Finite Group Databasebeta

← #22549663

Subgroups — #22549663

Order 8128.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16861126C211yesmaximal, characteristic, complemented
2#16861124C211yesmaximal, characteristic, complemented
3#120×C127C211yesmaximal, characteristic
4#14523232—21no—
5C22⋊Dic127—21no—
6C24×C127C411yescharacteristic, complemented
7C2×D4×C127—21no—
8C2×D4×C127C2211yescharacteristic
9C22⋊C4×C127—21no—
10C22⋊C4×C127C411yescharacteristic, complemented
11C2×Dic127—41no—
12C127⋊C8—41no—
13C23×C127—21no—
14C23×C127—42no—
15C23×C127—41no—
16C23×C127C2×C411yescharacteristic
17C23×C127D411yescharacteristic
18D4×C127—41no—
19D4×C127—42no—
20C2×C4×C127—21no—
21C2×C4×C127D411yescharacteristic
22C22×C127—22no—
23C22×C127—21no—
24C22×C127—21no—
25C22×C127—41no—
26C22×C127—41no—
27C22×C127—41no—
28C22×C127—42no—
29C22×C127—42no—
30C22×C127—41no—
31C22×C127C22⋊C411yescharacteristic
32C4×C127—21no—
33C4×C127—41no—
34Dic127—81no—
35C2×C127—21no—
36C2×C127—41no—
37C2×C127—42no—
38C2×C127—41no—
39C2×C127#9911yescharacteristic
40C127AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
41AΣL(1,𝔽16)—1271nomaximal, Sylow
42#120D12711yescharacteristic
43#100—1271no—
44#99—1271no—
45C24Dic12711yescharacteristic, complemented
46C2×D4—21no—
47C2×D4C2×D12711yescharacteristic
48M16—2541no—
49C22⋊C4—21no—
50C22⋊C4—2541no—
51C22⋊C4Dic12711yescharacteristic, complemented
52C23—21no—
53C23—42no—
54C23—41no—
55C23C2×Dic12711yescharacteristic
56C23C22⋊D12711yescharacteristic
57D4—41no—
58D4—42no—
59C2×C4—21no—
60C2×C4—5081no—
61C2×C4C22⋊D12711yescharacteristic
62C8—5081no—
63C22—22no—
64C22—21no—
65C22—21no—
66C22—41no—
67C22—41no—
68C22—41no—
69C22—42no—
70C22—42no—
71C22—41no—
72C22C22⋊Dic12711yescharacteristic
73C4—21no—
74C4—41no—
75C4—10161no—
76C2—21no—
77C2—41no—
78C2—42no—
79C2—41no—
80C2#1686112411yescharacteristic
subgroupG/H
centerC2#16861124
commutatorC23×C127C2×C4
FrattiniC2×D4C2×D127
Fitting#120×C127C2
socleC2×C127#99
hypercenter#120D127
hypocenterC127AΣL(1,𝔽16)
LCSG ▷ C23×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #16861126C2semidirect
2. #16861124C2semidirect
6. C24×C127C4semidirect
10. C22⋊C4×C127C4semidirect
40. C127AΣL(1,𝔽16)semidirect
45. C24Dic127semidirect
51. C22⋊C4Dic127semidirect