Finite Group Databasebeta

← #20254123

Subgroups — #20254123

Order 6016.

446 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 119 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#15689670C212yesmaximal, complemented
2#15689520C211yesmaximal, characteristic, complemented
3#15689498C211yesmaximal, characteristic, complemented
4#15689468C212yesmaximal, complemented
5#15689377C211yesmaximal, characteristic, complemented
6#15689375C212yesmaximal, complemented
7#15689373C211yesmaximal, characteristic, complemented
8#15689236C211yesmaximal, characteristic, complemented
9#15689233C212yesmaximal, complemented
10#15689075C211yesmaximal, characteristic, complemented
11C47×#442C211yesmaximal, characteristic, complemented
12C2×#10625350—22no—
13C2×D376C2211yescharacteristic
14C2×#10625334C2212yes—
15C2×#10625324C2211yescharacteristic
16C2×#10625324C2211yescharacteristic
17#13094023C2212yes—
18#13094020C2212yes—
19#13094010—22no—
20#13093999C2212yes—
21#13093997—22no—
22#13093995C2212yes—
23C4×D188C2212yes—
24C4×C22⋊D47—22no—
25C42×D47C2211yescharacteristic
26#13093956C2211yescharacteristic
27#13093955C2212yes—
28#13093946C2212yes—
29#13093945C2212yes—
30#13093944C2212yes—
31#13093935C2211yescharacteristic
32C8×Dic47C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×D8×C47C2211yescharacteristic
35C4×D4×C47C2212yes—
36#106×C47C2211yescharacteristic
37#102×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×D4×C47C2312yes—
40C22×C4×C47—22no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47—22no—
43C2×C22⋊D47—22no—
44#10625350—48no—
45C2×D188—22no—
46C2×D188C2312yes—
47C2×C4×D47—22no—
48C2×C4×D47D412yes—
49C2×C4×D47C2311yescharacteristic
50C2×Dic94—22no—
51D8×C47—22no—
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2311yescharacteristic
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—22no—
56C42×C47C2311yescharacteristic
57C22⋊Dic47—22no—
58#10625334—24no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63C4×Dic47D412yes—
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66C2×C47⋊C8C2311yescharacteristic
67D376—22no—
68#10625324—22no—
69#10625324—22no—
70C23×C47—22no—
71C22×D47—22no—
72C22×D47C2×D411yescharacteristic
73D4×C47—22no—
74D4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—44no—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2411yescharacteristic
79C22⋊D47—44no—
80C22⋊D47—44no—
81C22⋊D47—44no—
82C2×Dic47—22no—
83C2×Dic47C2×D411yescharacteristic
84C2×Dic47C2×D412yes—
85D188—22no—
86D188—22no—
87D188—44no—
88C4×D47—21no—
89C4×D47—21no—
90C4×D47—24no—
91C4×D47—44no—
92Dic94—44no—
93C8×C47—21no—
94C8×C47#4112yescomplemented
95C47⋊C8—21no—
96C47⋊C8#4112yescomplemented
97C22×C47—42no—
98C22×C47—42no—
99C22×C47—42no—
100C22×C47C22×D411yescharacteristic
101C2×D47—21no—
102C2×D47—22no—
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C4×C47—22no—
107C4×C47—42no—
108C4×C47C2×#4111yescharacteristic
109C4×C47C2×#4111yescharacteristic
110Dic47—21no—
111Dic47—42no—
112Dic47AGL(1,ℤ/8)14yes—
113#3184—471nomaximal, Sylow
114C2×C47—82no—
115C2×C47#53211yescharacteristic
116C2×C47C2×AGL(1,ℤ/8)12yes—
117D47—41no—
118D47—82no—
119#532—472no—
120#498—471no—
121#493—471no—
122#486—472no—
123#469—471no—
124#469—471no—
125#469—472no—
126#442—472no—
127#442—471no—
128#442D4711yescharacteristic, complemented
129C4×M16—471no—
130C47#318411yescharacteristic, complemented, Sylow
131C2×#41—942no—
132C2×D8—472no—
133C2×D8—471no—
134C2×D8C2×D4711yescharacteristic
135C2×M16—471no—
136C2×M16—471no—
137C4⋊Q8—472no—
138#127—472no—
139#124—942no—
140#121—472no—
141#121—472no—
142#121—942no—
143C4×D4—472no—
144C4×D4—942no—
145C4×D4C2×D4712yes—
146C2×C42—471no—
147#106—471no—
148#106—472no—
149#106C2×D4711yescharacteristic
150#102—472no—
151#102—472no—
152#102—472no—
153#102C2×D4712yes—
154#97—471no—
155#97C2×D4711yescharacteristic
156C4×C8—471no—
157C4×C8—471no—
158#41—1888no—
159C2×Q8—942no—
160C2×D4—472no—
161C2×D4—942no—
162C2×D4—942no—
163C2×D4—942no—
164C2×D4—942no—
165C2×D4C22×D4712yes—
166C22×C4—22no—
167C22×C4—472no—
168C22×C4—471no—
169C22×C4—942no—
170D8—22no—
171D8—944no—
172D8—942no—
173M16—942no—
174M16—942no—
175C2×C8—471no—
176C2×C8—471no—
177C2×C8C22×D4711yescharacteristic
178C2×C8C22×D4711yescharacteristic
179C4⋊C4—472no—
180C4⋊C4—942no—
181C4⋊C4C22×D4712yes—
182C22⋊C4—22no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C42—472no—
187C42—471no—
188C42C22×D4711yescharacteristic
189C23—22no—
190C23—471no—
191C23—942no—
192Q8—1884no—
193D4—22no—
194D4—22no—
195D4—942no—
196D4—942no—
197D4—1884no—
198D4—1884no—
199D4—1884no—
200D4—1884no—
201C2×C4—22no—
202C2×C4—44no—
203C2×C4—472no—
204C2×C4—471no—
205C2×C4—944no—
206C2×C4—941no—
207C2×C4—941no—
208C2×C4—942no—
209C2×C4—1884no—
210C2×C4D4×D4712yes—
211C2×C4C23×D4711yescharacteristic
212C8—21no—
213C8—472no—
214C8—941no—
215C8#1062535012yescomplemented
216C22—42no—
217C22—42no—
218C22—42no—
219C22—942no—
220C22—941no—
221C22—1882no—
222C22—1882no—
223C22—1882no—
224C22C2×D4×D4711yescharacteristic
225C4—22no—
226C4—42no—
227C4—474no—
228C4—941no—
229C4—1882no—
230C4#41×D4711yescharacteristic
231C4C2×#1062535011yescharacteristic
232C2—82no—
233C2—3762no—
234C2—1881no—
235C2#1568967011yescharacteristic
236C2AGL(1,ℤ/8)×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3184
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689670C2semidirect
2. #15689520C2semidirect
3. #15689498C2semidirect
4. #15689468C2semidirect
5. #15689377C2semidirect
6. #15689375C2semidirect
7. #15689373C2semidirect
8. #15689236C2semidirect
9. #15689233C2semidirect
10. #15689075C2semidirect
11. C47×#442C2semidirect
94. C8×C47#41semidirect
96. C47⋊C8#41semidirect
128. #442D47semidirect
130. C47#3184semidirect
215. C8#10625350semidirect