Finite Group Databasebeta

← #20268182

Subgroups — #20268182

Order 6592.

124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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×Dic412C211yesmaximal, characteristic, complemented
2C2×#13110095C211yesmaximal, characteristic, complemented
3C2×#13110093C211yesmaximal, characteristic
4#15693019C211yesmaximal, characteristic, complemented
5#15693008C211yesmaximal, characteristic
6#15692931C211yesmaximal, characteristic, complemented
7C2×SD16×C103C211yesmaximal, characteristic
8C2×Dic206C2211yescharacteristic
9C2×Dic206C2211yescharacteristic
10Dic412—22no—
11#13110095—22no—
12#13110093—22no—
13C2×C103⋊C8C2211yescharacteristic
14Dic103⋊C4—22no—
15C22⋊Dic103—22no—
16C4×Dic103C2211yescharacteristic
17C2×Q8×C103C2211yescharacteristic
18C2×D4×C103C2211yescharacteristic
19SD16×C103—22no—
20C2×C8×C103C2211yescharacteristic
21C23×C103—21no—
22Q8×C103—21no—
23Q8×C103—21no—
24D4×C103—21no—
25D4×C103—21no—
26C2×C4×C103—21no—
27C2×C4×C103C2311yescharacteristic
28C2×Dic103—21no—
29C2×Dic103—21no—
30C2×Dic103D412yes—
31Dic206—21no—
32Dic206—21no—
33Dic206—21no—
34Dic206—21no—
35C8×C103D412yes—
36C103⋊C8D412yes—
37C22×C103—41no—
38C22×C103—42no—
39C22×C103C2×D411yescharacteristic
40C4×C103—41no—
41C4×C103C2×D411yescharacteristic
42C4×C103C2×D411yescharacteristic
43Dic103—22no—
44Dic103—41no—
45Dic103—41no—
46C2×C103—81no—
47C2×C103#12711yescharacteristic
48C2×C103#13712yes—
49C103#49711yescharacteristic, complemented, Sylow
50#497—1031nomaximal, Sylow
51C2×Q16—1031no—
52C2×Q16—1031no—
53C2×SD16—1031no—
54C2×SD16D10311yescharacteristic
55C4⋊Q8—1031no—
56#124—1031no—
57#97—1031no—
58C2×Q8—1031no—
59C2×Q8—1031no—
60C2×Q8C2×D10311yescharacteristic
61C2×D4C2×D10311yescharacteristic
62Q16—2062no—
63Q16—2062no—
64SD16—22no—
65SD16—2062no—
66C2×C8—1031no—
67C2×C8C2×D10311yescharacteristic
68C4⋊C4—2062no—
69C22⋊C4—2062no—
70C42—1031no—
71C23—21no—
72Q8—21no—
73Q8—21no—
74Q8—2061no—
75Q8—2061no—
76Q8—2061no—
77Q8—2061no—
78D4—21no—
79D4—21no—
80C2×C4—21no—
81C2×C4—1032no—
82C2×C4—2061no—
83C2×C4—2061no—
84C2×C4C22×D10311yescharacteristic
85C8—1032no—
86C8C22⋊D10312yes—
87C22—41no—
88C22—42no—
89C22D4×D10311yescharacteristic
90C4—41no—
91C4—4121no—
92C4—4121no—
93C4—2062no—
94C4D4×D10311yescharacteristic
95C4C2×C22⋊D10311yescharacteristic
96C2—81no—
97C2#1569301711yescharacteristic
98C2#1569305012yes—
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×SD16×C103C2
socleC22×C103C2×D4
hypercenterC2×SD16D103
hypocenterC103#497
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Dic412C2semidirect
2. C2×#13110095C2semidirect
4. #15693019C2semidirect
6. #15692931C2semidirect
49. C103#497semidirect