Finite Group Databasebeta

← #27193020

Subgroups — #27193020

Order 13184.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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#20267755C211yesmaximal, characteristic
2C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic
3#407×C103C211yesmaximal, characteristic
4C2×#13110089—21no—
5C22×C103⋊C8C412yes—
6C22⋊(C103⋊C8)—21no—
7C22⋊(C103⋊C8)—21no—
8C22⋊(C103⋊C8)—21no—
9C22⋊(C103⋊C8)C412yes—
10C23×C4×C103C2211yescharacteristic
11C2×M16×C103—21no—
12C22⋊C8×C103—21no—
13C22⋊C8×C103C412yes—
14#13110089—42no—
15C2×C103⋊C8—22no—
16C2×C103⋊C8—22no—
17C2×C103⋊C8—42no—
18C24×C103Q811yescharacteristic
19C22×C4×C103—42no—
20C22×C4×C103C2×C411yescharacteristic
21C22×C4×C103C2×C411yescharacteristic
22C22×C4×C103C2×C411yescharacteristic
23C22×C4×C103D411yescharacteristic
24C22×C4×C103D411yescharacteristic
25C22×C4×C103D411yescharacteristic
26M16×C103—42no—
27C2×C8×C103—22no—
28C23×C103—22no—
29C23×C103—41no—
30C23×C103—41no—
31C23×C103C4⋊C411yescharacteristic
32C23×C103C4⋊C411yescharacteristic
33C23×C103C4⋊C411yescharacteristic
34C2×C4×C103—22no—
35C2×C4×C103—22no—
36C2×C4×C103—22no—
37C2×C4×C103—41no—
38C2×C4×C103—41no—
39C2×C4×C103—41no—
40C2×C4×C103C4211yescharacteristic
41C2×C4×C103C22⋊C411yescharacteristic
42C2×C4×C103C22⋊C411yescharacteristic
43C2×C4×C103C22⋊C411yescharacteristic
44C8×C103—42no—
45C103⋊C8—42no—
46C103⋊C8—42no—
47C22×C103—21no—
48C22×C103—21no—
49C22×C103—21no—
50C22×C103—21no—
51C22×C103—21no—
52C22×C103—21no—
53C22×C103—21no—
54C22×C103—21no—
55C22×C103—44no—
56C22×C103#9511yescharacteristic
57C22×C103#10812yes—
58C4×C103—21no—
59C4×C103—21no—
60C4×C103—21no—
61C4×C103#9912yes—
62C2×C103—22no—
63C2×C103—41no—
64C2×C103—41no—
65C2×C103#33811yescharacteristic
66C2×C103#34111yescharacteristic
67C2×C103#34211yescharacteristic
68#1293—1031nomaximal, Sylow
69C103#129311yescharacteristic, complemented, Sylow
70#407—1031no—
71#407D10311yescharacteristic
72C2×C22⋊C8—1031no—
73C23×C4C2×D10311yescharacteristic
74C2×M16—21no—
75C2×M16—2061no—
76C22×C8—1032no—
77C22⋊C8—21no—
78C22⋊C8—1032no—
79C22⋊C8—2061no—
80C22⋊C8—2061no—
81C22⋊C8—2061no—
82C22⋊C8Dic10312yes—
83C24Dic20611yescharacteristic
84C22×C4—42no—
85C22×C4C4×D10311yescharacteristic
86C22×C4C4×D10311yescharacteristic
87C22×C4D41211yescharacteristic
88C22×C4C2×Dic10311yescharacteristic
89C22×C4C22⋊D10311yescharacteristic
90C22×C4C22⋊D10311yescharacteristic
91M16—42no—
92M16—4122no—
93C2×C8—22no—
94C2×C8—4122no—
95C2×C8—2062no—
96C2×C8—2062no—
97C23—22no—
98C23—41no—
99C23—41no—
100C23Dic103⋊C411yescharacteristic
101C23Dic103⋊C411yescharacteristic
102C23C4⋊Dic10311yescharacteristic
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4C4×Dic10311yescharacteristic
110C2×C4(C2×D103)⋊C411yescharacteristic
111C2×C4(C2×D103)⋊C411yescharacteristic
112C2×C4C22⋊Dic10311yescharacteristic
113C8—42no—
114C8—4122no—
115C8—4122no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—21no—
120C22—21no—
121C22—21no—
122C22—21no—
123C22—21no—
124C22—44no—
125C22C103⋊#9511yescharacteristic
126C22#1569295612yes—
127C4—21no—
128C4—21no—
129C4—21no—
130C4#1569293512yes—
131C2—22no—
132C2—41no—
133C2—41no—
134C2C103⋊#33811yescharacteristic
135C2#2026755511yescharacteristic
136C2#2026755711yescharacteristic
subgroupG/H
centerC22C103⋊#95
commutatorC2×C4×C103C42
FrattiniC23×C4C2×D103
Fitting#407×C103C2
socleC22×C103#95
prime radicalC24×C103Q8
cosocleC23×C4×C103C22
hypercenter#407D103
hypocenterC103#1293
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
69. C103#1293semidirect

Maximal subgroups

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

subgroupindex
#202677552
C2×C22⋊(C103⋊C8)2
#407×C1032
#1293103