Finite Group Databasebeta

← #30636900

Subgroups — #30636900

Order 16256.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22550240C211yesmaximal, characteristic
2#22549669C211yesmaximal, characteristic
3#353×C127C211yesmaximal, characteristic
4#16861201C411yescharacteristic, complemented
5#16861130—21no—
6#16861130—21no—
7#16861124—21no—
8#16861120C411yescharacteristic, complemented
9#127×C127C2211yescharacteristic
10#99×C127—21no—
11C2×C127⋊C8—21no—
12C4⋊Dic127—21no—
13Dic127⋊C4—41no—
14C22⋊Dic127—41no—
15C2×D4×C127—41no—
16C2×D4×C127D411yescharacteristic
17C2×D4×C127D411yescharacteristic
18C22⋊C4×C127—41no—
19C42×C127C2×C411yescharacteristic
20C2×Dic127—41no—
21C2×Dic127—81no—
22C127⋊C8—41no—
23C23×C127—21no—
24C23×C127—21no—
25D4×C127—41no—
26D4×C127—41no—
27D4×C127—82no—
28C2×C4×C127—21no—
29C2×C4×C127—81no—
30C2×C4×C127C22⋊C411yescharacteristic
31C22×C127—41no—
32C22×C127—41no—
33C22×C127—81no—
34C22×C127—81no—
35C22×C127#9911yescharacteristic
36C4×C127—21no—
37C4×C127—41no—
38C4×C127—161no—
39Dic127—81no—
40Dic127—161no—
41C2×C127—21no—
42C2×C127—81no—
43C2×C127—81no—
44C2×C127#35411yescharacteristic
45#1412—1271nomaximal, Sylow
46C127#141211yescharacteristic, complemented, Sylow
47#490—1271no—
48#353—1271no—
49#353D12711yescharacteristic
50#127C2×D12711yescharacteristic
51#125—1271no—
52#102—2541no—
53#102—2541no—
54#99—21no—
55#99—2541no—
56#97—1271no—
57C2×D4—41no—
58C2×D4C22⋊D12711yescharacteristic
59C2×D4D50811yescharacteristic
60C2×C8—2541no—
61C4⋊C4—5081no—
62C4⋊C4—2541no—
63C22⋊C4—41no—
64C22⋊C4—5081no—
65C42C4×D12711yescharacteristic
66C23—21no—
67C23—21no—
68D4—41no—
69D4—41no—
70D4—82no—
71C2×C4—21no—
72C2×C4—81no—
73C2×C4—10161no—
74C2×C4—5081no—
75C2×C4(C2×D127)⋊C411yescharacteristic
76C8—5081no—
77C22—41no—
78C22—41no—
79C22—81no—
80C22—81no—
81C22#1686112311yescharacteristic
82C4—21no—
83C4—41no—
84C4—161no—
85C4—20321no—
86C4—10161no—
87C2—21no—
88C2—81no—
89C2—81no—
90C2#2254967011yescharacteristic
subgroupG/H
centerC2#22549670
commutatorC42×C127C2×C4
Frattini#127C2×D127
Fitting#353×C127C2
socleC2×C127#354
prime radical, cosocle#127×C127C22
hypercenter#353D127
hypocenterC127#1412
LCSG ▷ C42×C127 ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
4. #16861201C4semidirect
8. #16861120C4semidirect
46. C127#1412semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225502402
#225496692
#353×C1272
#1412127