Finite Group Databasebeta

← #27192988

Subgroups — #27192988

Order 13184.

152 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 77 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#20267844C211yesmaximal, characteristic
2C2×#15692932C211yesmaximal, characteristic
3#431×C103C211yesmaximal, characteristic
4C22×C103⋊C8C412yes—
5C4⋊(C103⋊C8)—21no—
6C22⋊(C103⋊C8)C412yes—
7#15692932—21no—
8#15692932—21no—
9C4×C103⋊C8—21no—
10C2×C42×C103C2211yescharacteristic
11C4⋊C8×C103—21no—
12C22⋊C8×C103C412yes—
13C4×C8×C103—21no—
14C2×C103⋊C8—22no—
15C2×C103⋊C8—22no—
16C2×C103⋊C8—22no—
17C2×C103⋊C8C814yescomplemented
18C22×C4×C103C2×C411yescharacteristic
19C22×C4×C103C2×C411yescharacteristic
20C22×C4×C103C2×C411yescharacteristic
21C2×C8×C103—22no—
22C42×C103D411yescharacteristic
23C42×C103D411yescharacteristic
24C42×C103D411yescharacteristic
25C42×C103Q811yescharacteristic
26C23×C103C4211yescharacteristic
27C2×C4×C103—41no—
28C2×C4×C103—41no—
29C2×C4×C103C22⋊C411yescharacteristic
30C2×C4×C103C22⋊C411yescharacteristic
31C2×C4×C103C22⋊C411yescharacteristic
32C2×C4×C103C4⋊C411yescharacteristic
33C2×C4×C103C4⋊C411yescharacteristic
34C2×C4×C103C4⋊C411yescharacteristic
35C2×C4×C103C2×C812yes—
36C2×C4×C103M1612yes—
37C8×C103—42no—
38C103⋊C8—24no—
39C103⋊C8—42no—
40C22×C103—21no—
41C22×C103—21no—
42C22×C103#9511yescharacteristic
43C22×C103C4×C811yescharacteristic
44C22×C103#9711yescharacteristic
45C4×C103—21no—
46C4×C103—21no—
47C4×C103—21no—
48C4×C103—21no—
49C4×C103C22⋊C812yes—
50C4×C103C4⋊C812yes—
51C2×C103—21no—
52C2×C103—21no—
53C2×C103#33611yescharacteristic
54C2×C103#34411yescharacteristic
55C2×C103#34411yescharacteristic
56#1281—1031nomaximal, Sylow
57C103#128111yescharacteristic, complemented, Sylow
58#431—1031no—
59#431D10311yescharacteristic
60C2×#97—1031no—
61C22×C8—1032no—
62C2×C42C2×D10311yescharacteristic
63C4⋊C8—21no—
64C4⋊C8—2061no—
65C22⋊C8—1032no—
66C22⋊C8Dic10312yes—
67#97—2061no—
68#97—2061no—
69C4×C8—21no—
70C4×C8—2061no—
71C22×C4C4×D10311yescharacteristic
72C22×C4C4×D10311yescharacteristic
73C22×C4C2×Dic10311yescharacteristic
74C2×C8—22no—
75C2×C8—1034no—
76C2×C8—2062no—
77C2×C8—2062no—
78C2×C8—2062no—
79C42Dic20611yescharacteristic
80C42D41211yescharacteristic
81C42C22⋊D10311yescharacteristic
82C42C22⋊D10311yescharacteristic
83C23C4×Dic10311yescharacteristic
84C2×C4—41no—
85C2×C4—41no—
86C2×C4(C2×D103)⋊C411yescharacteristic
87C2×C4(C2×D103)⋊C411yescharacteristic
88C2×C4C22⋊Dic10311yescharacteristic
89C2×C4Dic103⋊C411yescharacteristic
90C2×C4Dic103⋊C411yescharacteristic
91C2×C4C4⋊Dic10311yescharacteristic
92C2×C4C8×D10312yes—
93C2×C4#1311008812yes—
94C8—42no—
95C8—4122no—
96C8—2064no—
97C22—21no—
98C22—21no—
99C22C103⋊#9511yescharacteristic
100C22C8×Dic10311yescharacteristic
101C22#1569293111yescharacteristic
102C4—21no—
103C4—21no—
104C4—21no—
105C4—21no—
106C4(C2×D103)⋊C812yes—
107C4Dic103⋊C812yes—
108C2—21no—
109C2—21no—
110C2#2026754511yescharacteristic
111C2#2026756111yescharacteristic
112C2#2026756311yescharacteristic
subgroupG/H
centerC2×C4(C2×D103)⋊C4
commutatorC22×C103C4×C8
FrattiniC2×C42C2×D103
Fitting#431×C103C2
socleC22×C103#95
prime radicalC23×C103C42
cosocleC2×C42×C103C22
hypercenter#431D103
hypocenterC103#1281
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
17. C2×C103⋊C8C8semidirect
57. C103#1281semidirect

Maximal subgroups

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

subgroupindex
#202678442
C2×#156929322
#431×C1032
#1281103