D8—472no—
145C2×M16—471no—
146C2×M16C2×D4711yescharacteristic
147#124—474no—
148#124—941no—
149#124—941no—
150C4×Q8—472no—
151C4×D4—472no—
152C4×D4—942no—
153#117—941no—
154#117C2×D4711yescharacteristic
155C2×C22⋊C4—942no—
156C2×C42—471no—
157C2×C42—941no—
158C4⋊C8—474no—
159#103C2×D4714yescomplemented
160#102—474no—
161C24—941no—
162#41—474no—
163#41—942no—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—471no—
168C2×Q8C22×D4712yes—
169C2×D4—471no—
170C2×D4—472no—
171C2×D4—941no—
172C2×D4—942no—
173C2×D4—942no—
174C2×D4—941no—
175C22×C4—21no—
176C22×C4—472no—
177C22×C4—942no—
178C22×C4—941no—
179C22×C4C22×D4711yescharacteristic
180Q16—944no—
181SD16—944no—
182SD16—944no—
183D8—944no—
184M16—22no—
185M16—942no—
186C2×C8—472no—
187C2×C8C22×D4712yes—
188C4⋊C4—942no—
189C4⋊C4C22×D4712yes—
190C22⋊C4—21no—
191C22⋊C4—944no—
192C22⋊C4—944no—
193C22⋊C4—942no—
194C42—21no—
195C42—471no—
196C42—471no—
197C42—472no—
198C42—942no—
199C23—941no—
200C23—942no—
201C23—1884no—
202C23—1882no—
203C23D4×D4711yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—42no—
207Q8—472no—
208Q8—941no—
209D4—472no—
210D4—944no—
211D4—942no—
212D4—941no—
213D4—942no—
214D4—1882no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—472no—
219C2×C4—472no—
220C2×C4—941no—
221C2×C4—944no—
222C2×C4—1884no—
223C2×C4—1882no—
224C2×C4#1062535012yes—
225C2×C4D4×D4711yescharacteristic
226C2×C4D4×D4712yes—
227C2×C4C23×D4711yescharacteristic
228C8—22no—
229C8—942no—
230C22—22no—
231C22—942no—
232C22—3764no—
233C22—1882no—
234C22—1884no—
235C22—1882no—
236C22#1309399712yes—
237C22C2×D4×D4711yescharacteristic
238C4—42no—
239C4—42no—
240C4—942no—
241C4—942no—
242C4—942no—
243C4#1309399712yes—
244C4C2×D4×D4711yescharacteristic
245C4C2×#1062535011yescharacteristic
246C2—22no—
247C2—3762no—
248C2—1882no—
249C2C2×#1309399711yescharacteristic
250C2#1568992212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#419C2
socleC22×C47C22×D4
hypercenter#419D47
hypocenterC47#3040
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
3. C2×#13094013C2semidirect
4. #15689591C2semidirect
5. #15689348C2semidirect
6. #15689341C2semidirect
7. #15689146C2semidirect
8. #15689127C2semidirect
9. C47×#419C2semidirect
14. C2×#10625337C22semidirect
16. C2×#10625336C22semidirect
22. #13093989C22semidirect
23. #13093986C22semidirect
29. Dic47⋊C8C22semidirect
34. #103×C47C22semidirect
133. #419D47semidirect
135. C47#3040semidirect
159. #103C2×D47semidirect