Finite Group Databasebeta

← #27193245

Subgroups — #27193245

Order 13184.

132 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 69 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
2#20267829C211yesmaximal, characteristic
3#427×C103C211yesmaximal, characteristic
4#15692980—21no—
5#15692961—21no—
6#15692961—21no—
7C2×C103⋊C16C412yescomplemented
8#15692955—21no—
9#15692953C412yescomplemented
10C22×C8×C103C2211yescharacteristic
11#117×C103—21no—
12#107×C103—21no—
13#106×C103C412yescomplemented
14C4⋊Dic103—22no—
15C22⋊Dic103—41no—
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—
37C8×C103C4211yescharacteristic
38C8×C103C22⋊C411yescharacteristic
39C8×C103C4⋊C411yescharacteristic
40C8×C103C4⋊C411yescharacteristic
41C22×C103—41no—
42C22×C103#10211yescharacteristic
43C22×C103#10211yescharacteristic
44C22×C103#10711yescharacteristic
45C4×C103—82no—
46C4×C103#9511yescharacteristic
47C4×C103#10311yescharacteristic
48C4×C103#10311yescharacteristic
49C4×C103#10611yescharacteristic
50Dic103—82no—
51C2×C103—21no—
52C2×C103—21no—
53C2×C103—21no—
54C2×C103#34011yescharacteristic
55#1384—1031nomaximal, Sylow
56C103#138411yescharacteristic, complemented, Sylow
57C2×M32—1031no—
58#427—1031no—
59#427D10311yescharacteristic
60C22×C8C2×D10311yescharacteristic
61#117—21no—
62#117—2061no—
63M32—2061no—
64M32—2061no—
65C2×C16—1032no—
66#107—21no—
67#107—2061no—
68#106—1032no—
69#106Dic10312yescomplemented
70C22×C4C22⋊D10311yescharacteristic
71C2×C8Dic20611yescharacteristic
72C2×C8C4×D10311yescharacteristic
73C2×C8C4×D10311yescharacteristic
74C2×C8D41211yescharacteristic
75C2×C8C2×Dic10311yescharacteristic
76C2×C8C22⋊D10311yescharacteristic
77C4⋊C4—22no—
78C4⋊C4—2062no—
79C22⋊C4—41no—
80C22⋊C4—4121no—
81C42—41no—
82C42—4121no—
83C16—2062no—
84C23#1311009011yescharacteristic
85C2×C4—42no—
86C2×C4—4122no—
87C2×C4(C2×D103)⋊C411yescharacteristic
88C2×C4C22⋊Dic10311yescharacteristic
89C2×C4Dic103⋊C411yescharacteristic
90C2×C4#1311009211yescharacteristic
91C2×C4#1311009311yescharacteristic
92C2×C4#1311009511yescharacteristic
93C8C4×Dic10311yescharacteristic
94C8(C2×D103)⋊C411yescharacteristic
95C8Dic103⋊C411yescharacteristic
96C8C4⋊Dic10311yescharacteristic
97C22—41no—
98C22#1569294111yescharacteristic
99C22#1569294211yescharacteristic
100C22#1569295411yescharacteristic
101C4—82no—
102C4—8242no—
103C4C103⋊#9511yescharacteristic
104C4#1569294411yescharacteristic
105C4#1569294511yescharacteristic
106C4#1569295211yescharacteristic
107C2—21no—
108C2—21no—
109C2—21no—
110C2#2026755311yescharacteristic
subgroupG/H
centerC4#15692952
commutatorC8×C103C42
FrattiniC22×C8C2×D103
Fitting#427×C103C2
socleC2×C103#340
prime radicalC23×C103D8
cosocleC22×C8×C103C22
hypercenter#427D103
hypocenterC103#1384
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
7. C2×C103⋊C16C4semidirect
9. #15692953C4semidirect
13. #106×C103C4semidirect
56. C103#1384semidirect
69. #106Dic103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929612
#202678292
#427×C1032
#1384103