Finite Group Databasebeta

← #20242716

Subgroups — #20242716

Order 6016.

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

normal subgroups only

This group has 172 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
2#15689493C211yesmaximal, characteristic
3#15688865C211yesmaximal, characteristic
4#15688865C212yesmaximal
5C47×#564C211yesmaximal, characteristic
6#13094024C2211yescharacteristic
7#13093957—22no—
8#13093955—22no—
9#13093947—22no—
10#13093935C2211yescharacteristic
11#13093935C2212yes—
12#125×C47—22no—
13#125×C47—22no—
14#125×C47—22no—
15#125×C47C2211yescharacteristic
16#125×C47C2212yes—
17C2×Dic94—21no—
18C4⋊C4×C47—22no—
19C4⋊C4×C47—22no—
20C4⋊C4×C47—22no—
21C4⋊C4×C47—22no—
22C4⋊C4×C47—22no—
23C4⋊C4×C47—22no—
24C4⋊C4×C47D412yes—
25C4⋊C4×C47D412yes—
26C4⋊C4×C47D412yes—
27C42×C47—22no—
28C42×C47C2311yescharacteristic
29C4⋊Dic47—22no—
30C2×C47⋊C8—22no—
31C2×C47⋊C8—21no—
32C2×C4×C47—22no—
33C2×C4×C47—22no—
34C2×C4×C47—22no—
35C2×C4×C47C2×D412yes—
36C2×C4×C47C2×D411yescharacteristic
37C2×Dic47—41no—
38Dic94—42no—
39C47⋊C8—24no—
40C47⋊C8—41no—
41C22×C47#12011yescharacteristic
42C4×C47—21no—
43C4×C47—22no—
44C4×C47—42no—
45C4×C47—42no—
46C4×C47—42no—
47Dic47—81no—
48#1663—471nomaximal, Sylow
49C2×C47#45411yescharacteristic
50C2×C47#45612yes—
51#564D4711yescharacteristic
52#501—472no—
53#491—471no—
54#330—472no—
55#330—471no—
56C47#166311yescharacteristic, complemented, Sylow
57C4⋊Q8—471no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D4711yescharacteristic
62#125C2×D4712yes—
63#107—942no—
64#106—942no—
65#103—942no—
66#97—471no—
67#97—472no—
68C2×Q8—941no—
69C2×C8—942no—
70C2×C8—941no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—942no—
78C4⋊C4C22⋊D4712yes—
79C4⋊C4C22⋊D4712yes—
80C4⋊C4C22⋊D4712yes—
81C42—22no—
82C42C22×D4711yescharacteristic
83Q8—1882no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—1881no—
88C2×C4C2×C22⋊D4712yes—
89C2×C4C2×C22⋊D4711yescharacteristic
90C8—944no—
91C8—1881no—
92C22#1309399311yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—3761no—
99C2#1568929611yescharacteristic
100C2#1568930612yes—
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#564C2
socleC22×C47#120
hypercenter#564D47
hypocenterC47#1663
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
56. C47#1663semidirect