Finite Group Databasebeta

← #20241534

Subgroups — #20241534

Order 6016.

122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 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#15689290C211yesmaximal, characteristic
2#15688916C211yesmaximal, characteristic, complemented
3C47×#331C211yesmaximal, characteristic, complemented
4#13094069C411yescharacteristic, complemented
5#13094050—21no—
6#13093952—21no—
7#13093941C411yescharacteristic, complemented
8#13093939—21no—
9#127×C47C2211yescharacteristic
10C4⋊C8×C47—21no—
11C2×D4×C47—41no—
12C2×D4×C47C2×C411yescharacteristic
13C2×D4×C47D411yescharacteristic
14C2×C22⋊D47—41no—
15#10625352—41no—
16D4×D47—41no—
17#10625350—21no—
18C2×C8×C47—41no—
19C42×C47D411yescharacteristic
20C22⋊Dic47—41no—
21#10625335—41no—
22#10625334—41no—
23#10625329—21no—
24C23×C47—21no—
25C23×C47—21no—
26C22×D47—41no—
27D4×C47—41no—
28D4×C47—41no—
29D4×C47—81no—
30D4×C47—81no—
31C2×C4×C47—21no—
32C2×C4×C47C22⋊C411yescharacteristic
33C22⋊D47—42no—
34C22⋊D47—41no—
35C2×Dic47—41no—
36C2×Dic47—81no—
37D188—21no—
38C4×D47—41no—
39Dic94—21no—
40C8×C47—81no—
41C47⋊C8—41no—
42C22×C47—41no—
43C22×C47—41no—
44C22×C47—81no—
45C22×C47—81no—
46C22×C47#9911yescharacteristic
47C2×D47—41no—
48C2×D47—161no—
49C4×C47—21no—
50C4×C47—21no—
51C4×C47—21no—
52Dic47—41no—
53Dic47—161no—
54#1402—471nomaximal, Sylow
55C2×C47—21no—
56C2×C47—81no—
57C2×C47—81no—
58C2×C47AΣL(1,𝔽16)11yescharacteristic
59D47—81no—
60#453—471no—
61#353—471no—
62#331D4711yescharacteristic, complemented
63C47#140211yescharacteristic, complemented, Sylow
64H(5,𝔽2)—471no—
65AGL(1,ℤ/8)—941no—
66#127C2×D4711yescharacteristic
67C4⋊C8—21no—
68#104—941no—
69#100—471no—
70#99—941no—
71#41—941no—
72#41—1881no—
73C2×D4—41no—
74C2×D4—1881no—
75C2×D4—1881no—
76C2×D4C4×D4711yescharacteristic
77C2×D4D18811yescharacteristic
78SD16—1881no—
79D8—1881no—
80M16—941no—
81C2×C8—41no—
82C22⋊C4—1881no—
83C42C22⋊D4711yescharacteristic
84C23—21no—
85C23—21no—
86C23—1881no—
87Q8—941no—
88D4—41no—
89D4—41no—
90D4—81no—
91D4—81no—
92D4—941no—
93D4—1882no—
94D4—1881no—
95C2×C4—21no—
96C2×C4—3761no—
97C2×C4—1881no—
98C2×C4—1881no—
99C2×C4(C2×D47)⋊C411yescharacteristic
100C8—81no—
101C8—1881no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—1881no—
107C22—7521no—
108C22#1309393811yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—1881no—
113C4—7521no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—3761no—
118C2#1568891111yescharacteristic
subgroupG/H
centerC2#15688911
commutatorC2×D4×C47C2×C4
Frattini#127C2×D47
FittingC47×#331C2
socleC2×C47AΣL(1,𝔽16)
hypercenter#331D47
hypocenterC47#1402
LCSG ▷ C2×D4×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #15688916C2semidirect
3. C47×#331C2semidirect
4. #13094069C4semidirect
7. #13093941C4semidirect
62. #331D47semidirect
63. C47#1402semidirect