Finite Group Databasebeta

← #20241317

Subgroups — #20241317

Order 6016.

150 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 37 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#15688984C211yesmaximal, characteristic
2#15688847C211yesmaximal, characteristic
3C47×#323C211yesmaximal, characteristic
4C23×Dic47C411yescharacteristic
5C2×C22⋊Dic47C411yescharacteristic
6C22⋊(C47⋊C8)—21no—
7C47⋊#95—21no—
8C47⋊#95—21no—
9C2×C22⋊C4×C47C2211yescharacteristic
10C22⋊C8×C47—21no—
11C24×C47C2×C411yescharacteristic
12C22×C4×C47D411yescharacteristic
13C22×C4×C47D411yescharacteristic
14C22×Dic47—21no—
15C22×Dic47—21no—
16C22×Dic47—21no—
17C22×Dic47—41no—
18C22×Dic47—41no—
19C22×Dic47C812yescomplemented
20C2×C8×C47—41no—
21C22⋊C4×C47—41no—
22C22⋊Dic47—41no—
23C2×C47⋊C8—41no—
24C23×C47—21no—
25C23×C47—21no—
26C23×C47—41no—
27C23×C47—41no—
28C23×C47C22⋊C411yescharacteristic
29C23×C47C2×C811yescharacteristic
30C23×C47M1611yescharacteristic
31C2×C4×C47—21no—
32C2×C4×C47—21no—
33C2×C4×C47—41no—
34C2×C4×C47—41no—
35C2×Dic47—22no—
36C2×Dic47—42no—
37C2×Dic47—41no—
38C2×Dic47—41no—
39C2×Dic47—42no—
40C2×Dic47—41no—
41C2×Dic47—41no—
42C2×Dic47—41no—
43C8×C47—81no—
44C47⋊C8—81no—
45C22×C47—21no—
46C22×C47—21no—
47C22×C47—21no—
48C22×C47—21no—
49C22×C47—41no—
50C22×C47—41no—
51C22×C47—42no—
52C22×C47—41no—
53C22×C47—41no—
54C22×C47C22⋊C811yescharacteristic
55C22×C47#9911yescharacteristic
56C22×C47#10011yescharacteristic
57C4×C47—41no—
58C4×C47—41no—
59Dic47—42no—
60Dic47—81no—
61#1317—471nomaximal, Sylow
62C2×C47—21no—
63C2×C47—21no—
64C2×C47—41no—
65C2×C47—41no—
66C2×C47#32311yescharacteristic
67C2×C47#35211yescharacteristic
68C2×C47#35211yescharacteristic
69#381—471no—
70#323—471no—
71#323D4711yescharacteristic
72C47#131711yescharacteristic, complemented, Sylow
73C23×C4—471no—
74C2×C22⋊C4—471no—
75C2×C22⋊C4C2×D4711yescharacteristic
76C22⋊C8—21no—
77C22⋊C8—941no—
78#95—941no—
79#95—941no—
80C24C4×D4711yescharacteristic
81C22×C4—472no—
82C22×C4—941no—
83C22×C4—941no—
84C22×C4—941no—
85C22×C4—1881no—
86C22×C4—1881no—
87C22×C4D18811yescharacteristic
88C22×C4C22⋊D4711yescharacteristic
89C2×C8—41no—
90C2×C8—1881no—
91C22⋊C4—41no—
92C22⋊C4—1881no—
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23C8×D4711yescharacteristic
98C23#1062532411yescharacteristic
99C23(C2×D47)⋊C411yescharacteristic
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—942no—
105C2×C4—1881no—
106C2×C4—1881no—
107C2×C4—1881no—
108C2×C4—1882no—
109C2×C4—1881no—
110C2×C4—1881no—
111C2×C4—1882no—
112C8—81no—
113C8—3761no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22(C2×D47)⋊C811yescharacteristic
124C22#1309393811yescharacteristic
125C22#1309394011yescharacteristic
126C4—41no—
127C4—41no—
128C4—3761no—
129C4—1882no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#1568884611yescharacteristic
135C2#1568891211yescharacteristic
136C2#1568891411yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC23×C47C2×C8
FrattiniC2×C22⋊C4C2×D47
FittingC47×#323C2
socleC22×C47#99
hypercenter#323D47
hypocenterC47#1317
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
19. C22×Dic47C8semidirect
72. C47#1317semidirect