Finite Group Databasebeta

← #20267798

Subgroups — #20267798

Order 6592.

150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 55 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×Q8×D103C211yesmaximal, characteristic
2C2×#13110088C211yesmaximal, characteristic
3#15692979C211yesmaximal, characteristic
4#15692946C211yesmaximal, characteristic, complemented
5#15692945C211yesmaximal, characteristic, complemented
6#15692944C211yesmaximal, characteristic, complemented
7#103×C103C211yesmaximal, characteristic, complemented
8C2×Dic206—21no—
9C2×Dic206C2211yescharacteristic
10Q8×D103—22no—
11Q8×D103C414yescomplemented
12C2×C4×D103—21no—
13C2×C4×D103C2211yescharacteristic
14#13110088—22no—
15C2×C103⋊C8C2211yescharacteristic
16C4⋊Dic103C2211yescharacteristic
17(C2×D103)⋊C4—21no—
18C4×Dic103—21no—
19C2×Q8×C103C2211yescharacteristic
20C2×C8×C103C2211yescharacteristic
21C4⋊C4×C103C2211yescharacteristic
22C22×D103D411yescharacteristic
23Q8×C103—21no—
24Q8×C103C2×C412yes—
25C2×C4×C103—21no—
26C2×C4×C103—21no—
27C2×C4×C103C2311yescharacteristic
28C2×Dic103—21no—
29C2×Dic103—21no—
30C2×Dic103D411yescharacteristic
31C4×D103—24no—
32C4×D103C2×C412yes—
33C4×D103D412yes—
34Dic206—21no—
35Dic206—24no—
36Dic206C2×C412yes—
37C8×C103—21no—
38C103⋊C8—21no—
39C22×C103C2×D411yescharacteristic
40C2×D103—21no—
41C2×D103—21no—
42C2×D103C22⋊C412yes—
43C4×C103—22no—
44C4×C103—41no—
45C4×C103C22×C411yescharacteristic
46C4×C103C2×D411yescharacteristic
47Dic103—22no—
48Dic103—41no—
49Dic103C22⋊C412yes—
50C2×C103C2×C22⋊C411yescharacteristic
51C2×C103#13711yescharacteristic
52C2×C103#13711yescharacteristic
53D103—22no—
54C103#41911yescharacteristic, complemented, Sylow
55#419—1031nomaximal, Sylow
56C22×Q8—1031no—
57C2×M16—1031no—
58#117—1031no—
59#103—1031no—
60#103—1031no—
61#103—1031no—
62#103D10311yescharacteristic, complemented
63C2×Q8—1034no—
64C2×Q8—1031no—
65C2×Q8—2061no—
66C2×Q8—2062no—
67C2×Q8C2×D10311yescharacteristic
68C22×C4—1031no—
69C22×C4—2061no—
70M16—2062no—
71C2×C8—1031no—
72C2×C8C2×D10311yescharacteristic
73C4⋊C4—1031no—
74C4⋊C4C2×D10311yescharacteristic
75C22⋊C4—2061no—
76C42—2061no—
77C23—1031no—
78Q8—21no—
79Q8—1032no—
80Q8—2064no—
81Q8—2061no—
82Q8C4×D10312yes—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—1031no—
86C2×C4—1032no—
87C2×C4—1032no—
88C2×C4—2064no—
89C2×C4—2061no—
90C2×C4—2061no—
91C2×C4C22×D10311yescharacteristic
92C8—21no—
93C8—2061no—
94C22—1032no—
95C22—2061no—
96C22—2061no—
97C22D4×D10311yescharacteristic
98C4—22no—
99C4—41no—
100C4—1032no—
101C4—4121no—
102C4—2062no—
103C4C2×C4×D10311yescharacteristic
104C4D4×D10311yescharacteristic
105C2—2062no—
106C2C22⋊C4×D10311yescharacteristic
107C2#1569305011yescharacteristic
108C2#1569305311yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#103×C103C2
socleC22×C103C2×D4
hypercenter#103D103
hypocenterC103#419
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
4. #15692946C2semidirect
5. #15692945C2semidirect
6. #15692944C2semidirect
7. #103×C103C2semidirect
11. Q8×D103C4semidirect
54. C103#419semidirect
62. #103D103semidirect