Finite Group Databasebeta

← #20254318

Subgroups — #20254318

Order 6016.

438 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689674C211yesmaximal, characteristic, complemented
2#15689671C211yesmaximal, characteristic, complemented
3#15689499C211yesmaximal, characteristic, complemented
4#15689473C211yesmaximal, characteristic, complemented
5#15689470C211yesmaximal, characteristic, complemented
6#15689340C214yesmaximal, complemented
7#15689267C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic, complemented
9C47×#492C211yesmaximal, characteristic, complemented
10C2×#10625354C2212yes—
11C2×#10625352—21no—
12C2×#10625334C2214yes—
13#13094024C2211yescharacteristic
14#13094021C2211yescharacteristic
15#13094013C2212yes—
16#13094011—21no—
17#13093999—21no—
18#13093999—21no—
19#13093995—21no—
20#13093995C2212yes—
21D4×Dic47—21no—
22D4×Dic47C2212yes—
23#13093986—21no—
24#13093986—21no—
25C42×D47C2211yescharacteristic
26Dic47⋊C8C2212yes—
27#13093948C2214yes—
28#13093946C2214yes—
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C2×SD16×C47C2214yes—
32C4⋊Q8×C47C2211yescharacteristic
33#127×C47C2211yescharacteristic
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47C2312yes—
36C2×D4×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47C2312yes—
39C2×C22⋊D47—22no—
40C22×Dic47—22no—
41#10625354—44no—
42#10625352—44no—
43C2×D188—22no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188C2312yes—
47C2×C4×D47—22no—
48C2×C4×D47D411yescharacteristic
49C2×C4×D47D411yescharacteristic
50C2×C4×D47C2311yescharacteristic
51C2×Dic94—21no—
52SD16×C47—44no—
53C2×C8×C47C2312yes—
54C4⋊C4×C47—21no—
55C4⋊C4×C47—21no—
56C42×C47C2311yescharacteristic
57C22⋊Dic47—22no—
58C22⋊Dic47—22no—
59#10625334—44no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62C4⋊Dic47—21no—
63C4⋊Dic47C2312yes—
64C4×Dic47D411yescharacteristic
65C4×Dic47D411yescharacteristic
66C4×Dic47C2311yescharacteristic
67C2×C47⋊C8C2312yes—
68C23×C47—22no—
69C22×D47—22no—
70C22×D47C2×D411yescharacteristic
71Q8×C47—24no—
72D4×C47—24no—
73D4×C47—42no—
74D4×C47—42no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2411yescharacteristic
79C22⋊D47—44no—
80C2×Dic47—22no—
81C2×Dic47—44no—
82C2×Dic47C2×D411yescharacteristic
83C2×Dic47C2×D411yescharacteristic
84C2×Dic47C2×D411yescharacteristic
85D188—24no—
86D188—44no—
87D188—42no—
88D188—42no—
89C4×D47—22no—
90C4×D47—22no—
91C4×D47—22no—
92C4×D47—44no—
93Dic94—42no—
94C8×C47—22no—
95C47⋊C8—22no—
96C22×C47—42no—
97C22×C47—42no—
98C22×C47—42no—
99C22×C47C22×D411yescharacteristic
100C2×D47—21no—
101C2×D47—21no—
102C2×D47—21no—
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C4×C47—42no—
107C4×C47#13512yes—
108C4×C47AGL(1,ℤ/8)12yes—
109C4×C47H(5,𝔽2)12yes—
110Dic47—21no—
111Dic47—21no—
112Dic47—21no—
113Dic47—42no—
114#3207—471nomaximal, Sylow
115C2×C47—82no—
116C2×C47#53511yescharacteristic
117C2×C47C2×#13511yescharacteristic
118C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
119D47—41no—
120D47—82no—
121#532—471no—
122#532—471no—
123#493—471no—
124#492D4711yescharacteristic, complemented
125#487—471no—
126#486—471no—
127#463—474no—
128#449—474no—
129#431—471no—
130C47#320711yescharacteristic, complemented, Sylow
131C2×#41—472no—
132C2×#41—941no—
133C2×SD16C2×D4714yes—
134C2×D8—474no—
135C4⋊Q8—471no—
136C4⋊Q8C2×D4711yescharacteristic
137#127—471no—
138#127C2×D4711yescharacteristic
139#124—472no—
140#124—941no—
141#121—472no—
142#121—941no—
143#121—941no—
144#121—941no—
145C4×D4—472no—
146C4×D4—941no—
147C4×D4—941no—
148C4×D4—941no—
149C2×C42—471no—
150C4⋊C8—472no—
151#103—474no—
152#102—474no—
153C22⋊C8—472no—
154C4×C8—471no—
155C4×C8C2×D4711yescharacteristic
156#41—1884no—
157#41—1884no—
158C2×Q8—941no—
159C2×Q8C22×D4712yes—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—472no—
163C2×D4—942no—
164C2×D4—942no—
165C2×D4—941no—
166C2×D4—941no—
167C2×D4C22×D4712yes—
168C22×C4—471no—
169C22×C4—471no—
170C22×C4—471no—
171C22×C4—942no—
172C22×C4—942no—
173SD16—44no—
174D8—1884no—
175C2×C8—472no—
176C2×C8C22×D4712yes—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—472no—
180C4⋊C4—941no—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C42—471no—
186C42—471no—
187C42—471no—
188C42C22×D4711yescharacteristic
189C23—22no—
190C23—471no—
191C23—942no—
192Q8—24no—
193Q8—1882no—
194D4—24no—
195D4—42no—
196D4—42no—
197D4—944no—
198D4—1884no—
199D4—1884no—
200D4—1882no—
201D4—1882no—
202C2×C4—22no—
203C2×C4—471no—
204C2×C4—471no—
205C2×C4—471no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—1884no—
211C2×C4—1884no—
212C2×C4D4×D4711yescharacteristic
213C2×C4D4×D4711yescharacteristic
214C2×C4C23×D4711yescharacteristic
215C8—22no—
216C8—942no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—941no—
221C22—941no—
222C22—941no—
223C22—1882no—
224C22—1882no—
225C22—1882no—
226C22C2×D4×D4711yescharacteristic
227C4—42no—
228C4—941no—
229C4—941no—
230C4—941no—
231C4—1882no—
232C4#1309404512yes—
233C4#1309405112yes—
234C4#1309406912yes—
235C2—82no—
236C2—3762no—
237C2—1881no—
238C2#1568968611yescharacteristic
239C2C2×#1309404511yescharacteristic
240C2C2×#1309405111yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#492C2
socleC22×C47C22×D4
hypercenter#492D47
hypocenterC47#3207
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #15689674C2semidirect
2. #15689671C2semidirect
3. #15689499C2semidirect
4. #15689473C2semidirect
5. #15689470C2semidirect
6. #15689340C2semidirect
7. #15689267C2semidirect
8. #15689174C2semidirect
9. C47×#492C2semidirect
124. #492D47semidirect
130. C47#3207semidirect