Finite Group Databasebeta

← #20241539

Subgroups — #20241539

Order 6016.

112 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 25 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#15688918C211yesmaximal, characteristic, complemented
2#15688863C211yesmaximal, characteristic, complemented
3C47×#454C211yesmaximal, characteristic
4#13093939—21no—
5#13093935—21no—
62−1+4×C47C411yescharacteristic, complemented
7AGL(1,ℤ/8)×C47—21no—
8#124×C47C2211yescharacteristic
9#104×C47—21no—
10#101×C47C411yescharacteristic, complemented
11#41×C47—21no—
12#41×C47—41no—
13#41×C47—41no—
14C2×Q8×C47—41no—
15C2×Q8×C47C2×C411yescharacteristic
16C2×D4×C47D411yescharacteristic
17SD16×C47—41no—
18D8×C47—41no—
19M16×C47—21no—
20C22⋊C4×C47—41no—
21C42×C47D411yescharacteristic
22C22⋊Dic47—41no—
23C2×C47⋊C8—41no—
24C23×C47—21no—
25Q8×C47—21no—
26Q8×C47—41no—
27Q8×C47—41no—
28D4×C47—21no—
29D4×C47—41no—
30D4×C47—41no—
31D4×C47—41no—
32C2×C4×C47—21no—
33C2×C4×C47—21no—
34C2×C4×C47—41no—
35C2×C4×C47—42no—
36C2×C4×C47C22⋊C411yescharacteristic
37C2×Dic47—81no—
38C8×C47—41no—
39C47⋊C8—42no—
40C22×C47—41no—
41C22×C47—41no—
42C22×C47—81no—
43C22×C47#9911yescharacteristic
44C4×C47—21no—
45C4×C47—41no—
46C4×C47—41no—
47C4×C47—41no—
48Dic47—161no—
49#1404—471nomaximal, Sylow
50C2×C47—21no—
51C2×C47—81no—
52C2×C47—81no—
53C2×C47AΣL(1,𝔽16)11yescharacteristic
54#454D4711yescharacteristic
55#354—471no—
56#329—471no—
57C47#140411yescharacteristic, complemented, Sylow
582−1+4Dic4711yescharacteristic, complemented
59AGL(1,ℤ/8)—21no—
60#124C2×D4711yescharacteristic
61#104—21no—
62#101Dic4711yescharacteristic, complemented
63#99—941no—
64#97—941no—
65#41—21no—
66#41—41no—
67#41—41no—
68C2×Q8—41no—
69C2×Q8C2×Dic4711yescharacteristic
70C2×D4C22⋊D4711yescharacteristic
71SD16—41no—
72D8—41no—
73M16—21no—
74C2×C8—1881no—
75C22⋊C4—41no—
76C22⋊C4—1881no—
77C42C22⋊D4711yescharacteristic
78C23—21no—
79Q8—21no—
80Q8—41no—
81Q8—41no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—41no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—41no—
89C2×C4—42no—
90C2×C4—3761no—
91C2×C4C22⋊Dic4711yescharacteristic
92C8—41no—
93C8—1882no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22#1309393911yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—41no—
102C4—7521no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#1568891011yescharacteristic
subgroupG/H
centerC2#15688910
commutatorC2×Q8×C47C2×C4
Frattini#124C2×D47
FittingC47×#454C2
socleC2×C47AΣL(1,𝔽16)
hypercenter#454D47
hypocenterC47#1404
LCSG ▷ C2×Q8×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #15688918C2semidirect
2. #15688863C2semidirect
6. 2−1+4×C47C4semidirect
10. #101×C47C4semidirect
57. C47#1404semidirect
58. 2−1+4Dic47semidirect
62. #101Dic47semidirect