Finite Group Databasebeta

← #27193083

Subgroups — #27193083

Order 13184.

108 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 43 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×Dic103⋊C8C211yesmaximal, characteristic
2C22⋊(C103⋊C16)C211yesmaximal, characteristic
3C22⋊C16×C103C211yesmaximal, characteristic
4C22×C103⋊C8C411yescharacteristic
5C2×C4×Dic103C411yescharacteristic
6C2×C103⋊C16—21no—
7Dic103⋊C8—21no—
8Dic103⋊C8—21no—
9C22×C8×C103C2211yescharacteristic
10C2×C16×C103—21no—
11C22×Dic103C811yescharacteristic
12C22×Dic103C811yescharacteristic
13C2×C103⋊C8—21no—
14C2×C103⋊C8—41no—
15C4×Dic103—21no—
16C4×Dic103—21no—
17C103⋊C16—41no—
18C22×C4×C103C2×C411yescharacteristic
19C2×C8×C103—41no—
20C2×C8×C103D411yescharacteristic
21C2×C8×C103D411yescharacteristic
22C16×C103—41no—
23C23×C103C2×C811yescharacteristic
24C2×C4×C103—21no—
25C2×C4×C103—21no—
26C2×C4×C103C22⋊C411yescharacteristic
27C2×C4×C103M1611yescharacteristic
28C2×Dic103—21no—
29C2×Dic103—21no—
30C2×Dic103—21no—
31C2×Dic103—41no—
32C2×Dic103C1612yescomplemented
33C8×C103—21no—
34C8×C103—21no—
35C103⋊C8—41no—
36C22×C103—21no—
37C22×C103—21no—
38C22×C103C22⋊C811yescharacteristic
39C22×C103C2×C1611yescharacteristic
40C22×C103M3211yescharacteristic
41C4×C103—21no—
42C4×C103#9911yescharacteristic
43C4×C103#10111yescharacteristic
44Dic103—22no—
45Dic103—41no—
46C2×C103—21no—
47C2×C103—21no—
48C2×C103#32411yescharacteristic
49C2×C103C22⋊C1611yescharacteristic
50C2×C103#34911yescharacteristic
51#1322—1031nomaximal, Sylow
52C103#132211yescharacteristic, complemented, Sylow
53C2×C4⋊C8—1031no—
54C22⋊C16—1031no—
55C22⋊C16D10311yescharacteristic
56C22×C8—1031no—
57C22×C8C2×D10311yescharacteristic
58C2×C42—1031no—
59C2×C16—21no—
60C2×C16—2061no—
61C4⋊C8—2061no—
62C4⋊C8—2061no—
63C22×C4—1031no—
64C22×C4—1031no—
65C22×C4C4×D10311yescharacteristic
66C2×C8—41no—
67C2×C8—4121no—
68C2×C8—2061no—
69C2×C8D41211yescharacteristic
70C2×C8C22⋊D10311yescharacteristic
71C42—2061no—
72C42—2061no—
73C16—41no—
74C16—4121no—
75C23C8×D10311yescharacteristic
76C2×C4—21no—
77C2×C4—21no—
78C2×C4—1032no—
79C2×C4—4121no—
80C2×C4—2061no—
81C2×C4—2061no—
82C2×C4—2061no—
83C2×C4(C2×D103)⋊C411yescharacteristic
84C2×C4#1311008811yescharacteristic
85C8—21no—
86C8—21no—
87C8—4121no—
88C22—21no—
89C22—21no—
90C22(C2×D103)⋊C811yescharacteristic
91C22C16×D10311yescharacteristic
92C22#1569296011yescharacteristic
93C4—21no—
94C4—4121no—
95C4—2062no—
96C4#1569293511yescharacteristic
97C4#1569293911yescharacteristic
98C2—21no—
99C2—21no—
100C2#2026751611yescharacteristic
101C2(C2×D103)⋊C1611yescharacteristic
102C2#2026757211yescharacteristic
subgroupG/H
centerC2×C4(C2×D103)⋊C4
commutatorC22×C103C2×C16
FrattiniC22×C8C2×D103
FittingC22⋊C16×C103C2
socleC22×C103C22⋊C8
prime radicalC23×C103C2×C8
cosocleC22×C8×C103C22
hypercenterC22⋊C16D103
hypocenterC103#1322
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
32. C2×Dic103C16semidirect
52. C103#1322semidirect

Maximal subgroups

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

subgroupindex
C2×Dic103⋊C82
C22⋊(C103⋊C16)2
C22⋊C16×C1032
#1322103