Finite Group Databasebeta

← #20245614

Subgroups — #20245614

Order 6016.

140 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 51 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#15689527C211yesmaximal, characteristic
2#15689501C211yesmaximal, characteristic
3#15688928C211yesmaximal, characteristic
4#15688927C211yesmaximal, characteristic
5#15688926C211yesmaximal, characteristic
6C16×Dic47C211yesmaximal, characteristic
7C47×#358C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9C2×#10625337—21no—
10#13094023—21no—
11#13094022—21no—
12C2×C47⋊C16C2211yescharacteristic
13#13093958C2211yescharacteristic
14#13093957—21no—
15C8×Dic47C2211yescharacteristic
16C2×Q16×C47C2211yescharacteristic
17C2×C16×C47C2211yescharacteristic
18#107×C47C2211yescharacteristic
19C2×Q8×C47—21no—
20C2×Dic94—21no—
21C2×Dic94—41no—
22Q16×C47—21no—
23Q16×C47—21no—
24C2×C8×C47C2311yescharacteristic
25C4⋊C4×C47—21no—
26#10625337—42no—
27C4⋊Dic47—21no—
28Dic47⋊C4—41no—
29Dic47⋊C4—41no—
30Dic47⋊C4—41no—
31C4×Dic47D411yescharacteristic
32C2×C47⋊C8D411yescharacteristic
33Dic188—21no—
34Dic188—21no—
35C16×C47—21no—
36C47⋊C16—21no—
37Q8×C47—41no—
38Q8×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47—41no—
41C2×C4×C47C2×D411yescharacteristic
42C2×Dic47—41no—
43C2×Dic47—41no—
44C2×Dic47D811yescharacteristic
45C2×Dic47D811yescharacteristic
46Dic94—41no—
47Dic94—41no—
48Dic94—82no—
49C8×C47#4111yescharacteristic
50C8×C47#4111yescharacteristic
51C47⋊C8SD1612yes—
52C22×C47C2×D811yescharacteristic
53C4×C47—81no—
54C4×C47—81no—
55C4×C47#12411yescharacteristic
56C4×C47C2×SD1611yescharacteristic
57Dic47—81no—
58Dic47—81no—
59Dic47SD3212yes—
60Dic47Q3212yes—
61#2241—471nomaximal, Sylow
62C2×C47#48611yescharacteristic
63C2×C47C2×SD3211yescharacteristic
64C2×C47C2×Q3211yescharacteristic
65#500—471no—
66#494—471no—
67#358—471no—
68#358—471no—
69#358—471no—
70#358D4711yescharacteristic
71C4×C16—471no—
72C47#224111yescharacteristic, complemented, Sylow
73C2×Q16—471no—
74C2×Q16—941no—
75C2×Q16C2×D4711yescharacteristic
76C4⋊Q8—941no—
77C4⋊Q8—941no—
78C2×C16—471no—
79C2×C16C2×D4711yescharacteristic
80#107—471no—
81#107—941no—
82#107C2×D4711yescharacteristic
83C4×C8—471no—
84C2×Q8—21no—
85C2×Q8—941no—
86C2×Q8—1881no—
87Q16—21no—
88Q16—21no—
89Q16—941no—
90Q16—941no—
91Q16—1882no—
92C2×C8—471no—
93C2×C8C22×D4711yescharacteristic
94C4⋊C4—21no—
95C4⋊C4—941no—
96C4⋊C4—1881no—
97C4⋊C4—1881no—
98C4⋊C4—1881no—
99C42—471no—
100C16—21no—
101C16—941no—
102Q8—41no—
103Q8—41no—
104Q8—3762no—
105Q8—1881no—
106Q8—1881no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—471no—
110C2×C4—471no—
111C2×C4—1881no—
112C2×C4—1881no—
113C2×C4D4×D4711yescharacteristic
114C8—472no—
115C8#1062535011yescharacteristic
116C8#1062535211yescharacteristic
117C22D8×D4711yescharacteristic
118C4—81no—
119C4—81no—
120C4—472no—
121C4—472no—
122C4—3761no—
123C4—3761no—
124C4#1309401011yescharacteristic
125C4SD16×D4711yescharacteristic
126C2#1568946811yescharacteristic
127C2SD32×D4711yescharacteristic
128C2Q32×D4711yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#358C2
socleC22×C47C2×D8
hypercenter#358D47
hypocenterC47#2241
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
72. C47#2241semidirect