Finite Group Databasebeta

← #20241515

Subgroups — #20241515

Order 6016.

172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#13093943C212yesmaximal
2C47×#391C211yesmaximal, characteristic
3C2×#10625329—22no—
4#13093943—22no—
5#13093943C414yescomplemented
6C22×Q8×C47C2211yescharacteristic
7C2×C4⋊C4×C47C411yescharacteristic
8C2×C42×C47C411yescharacteristic
9#95×C47—22no—
10C2×Q8×C47—41no—
11C2×Q8×C47—41no—
12C2×Q8×C47C2×C412yes—
13C2×Q8×C47D411yescharacteristic
14C2×Q8×C47Q811yescharacteristic
15C22×C4×C47—21no—
16C22×C4×C47—21no—
17C22×C4×C47C2×C411yescharacteristic
18C22×C4×C47D412yes—
19C4⋊C4×C47—41no—
20C42×C47—41no—
21#10625329—24no—
22#10625329—42no—
23C2×C47⋊C8—42no—
24C23×C47C22⋊C411yescharacteristic
25Q8×C47—42no—
26Q8×C47—41no—
27Q8×C47—41no—
28C2×C4×C47—22no—
29C2×C4×C47—22no—
30C2×C4×C47—21no—
31C2×C4×C47—21no—
32C2×C4×C47—22no—
33C2×C4×C47—41no—
34C2×C4×C47—41no—
35C2×C4×C47—42no—
36C2×C4×C47—41no—
37C2×C4×C47C4211yescharacteristic
38C2×C4×C47C22⋊C412yes—
39C2×C4×C47C4⋊C412yes—
40C2×C4×C47C4⋊C411yescharacteristic
41C47⋊C8—44no—
42C22×C47—21no—
43C22×C47—21no—
44C22×C47#9511yescharacteristic
45C22×C47#9911yescharacteristic
46C22×C47#9911yescharacteristic
47C4×C47—22no—
48C4×C47—21no—
49C4×C47—22no—
50C4×C47—21no—
51C4×C47—42no—
52C4×C47—81no—
53#1394—471nomaximal, Sylow
54C2×C47—21no—
55C2×C47—21no—
56C2×C47#34211yescharacteristic
57C2×C47#35511yescharacteristic
58C2×C47#35611yescharacteristic
59C2×#101—472no—
60#391D4711yescharacteristic
61C47#139411yescharacteristic, complemented, Sylow
62C22×Q8C2×D4711yescharacteristic
63C2×M16—942no—
64C2×C4⋊C4Dic4711yescharacteristic
65C2×C42Dic4711yescharacteristic
66#101—474no—
67#101—942no—
68#95—22no—
69C2×Q8—41no—
70C2×Q8—41no—
71C2×Q8Dic9411yescharacteristic
72C2×Q8C4×D4712yes—
73C2×Q8D18811yescharacteristic
74C22×C4—21no—
75C22×C4—21no—
76C22×C4C2×Dic4711yescharacteristic
77C22×C4C22⋊D4712yes—
78M16—944no—
79M16—1882no—
80C2×C8—1882no—
81C4⋊C4—41no—
82C42—41no—
83C23C22⋊Dic4711yescharacteristic
84Q8—41no—
85Q8—42no—
86Q8—41no—
87C2×C4—21no—
88C2×C4—22no—
89C2×C4—21no—
90C2×C4—22no—
91C2×C4—22no—
92C2×C4—41no—
93C2×C4—41no—
94C2×C4—42no—
95C2×C4—41no—
96C2×C4C4×Dic4711yescharacteristic
97C2×C4Dic47⋊C412yes—
98C2×C4C4⋊Dic4711yescharacteristic
99C2×C4(C2×D47)⋊C412yes—
100C8—1884no—
101C22—21no—
102C22—21no—
103C22C47⋊#9511yescharacteristic
104C22#1309393911yescharacteristic
105C22#1309393911yescharacteristic
106C4—22no—
107C4—21no—
108C4—22no—
109C4—21no—
110C4—42no—
111C4—81no—
112C2—21no—
113C2—21no—
114C2#1568889011yescharacteristic
115C2#1568892011yescharacteristic
116C2#1568892211yescharacteristic
subgroupG/H
centerC22#13093939
commutatorC2×C4×C47C42
FrattiniC22×Q8C2×D47
FittingC47×#391C2
socleC22×C47#99
hypercenter#391D47
hypocenterC47#1394
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
5. #13093943C4semidirect
61. C47#1394semidirect