Finite Group Databasebeta

← #20245177

Subgroups — #20245177

Order 6016.

156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13093964C211yesmaximal, characteristic
2C2×#13093958C211yesmaximal, characteristic
3#15688950C212yesmaximal, complemented
4#15688948C212yesmaximal, complemented
5C47×#427C211yesmaximal, characteristic
6C2×C4⋊Dic47—21no—
7#13093964C414yescomplemented
8C2×C47⋊C16C2212yes—
9#13093958—21no—
10#13093958C2212yes—
11C22×C8×C47C2211yescharacteristic
12#117×C47—21no—
13#107×C47C2211yescharacteristic
14#107×C47C2211yescharacteristic
15#106×C47—21no—
16C22×C4×C47D411yescharacteristic
17C22×Dic47—41no—
18C2×C8×C47C2×C412yes—
19C2×C8×C47D411yescharacteristic
20C2×C8×C47Q812yes—
21C2×C8×C47C2311yescharacteristic
22C4⋊C4×C47—21no—
23C4⋊C4×C47—21no—
24C22⋊C4×C47—41no—
25C42×C47—41no—
26C4⋊Dic47—22no—
27C4⋊Dic47—41no—
28C47⋊C16C2×C414yescomplemented
29C23×C47D811yescharacteristic
30C2×C4×C47—41no—
31C2×C4×C47—41no—
32C2×C4×C47C4⋊C412yes—
33C2×C4×C47D811yescharacteristic
34C2×C4×C47Q1612yes—
35C2×C4×C47C2×D411yescharacteristic
36C2×Dic47—42no—
37C2×Dic47—82no—
38C8×C47C4⋊C412yes—
39C8×C47C22×C411yescharacteristic
40C8×C47C2×Q811yescharacteristic
41C22×C47—21no—
42C22×C47—21no—
43C22×C47#10712yes—
44C22×C47C2×D811yescharacteristic
45C4×C47—81no—
46C4×C47—81no—
47C4×C47#10712yes—
48C4×C47C2×C4⋊C411yescharacteristic
49C4×C47C2×Q1611yescharacteristic
50Dic47—82no—
51#2159—471nomaximal, Sylow
52C2×C47—22no—
53C2×C47C2×#10711yescharacteristic
54C2×C47#50911yescharacteristic
55C2×C47#51011yescharacteristic
56C2×M32—471no—
57#427D4711yescharacteristic
58C2×#107—471no—
59#367—472no—
60#366—472no—
61C47#215911yescharacteristic, complemented, Sylow
62C22×C8C2×D4711yescharacteristic
63#117—21no—
64C2×C4⋊C4—941no—
65M32—474no—
66C2×C16—472no—
67#107—472no—
68#107—941no—
69#107C2×D4711yescharacteristic
70#107C2×D4711yescharacteristic
71#106—21no—
72C22×C4—1881no—
73C22×C4C22⋊D4711yescharacteristic
74C2×C8Dic9412yes—
75C2×C8C4×D4712yes—
76C2×C8C22⋊D4711yescharacteristic
77C2×C8C22×D4711yescharacteristic
78C4⋊C4—21no—
79C4⋊C4—21no—
80C4⋊C4—942no—
81C4⋊C4—1881no—
82C22⋊C4—41no—
83C42—41no—
84C16—474no—
85C23#1062533411yescharacteristic
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—3762no—
89C2×C4—1882no—
90C2×C4Dic47⋊C412yes—
91C2×C4#1062533411yescharacteristic
92C2×C4#1062533712yes—
93C2×C4C2×C22⋊D4711yescharacteristic
94C8Dic47⋊C412yes—
95C8C2×Dic9411yescharacteristic
96C8C2×C4×D4711yescharacteristic
97C22—21no—
98C22—21no—
99C22#1309395712yes—
100C22C2×#1062533411yescharacteristic
101C4—81no—
102C4—81no—
103C4—3762no—
104C4#1309395712yes—
105C4C2×Dic47⋊C411yescharacteristic
106C4C2×#1062533711yescharacteristic
107C2—22no—
108C2C2×#1309395711yescharacteristic
109C2#1568955811yescharacteristic
110C2#1568956311yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC47×#427C2
socleC22×C47C2×D8
hypercenter#427D47
hypocenterC47#2159
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
3. #15688950C2semidirect
4. #15688948C2semidirect
7. #13093964C4semidirect
28. C47⋊C16C2×C4semidirect
61. C47#2159semidirect