Finite Group Databasebeta

← #27193012

Subgroups — #27193012

Order 13184.

228 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 77 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#20267651C212yesmaximal
2C2×C22⋊C8×C103C211yesmaximal, characteristic
3C2×C4⋊Dic103—22no—
4C2×C22⋊Dic103—22no—
5C103⋊#95C414yescomplemented
6C23×C4×C103C2211yescharacteristic
7C22×C8×C103C412yescomplemented
8C22⋊C8×C103—22no—
9C22×Dic103—24no—
10C4⋊Dic103—44no—
11C22⋊Dic103—42no—
12C22⋊Dic103—42no—
13C24×C103D411yescharacteristic
14C22×C4×C103—42no—
15C22×C4×C103C2×C412yes—
16C22×C4×C103C2×C411yescharacteristic
17C22×C4×C103D412yes—
18C22×C4×C103Q811yescharacteristic
19C2×C8×C103—22no—
20C2×C8×C103—42no—
21C23×C103—41no—
22C23×C103—41no—
23C23×C103C22⋊C412yes—
24C23×C103C4⋊C411yescharacteristic
25C23×C103D811yescharacteristic
26C23×C103SD1612yes—
27C23×C103Q1611yescharacteristic
28C2×C4×C103—22no—
29C2×C4×C103—24no—
30C2×C4×C103—42no—
31C2×C4×C103—41no—
32C2×C4×C103C4211yescharacteristic
33C2×C4×C103C22⋊C411yescharacteristic
34C2×C4×C103C4⋊C412yes—
35C2×Dic103—44no—
36C2×Dic103—44no—
37C2×Dic103—44no—
38C8×C103—42no—
39C22×C103—22no—
40C22×C103—21no—
41C22×C103—22no—
42C22×C103—21no—
43C22×C103—41no—
44C22×C103—42no—
45C22×C103—41no—
46C22×C103#9511yescharacteristic
47C22×C103#10212yes—
48C22×C103#10312yes—
49C22×C103#10611yescharacteristic
50C22×C103#10711yescharacteristic
51C4×C103—21no—
52C4×C103—22no—
53C4×C103#9912yes—
54Dic103—84no—
55C2×C103—22no—
56C2×C103—22no—
57C2×C103—21no—
58C2×C103—21no—
59C2×C103H(3,ℤ/4)11yescharacteristic
60C2×C103#34011yescharacteristic
61C2×C103#34211yescharacteristic
62#1289—1031nomaximal, Sylow
63C103#128911yescharacteristic, complemented, Sylow
64C2×C22⋊C8D10311yescharacteristic
65#380—1032no—
66C23×C4C2×D10311yescharacteristic
67C22×C8Dic10312yescomplemented
68C2×C4⋊C4—2062no—
69C2×C22⋊C4—2062no—
70C22⋊C8—22no—
71#95—1034no—
72C24D41211yescharacteristic
73C22×C4—42no—
74C22×C4—2064no—
75C22×C4Dic20611yescharacteristic
76C22×C4C4×D10312yes—
77C22×C4C2×Dic10311yescharacteristic
78C22×C4C22⋊D10312yes—
79C2×C8—22no—
80C2×C8—42no—
81C4⋊C4—4124no—
82C22⋊C4—4122no—
83C22⋊C4—4122no—
84C23—41no—
85C23—41no—
86C23(C2×D103)⋊C412yes—
87C23C4⋊Dic10311yescharacteristic
88C23D82411yescharacteristic
89C23#1311009412yes—
90C23Dic41211yescharacteristic
91C2×C4—24no—
92C2×C4—22no—
93C2×C4—41no—
94C2×C4—42no—
95C2×C4—4124no—
96C2×C4—4124no—
97C2×C4—4124no—
98C2×C4C4×Dic10311yescharacteristic
99C2×C4C22⋊Dic10311yescharacteristic
100C2×C4Dic103⋊C412yes—
101C8—42no—
102C22—22no—
103C22—21no—
104C22—22no—
105C22—21no—
106C22—41no—
107C22—42no—
108C22—41no—
109C22C103⋊#9511yescharacteristic
110C22#1569294312yes—
111C22#1569294612yes—
112C22#1569295311yescharacteristic
113C22#1569295511yescharacteristic
114C4—21no—
115C4—22no—
116C4—8244no—
117C4#1569293612yes—
118C2—22no—
119C2—22no—
120C2—21no—
121C2—21no—
122C2#2026754811yescharacteristic
123C2#2026755411yescharacteristic
124C2#2026755811yescharacteristic
subgroupG/H
centerC22C103⋊#95
commutatorC2×C4×C103C42
FrattiniC23×C4C2×D103
FittingC2×C22⋊C8×C103C2
socleC22×C103#95
prime radicalC24×C103D4
cosocleC23×C4×C103C22
hypercenterC2×C22⋊C8D103
hypocenterC103#1289
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
5. C103⋊#95C4semidirect
7. C22×C8×C103C4semidirect
63. C103#1289semidirect
67. C22×C8Dic103semidirect

Maximal subgroups

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

subgroupindex
#202676512
C2×C22⋊C8×C1032
#1289103