Finite Group Databasebeta

← #20245060

Subgroups — #20245060

Order 6016.

270 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689097C212yesmaximal, complemented
2#15688916C214yesmaximal, complemented
3C47×#535C211yesmaximal, characteristic
4#13093983—22no—
5#13093939—22no—
6#13093939C2214yescomplemented
7C2×#41×C47C2211yescharacteristic
8C22×D4×C47C411yescharacteristic, complemented
9#127×C47C2212yes—
10#124×C47C412yescomplemented
11#121×C47—22no—
12#120×C47—22no—
13#117×C47C411yescharacteristic, complemented
14C24×C47—21no—
15#41×C47—42no—
16C2×Q8×C47C2×C411yescharacteristic
17C2×D4×C47—24no—
18C2×D4×C47—21no—
19C2×D4×C47—42no—
20C2×D4×C47C2×C412yes—
21C2×D4×C47D412yes—
22C2×D4×C47C2311yescharacteristic
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D412yes—
25C4⋊C4×C47—21no—
26C22⋊C4×C47—21no—
27C22⋊C4×C47—24no—
28C42×C47C2×C412yes—
29C22⋊Dic47—24no—
30C4⋊Dic47—42no—
31C4×Dic47—42no—
32C23×C47—22no—
33C23×C47—42no—
34C23×C47—82no—
35C23×C47C22⋊C411yescharacteristic
36C23×C47C2×D412yes—
37Q8×C47—41no—
38D4×C47—42no—
39D4×C47—41no—
40D4×C47—42no—
41D4×C47—42no—
42D4×C47—84no—
43C2×C4×C47—22no—
44C2×C4×C47—22no—
45C2×C4×C47—22no—
46C2×C4×C47—22no—
47C2×C4×C47C22⋊C412yes—
48C2×C4×C47C22⋊C411yescharacteristic
49C2×C4×C47C22×C411yescharacteristic
50C2×Dic47—44no—
51C22×C47—22no—
52C22×C47—21no—
53C22×C47—42no—
54C22×C47—41no—
55C22×C47—44no—
56C22×C47—42no—
57C22×C47—84no—
58C22×C47C2×C22⋊C411yescharacteristic
59C4×C47—22no—
60C4×C47—21no—
61C4×C47—42no—
62C4×C47#9912yes—
63Dic47—84no—
64#2128—471nomaximal, Sylow
65C2×C47—21no—
66C2×C47—42no—
67C2×C47—41no—
68C2×C47—82no—
69C2×C47C2×#9911yescharacteristic
70#535D4711yescharacteristic
71#410—472no—
72#353—474no—
73C47#212811yescharacteristic, complemented, Sylow
74C2×#41C2×D4711yescharacteristic
75C22×D4Dic4711yescharacteristic, complemented
76#127C2×D4712yes—
77#124Dic4712yescomplemented
78#121—22no—
79#120—22no—
80#117—942no—
81#117Dic4711yescharacteristic, complemented
82#99—474no—
83#99—942no—
84C24—21no—
85#41—42no—
86C2×Q8C2×Dic4711yescharacteristic
87C2×D4—24no—
88C2×D4—21no—
89C2×D4—42no—
90C2×D4C2×Dic4712yes—
91C2×D4C22⋊D4712yes—
92C2×D4C22×D4711yescharacteristic
93C22×C4C2×Dic4711yescharacteristic
94C22×C4C22⋊D4712yes—
95C4⋊C4—21no—
96C4⋊C4—1882no—
97C22⋊C4—21no—
98C22⋊C4—24no—
99C22⋊C4—944no—
100C42—1882no—
101C42C2×Dic4712yes—
102C23—22no—
103C23—42no—
104C23—82no—
105C23C22⋊Dic4711yescharacteristic
106C23C2×C22⋊D4712yes—
107Q8—41no—
108D4—42no—
109D4—41no—
110D4—42no—
111D4—42no—
112D4—84no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—1884no—
118C2×C4C22⋊Dic4712yes—
119C2×C4C22⋊Dic4711yescharacteristic
120C2×C4C22×Dic4711yescharacteristic
121C22—22no—
122C22—21no—
123C22—42no—
124C22—41no—
125C22—44no—
126C22—42no—
127C22—84no—
128C22C2×C22⋊Dic4711yescharacteristic
129C4—22no—
130C4—21no—
131C4—42no—
132C4—3764no—
133C4#1309393912yes—
134C2—21no—
135C2—42no—
136C2—41no—
137C2—82no—
138C2C2×#1309393911yescharacteristic
subgroupG/H
centerC2C2×#13093939
commutatorC2×C4×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#535C2
socleC2×C47C2×#99
hypercenter#535D47
hypocenterC47#2128
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #15689097C2semidirect
2. #15688916C2semidirect
6. #13093939C22semidirect
8. C22×D4×C47C4semidirect
10. #124×C47C4semidirect
13. #117×C47C4semidirect
73. C47#2128semidirect
75. C22×D4Dic47semidirect
77. #124Dic47semidirect
81. #117Dic47semidirect