Finite Group Databasebeta

← #20245284

Subgroups — #20245284

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#15689559C211yesmaximal, characteristic
2#15689246C211yesmaximal, characteristic, complemented
3#15688945C211yesmaximal, characteristic, complemented
4#15688936C211yesmaximal, characteristic, complemented
5#15688932C211yesmaximal, characteristic, complemented
6#15688901C211yesmaximal, characteristic, complemented
7C47×#442C211yesmaximal, characteristic, complemented
8#13094046C2211yescharacteristic
9#13094030—21no—
10#13093968C412yescomplemented
11#13093965C412yescomplemented
12#13093964C2211yescharacteristic
13#13093964C2211yescharacteristic
14#13093960C2211yescharacteristic
15#13093952—21no—
16C2×D8×C47C2211yescharacteristic
17C4×D4×C47—21no—
18#106×C47C2211yescharacteristic
19#102×C47—21no—
20#97×C47C2211yescharacteristic
21C2×D4×C47—21no—
22C22×C4×C47—41no—
23#10625350—21no—
24D8×C47—21no—
25D8×C47C2×C412yes—
26C2×C8×C47D411yescharacteristic
27C2×C8×C47C2311yescharacteristic
28C4⋊C4×C47—21no—
29C22⋊C4×C47—41no—
30C42×C47D411yescharacteristic
31#10625329—21no—
32Dic188C2×C411yescharacteristic, complemented
33D376C2×C411yescharacteristic, complemented
34#10625325—21no—
35#10625324—41no—
36C8×D47—41no—
37C47⋊C16—21no—
38C47⋊C16C2×C412yescomplemented
39C23×C47—41no—
40D4×C47—22no—
41D4×C47—41no—
42C2×C4×C47—21no—
43C2×C4×C47—41no—
44C2×C4×C47—82no—
45C2×C4×C47C2×D411yescharacteristic
46C22⋊D47—41no—
47D188—21no—
48C4×D47—41no—
49Dic94—21no—
50C8×C47—21no—
51C8×C47C22×C411yescharacteristic
52C8×C47#4111yescharacteristic
53C47⋊C8—41no—
54C22×C47—42no—
55C22×C47—81no—
56C22×C47—81no—
57C22×C47AGL(1,ℤ/8)11yescharacteristic
58C2×D47—41no—
59C4×C47—41no—
60C4×C47—81no—
61C4×C47C4×D411yescharacteristic
62C4×C47AGL(1,ℤ/8)11yescharacteristic
63Dic47—41no—
64AGL(1,ℤ/16)—471nomaximal, Sylow
65C2×C47—21no—
66C2×C47—82no—
67C2×C47#44211yescharacteristic
68D47—81no—
69#509—471no—
70#444—471no—
71#442D4711yescharacteristic, complemented
72#365—471no—
73#361—471no—
74#360—471no—
75#347—471no—
76C47AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
77#135—471no—
78C2×D8C2×D4711yescharacteristic
79#131—941no—
80C4×D4—21no—
81SD32—472no—
82D16—472no—
83M32—471no—
84M32—471no—
85#108—471no—
86#106C2×D4711yescharacteristic
87#104—941no—
88#102—21no—
89#97C2×D4711yescharacteristic
90#41—941no—
91C2×D4—21no—
92C22×C4—41no—
93Q16—471no—
94SD16—941no—
95D8—21no—
96D8—471no—
97D8C4×D4712yes—
98M16—941no—
99M16—1881no—
100C2×C8—1881no—
101C2×C8C22⋊D4711yescharacteristic
102C2×C8C22×D4711yescharacteristic
103C4⋊C4—21no—
104C22⋊C4—41no—
105C42C22⋊D4711yescharacteristic
106C16—472no—
107C16—941no—
108C23—41no—
109Q8—941no—
110D4—22no—
111D4—41no—
112D4—941no—
113D4—1881no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—82no—
117C2×C4—1881no—
118C2×C4C2×C22⋊D4711yescharacteristic
119C8—21no—
120C8—1881no—
121C8C2×C4×D4711yescharacteristic
122C8#1062535011yescharacteristic
123C22—42no—
124C22—81no—
125C22—81no—
126C22—1881no—
127C22#1309405011yescharacteristic
128C4—41no—
129C4—81no—
130C4—1881no—
131C4C4×C22⋊D4711yescharacteristic
132C4#1309404911yescharacteristic
133C2—21no—
134C2—82no—
135C2—3761no—
136C2#1568923311yescharacteristic
subgroupG/H
centerC2#15689233
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC47×#442C2
socleC2×C47#442
hypercenter#442D47
hypocenterC47AGL(1,ℤ/16)
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #15689246C2semidirect
3. #15688945C2semidirect
4. #15688936C2semidirect
5. #15688932C2semidirect
6. #15688901C2semidirect
7. C47×#442C2semidirect
10. #13093968C4semidirect
11. #13093965C4semidirect
32. Dic188C2×C4semidirect
33. D376C2×C4semidirect
38. C47⋊C16C2×C4semidirect
71. #442D47semidirect
76. C47AGL(1,ℤ/16)semidirect