Finite Group Databasebeta

← #20245288

Subgroups — #20245288

Order 6016.

154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689561C211yesmaximal, characteristic
2#15689246C211yesmaximal, characteristic, complemented
3#15689236C211yesmaximal, characteristic, complemented
4#15688946C211yesmaximal, characteristic, complemented
5#15688937C211yesmaximal, characteristic, complemented
6#15688934C211yesmaximal, characteristic, complemented
7C47×#347C211yesmaximal, characteristic, complemented
8#13094046C2211yescharacteristic
9C2×D376C2211yescharacteristic
10#13094030—21no—
11C4×D188—21no—
12#13093969C412yescomplemented
13D752C412yescomplemented
14#13093960C2211yescharacteristic
15#13093956C2211yescharacteristic
16#13093952—21no—
17#13093946—21no—
18M32×C47C2211yescharacteristic
19M32×C47C2211yescharacteristic
20#97×C47C2211yescharacteristic
21#10625350—21no—
22C2×D188—21no—
23C2×C4×D47—41no—
24C2×C8×C47D411yescharacteristic
25C2×C8×C47C2311yescharacteristic
26C42×C47D411yescharacteristic
27(C2×D47)⋊C4—41no—
28C4⋊Dic47—21no—
29#10625329—21no—
30Dic188C2×C411yescharacteristic, complemented
31D376—21no—
32D376C2×C412yes—
33D376C2×C411yescharacteristic, complemented
34#10625325—21no—
35#10625324—41no—
36C8×D47—41no—
37C16×C47—21no—
38C16×C47C2×C412yescomplemented
39C22×D47—41no—
40C2×C4×C47—21no—
41C2×C4×C47C2×D411yescharacteristic
42C22⋊D47—41no—
43C2×Dic47—41no—
44D188—21no—
45D188—22no—
46D188—41no—
47C4×D47—41no—
48C4×D47—82no—
49Dic94—21no—
50C8×C47—21no—
51C8×C47C22×C411yescharacteristic
52C8×C47#4111yescharacteristic
53C47⋊C8—41no—
54C22×C47AGL(1,ℤ/8)11yescharacteristic
55C2×D47—41no—
56C2×D47—42no—
57C2×D47—81no—
58C2×D47—81no—
59C4×C47—41no—
60C4×C47C4×D411yescharacteristic
61C4×C47AGL(1,ℤ/8)11yescharacteristic
62Dic47—41no—
63Dic47—81no—
64AGL(1,ℤ/16)—471nomaximal, Sylow
65C2×C47—21no—
66C2×C47#44211yescharacteristic
67D47—81no—
68D47—82no—
69#509—471no—
70#444—471no—
71#442—471no—
72#365—471no—
73#361—471no—
74#360—471no—
75#347D4711yescharacteristic, complemented
76C47AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
77#135—471no—
78C2×D8—471no—
79#131—941no—
80C4×D4—941no—
81SD32—472no—
82D16—472no—
83M32C2×D4711yescharacteristic
84M32C2×D4711yescharacteristic
85#108—471no—
86#106—471no—
87#104—941no—
88#102—941no—
89#97C2×D4711yescharacteristic
90#41—941no—
91C2×D4—941no—
92C22×C4—1881no—
93Q16—471no—
94SD16—941no—
95D8—472no—
96D8—471no—
97D8—941no—
98M16—941no—
99M16—1881no—
100C2×C8—1881no—
101C2×C8D18811yescharacteristic
102C2×C8C22×D4711yescharacteristic
103C4⋊C4—941no—
104C22⋊C4—1881no—
105C42D18811yescharacteristic
106C16—21no—
107C16C4×D4712yescomplemented
108C23—1881no—
109Q8—941no—
110D4—942no—
111D4—941no—
112D4—1881no—
113D4—1881no—
114C2×C4—21no—
115C2×C4—3762no—
116C2×C4—1881no—
117C2×C4—1881no—
118C2×C4C2×D18811yescharacteristic
119C8—21no—
120C8—1881no—
121C8C2×C4×D4711yescharacteristic
122C8#1062535011yescharacteristic
123C22—3761no—
124C22—3761no—
125C22—1881no—
126C22—1882no—
127C22#1309405211yescharacteristic
128C4—41no—
129C4—3761no—
130C4—1881no—
131C4C4×D18811yescharacteristic
132C4#1309405211yescharacteristic
133C2—21no—
134C2—3762no—
135C2—3761no—
136C2#1568923611yescharacteristic
subgroupG/H
centerC2#15689236
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC47×#347C2
socleC2×C47#442
hypercenter#347D47
hypocenterC47AGL(1,ℤ/16)
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #347

Complements

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

NH ≅ G/Ntype
2. #15689246C2semidirect
3. #15689236C2semidirect
4. #15688946C2semidirect
5. #15688937C2semidirect
6. #15688934C2semidirect
7. C47×#347C2semidirect
12. #13093969C4semidirect
13. D752C4semidirect
30. Dic188C2×C4semidirect
33. D376C2×C4semidirect
38. C16×C47C2×C4semidirect
75. #347D47semidirect
76. C47AGL(1,ℤ/16)semidirect
107. C16C4×D47semidirect