Finite Group Databasebeta

← #27193267

Subgroups — #27193267

Order 13184.

158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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#20267775C212yesmaximal
2#408×C103C211yesmaximal, characteristic
3C2×#13110089—22no—
4#15692940—22no—
5#15692938C414yes—
6C2×#41×C103C2211yescharacteristic
7C2×M16×C103C411yescharacteristic
8C22×C8×C103C411yescharacteristic
9C22⋊C8×C103—22no—
10#13110089—24no—
11#13110089—42no—
12C2×C103⋊C8—42no—
13#41×C103—41no—
14#41×C103—41no—
15C2×Q8×C103D411yescharacteristic
16C2×D4×C103C2×C412yes—
17C2×D4×C103Q811yescharacteristic
18C22×C4×C103C2×C411yescharacteristic
19C22×C4×C103D412yes—
20M16×C103—41no—
21C2×C8×C103—21no—
22C2×C8×C103—21no—
23C2×C8×C103—41no—
24C23×C103C4211yescharacteristic
25C23×C103C4⋊C412yes—
26Q8×C103—41no—
27D4×C103—42no—
28D4×C103—41no—
29C2×C4×C103—21no—
30C2×C4×C103—21no—
31C2×C4×C103—22no—
32C2×C4×C103—22no—
33C2×C4×C103C22⋊C412yes—
34C2×C4×C103C22⋊C411yescharacteristic
35C2×C4×C103C4⋊C411yescharacteristic
36C8×C103—41no—
37C8×C103—41no—
38C103⋊C8—44no—
39C22×C103—21no—
40C22×C103—22no—
41C22×C103—41no—
42C22×C103—42no—
43C22×C103#9511yescharacteristic
44C4×C103—22no—
45C4×C103—21no—
46C4×C103#9911yescharacteristic
47C4×C103#9911yescharacteristic
48C2×C103—21no—
49C2×C103—41no—
50C2×C103—42no—
51C2×C103#34211yescharacteristic
52#1392—1031nomaximal, Sylow
53C103#139211yescharacteristic, complemented, Sylow
54#413—1032no—
55#408D10311yescharacteristic
56C2×#41C2×D10311yescharacteristic
57C2×M16—2062no—
58C2×M16Dic10311yescharacteristic
59C22×C8Dic10311yescharacteristic
60#101—2062no—
61#100—1034no—
62C22⋊C8—22no—
63#41—41no—
64#41—41no—
65C2×Q8D41211yescharacteristic
66C2×D4Dic20611yescharacteristic
67C2×D4C4×D10312yes—
68C22×C4C2×Dic10311yescharacteristic
69C22×C4C22⋊D10312yes—
70M16—41no—
71M16—4122no—
72M16—2064no—
73C2×C8—21no—
74C2×C8—21no—
75C2×C8—41no—
76C2×C8—4122no—
77C23C4×Dic10311yescharacteristic
78C23Dic103⋊C412yes—
79Q8—41no—
80D4—41no—
81D4—42no—
82C2×C4—21no—
83C2×C4—22no—
84C2×C4—21no—
85C2×C4—22no—
86C2×C4(C2×D103)⋊C412yes—
87C2×C4C22⋊Dic10311yescharacteristic
88C2×C4C4⋊Dic10311yescharacteristic
89C8—41no—
90C8—41no—
91C8—4124no—
92C22—21no—
93C22—22no—
94C22—41no—
95C22—42no—
96C22C103⋊#9511yescharacteristic
97C4—22no—
98C4—21no—
99C4#1569293611yescharacteristic
100C4#1569293611yescharacteristic
101C2—21no—
102C2—41no—
103C2—42no—
104C2#2026755811yescharacteristic
subgroupG/H
centerC4#15692936
commutatorC23×C103C42
FrattiniC2×#41C2×D103
Fitting#408×C103C2
socleC2×C103#342
prime radical, cosocleC2×#41×C103C22
hypercenter#408D103
hypocenterC103#1392
LCSG ▷ C23×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
53. C103#1392semidirect

Maximal subgroups

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

subgroupindex
#202677752
#408×C1032
#1392103