Finite Group Databasebeta

← #20245624

Subgroups — #20245624

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#15688927C212yesmaximal, complemented
3#15688924C212yesmaximal
4#15688899C211yesmaximal, characteristic, complemented
5C47×#495C211yesmaximal, characteristic
6#13094024—21no—
7C2×C47⋊C16C2212yes—
8#13093958—21no—
9#13093958C2212yes—
10C2×Q16×C47C2211yescharacteristic
11C2×SD16×C47—21no—
12C2×D8×C47C2211yescharacteristic
13#124×C47—21no—
14C4×C8×C47C2211yescharacteristic
15C2×Q8×C47—21no—
16C2×D4×C47—21no—
17C2×Dic94—41no—
18Q16×C47—22no—
19SD16×C47—42no—
20D8×C47—22no—
21C2×C8×C47D411yescharacteristic
22C2×C8×C47C2311yescharacteristic
23C22⋊C4×C47—41no—
24C22⋊C4×C47—41no—
25C42×C47D411yescharacteristic
26C4⋊Dic47—22no—
27C4⋊Dic47—41no—
28C47⋊C16—22no—
29C23×C47—41no—
30Q8×C47—41no—
31Q8×C47—41no—
32D4×C47—41no—
33D4×C47—41no—
34C2×C4×C47—41no—
35C2×C4×C47D811yescharacteristic
36C2×C4×C47D811yescharacteristic
37C2×C4×C47C2×D411yescharacteristic
38C2×Dic47—42no—
39Dic94—82no—
40C8×C47SD1612yes—
41C8×C47#4112yes—
42C22×C47—81no—
43C22×C47—81no—
44C22×C47—81no—
45C22×C47C2×D811yescharacteristic
46C4×C47—21no—
47C4×C47—21no—
48C4×C47—81no—
49C4×C47#12411yescharacteristic
50C4×C47C2×SD1611yescharacteristic
51Dic47—82no—
52#2243—471nomaximal, Sylow
53C2×C47—161no—
54C2×C47#48611yescharacteristic
55C2×C47#50911yescharacteristic
56C2×C47#51011yescharacteristic
57#500—471no—
58#495D4711yescharacteristic
59#358—472no—
60#357—472no—
61#346—471no—
62C47#224311yescharacteristic, complemented, Sylow
63C2×Q16C2×D4711yescharacteristic
64C2×SD16—21no—
65C2×D8C2×D4711yescharacteristic
66C4⋊Q8—941no—
67#124—21no—
68C2×C16—472no—
69#107—472no—
70#107—941no—
71C4×C8C2×D4711yescharacteristic
72C2×Q8—21no—
73C2×Q8—1881no—
74C2×D4—21no—
75Q16—22no—
76SD16—42no—
77D8—22no—
78C2×C8C22⋊D4711yescharacteristic
79C2×C8C22×D4711yescharacteristic
80C4⋊C4—942no—
81C4⋊C4—1881no—
82C22⋊C4—41no—
83C22⋊C4—41no—
84C42C22⋊D4711yescharacteristic
85C16—942no—
86C23—41no—
87Q8—41no—
88Q8—41no—
89Q8—3762no—
90D4—41no—
91D4—41no—
92C2×C4—41no—
93C2×C4—1882no—
94C2×C4#1062533411yescharacteristic
95C2×C4#1062533411yescharacteristic
96C2×C4C2×C22⋊D4711yescharacteristic
97C8#1062533512yes—
98C8#1062535212yes—
99C22—81no—
100C22—81no—
101C22—81no—
102C22C2×#1062533411yescharacteristic
103C4—21no—
104C4—21no—
105C4—81no—
106C4—3762no—
107C4#1309401111yescharacteristic
108C4C2×#1062533511yescharacteristic
109C2—161no—
110C2#1568946911yescharacteristic
111C2#1568955811yescharacteristic
112C2#1568956311yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#495C2
socleC22×C47C2×D8
hypercenter#495D47
hypocenterC47#2243
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #15689528C2semidirect
2. #15688927C2semidirect
4. #15688899C2semidirect
62. C47#2243semidirect