Finite Group Databasebeta

← #27193241

Subgroups — #27193241

Order 13184.

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

normal subgroups only

This group has 132 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
1C22×C103⋊C16C211yesmaximal, characteristic
2#20267829C211yesmaximal, characteristic
3C2×#108×C103C211yesmaximal, characteristic
4#15692980—21no—
5C2×C103⋊C16—21no—
6C2×C103⋊C16—21no—
7C2×C103⋊C16C412yescomplemented
8#15692955C412yes—
9#15692953—21no—
10C2×M16×C103—21no—
11C22×C8×C103C2211yescharacteristic
12#108×C103—21no—
13#108×C103C412yescomplemented
14C4⋊Dic103—22no—
15C22⋊Dic103—41no—
16C4×Dic103—41no—
17C103⋊C16—22no—
18C22×C4×C103D411yescharacteristic
19M16×C103—22no—
20M16×C103—41no—
21C2×C8×C103—41no—
22C2×C8×C103C2×C411yescharacteristic
23C2×C8×C103C2×C411yescharacteristic
24C2×C8×C103C2×C411yescharacteristic
25C2×C8×C103D411yescharacteristic
26C2×C8×C103D411yescharacteristic
27C2×C8×C103Q811yescharacteristic
28C23×C103SD1611yescharacteristic
29C2×C4×C103C22⋊C411yescharacteristic
30C2×C4×C103C22⋊C411yescharacteristic
31C2×C4×C103C4⋊C411yescharacteristic
32C2×C4×C103D811yescharacteristic
33C2×C4×C103SD1611yescharacteristic
34C2×C4×C103Q1611yescharacteristic
35C2×Dic103—42no—
36C8×C103—42no—
37C8×C103C4211yescharacteristic
38C8×C103C22⋊C411yescharacteristic
39C8×C103C4⋊C411yescharacteristic
40C8×C103C4⋊C411yescharacteristic
41C22×C103—22no—
42C22×C103#10211yescharacteristic
43C22×C103#10311yescharacteristic
44C22×C103#10611yescharacteristic
45C4×C103#9511yescharacteristic
46C4×C103#10211yescharacteristic
47C4×C103#10311yescharacteristic
48C4×C103#10711yescharacteristic
49Dic103—82no—
50C2×C103—21no—
51C2×C103—21no—
52C2×C103#34011yescharacteristic
53C2×C103#35912yes—
54#1382—1031nomaximal, Sylow
55C103#138211yescharacteristic, complemented, Sylow
56C22×C16—1031no—
57C2×#108D10311yescharacteristic
58#427—1031no—
59C2×M16—21no—
60C22×C8C2×D10311yescharacteristic
61#117—2061no—
62C2×C16—1032no—
63C2×C16—2061no—
64C2×C16—2061no—
65#108—21no—
66#108Dic10312yescomplemented
67#107—1032no—
68#106—2061no—
69C22×C4C22⋊D10311yescharacteristic
70M16—22no—
71M16—41no—
72C2×C8—41no—
73C2×C8Dic20611yescharacteristic
74C2×C8C4×D10311yescharacteristic
75C2×C8C4×D10311yescharacteristic
76C2×C8D41211yescharacteristic
77C2×C8C2×Dic10311yescharacteristic
78C2×C8C22⋊D10311yescharacteristic
79C4⋊C4—2062no—
80C22⋊C4—4121no—
81C42—4121no—
82C16—2062no—
83C23#1311009211yescharacteristic
84C2×C4—4122no—
85C2×C4(C2×D103)⋊C411yescharacteristic
86C2×C4C22⋊Dic10311yescharacteristic
87C2×C4Dic103⋊C411yescharacteristic
88C2×C4#1311009011yescharacteristic
89C2×C4#1311009311yescharacteristic
90C2×C4#1311009511yescharacteristic
91C8—42no—
92C8C4×Dic10311yescharacteristic
93C8(C2×D103)⋊C411yescharacteristic
94C8Dic103⋊C411yescharacteristic
95C8C4⋊Dic10311yescharacteristic
96C22—22no—
97C22#1569294111yescharacteristic
98C22#1569294511yescharacteristic
99C22#1569295211yescharacteristic
100C4—8242no—
101C4C103⋊#9511yescharacteristic
102C4#1569294211yescharacteristic
103C4#1569294411yescharacteristic
104C4#1569295411yescharacteristic
105C2—21no—
106C2—21no—
107C2#2026755311yescharacteristic
108C2#2026759712yes—
subgroupG/H
centerC2×C4#13110090
commutatorC8×C103C42
FrattiniC22×C8C2×D103
FittingC2×#108×C103C2
socleC22×C103#102
prime radicalC23×C103SD16
cosocleC22×C8×C103C22
hypercenterC2×#108D103
hypocenterC103#1382
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
7. C2×C103⋊C16C4semidirect
13. #108×C103C4semidirect
55. C103#1382semidirect
66. #108Dic103semidirect

Maximal subgroups

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

subgroupindex
C22×C103⋊C162
#202678292
C2×#108×C1032
#1382103