Finite Group Databasebeta

← #20267809

Subgroups — #20267809

Order 6592.

154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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#15692949C214yesmaximal, complemented
4#117×C103C211yesmaximal, characteristic, complemented
5#13110105—21no—
6#13110105—21no—
7#13110105C412yescomplemented
8#13110105C2212yes—
9C2×Dic206C411yescharacteristic, complemented
10C2×D412C411yescharacteristic, complemented
11C2×C22⋊D103—21no—
12C2×C4×D103—21no—
13#13110089—21no—
14#13110089C2212yescomplemented
15C2×C103⋊C8—21no—
16C22×C4×C103C2211yescharacteristic
17C4⋊C4×C103—21no—
18C22⋊C4×C103—21no—
19C42×C103C2212yescomplemented
20C23×C103D411yescharacteristic
21C22×D103—21no—
22C2×C4×C103—22no—
23C2×C4×C103C2×C411yescharacteristic
24C2×C4×C103C2×C411yescharacteristic
25C2×C4×C103D411yescharacteristic
26C2×C4×C103D411yescharacteristic
27C2×C4×C103D411yescharacteristic
28C2×C4×C103C2311yescharacteristic
29C22⋊D103—22no—
30C22⋊D103—22no—
31C2×Dic103—21no—
32D412—21no—
33D412C2×C412yes—
34C4×D103—22no—
35C4×D103—22no—
36Dic206—21no—
37Dic206C2×C412yes—
38C103⋊C8—22no—
39C22×C103—41no—
40C22×C103C22⋊C411yescharacteristic
41C22×C103C22⋊C411yescharacteristic
42C22×C103C2×D411yescharacteristic
43C2×D103—22no—
44C2×D103—42no—
45C4×C103—42no—
46C4×C103C22⋊C411yescharacteristic
47C4×C103C22⋊C411yescharacteristic
48C4×C103C22×C411yescharacteristic
49C4×C103C2×D411yescharacteristic
50Dic103—22no—
51C2×C103—21no—
52C2×C103—21no—
53C2×C103—21no—
54C2×C103C2×C22⋊C411yescharacteristic
55D103—42no—
56C103#42111yescharacteristic, complemented, Sylow
57#421—1031nomaximal, Sylow
58C2×#41—1031no—
59C2×M16—1031no—
60#117D10311yescharacteristic, complemented
61#104—1034no—
62#41—1032no—
63#41—1032no—
64#41—2061no—
65#41—2061no—
66C2×Q8—1031no—
67C2×D4—1031no—
68C2×D4—2061no—
69C22×C4—2061no—
70C22×C4C2×D10311yescharacteristic
71M16—1032no—
72M16—2061no—
73C2×C8—2061no—
74C4⋊C4—21no—
75C22⋊C4—21no—
76C42C2×D10312yescomplemented
77C23—2061no—
78C23C22⋊D10311yescharacteristic
79Q8—1032no—
80Q8—2061no—
81D4—1032no—
82D4—2062no—
83D4—2062no—
84D4—2061no—
85C2×C4—22no—
86C2×C4—2061no—
87C2×C4—2062no—
88C2×C4—2062no—
89C2×C4C4×D10311yescharacteristic
90C2×C4C4×D10311yescharacteristic
91C2×C4D41211yescharacteristic
92C2×C4D41211yescharacteristic
93C2×C4C22⋊D10311yescharacteristic
94C2×C4C22×D10311yescharacteristic
95C8—2062no—
96C22—41no—
97C22—4122no—
98C22—2062no—
99C22(C2×D103)⋊C411yescharacteristic
100C22(C2×D103)⋊C411yescharacteristic
101C22C2×C22⋊D10311yescharacteristic
102C4—42no—
103C4—2062no—
104C4(C2×D103)⋊C411yescharacteristic
105C4(C2×D103)⋊C411yescharacteristic
106C4C2×C4×D10311yescharacteristic
107C4C2×D41211yescharacteristic
108C2—21no—
109C2—21no—
110C2—21no—
111C2—4122no—
112C2C2×(C2×D103)⋊C411yescharacteristic
subgroupG/H
centerC4C2×D412
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#117×C103C2
socleC2×C103C2×C22⋊C4
hypercenter#117D103
hypocenterC103#421
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#13110089C2semidirect
3. #15692949C2semidirect
4. #117×C103C2semidirect
7. #13110105C4semidirect
9. C2×Dic206C4semidirect
10. C2×D412C4semidirect
14. #13110089C22semidirect
19. C42×C103C22semidirect
56. C103#421semidirect
60. #117D103semidirect
76. C42C2×D103semidirect