Finite Group Databasebeta

← #20245625

Subgroups — #20245625

Order 6016.

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

normal subgroups only

This group has 142 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#15689528C211yesmaximal, characteristic, complemented
2#15689507C211yesmaximal, characteristic
3#15688928C212yesmaximal, complemented
4#15688925C212yesmaximal
5C47×#346C211yesmaximal, characteristic, complemented
6C2×Dic188C2211yescharacteristic
7C2×#10625325—21no—
8C2×D376C2211yescharacteristic
9#13094024—21no—
10#13094012—21no—
11#13093958—21no—
12#13093958C2212yes—
13C2×C16×C47C2212yes—
14C4×C8×C47C2211yescharacteristic
15C2×D188—21no—
16C2×Dic94—21no—
17C2×Dic94—41no—
18C2×C8×C47D411yescharacteristic
19C2×C8×C47C2311yescharacteristic
20C42×C47D411yescharacteristic
21(C2×D47)⋊C4—41no—
22(C2×D47)⋊C4—41no—
23C4⋊Dic47—22no—
24C4⋊Dic47—41no—
25Dic188—22no—
26D376—22no—
27#10625325—42no—
28C16×C47—22no—
29C22×D47—41no—
30C2×C4×C47D811yescharacteristic
31C2×C4×C47D811yescharacteristic
32C2×C4×C47C2×D411yescharacteristic
33C2×Dic47—42no—
34C2×Dic47—41no—
35D188—41no—
36D188—41no—
37Dic94—41no—
38Dic94—41no—
39Dic94—82no—
40C8×C47SD1612yes—
41C8×C47#4112yes—
42C22×C47C2×D811yescharacteristic
43C2×D47—81no—
44C2×D47—81no—
45C2×D47—81no—
46C4×C47—21no—
47C4×C47—21no—
48C4×C47#12411yescharacteristic
49C4×C47C2×SD1611yescharacteristic
50Dic47—81no—
51Dic47—82no—
52#2243—471nomaximal, Sylow
53C2×C47#48611yescharacteristic
54C2×C47#50911yescharacteristic
55C2×C47#51011yescharacteristic
56D47—161no—
57#500—471no—
58#495—471no—
59#358—472no—
60#357—472no—
61#346D4711yescharacteristic, complemented
62C47#224311yescharacteristic, complemented, Sylow
63C2×Q16—471no—
64C2×SD16—941no—
65C2×D8—471no—
66C4⋊Q8—941no—
67#124—941no—
68C2×C16C2×D4712yes—
69#107—472no—
70#107—941no—
71C4×C8C2×D4711yescharacteristic
72C2×Q8—941no—
73C2×Q8—1881no—
74C2×D4—941no—
75Q16—942no—
76SD16—1882no—
77D8—942no—
78C2×C8D18811yescharacteristic
79C2×C8C22×D4711yescharacteristic
80C4⋊C4—942no—
81C4⋊C4—1881no—
82C22⋊C4—1881no—
83C22⋊C4—1881no—
84C42D18811yescharacteristic
85C16—22no—
86C23—1881no—
87Q8—3762no—
88Q8—1881no—
89Q8—1881no—
90D4—1881no—
91D4—1881no—
92C2×C4—1881no—
93C2×C4—1882no—
94C2×C4D37611yescharacteristic
95C2×C4D37611yescharacteristic
96C2×C4C2×D18811yescharacteristic
97C8#1062532512yes—
98C8#1062535012yes—
99C22—3761no—
100C22—3761no—
101C22—3761no—
102C22C2×D37611yescharacteristic
103C4—21no—
104C4—21no—
105C4—3762no—
106C4—3761no—
107C4#1309401211yescharacteristic
108C4C2×#1062532511yescharacteristic
109C2—7521no—
110C2#1568947011yescharacteristic
111C2#1568956111yescharacteristic
112C2#1568956611yescharacteristic
subgroupG/H
centerC22C2×D376
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#346C2
socleC22×C47C2×D8
hypercenter#346D47
hypocenterC47#2243
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #346

Complements

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

NH ≅ G/Ntype
1. #15689528C2semidirect
3. #15688928C2semidirect
5. C47×#346C2semidirect
61. #346D47semidirect
62. C47#2243semidirect