Finite Group Databasebeta

← #20268064

Subgroups — #20268064

Order 6592.

100 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 37 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#15693051C211yesmaximal, characteristic
2C2×#13110095C211yesmaximal, characteristic, complemented
3#15693028C211yesmaximal, characteristic
4#15692956C211yesmaximal, characteristic, complemented
5#15692940C211yesmaximal, characteristic, complemented
6#15692939C211yesmaximal, characteristic, complemented
7#137×C103C211yesmaximal, characteristic
8C2×Dic206C2211yescharacteristic
9#13110095—21no—
10#13110095—21no—
11#13110095—21no—
12#13110093—21no—
13#13110089—21no—
14#13110089C2211yescharacteristic
15#13110089C2211yescharacteristic
16C2×C103⋊C8—21no—
17C2×C103⋊C8C2211yescharacteristic
18#41×C103C2211yescharacteristic
19C2×Q8×C103C2211yescharacteristic
20Q16×C103—21no—
21SD16×C103—21no—
22M16×C103C2211yescharacteristic
23Q8×C103—21no—
24Q8×C103—21no—
25Q8×C103D411yescharacteristic
26D4×C103—21no—
27D4×C103D411yescharacteristic
28C2×C4×C103—21no—
29C2×C4×C103—21no—
30C2×C4×C103C2311yescharacteristic
31C2×Dic103—21no—
32Dic206—21no—
33Dic206—21no—
34C8×C103—21no—
35C103⋊C8—21no—
36C103⋊C8—21no—
37C103⋊C8D411yescharacteristic
38C103⋊C8D411yescharacteristic
39C22×C103—21no—
40C22×C103#4111yescharacteristic
41C4×C103—21no—
42C4×C103—41no—
43C4×C103C2×D411yescharacteristic
44C4×C103C2×D411yescharacteristic
45Dic103—41no—
46C2×C103—21no—
47C2×C103—41no—
48C2×C103#12111yescharacteristic
49C103#47311yescharacteristic, complemented, Sylow
50#473—1031nomaximal, Sylow
51#137—1031no—
52#137D10311yescharacteristic
53C2×Q16—1031no—
54#131—1031no—
55#108—1031no—
56#101—1031no—
57#101—1031no—
58#41C2×D10311yescharacteristic
59C2×Q8—1031no—
60C2×Q8C2×D10311yescharacteristic
61Q16—21no—
62Q16—2061no—
63Q16—2061no—
64Q16—2061no—
65SD16—21no—
66SD16—2061no—
67M16—1031no—
68M16—1031no—
69M16—2061no—
70M16C2×D10311yescharacteristic
71C2×C8—1031no—
72C2×C8—2061no—
73Q8—21no—
74Q8—21no—
75Q8—2061no—
76Q8—2061no—
77Q8C22⋊D10311yescharacteristic
78D4—21no—
79D4C22⋊D10311yescharacteristic
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—2061no—
83C2×C4C22×D10311yescharacteristic
84C8—21no—
85C8—1031no—
86C8—1031no—
87C8—2061no—
88C8—2061no—
89C22—21no—
90C22#1311010411yescharacteristic
91C4—21no—
92C4—41no—
93C4—4121no—
94C4D4×D10311yescharacteristic
95C4C2×C22⋊D10311yescharacteristic
96C2—21no—
97C2—41no—
98C2#1569299311yescharacteristic
subgroupG/H
centerC2#15692993
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#137×C103C2
socleC2×C103#121
hypercenter#137D103
hypocenterC103#473
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. C2×#13110095C2semidirect
4. #15692956C2semidirect
5. #15692940C2semidirect
6. #15692939C2semidirect
49. C103#473semidirect