Finite Group Databasebeta

← #27193249

Subgroups — #27193249

Order 13184.

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

normal subgroups only

This group has 140 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
1C2×#15692961C211yesmaximal, characteristic
2C2×#15692953C211yesmaximal, characteristic
3#427×C103C211yesmaximal, characteristic
4C2×C4⋊Dic103—21no—
5#15692961—21no—
6#15692961C412yescomplemented
7C2×C103⋊C16—21no—
8#15692953—21no—
9#15692953C412yescomplemented
10C22×C8×C103C2211yescharacteristic
11#117×C103—21no—
12#107×C103C412yescomplemented
13#106×C103—21no—
14C22×Dic103—41no—
15C4⋊Dic103—22no—
16C4⋊Dic103—41no—
17C103⋊C16—22no—
18C22×C4×C103D411yescharacteristic
19C2×C8×C103C2×C411yescharacteristic
20C2×C8×C103C2×C411yescharacteristic
21C2×C8×C103C2×C411yescharacteristic
22C2×C8×C103D411yescharacteristic
23C2×C8×C103D411yescharacteristic
24C2×C8×C103Q811yescharacteristic
25C4⋊C4×C103—22no—
26C22⋊C4×C103—41no—
27C42×C103—41no—
28C23×C103D811yescharacteristic
29C2×C4×C103—42no—
30C2×C4×C103C22⋊C411yescharacteristic
31C2×C4×C103C22⋊C411yescharacteristic
32C2×C4×C103C4⋊C411yescharacteristic
33C2×C4×C103SD1611yescharacteristic
34C2×C4×C103SD1611yescharacteristic
35C2×C4×C103Q1611yescharacteristic
36C2×Dic103—42no—
37C2×Dic103—82no—
38C8×C103C4211yescharacteristic
39C8×C103C22⋊C411yescharacteristic
40C8×C103C4⋊C411yescharacteristic
41C8×C103C4⋊C411yescharacteristic
42C22×C103—22no—
43C22×C103#10211yescharacteristic
44C22×C103#10211yescharacteristic
45C22×C103#10711yescharacteristic
46C4×C103—82no—
47C4×C103#9511yescharacteristic
48C4×C103#10311yescharacteristic
49C4×C103#10311yescharacteristic
50C4×C103#10611yescharacteristic
51Dic103—82no—
52C2×C103—21no—
53C2×C103—21no—
54C2×C103#34011yescharacteristic
55C2×C103#36012yes—
56#1386—1031nomaximal, Sylow
57C103#138611yescharacteristic, complemented, Sylow
58C2×M32—1031no—
59#427D10311yescharacteristic
60C2×#106—1031no—
61C22×C8C2×D10311yescharacteristic
62#117—21no—
63C2×C4⋊C4—2061no—
64M32—1032no—
65M32—2061no—
66C2×C16—2061no—
67#107Dic10312yescomplemented
68#106—21no—
69#106—1032no—
70#106—2061no—
71C22×C4—4121no—
72C22×C4C22⋊D10311yescharacteristic
73C2×C8Dic20611yescharacteristic
74C2×C8C4×D10311yescharacteristic
75C2×C8C4×D10311yescharacteristic
76C2×C8D41211yescharacteristic
77C2×C8C2×Dic10311yescharacteristic
78C2×C8C22⋊D10311yescharacteristic
79C4⋊C4—22no—
80C4⋊C4—4121no—
81C4⋊C4—2062no—
82C22⋊C4—41no—
83C42—41no—
84C16—2062no—
85C23#1311009011yescharacteristic
86C2×C4—42no—
87C2×C4—8242no—
88C2×C4—4122no—
89C2×C4(C2×D103)⋊C411yescharacteristic
90C2×C4C22⋊Dic10311yescharacteristic
91C2×C4Dic103⋊C411yescharacteristic
92C2×C4#1311009211yescharacteristic
93C2×C4#1311009311yescharacteristic
94C2×C4#1311009511yescharacteristic
95C8C4×Dic10311yescharacteristic
96C8(C2×D103)⋊C411yescharacteristic
97C8Dic103⋊C411yescharacteristic
98C8C4⋊Dic10311yescharacteristic
99C22—22no—
100C22#1569294111yescharacteristic
101C22#1569294211yescharacteristic
102C22#1569295411yescharacteristic
103C4—82no—
104C4—8242no—
105C4C103⋊#9511yescharacteristic
106C4#1569294411yescharacteristic
107C4#1569294511yescharacteristic
108C4#1569295211yescharacteristic
109C2—21no—
110C2—21no—
111C2#2026755311yescharacteristic
112C2#2026760112yes—
subgroupG/H
centerC22#15692942
commutatorC8×C103C42
FrattiniC22×C8C2×D103
Fitting#427×C103C2
socleC22×C103#102
prime radicalC23×C103D8
cosocleC22×C8×C103C22
hypercenter#427D103
hypocenterC103#1386
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
6. #15692961C4semidirect
9. #15692953C4semidirect
12. #107×C103C4semidirect
57. C103#1386semidirect
67. #107Dic103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929612
C2×#156929532
#427×C1032
#1386103