Finite Group Databasebeta

← #20245603

Subgroups — #20245603

Order 6016.

134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689376C211yesmaximal, characteristic
2#15689172C211yesmaximal, characteristic, complemented
3#15688946C212yesmaximal, complemented
4#15688937C212yesmaximal, complemented
5C47×#349C211yesmaximal, characteristic, complemented
6C2×D376C2211yescharacteristic
7C2×#10625329—21no—
8#13093998—21no—
9#13093960—21no—
10#13093960C2212yes—
11#13093956C2211yescharacteristic
12#13093946—21no—
13C2×M16×C47C2211yescharacteristic
14M32×C47C2212yes—
15C22×C4×C47D411yescharacteristic
16C2×C22⋊D47—41no—
17C2×D188—21no—
18M16×C47—22no—
19C2×C8×C47D411yescharacteristic
20C2×C8×C47C2311yescharacteristic
21(C2×D47)⋊C4—41no—
22C4⋊Dic47—21no—
23#10625329—22no—
24#10625329—41no—
25C2×C47⋊C8—41no—
26D376—22no—
27C16×C47—22no—
28C23×C47SD1611yescharacteristic
29C22×D47—41no—
30C2×C4×C47—21no—
31C2×C4×C47—21no—
32C2×C4×C47SD1611yescharacteristic
33C2×C4×C47C2×D411yescharacteristic
34C22⋊D47—82no—
35C2×Dic47—41no—
36D188—41no—
37D188—41no—
38C8×C47—21no—
39C8×C47#4112yes—
40C47⋊C8—42no—
41C22×C47—21no—
42C22×C47—41no—
43C22×C47C2×SD1611yescharacteristic
44C2×D47—81no—
45C2×D47—81no—
46C2×D47—81no—
47C4×C47—21no—
48C4×C47#12311yescharacteristic
49C4×C47AGL(1,ℤ/8)11yescharacteristic
50Dic47—81no—
51#2238—471nomaximal, Sylow
52C2×C47—21no—
53C2×C47—41no—
54C2×C47#48111yescharacteristic
55D47—161no—
56#469—471no—
57#430—471no—
58#365—472no—
59#361—472no—
60#349D4711yescharacteristic, complemented
61C47#223811yescharacteristic, complemented, Sylow
62C2×D8—471no—
63C2×M16—941no—
64C2×M16C2×D4711yescharacteristic
65#121—941no—
66M32C2×D4712yes—
67#108—472no—
68#108—941no—
69#106—471no—
70#102—941no—
71C2×D4—941no—
72C2×D4—1881no—
73C22×C4D18811yescharacteristic
74D8—942no—
75M16—22no—
76M16—942no—
77M16—1881no—
78C2×C8—1881no—
79C2×C8D18811yescharacteristic
80C2×C8C22×D4711yescharacteristic
81C4⋊C4—941no—
82C22⋊C4—1881no—
83C16—22no—
84C23—1881no—
85C23#1062532511yescharacteristic
86D4—3762no—
87D4—1881no—
88D4—1881no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—1881no—
92C2×C4#1062532511yescharacteristic
93C2×C4C2×D18811yescharacteristic
94C8—21no—
95C8—1882no—
96C8#1062535212yes—
97C22—21no—
98C22—41no—
99C22—3761no—
100C22—3761no—
101C22—3761no—
102C22C2×#1062532511yescharacteristic
103C4—21no—
104C4—3761no—
105C4#1309400811yescharacteristic
106C4#1309405211yescharacteristic
107C2—21no—
108C2—41no—
109C2—7521no—
110C2#1568944211yescharacteristic
subgroupG/H
centerC2#15689442
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#349C2
socleC2×C47#481
hypercenter#349D47
hypocenterC47#2238
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #15689172C2semidirect
3. #15688946C2semidirect
4. #15688937C2semidirect
5. C47×#349C2semidirect
60. #349D47semidirect
61. C47#2238semidirect