Finite Group Databasebeta

← #20245479

Subgroups — #20245479

Order 6016.

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

normal subgroups only

This group has 154 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×Dic376C211yesmaximal, characteristic, complemented
2#15689364C212yesmaximal
3#15688949C211yesmaximal, characteristic, complemented
4#15688928C212yesmaximal, complemented
5C22×C16×C47C211yesmaximal, characteristic
6C2×Dic188C2212yes—
7#13094003—22no—
8Dic376—22no—
9#13093958C2212yes—
10#13093949—22no—
11C22×C8×C47C2211yescharacteristic
12C2×C16×C47—22no—
13C2×C16×C47C2211yescharacteristic
14C2×C16×C47C2211yescharacteristic
15C22×C4×C47D411yescharacteristic
16C2×Dic94—22no—
17C2×C8×C47—21no—
18C2×C8×C47—21no—
19C2×C8×C47D411yescharacteristic
20C2×C8×C47C2311yescharacteristic
21C22⋊Dic47—42no—
22C4⋊Dic47—22no—
23Dic47⋊C4—42no—
24Dic188—22no—
25Dic188—22no—
26C16×C47—21no—
27C16×C47D412yes—
28C23×C47D811yescharacteristic
29C2×C4×C47—21no—
30C2×C4×C47—21no—
31C2×C4×C47D811yescharacteristic
32C2×C4×C47C2×D411yescharacteristic
33C2×Dic47—42no—
34C2×Dic47—42no—
35Dic94—42no—
36Dic94—42no—
37C8×C47—21no—
38C8×C47C2×D411yescharacteristic
39C8×C47#4111yescharacteristic
40C22×C47—21no—
41C22×C47—21no—
42C22×C47Q3212yescomplemented
43C22×C47C2×D811yescharacteristic
44C4×C47—21no—
45C4×C47#12111yescharacteristic
46C4×C47#13511yescharacteristic
47Dic47—82no—
48Dic47—82no—
49#2216—471nomaximal, Sylow
50C2×C47—22no—
51C2×C47#46611yescharacteristic
52C2×C47C2×Q3211yescharacteristic
53C2×C47#50811yescharacteristic
54C2×Q32—471no—
55C22×C16D4711yescharacteristic
56#467—472no—
57#366—471no—
58#358—472no—
59C47#221611yescharacteristic, complemented, Sylow
60C2×Q16—472no—
61C22×C8C2×D4711yescharacteristic
62C22⋊Q8—942no—
63Q32—942no—
64C2×C16—22no—
65C2×C16C2×D4711yescharacteristic
66C2×C16C2×D4711yescharacteristic
67#107—472no—
68#103—942no—
69C2×Q8—942no—
70C22×C4D18811yescharacteristic
71Q16—942no—
72Q16—942no—
73C2×C8—21no—
74C2×C8—21no—
75C2×C8D18811yescharacteristic
76C2×C8C22×D4711yescharacteristic
77C4⋊C4—942no—
78C4⋊C4—1882no—
79C22⋊C4—1882no—
80C16—21no—
81C16C22⋊D4712yes—
82C23D37611yescharacteristic
83Q8—1882no—
84Q8—1882no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—1882no—
88C2×C4—1882no—
89C2×C4D37611yescharacteristic
90C2×C4C2×D18811yescharacteristic
91C8—21no—
92C8#1062535011yescharacteristic
93C8C2×C22⋊D4711yescharacteristic
94C22—21no—
95C22—21no—
96C22Dic37612yescomplemented
97C22C2×D37611yescharacteristic
98C4—21no—
99C4—3762no—
100C4—3762no—
101C4#1309399811yescharacteristic
102C4#1309404611yescharacteristic
103C2—22no—
104C2#1568935911yescharacteristic
105C2C2×Dic37611yescharacteristic
106C2#1568955511yescharacteristic
subgroupG/H
centerC22C2×D376
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC22×C16×C47C2
socleC22×C47C2×D8
hypercenterC22×C16D47
hypocenterC47#2216
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
1. C2×Dic376C2semidirect
3. #15688949C2semidirect
4. #15688928C2semidirect
42. C22×C47Q32semidirect
59. C47#2216semidirect
96. C22Dic376semidirect