Finite Group Databasebeta

← #20267790

Subgroups — #20267790

Order 6592.

162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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×#13110105C211yesmaximal, characteristic
2C2×#13110089C211yesmaximal, characteristic, complemented
3#15692944C212yesmaximal, complemented
4#15692941C212yesmaximal, complemented
5C2×C4⋊C4×C103C211yesmaximal, characteristic, complemented
6#13110105—22no—
7#13110105C414yescomplemented
8C2×Dic206C2211yescharacteristic
9C2×D412C2211yescharacteristic
10C2×C22⋊D103—21no—
11C2×C4×D103—21no—
12#13110089—22no—
13C2×C103⋊C8C2212yes—
14C22×C4×C103—21no—
15C22×C4×C103C2211yescharacteristic
16C4⋊C4×C103—21no—
17C4⋊C4×C103C2212yes—
18C23×C103D411yescharacteristic
19C22×D103—21no—
20C2×C4×C103—22no—
21C2×C4×C103—42no—
22C2×C4×C103C2×C412yes—
23C2×C4×C103D412yes—
24C2×C4×C103D411yescharacteristic
25C2×C4×C103C2311yescharacteristic
26C22⋊D103—24no—
27C2×Dic103—21no—
28D412—21no—
29D412C2×C412yescomplemented
30C4×D103—24no—
31Dic206—21no—
32Dic206C2×C412yescomplemented
33C103⋊C8—22no—
34C22×C103—21no—
35C22×C103—21no—
36C22×C103C22⋊C412yes—
37C22×C103C2×D411yescharacteristic
38C2×D103—22no—
39C2×D103—41no—
40C2×D103—41no—
41C4×C103—42no—
42C4×C103C22⋊C412yes—
43C4×C103C22×C411yescharacteristic
44C4×C103C2×D411yescharacteristic
45Dic103—22no—
46C2×C103—22no—
47C2×C103C2×C22⋊C411yescharacteristic
48C2×C103AGL(1,ℤ/8)11yescharacteristic
49C2×C103#13711yescharacteristic
50D103—42no—
51C103#41711yescharacteristic, complemented, Sylow
52#417—1031nomaximal, Sylow
53C2×#41—1031no—
54C2×M16—1031no—
55C2×C4⋊C4D10311yescharacteristic, complemented
56#103—1032no—
57#102—1032no—
58#41—1034no—
59#41—2062no—
60C2×Q8—1031no—
61C2×D4—1031no—
62C2×D4—2061no—
63C22×C4—21no—
64C22×C4—2061no—
65C22×C4C2×D10311yescharacteristic
66M16—2062no—
67C2×C8—1032no—
68C4⋊C4—21no—
69C4⋊C4C2×D10312yes—
70C23—2061no—
71C23C22⋊D10311yescharacteristic
72Q8—1032no—
73Q8—2061no—
74D4—1032no—
75D4—2064no—
76D4—2061no—
77C2×C4—22no—
78C2×C4—42no—
79C2×C4—2061no—
80C2×C4—2064no—
81C2×C4C4×D10312yes—
82C2×C4D41212yes—
83C2×C4C22⋊D10311yescharacteristic
84C2×C4C22×D10311yescharacteristic
85C8—2062no—
86C22—21no—
87C22—21no—
88C22—4121no—
89C22—4121no—
90C22—2062no—
91C22(C2×D103)⋊C412yes—
92C22C2×C22⋊D10311yescharacteristic
93C4—42no—
94C4—2062no—
95C4(C2×D103)⋊C412yes—
96C4C2×C4×D10311yescharacteristic
97C4C2×D41211yescharacteristic
98C2—22no—
99C2—4122no—
100C2C2×(C2×D103)⋊C411yescharacteristic
101C2#1569304711yescharacteristic
102C2#1569305211yescharacteristic
subgroupG/H
centerC22C2×C22⋊D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
FittingC2×C4⋊C4×C103C2
socleC22×C103C2×D4
hypercenterC2×C4⋊C4D103
hypocenterC103#417
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#13110089C2semidirect
3. #15692944C2semidirect
4. #15692941C2semidirect
5. C2×C4⋊C4×C103C2semidirect
7. #13110105C4semidirect
29. D412C2×C4semidirect
32. Dic206C2×C4semidirect
51. C103#417semidirect
55. C2×C4⋊C4D103semidirect