Finite Group Databasebeta

← #20245480

Subgroups — #20245480

Order 6016.

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

normal subgroups only

This group has 154 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
1C2×Dic376C211yesmaximal, characteristic, complemented
2C2×C16×D47C211yesmaximal, characteristic
3#15689365C212yesmaximal
4#15688926C212yesmaximal, complemented
5C47×#366C211yesmaximal, characteristic, complemented
6C2×Dic188C2212yes—
7C2×C8×D47C2211yescharacteristic
8#13094004—22no—
9Dic376—22no—
10C2×C47⋊C16C2211yescharacteristic
11C16×D47—22no—
12#13093947—22no—
13C2×C16×C47C2211yescharacteristic
14#107×C47C2212yes—
15C2×C4×D47D411yescharacteristic
16C2×Dic94—22no—
17C2×C8×C47C2311yescharacteristic
18C4⋊C4×C47—22no—
19(C2×D47)⋊C4—42no—
20C4⋊Dic47—42no—
21C2×C47⋊C8D411yescharacteristic
22Dic188—22no—
23Dic188—22no—
24C8×D47—21no—
25C8×D47—21no—
26C16×C47D412yes—
27C47⋊C16—21no—
28C22×D47D811yescharacteristic
29C2×C4×C47—42no—
30C2×C4×C47C2×D411yescharacteristic
31C2×Dic47—42no—
32C2×Dic47D811yescharacteristic
33C4×D47—21no—
34C4×D47—21no—
35Dic94—42no—
36Dic94—42no—
37C8×C47C2×D411yescharacteristic
38C8×C47#4111yescharacteristic
39C47⋊C8—21no—
40C22×C47C2×D811yescharacteristic
41C2×D47—21no—
42C2×D47—21no—
43C2×D47Q3212yescomplemented
44C4×C47—82no—
45C4×C47#12111yescharacteristic
46C4×C47#13511yescharacteristic
47Dic47—21no—
48Dic47—82no—
49#2216—471nomaximal, Sylow
50C2×C47#46611yescharacteristic
51C2×C47C2×Q3211yescharacteristic
52C2×C47#50811yescharacteristic
53D47—22no—
54C2×Q32—471no—
55C22×C16—471no—
56#467—472no—
57#366D4711yescharacteristic, complemented
58#358—472no—
59C47#221611yescharacteristic, complemented, Sylow
60C2×Q16—472no—
61C22×C8—471no—
62C22⋊Q8—942no—
63Q32—942no—
64C2×C16—471no—
65C2×C16—942no—
66C2×C16C2×D4711yescharacteristic
67#107C2×D4712yes—
68#103—942no—
69C2×Q8—942no—
70C22×C4—471no—
71Q16—942no—
72Q16—942no—
73C2×C8—471no—
74C2×C8—941no—
75C2×C8—941no—
76C2×C8C22×D4711yescharacteristic
77C4⋊C4—22no—
78C4⋊C4—1882no—
79C22⋊C4—1882no—
80C16—941no—
81C16D18812yes—
82C23—471no—
83Q8—1882no—
84Q8—1882no—
85C2×C4—42no—
86C2×C4—471no—
87C2×C4—941no—
88C2×C4—941no—
89C2×C4—1882no—
90C2×C4D4×D4711yescharacteristic
91C8—941no—
92C8C2×D18811yescharacteristic
93C8#1062535411yescharacteristic
94C22—472no—
95C22—941no—
96C22—941no—
97C22D8×D4711yescharacteristic
98C4—82no—
99C4—941no—
100C4—3762no—
101C4#1309399911yescharacteristic
102C4#1309404711yescharacteristic
103C2—942no—
104C2#1568936011yescharacteristic
105C2Q32×D4711yescharacteristic
106C2#1568955211yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#366C2
socleC22×C47C2×D8
hypercenter#366D47
hypocenterC47#2216
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
1. C2×Dic376C2semidirect
4. #15688926C2semidirect
5. C47×#366C2semidirect
43. C2×D47Q32semidirect
57. #366D47semidirect
59. C47#2216semidirect