Finite Group Databasebeta

← #27193021

Subgroups — #27193021

Order 13184.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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#20267755C212yesmaximal
2C2×C22⋊C8×C103C211yesmaximal, characteristic
3C2×#13110089—22no—
4C22⋊(C103⋊C8)—22no—
5C22⋊(C103⋊C8)C414yes—
6C23×C4×C103C2211yescharacteristic
7C22×C8×C103C412yes—
8C22⋊C8×C103—22no—
9#13110089—44no—
10C2×C103⋊C8—24no—
11C24×C103Q811yescharacteristic
12C22×C4×C103—42no—
13C22×C4×C103C2×C412yes—
14C22×C4×C103C2×C411yescharacteristic
15C22×C4×C103D411yescharacteristic
16C22×C4×C103D412yes—
17C2×C8×C103—22no—
18C2×C8×C103—42no—
19C23×C103—22no—
20C23×C103—41no—
21C23×C103—41no—
22C23×C103C4⋊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⋊C412yes—
30C2×C4×C103C22⋊C411yescharacteristic
31C8×C103—42no—
32C103⋊C8—44no—
33C22×C103—21no—
34C22×C103—21no—
35C22×C103—22no—
36C22×C103—22no—
37C22×C103—22no—
38C22×C103—44no—
39C22×C103#9511yescharacteristic
40C22×C103#10812yes—
41C4×C103—22no—
42C4×C103—21no—
43C4×C103#9912yes—
44C2×C103—22no—
45C2×C103—42no—
46C2×C103#33811yescharacteristic
47C2×C103#34111yescharacteristic
48C2×C103#34211yescharacteristic
49#1293—1031nomaximal, Sylow
50C103#129311yescharacteristic, complemented, Sylow
51#407—1032no—
52C2×C22⋊C8D10311yescharacteristic
53C23×C4C2×D10311yescharacteristic
54C2×M16—2062no—
55C22×C8Dic10312yes—
56C22⋊C8—22no—
57C22⋊C8—1034no—
58C22⋊C8—2062no—
59C24Dic20611yescharacteristic
60C22×C4—42no—
61C22×C4C4×D10312yes—
62C22×C4D41211yescharacteristic
63C22×C4C2×Dic10311yescharacteristic
64C22×C4C22⋊D10312yes—
65M16—4124no—
66C2×C8—22no—
67C2×C8—42no—
68C2×C8—2064no—
69C23—22no—
70C23—41no—
71C23—41no—
72C23Dic103⋊C412yes—
73C23C4⋊Dic10311yescharacteristic
74C2×C4—22no—
75C2×C4—24no—
76C2×C4—42no—
77C2×C4—41no—
78C2×C4C4×Dic10311yescharacteristic
79C2×C4(C2×D103)⋊C412yes—
80C2×C4C22⋊Dic10311yescharacteristic
81C8—42no—
82C8—4124no—
83C22—21no—
84C22—21no—
85C22—22no—
86C22—22no—
87C22—22no—
88C22—44no—
89C22C103⋊#9511yescharacteristic
90C22#1569295712yes—
91C4—22no—
92C4—21no—
93C4#1569293612yes—
94C2—22no—
95C2—42no—
96C2C103⋊#33811yescharacteristic
97C2#2026755611yescharacteristic
98C2#2026755811yescharacteristic
subgroupG/H
centerC22C103⋊#95
commutatorC2×C4×C103C42
FrattiniC23×C4C2×D103
FittingC2×C22⋊C8×C103C2
socleC22×C103#95
prime radicalC24×C103Q8
cosocleC23×C4×C103C22
hypercenterC2×C22⋊C8D103
hypocenterC103#1293
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
50. C103#1293semidirect

Maximal subgroups

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

subgroupindex
#202677552
C2×C22⋊C8×C1032
#1293103