Finite Group Databasebeta

← #27195293

Subgroups — #27195293

Order 13184.

162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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#20267562C212yesmaximal
2#20267551C212yesmaximal
3C103⋊#338C211yesmaximal, characteristic
4#20267548C211yesmaximal, characteristic
5C4×M16×C103C211yesmaximal, characteristic
6C2×#13110089C2212yes—
7#15692980C2212yes—
8C2×M16×C103C2211yescharacteristic
9C2×M16×C103C2211yescharacteristic
10C2×C42×C103C2211yescharacteristic
11#97×C103C412yescomplemented
12C4×C8×C103C412yescomplemented
13#13110089—22no—
14#13110089—22no—
15C2×C103⋊C8—22no—
16C4⋊Dic103—22no—
17C22⋊Dic103—22no—
18C4×Dic103—22no—
19C22×C4×C103—21no—
20C22×C4×C103C2311yescharacteristic
21M16×C103—22no—
22M16×C103—22no—
23C2×C8×C103C2×C412yes—
24C2×C8×C103C2×C412yes—
25C42×C103—21no—
26C42×C103C2×C411yescharacteristic
27C42×C103C2×C411yescharacteristic
28C23×C103#4111yescharacteristic
29C2×C4×C103—21no—
30C2×C4×C103—21no—
31C2×C4×C103—42no—
32C2×C4×C103C22×C411yescharacteristic
33C2×C4×C103#4112yes—
34C2×C4×C103#4112yes—
35C2×C4×C103#4111yescharacteristic
36C2×Dic103—42no—
37C8×C103—22no—
38C8×C103—22no—
39C103⋊C8—42no—
40C22×C103—41no—
41C22×C103#11711yescharacteristic
42C22×C103#12612yes—
43C4×C103—22no—
44C4×C103—41no—
45C4×C103#11711yescharacteristic
46C4×C103#11711yescharacteristic
47C4×C103#12612yes—
48Dic103—82no—
49C2×C103—22no—
50C2×C103—21no—
51C2×C103#38311yescharacteristic
52#1841—1031nomaximal, Sylow
53C103#184111yescharacteristic, complemented, Sylow
54C4×M16D10311yescharacteristic
55#344—1032no—
56#339—1032no—
57#338—1031no—
58H(3,ℤ/4)—1031no—
59C2×M16—1032no—
60C2×M16C2×D10311yescharacteristic
61C2×M16C2×D10311yescharacteristic
62#117—1032no—
63C2×C42C2×D10311yescharacteristic
64#97Dic10312yescomplemented
65C4×C8Dic10312yescomplemented
66C22×C4—21no—
67C22×C4C22×D10311yescharacteristic
68M16—22no—
69M16—22no—
70M16—2062no—
71M16—2062no—
72C2×C8—2062no—
73C2×C8C2×Dic10312yes—
74C2×C8C2×Dic10312yes—
75C4⋊C4—2062no—
76C22⋊C4—2062no—
77C42—21no—
78C42—2062no—
79C42C2×Dic10311yescharacteristic
80C42C2×Dic10311yescharacteristic
81C23#1311010511yescharacteristic
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—42no—
85C2×C4—4122no—
86C2×C4C22×Dic10311yescharacteristic
87C2×C4#1311010512yes—
88C2×C4#1311010512yes—
89C2×C4#1311010511yescharacteristic
90C8—22no—
91C8—22no—
92C8—4122no—
93C22—41no—
94C22#1569298011yescharacteristic
95C22#1569301512yes—
96C4—22no—
97C4—41no—
98C4—8242no—
99C4#1569298011yescharacteristic
100C4#1569298011yescharacteristic
101C4#1569301512yes—
102C2—21no—
103C2—22no—
104C2#2026765911yescharacteristic
subgroupG/H
centerC4#15692980
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC4×M16×C103C2
socleC2×C103#383
prime radicalC23×C103#41
cosocleC22×C4×C103C23
hypercenterC4×M16D103
hypocenterC103#1841
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C2×M16 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
11. #97×C103C4semidirect
12. C4×C8×C103C4semidirect
53. C103#1841semidirect
64. #97Dic103semidirect
65. C4×C8Dic103semidirect

Maximal subgroups

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

subgroupindex
#202675622
#202675512
C103⋊#3382
#202675482
C4×M16×C1032
#1841103