Finite Group Databasebeta

← #20268172

Subgroups — #20268172

Order 6592.

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

normal subgroups only

This group has 130 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×#13110095C211yesmaximal, characteristic, complemented
2C2×#13110094C211yesmaximal, characteristic, complemented
3C2×#13110090C211yesmaximal, characteristic
4#15693010C211yesmaximal, characteristic, complemented
5#15693008C211yesmaximal, characteristic, complemented
6C8×Dic103C211yesmaximal, characteristic, complemented
7C2×SD16×C103C211yesmaximal, characteristic, complemented
8C2×Dic206C2211yescharacteristic
9C2×D412C2211yescharacteristic
10#13110095—22no—
11#13110094—22no—
12#13110090—22no—
13C2×C103⋊C8C2211yescharacteristic
14C22⋊Dic103—22no—
15(C2×D103)⋊C4—22no—
16C4×Dic103C2211yescharacteristic
17C2×Q8×C103C2211yescharacteristic
18C2×D4×C103C2211yescharacteristic
19SD16×C103—22no—
20C2×C8×C103C2211yescharacteristic
21C23×C103—21no—
22C22×D103—21no—
23Q8×C103—21no—
24Q8×C103—21no—
25D4×C103—21no—
26D4×C103—21no—
27C2×C4×C103—21no—
28C2×C4×C103C2311yescharacteristic
29C2×Dic103—21no—
30C2×Dic103D412yes—
31D412—21no—
32D412—21no—
33Dic206—21no—
34Dic206—21no—
35C8×C103D412yes—
36C103⋊C8D412yes—
37C22×C103—41no—
38C22×C103—42no—
39C22×C103C2×D411yescharacteristic
40C2×D103—41no—
41C2×D103—42no—
42C4×C103—41no—
43C4×C103C2×D411yescharacteristic
44C4×C103C2×D411yescharacteristic
45Dic103—22no—
46Dic103—41no—
47C2×C103—81no—
48C2×C103#12711yescharacteristic
49C2×C103#13512yes—
50D103—81no—
51C103#49511yescharacteristic, complemented, Sylow
52#495—1031nomaximal, Sylow
53C2×Q16—1031no—
54C2×SD16—1031no—
55C2×SD16D10311yescharacteristic, complemented
56C2×D8—1031no—
57#124—1031no—
58#124—1031no—
59C4×C8—1031no—
60C2×Q8—1031no—
61C2×Q8C2×D10311yescharacteristic
62C2×D4—1031no—
63C2×D4C2×D10311yescharacteristic
64Q16—2062no—
65SD16—22no—
66SD16—2062no—
67D8—2062no—
68C2×C8—1031no—
69C2×C8C2×D10311yescharacteristic
70C22⋊C4—2062no—
71C22⋊C4—2062no—
72C42—1031no—
73C23—21no—
74C23—2061no—
75Q8—21no—
76Q8—21no—
77Q8—2061no—
78Q8—2061no—
79D4—21no—
80D4—21no—
81D4—2061no—
82D4—2061no—
83C2×C4—21no—
84C2×C4—1032no—
85C2×C4—2061no—
86C2×C4C22×D10311yescharacteristic
87C8—1032no—
88C8C22⋊D10312yes—
89C22—41no—
90C22—42no—
91C22—4121no—
92C22—4122no—
93C22D4×D10311yescharacteristic
94C4—41no—
95C4—4121no—
96C4—2062no—
97C4D4×D10311yescharacteristic
98C4C2×C22⋊D10311yescharacteristic
99C2—81no—
100C2—8241no—
101C2#1569301711yescharacteristic
102C2#1569304212yes—
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×SD16×C103C2
socleC22×C103C2×D4
hypercenterC2×SD16D103
hypocenterC103#495
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×#13110095C2semidirect
2. C2×#13110094C2semidirect
4. #15693010C2semidirect
5. #15693008C2semidirect
6. C8×Dic103C2semidirect
7. C2×SD16×C103C2semidirect
51. C103#495semidirect
55. C2×SD16D103semidirect