Finite Group Databasebeta

← #27193009

Subgroups — #27193009

Order 13184.

152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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#20267848C211yesmaximal, characteristic
2#20267659C211yesmaximal, characteristic
3C4×M16×C103C211yesmaximal, characteristic
4C4⋊(C103⋊C8)—21no—
5C22⋊(C103⋊C8)—21no—
6#15692932C412yescomplemented
7C103⋊#95—21no—
8C103⋊#95—21no—
9C103⋊#95C412yes—
10C2×M16×C103—21no—
11C2×C42×C103C2211yescharacteristic
12#97×C103—21no—
13C4×C8×C103C412yescomplemented
14C22×Dic103—22no—
15C2×C103⋊C8—22no—
16C22×C4×C103C2×C411yescharacteristic
17C22×C4×C103D411yescharacteristic
18C22×C4×C103D411yescharacteristic
19M16×C103—24no—
20C2×C8×C103—22no—
21C42×C103C2×C411yescharacteristic
22C42×C103C2×C411yescharacteristic
23C42×C103D411yescharacteristic
24C42×C103Q811yescharacteristic
25C23×C103C22⋊C411yescharacteristic
26C2×C4×C103—22no—
27C2×C4×C103—41no—
28C2×C4×C103—41no—
29C2×C4×C103C4211yescharacteristic
30C2×C4×C103C22⋊C411yescharacteristic
31C2×C4×C103C22⋊C411yescharacteristic
32C2×C4×C103C4⋊C411yescharacteristic
33C2×C4×C103C4⋊C411yescharacteristic
34C2×C4×C103C4⋊C411yescharacteristic
35C2×Dic103—42no—
36C2×Dic103—42no—
37C2×Dic103—42no—
38C8×C103—24no—
39C103⋊C8—42no—
40C22×C103—21no—
41C22×C103—21no—
42C22×C103#9511yescharacteristic
43C22×C103#10412yes—
44C4×C103—21no—
45C4×C103—21no—
46C4×C103—21no—
47C4×C103—21no—
48C4×C103—21no—
49C4×C103—21no—
50Dic103—82no—
51C2×C103—22no—
52C2×C103H(3,ℤ/4)11yescharacteristic
53C2×C103#33911yescharacteristic
54C2×C103#34411yescharacteristic
55#1288—1031nomaximal, Sylow
56C103#128811yescharacteristic, complemented, Sylow
57#432—1031no—
58C4×M16D10311yescharacteristic
59#383—1031no—
60C2×M16—21no—
61C2×C42C2×D10311yescharacteristic
62C4⋊C8—2061no—
63C22⋊C8—2061no—
64#97—21no—
65#97—1032no—
66C4×C8Dic10312yescomplemented
67#95—1032no—
68#95—2061no—
69#95—2061no—
70C22×C4—2062no—
71C22×C4C4×D10311yescharacteristic
72C22×C4D41211yescharacteristic
73C22×C4C22⋊D10311yescharacteristic
74M16—24no—
75C2×C8—22no—
76C2×C8—2062no—
77C42Dic20611yescharacteristic
78C42C4×D10311yescharacteristic
79C42C2×Dic10311yescharacteristic
80C42C22⋊D10311yescharacteristic
81C23(C2×D103)⋊C411yescharacteristic
82C2×C4—22no—
83C2×C4—41no—
84C2×C4—41no—
85C2×C4—4122no—
86C2×C4—4122no—
87C2×C4—4122no—
88C2×C4C4×Dic10311yescharacteristic
89C2×C4(C2×D103)⋊C411yescharacteristic
90C2×C4C22⋊Dic10311yescharacteristic
91C2×C4Dic103⋊C411yescharacteristic
92C2×C4Dic103⋊C411yescharacteristic
93C2×C4C4⋊Dic10311yescharacteristic
94C8—24no—
95C8—4122no—
96C22—21no—
97C22—21no—
98C22C103⋊#9511yescharacteristic
99C22#1569294912yes—
100C4—21no—
101C4—21no—
102C4—21no—
103C4—21no—
104C4—21no—
105C4—21no—
106C4—8242no—
107C2—22no—
108C2#2026754811yescharacteristic
109C2#2026755111yescharacteristic
110C2#2026756211yescharacteristic
subgroupG/H
centerC22C103⋊#95
commutatorC2×C4×C103C42
FrattiniC2×C42C2×D103
FittingC4×M16×C103C2
socleC22×C103#95
prime radicalC23×C103C22⋊C4
cosocleC2×C42×C103C22
hypercenterC4×M16D103
hypocenterC103#1288
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
6. #15692932C4semidirect
13. C4×C8×C103C4semidirect
56. C103#1288semidirect
66. C4×C8Dic103semidirect

Maximal subgroups

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

subgroupindex
#202678482
#202676592
C4×M16×C1032
#1288103