Finite Group Databasebeta

← #20245583

Subgroups — #20245583

Order 6016.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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×#13093958C211yesmaximal, characteristic
2#15688950C212yesmaximal, complemented
3#15688927C212yesmaximal, complemented
4C22⋊(C47⋊C16)C211yesmaximal, characteristic
5C47×#467C211yesmaximal, characteristic
6C2×C4⋊Dic47—21no—
7C2×C47⋊C16C2212yes—
8#13093958—21no—
9#13093958C2212yes—
10C2×Q16×C47C2211yescharacteristic
11C22×C8×C47C2211yescharacteristic
12C22⋊Q8×C47—21no—
13#107×C47C2211yescharacteristic
14#103×C47—21no—
15C2×Q8×C47—21no—
16C22×C4×C47D411yescharacteristic
17C22×Dic47—41no—
18Q16×C47—22no—
19C2×C8×C47—22no—
20C2×C8×C47D411yescharacteristic
21C2×C8×C47C2311yescharacteristic
22C4⋊C4×C47—21no—
23C4⋊C4×C47—41no—
24C22⋊C4×C47—41no—
25C4⋊Dic47—22no—
26C4⋊Dic47—41no—
27C47⋊C16—22no—
28C23×C47D811yescharacteristic
29Q8×C47—41no—
30Q8×C47—41no—
31C2×C4×C47—21no—
32C2×C4×C47—21no—
33C2×C4×C47—41no—
34C2×C4×C47—41no—
35C2×C4×C47D811yescharacteristic
36C2×C4×C47C2×D411yescharacteristic
37C2×Dic47—42no—
38C2×Dic47—82no—
39C8×C47—21no—
40C8×C47#4112yes—
41C22×C47—21no—
42C22×C47—21no—
43C22×C47SD3212yes—
44C22×C47C2×D811yescharacteristic
45C4×C47—21no—
46C4×C47—81no—
47C4×C47—81no—
48C4×C47#12311yescharacteristic
49C4×C47#13711yescharacteristic
50Dic47—82no—
51#2235—471nomaximal, Sylow
52C2×C47—22no—
53C2×C47#48011yescharacteristic
54C2×C47C2×SD3211yescharacteristic
55C2×C47#51011yescharacteristic
56#467D4711yescharacteristic
57C2×#107—471no—
58#367—472no—
59#358—472no—
60C22⋊C16—471no—
61C47#223511yescharacteristic, complemented, Sylow
62C2×Q16C2×D4711yescharacteristic
63C22×C8C2×D4711yescharacteristic
64C22⋊Q8—21no—
65C2×C4⋊C4—941no—
66C2×C16—472no—
67#107—472no—
68#107—941no—
69#107C2×D4711yescharacteristic
70#103—21no—
71C2×Q8—21no—
72C22×C4—1881no—
73C22×C4C22⋊D4711yescharacteristic
74Q16—22no—
75C2×C8—22no—
76C2×C8C22⋊D4711yescharacteristic
77C2×C8C22×D4711yescharacteristic
78C4⋊C4—21no—
79C4⋊C4—41no—
80C4⋊C4—942no—
81C4⋊C4—1881no—
82C22⋊C4—41no—
83C16—942no—
84C23#1062533411yescharacteristic
85Q8—41no—
86Q8—41no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—3762no—
92C2×C4—1882no—
93C2×C4#1062533411yescharacteristic
94C2×C4C2×C22⋊D4711yescharacteristic
95C8—21no—
96C8#1062535212yes—
97C22—21no—
98C22—21no—
99C22#1309396712yes—
100C22C2×#1062533411yescharacteristic
101C4—21no—
102C4—81no—
103C4—81no—
104C4—3762no—
105C4#1309400511yescharacteristic
106C4#1309405411yescharacteristic
107C2—22no—
108C2#1568943411yescharacteristic
109C2C2×#1309396711yescharacteristic
110C2#1568956311yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#467C2
socleC22×C47C2×D8
hypercenter#467D47
hypocenterC47#2235
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #15688950C2semidirect
3. #15688927C2semidirect
61. C47#2235semidirect