Finite Group Databasebeta

← #22580719

Subgroups — #22580719

Order 8896.

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

normal subgroups only

This group has 142 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×C22⋊Dic139C211yesmaximal, characteristic
2C2×C22⋊Dic139C211yesmaximal, characteristic
3C2×C22⋊C4×C139C211yesmaximal, characteristic
4C22×Dic139—21no—
5C22×Dic139C412yescomplemented
6C22⋊Dic139—21no—
7C22⋊Dic139—21no—
8C22⋊Dic139—21no—
9C22⋊Dic139C412yescomplemented
10C24×C139C2211yescharacteristic
11C22×C4×C139—21no—
12C22⋊C4×C139—21no—
13C22⋊C4×C139C412yescomplemented
14C2×Dic139—22no—
15C2×Dic139—22no—
16C2×Dic139—42no—
17C2×Dic139—42no—
18C23×C139—42no—
19C23×C139C2×C411yescharacteristic
20C23×C139C2×C411yescharacteristic
21C23×C139C2×C411yescharacteristic
22C23×C139D411yescharacteristic
23C23×C139D411yescharacteristic
24C23×C139D411yescharacteristic
25C23×C139Q811yescharacteristic
26C2×C4×C139—22no—
27C2×C4×C139—42no—
28C22×C139—22no—
29C22×C139—22no—
30C22×C139—22no—
31C22×C139—41no—
32C22×C139—41no—
33C22×C139—41no—
34C22×C139—41no—
35C22×C139C4211yescharacteristic
36C22×C139C22⋊C411yescharacteristic
37C22×C139C22⋊C411yescharacteristic
38C22×C139C22⋊C411yescharacteristic
39C22×C139C4⋊C411yescharacteristic
40C22×C139C4⋊C411yescharacteristic
41C22×C139C4⋊C411yescharacteristic
42C4×C139—42no—
43Dic139—42no—
44Dic139—42no—
45C2×C139—21no—
46C2×C139—21no—
47C2×C139—21no—
48C2×C139—21no—
49C2×C139—21no—
50C2×C139—21no—
51C2×C139#9511yescharacteristic
52C2×C139#9912yes—
53C139#34211yescharacteristic, complemented, Sylow
54#342—1391nomaximal, Sylow
55C2×C22⋊C4—1391no—
56C2×C22⋊C4—1391no—
57C2×C22⋊C4D13911yescharacteristic
58C24C2×D13911yescharacteristic
59C22×C4—21no—
60C22×C4—2781no—
61C22×C4—1392no—
62C22⋊C4—21no—
63C22⋊C4—2781no—
64C22⋊C4—2781no—
65C22⋊C4—2781no—
66C22⋊C4—1392no—
67C22⋊C4Dic13912yescomplemented
68C23—42no—
69C23C4×D13911yescharacteristic
70C23C4×D13911yescharacteristic
71C23C2×Dic13911yescharacteristic
72C23C22⋊D13911yescharacteristic
73C23C22⋊D13911yescharacteristic
74C23D55611yescharacteristic
75C23Dic27811yescharacteristic
76C2×C4—22no—
77C2×C4—42no—
78C2×C4—2782no—
79C2×C4—2782no—
80C2×C4—5562no—
81C2×C4—5562no—
82C22—22no—
83C22—22no—
84C22—22no—
85C22—41no—
86C22—41no—
87C22—41no—
88C22—41no—
89C22C4×Dic13911yescharacteristic
90C22(C2×D139)⋊C411yescharacteristic
91C22(C2×D139)⋊C411yescharacteristic
92C22C22⋊Dic13911yescharacteristic
93C22Dic139⋊C411yescharacteristic
94C22Dic139⋊C411yescharacteristic
95C22C4⋊Dic13911yescharacteristic
96C4—42no—
97C4—5562no—
98C4—5562no—
99C2—21no—
100C2—21no—
101C2—21no—
102C2—21no—
103C2—21no—
104C2—21no—
105C2C139⋊#9511yescharacteristic
106C2#1798475612yes—
subgroupG/H
centerC22(C2×D139)⋊C4
commutatorC22×C139C42
FrattiniC24C2×D139
FittingC2×C22⋊C4×C139C2
socleC22×C139C22⋊C4
hypercenterC2×C22⋊C4D139
hypocenterC139#342
LCSG ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C22×Dic139C4semidirect
9. C22⋊Dic139C4semidirect
13. C22⋊C4×C139C4semidirect
53. C139#342semidirect
67. C22⋊C4Dic139semidirect