Finite Group Databasebeta

← #20245627

Subgroups — #20245627

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#15689507C211yesmaximal, characteristic
2#15688926C212yesmaximal, complemented
3#15688923C212yesmaximal
4#15688899C211yesmaximal, characteristic, complemented
5C47×#500C211yesmaximal, characteristic, complemented
6C2×Dic188C2211yescharacteristic
7C2×#10625325—21no—
8C2×D376C2211yescharacteristic
9#13094012—21no—
10C2×C47⋊C16C2212yes—
11C4⋊Q8×C47—21no—
12#107×C47—21no—
13#107×C47C2212yes—
14C4×C8×C47C2211yescharacteristic
15C2×Q8×C47—41no—
16C2×D188—21no—
17C2×Dic94—21no—
18C2×C8×C47D411yescharacteristic
19C2×C8×C47C2311yescharacteristic
20C4⋊C4×C47—22no—
21C4⋊C4×C47—41no—
22C42×C47D411yescharacteristic
23(C2×D47)⋊C4—41no—
24(C2×D47)⋊C4—41no—
25Dic188—22no—
26D376—22no—
27#10625325—42no—
28C47⋊C16—22no—
29C22×D47—41no—
30Q8×C47—82no—
31C2×C4×C47—42no—
32C2×C4×C47D811yescharacteristic
33C2×C4×C47D811yescharacteristic
34C2×C4×C47C2×D411yescharacteristic
35C2×Dic47—41no—
36D188—41no—
37D188—41no—
38Dic94—41no—
39Dic94—41no—
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—82no—
49C4×C47#12411yescharacteristic
50C4×C47C2×SD1611yescharacteristic
51Dic47—81no—
52#2243—471nomaximal, Sylow
53C2×C47#48611yescharacteristic
54C2×C47#50911yescharacteristic
55C2×C47#51011yescharacteristic
56D47—161no—
57#500D4711yescharacteristic, complemented
58#495—471no—
59#358—472no—
60#357—472no—
61#346—471no—
62C47#224311yescharacteristic, complemented, Sylow
63C2×Q16—471no—
64C2×SD16—941no—
65C2×D8—471no—
66C4⋊Q8—21no—
67#124—941no—
68C2×C16—472no—
69#107—21no—
70#107C2×D4712yes—
71C4×C8C2×D4711yescharacteristic
72C2×Q8—41no—
73C2×Q8—941no—
74C2×D4—941no—
75Q16—942no—
76SD16—1882no—
77D8—942no—
78C2×C8C22⋊D4711yescharacteristic
79C2×C8C22×D4711yescharacteristic
80C4⋊C4—22no—
81C4⋊C4—41no—
82C22⋊C4—1881no—
83C22⋊C4—1881no—
84C42C22⋊D4711yescharacteristic
85C16—942no—
86C23—1881no—
87Q8—82no—
88Q8—1881no—
89Q8—1881no—
90D4—1881no—
91D4—1881no—
92C2×C4—42no—
93C2×C4—1881no—
94C2×C4#1062533411yescharacteristic
95C2×C4#1062533411yescharacteristic
96C2×C4C2×C22⋊D4711yescharacteristic
97C8#1062533612yes—
98C8#1062535412yes—
99C22—3761no—
100C22—3761no—
101C22—3761no—
102C22C2×#1062533411yescharacteristic
103C4—21no—
104C4—21no—
105C4—82no—
106C4—3761no—
107C4#1309401311yescharacteristic
108C4C2×#1062533611yescharacteristic
109C2—7521no—
110C2#1568947111yescharacteristic
111C2#1568955911yescharacteristic
112C2#1568956411yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#500C2
socleC22×C47C2×D8
hypercenter#500D47
hypocenterC47#2243
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #15688926C2semidirect
4. #15688899C2semidirect
5. C47×#500C2semidirect
57. #500D47semidirect
62. C47#2243semidirect