Finite Group Databasebeta

← #20254122

Subgroups — #20254122

Order 6016.

446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#15689673C211yesmaximal, characteristic, complemented
2#15689519C211yesmaximal, characteristic, complemented
3#15689499C211yesmaximal, characteristic, complemented
4#15689471C211yesmaximal, characteristic, complemented
5#15689469C211yesmaximal, characteristic, complemented
6#15689374C214yesmaximal, complemented
7#15689233C214yesmaximal, complemented
8C4×#10625329C211yesmaximal, characteristic, complemented
9C47×#532C211yesmaximal, characteristic, complemented
10C2×#10625350—21no—
11C2×#10625334C2214yes—
12C2×#10625329C2212yes—
13#13094024C2211yescharacteristic
14#13094021C2211yescharacteristic
15#13094012—21no—
16#13093998—21no—
17#13093998C2212yes—
18C4×D188—21no—
19C4×D188C2212yes—
20#13093955C2214yes—
21#13093945C2214yes—
22#13093944C2214yes—
23#13093935C2212yes—
24C4×C47⋊C8C2211yescharacteristic
25C4×C47⋊C8C2211yescharacteristic
26C2×#41×C47—21no—
27C4⋊Q8×C47C2211yescharacteristic
28#127×C47C2211yescharacteristic
29#124×C47—21no—
30#121×C47—21no—
31#121×C47C2212yes—
32C4×D4×C47—21no—
33C4×D4×C47C2212yes—
34C2×C42×C47C2211yescharacteristic
35#41×C47—44no—
36C2×Q8×C47—21no—
37C2×D4×C47—22no—
38C2×D4×C47—21no—
39C2×D4×C47—21no—
40C2×D4×C47C2312yes—
41C22×C4×C47—22no—
42C22×C4×C47D411yescharacteristic
43C22×C4×C47D411yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—22no—
46#10625350—44no—
47C2×D188—21no—
48C2×D188—21no—
49C2×D188C2312yes—
50C2×C4×D47—22no—
51C2×Dic94—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2312yes—
54C22⋊C4×C47—22no—
55C22⋊C4×C47—22no—
56C42×C47D411yescharacteristic
57C42×C47D411yescharacteristic
58C42×C47C2311yescharacteristic
59C42×C47C2311yescharacteristic
60#10625334—28no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—22no—
63C4⋊Dic47—21no—
64C4⋊Dic47C2312yes—
65#10625329—24no—
66C2×C47⋊C8C2312yes—
67C2×C47⋊C8C2312yes—
68C23×C47—22no—
69C23×C47C2×D411yescharacteristic
70C22×D47—22no—
71Q8×C47—42no—
72D4×C47—24no—
73D4×C47—44no—
74D4×C47—42no—
75D4×C47—42no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—44no—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2411yescharacteristic
87C22⋊D47—44no—
88C2×Dic47—22no—
89D188—24no—
90D188—42no—
91D188—42no—
92C4×D47—44no—
93Dic94—42no—
94C47⋊C8—22no—
95C47⋊C8#4114yescomplemented
96C22×C47—21no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47C22×D411yescharacteristic
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C4×C47—21no—
107C4×C47—21no—
108C4×C47—21no—
109C4×C47—42no—
110C4×C47AGL(1,ℤ/8)12yes—
111C4×C47AGL(1,ℤ/8)12yes—
112C4×C47C2×#4112yes—
113Dic47—42no—
114#3184—471nomaximal, Sylow
115C2×C47—41no—
116C2×C47—82no—
117C2×C47#53211yescharacteristic
118C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
119C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
120D47—82no—
121#532—471no—
122#532D4711yescharacteristic, complemented
123#498—471no—
124#493—471no—
125#486—471no—
126#486—471no—
127#469—474no—
128#442—474no—
129C4×M16—471no—
130C47#318411yescharacteristic, complemented, Sylow
131C2×#41—21no—
132C2×#41—941no—
133C2×D8—474no—
134C2×M16—472no—
135C4⋊Q8—471no—
136C4⋊Q8C2×D4711yescharacteristic
137#127—471no—
138#127C2×D4711yescharacteristic
139#124—21no—
140#124—941no—
141#121—21no—
142#121—472no—
143#121—941no—
144#121C2×D4712yes—
145C4×D4—21no—
146C4×D4—472no—
147C4×D4—941no—
148C4×D4C2×D4712yes—
149C2×C42C2×D4711yescharacteristic
150#106—474no—
151#102—474no—
152#102—474no—
153#97—472no—
154C4×C8—471no—
155C4×C8—471no—
156#41—44no—
157#41—1884no—
158C2×Q8—21no—
159C2×Q8—941no—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—472no—
164C2×D4—942no—
165C2×D4—941no—
166C2×D4—941no—
167C2×D4C22×D4712yes—
168C22×C4—22no—
169C22×C4—942no—
170C22×C4C22⋊D4711yescharacteristic
171C22×C4C22⋊D4711yescharacteristic
172C22×C4C22×D4711yescharacteristic
173D8—948no—
174M16—944no—
175C2×C8—472no—
176C2×C8—472no—
177C4⋊C4—21no—
178C4⋊C4—472no—
179C4⋊C4—941no—
180C4⋊C4C22×D4712yes—
181C22⋊C4—22no—
182C22⋊C4—22no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C42C22⋊D4711yescharacteristic
186C42C22⋊D4711yescharacteristic
187C42C22×D4711yescharacteristic
188C42C22×D4711yescharacteristic
189C23—22no—
190C23—942no—
191C23C2×C22⋊D4711yescharacteristic
192Q8—42no—
193Q8—1882no—
194D4—24no—
195D4—44no—
196D4—42no—
197D4—42no—
198D4—944no—
199D4—1884no—
200D4—1882no—
201D4—1882no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—44no—
207C2×C4—942no—
208C2×C4—1884no—
209C2×C4C2×C22⋊D4711yescharacteristic
210C2×C4C2×C22⋊D4711yescharacteristic
211C2×C4C2×C22⋊D4711yescharacteristic
212C2×C4C2×C22⋊D4711yescharacteristic
213C2×C4C2×C22⋊D4711yescharacteristic
214C2×C4C23×D4711yescharacteristic
215C8—474no—
216C8—942no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—1882no—
224C22—1882no—
225C22—1882no—
226C22C22×C22⋊D4711yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—42no—
231C4—1882no—
232C4#1309404912yes—
233C4#1309405012yes—
234C4#41×D4712yes—
235C2—41no—
236C2—82no—
237C2—3762no—
238C2#1568966911yescharacteristic
239C2C2×#1309404911yescharacteristic
240C2C2×#1309405011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#532C2
socleC22×C47C22×D4
hypercenter#532D47
hypocenterC47#3184
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #15689673C2semidirect
2. #15689519C2semidirect
3. #15689499C2semidirect
4. #15689471C2semidirect
5. #15689469C2semidirect
6. #15689374C2semidirect
7. #15689233C2semidirect
8. C4×#10625329C2semidirect
9. C47×#532C2semidirect
95. C47⋊C8#41semidirect
122. #532D47semidirect
130. C47#3184semidirect