Finite Group Databasebeta

← #27193029

Subgroups — #27193029

Order 13184.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C4×C22⋊Dic103C212yesmaximal
2#407×C103C211yesmaximal, characteristic
3C2×C22⋊Dic103—22no—
4C2×C4×Dic103—22no—
5C103⋊#95C414yescomplemented
6C23×C4×C103C2211yescharacteristic
7C2×M16×C103C412yescomplemented
8C22⋊C8×C103—22no—
9C22×Dic103—24no—
10C22⋊Dic103—28no—
11C4×Dic103—44no—
12C24×C103D411yescharacteristic
13C22×C4×C103—42no—
14C22×C4×C103C2×C412yes—
15C22×C4×C103C2×C411yescharacteristic
16C22×C4×C103D412yes—
17C22×C4×C103Q811yescharacteristic
18M16×C103—42no—
19C2×C8×C103—22no—
20C23×C103—24no—
21C23×C103—41no—
22C23×C103C22⋊C412yes—
23C23×C103C4⋊C411yescharacteristic
24C2×C4×C103—22no—
25C2×C4×C103—24no—
26C2×C4×C103—42no—
27C2×C4×C103—41no—
28C2×C4×C103C4211yescharacteristic
29C2×C4×C103C22⋊C411yescharacteristic
30C2×C4×C103C4⋊C412yes—
31C2×Dic103—28no—
32C2×Dic103—44no—
33C2×Dic103—44no—
34C8×C103—42no—
35C22×C103—22no—
36C22×C103—22no—
37C22×C103—22no—
38C22×C103—21no—
39C22×C103—44no—
40C22×C103#9511yescharacteristic
41C22×C103#10414yes—
42C4×C103—21no—
43C4×C103—22no—
44C4×C103#9912yes—
45Dic103—48no—
46C2×C103—24no—
47C2×C103—41no—
48C2×C103#33912yes—
49C2×C103#34211yescharacteristic
50#1297—1031nomaximal, Sylow
51C103#129711yescharacteristic, complemented, Sylow
52#407D10311yescharacteristic
53C4×C22⋊C4—1032no—
54C23×C4C2×D10311yescharacteristic
55C2×M16Dic10312yescomplemented
56C2×C22⋊C4—2062no—
57C2×C42—2062no—
58C22⋊C8—22no—
59#95—1034no—
60C24D41211yescharacteristic
61C22×C4—42no—
62C22×C4—2064no—
63C22×C4Dic20611yescharacteristic
64C22×C4C4×D10312yes—
65C22×C4C2×Dic10311yescharacteristic
66C22×C4C22⋊D10312yes—
67M16—42no—
68C2×C8—22no—
69C22⋊C4—2068no—
70C42—4124no—
71C23—24no—
72C23—41no—
73C23(C2×D103)⋊C412yes—
74C23C4⋊Dic10311yescharacteristic
75C2×C4—24no—
76C2×C4—22no—
77C2×C4—41no—
78C2×C4—42no—
79C2×C4—4124no—
80C2×C4—4124no—
81C2×C4—2068no—
82C2×C4C4×Dic10311yescharacteristic
83C2×C4C22⋊Dic10311yescharacteristic
84C2×C4Dic103⋊C412yes—
85C8—42no—
86C22—22no—
87C22—22no—
88C22—22no—
89C22—21no—
90C22—44no—
91C22C103⋊#9511yescharacteristic
92C22#1569294714yes—
93C4—21no—
94C4—22no—
95C4—4128no—
96C4#1569293612yes—
97C2—24no—
98C2—41no—
99C2#2026755212yes—
100C2#2026755811yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic103
commutatorC2×C4×C103C42
FrattiniC23×C4C2×D103
Fitting#407×C103C2
socleC22×C103#95
prime radicalC24×C103D4
cosocleC23×C4×C103C22
hypercenter#407D103
hypocenterC103#1297
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
5. C103⋊#95C4semidirect
7. C2×M16×C103C4semidirect
51. C103#1297semidirect
55. C2×M16Dic103semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊Dic1032
#407×C1032
#1297103