Finite Group Databasebeta

← #20242699

Subgroups — #20242699

Order 6016.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#15689533C212yesmaximal, complemented
2#15689518C211yesmaximal, characteristic
3#15688865C212yesmaximal, complemented
4#15688863C211yesmaximal, characteristic
5C47×#563C211yesmaximal, characteristic
6C2×#10625337—21no—
7C2×#10625335—21no—
8#13094024C2211yescharacteristic
9#13093957—22no—
10#13093955—22no—
11#13093935C2211yescharacteristic
12#13093935C2212yes—
13C4⋊Q8×C47—21no—
14#126×C47—22no—
15#125×C47C2212yes—
16#124×C47C2211yescharacteristic
17#123×C47—21no—
18C22⋊Q8×C47—22no—
19C2×Q8×C47—21no—
20C2×Q8×C47D411yescharacteristic
21C2×D4×C47D411yescharacteristic
22C22×C4×C47—21no—
23C2×Dic94—21no—
24C4⋊C4×C47—22no—
25C4⋊C4×C47—22no—
26C4⋊C4×C47—22no—
27C4⋊C4×C47D412yes—
28C4⋊C4×C47D412yes—
29C22⋊C4×C47—22no—
30C22⋊C4×C47—21no—
31C22⋊C4×C47—22no—
32C42×C47—21no—
33C42×C47C2311yescharacteristic
34#10625337—42no—
35#10625335—42no—
36C4⋊Dic47—22no—
37C2×C47⋊C8—22no—
38C2×C47⋊C8—21no—
39C23×C47—21no—
40Q8×C47—41no—
41Q8×C47—81no—
42D4×C47—41no—
43C2×C4×C47—22no—
44C2×C4×C47—21no—
45C2×C4×C47—22no—
46C2×C4×C47—81no—
47C2×C4×C47C2×D412yes—
48C2×C4×C47C2×D411yescharacteristic
49C2×Dic47—41no—
50Dic94—41no—
51Dic94—41no—
52C47⋊C8—24no—
53C47⋊C8—22no—
54C22×C47—41no—
55C22×C47—42no—
56C22×C47#12011yescharacteristic
57C4×C47—21no—
58C4×C47—22no—
59C4×C47—42no—
60C4×C47—41no—
61C4×C47—42no—
62Dic47—81no—
63#1660—471nomaximal, Sylow
64C2×C47—81no—
65C2×C47#45311yescharacteristic
66C2×C47#45612yes—
67#563D4711yescharacteristic
68#501—472no—
69#497—471no—
70#330—472no—
71#329—471no—
72C47#166011yescharacteristic, complemented, Sylow
73C2×Q16—941no—
74C2×SD16—941no—
75C4⋊Q8—21no—
76C4⋊Q8—471no—
77#126—22no—
78#125C2×D4712yes—
79#124C2×D4711yescharacteristic
80#123—21no—
81C22⋊Q8—22no—
82#107—942no—
83#106—942no—
84#97—472no—
85#97—471no—
86C2×Q8—21no—
87C2×Q8—941no—
88C2×Q8C22⋊D4711yescharacteristic
89C2×D4C22⋊D4711yescharacteristic
90C22×C4—21no—
91Q16—1882no—
92SD16—1882no—
93C2×C8—942no—
94C2×C8—941no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—942no—
99C4⋊C4C22⋊D4712yes—
100C4⋊C4C22⋊D4712yes—
101C22⋊C4—22no—
102C22⋊C4—21no—
103C22⋊C4—22no—
104C42—21no—
105C42C22×D4711yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—81no—
109Q8—1881no—
110Q8—1881no—
111D4—41no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—81no—
116C2×C4—1881no—
117C2×C4C2×C22⋊D4712yes—
118C2×C4C2×C22⋊D4711yescharacteristic
119C8—944no—
120C8—942no—
121C22—41no—
122C22—42no—
123C22#1309399311yescharacteristic
124C4—21no—
125C4—22no—
126C4—42no—
127C4—41no—
128C4—42no—
129C4—3761no—
130C2—81no—
131C2#1568929111yescharacteristic
132C2#1568930612yes—
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#563C2
socleC22×C47#120
hypercenter#563D47
hypocenterC47#1660
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #15689533C2semidirect
3. #15688865C2semidirect
72. C47#1660semidirect