Finite Group Databasebeta

← #27193003

Subgroups — #27193003

Order 13184.

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

normal subgroups only

This group has 156 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#20267815C211yesmaximal, characteristic
2#20267657C211yesmaximal, characteristic
3#431×C103C211yesmaximal, characteristic
4C2×#13110089—21no—
5C2×C4⋊Dic103—21no—
6C4⋊(C103⋊C8)—21no—
7C4⋊(C103⋊C8)C412yescomplemented
8C103⋊#95—21no—
9C103⋊#95C412yes—
10C2×C42×C103C2211yescharacteristic
11C4⋊C8×C103—21no—
12C22⋊C8×C103—21no—
13C4×C8×C103C412yescomplemented
14C22×Dic103—22no—
15#13110089—41no—
16#13110089—41no—
17C2×C103⋊C8—22no—
18C4⋊Dic103—41no—
19C4⋊Dic103—41no—
20C22×C4×C103C2×C411yescharacteristic
21C22×C4×C103D411yescharacteristic
22C22×C4×C103D411yescharacteristic
23C2×C8×C103—22no—
24C42×C103C2×C411yescharacteristic
25C42×C103C2×C411yescharacteristic
26C42×C103D411yescharacteristic
27C42×C103Q811yescharacteristic
28C23×C103C22⋊C411yescharacteristic
29C2×C4×C103—41no—
30C2×C4×C103—41no—
31C2×C4×C103C4211yescharacteristic
32C2×C4×C103C22⋊C411yescharacteristic
33C2×C4×C103C22⋊C411yescharacteristic
34C2×C4×C103C4⋊C411yescharacteristic
35C2×C4×C103C4⋊C411yescharacteristic
36C2×C4×C103C4⋊C411yescharacteristic
37C2×C4×C103D811yescharacteristic
38C2×C4×C103SD1611yescharacteristic
39C2×C4×C103SD1611yescharacteristic
40C2×C4×C103Q1611yescharacteristic
41C2×Dic103—42no—
42C2×Dic103—42no—
43C2×Dic103—42no—
44C8×C103—42no—
45C103⋊C8—42no—
46C22×C103—21no—
47C22×C103—21no—
48C22×C103#9511yescharacteristic
49C22×C103#10211yescharacteristic
50C22×C103#10311yescharacteristic
51C4×C103—21no—
52C4×C103—21no—
53C4×C103—21no—
54C4×C103—21no—
55C4×C103#10211yescharacteristic
56C4×C103#10311yescharacteristic
57C4×C103#10611yescharacteristic
58C4×C103#10711yescharacteristic
59Dic103—82no—
60C2×C103—21no—
61C2×C103—21no—
62C2×C103H(3,ℤ/4)11yescharacteristic
63C2×C103#34011yescharacteristic
64C2×C103#34411yescharacteristic
65#1286—1031nomaximal, Sylow
66C103#128611yescharacteristic, complemented, Sylow
67#431D10311yescharacteristic
68#423—1031no—
69#382—1031no—
70C2×M16—2061no—
71C2×C4⋊C4—2061no—
72C2×C42C2×D10311yescharacteristic
73C4⋊C8—21no—
74C4⋊C8—1032no—
75C4⋊C8—2061no—
76C22⋊C8—21no—
77C4×C8Dic10312yescomplemented
78#95—1032no—
79#95—2061no—
80C22×C4—2062no—
81C22×C4C4×D10311yescharacteristic
82C22×C4D41211yescharacteristic
83C22×C4C22⋊D10311yescharacteristic
84M16—4121no—
85M16—4121no—
86C2×C8—22no—
87C2×C8—2062no—
88C4⋊C4—4121no—
89C4⋊C4—4121no—
90C42Dic20611yescharacteristic
91C42C4×D10311yescharacteristic
92C42C2×Dic10311yescharacteristic
93C42C22⋊D10311yescharacteristic
94C23(C2×D103)⋊C411yescharacteristic
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—4122no—
98C2×C4—4122no—
99C2×C4—4122no—
100C2×C4C4×Dic10311yescharacteristic
101C2×C4(C2×D103)⋊C411yescharacteristic
102C2×C4C22⋊Dic10311yescharacteristic
103C2×C4Dic103⋊C411yescharacteristic
104C2×C4Dic103⋊C411yescharacteristic
105C2×C4C4⋊Dic10311yescharacteristic
106C2×C4D82411yescharacteristic
107C2×C4#1311009411yescharacteristic
108C2×C4#1311009411yescharacteristic
109C2×C4Dic41211yescharacteristic
110C8—42no—
111C8—4122no—
112C22—21no—
113C22—21no—
114C22C103⋊#9511yescharacteristic
115C22#1569294311yescharacteristic
116C22#1569294611yescharacteristic
117C4—21no—
118C4—21no—
119C4—21no—
120C4—21no—
121C4—8242no—
122C4#1569294311yescharacteristic
123C4#1569294611yescharacteristic
124C4#1569295311yescharacteristic
125C4#1569295511yescharacteristic
126C2—21no—
127C2—21no—
128C2#2026754711yescharacteristic
129C2#2026755411yescharacteristic
130C2#2026756211yescharacteristic
subgroupG/H
centerC22C103⋊#95
commutatorC2×C4×C103C42
FrattiniC2×C42C2×D103
Fitting#431×C103C2
socleC22×C103#95
prime radicalC23×C103C22⋊C4
cosocleC2×C42×C103C22
hypercenter#431D103
hypocenterC103#1286
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
7. C4⋊(C103⋊C8)C4semidirect
13. C4×C8×C103C4semidirect
66. C103#1286semidirect
77. C4×C8Dic103semidirect

Maximal subgroups

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

subgroupindex
#202678152
#202676572
#431×C1032
#1286103