Finite Group Databasebeta

← #103×D103 #20267780

Subgroups — #103×D103 #20267780

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×Q8×D103C211yesmaximal, characteristic
2C2×C8×D103C211yesmaximal, characteristic
3C4⋊C4×D103C211yesmaximal, 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×D103—21no—
14C2×C4×D103C2211yescharacteristic
15C2×C103⋊C8C2211yescharacteristic
16C8×D103—22no—
17C4⋊Dic103C2211yescharacteristic
18Dic103⋊C4—21no—
19C2×Q8×C103C2211yescharacteristic
20C2×C8×C103C2211yescharacteristic
21C4⋊C4×C103C2211yescharacteristic
22C22×D103D411yescharacteristic
23Q8×C103—21no—
24Q8×C103C2×C412yescomplemented
25C2×C4×C103—21no—
26C2×C4×C103—21no—
27C2×C4×C103C2311yescharacteristic
28C2×Dic103—21no—
29C2×Dic103—21no—
30C2×Dic103D411yescharacteristic
31C4×D103—24no—
32C4×D103—42no—
33C4×D103C2×C412yes—
34C4×D103D412yes—
35Dic206—21no—
36Dic206—24no—
37Dic206C2×C412yescomplemented
38C8×C103—21no—
39C103⋊C8—21no—
40C22×C103C2×D411yescharacteristic
41C2×D103C22⋊C412yes—
42C2×D103SD1612yes—
43C2×D103Q1612yes—
44C4×C103—22no—
45C4×C103—41no—
46C4×C103C22×C411yescharacteristic
47C4×C103C2×D411yescharacteristic
48Dic103—22no—
49Dic103—41no—
50Dic103C22⋊C412yes—
51C2×C103C2×C22⋊C411yescharacteristic
52C2×C103C2×SD1611yescharacteristic
53C2×C103C2×Q1611yescharacteristic
54D103#10314yesdirect product factor
55C103C2×#10311yescharacteristic, complemented, Sylow
56C2×#103—1031nomaximal, Sylow
57C22×Q8—1031no—
58C22×C8—1031no—
59C2×C4⋊C4—1031no—
60#103—1031no—
61#103—1031no—
62#103—1031no—
63#103D10311yescharacteristic, direct product factor
64C2×Q8—1034no—
65C2×Q8—1031no—
66C2×Q8—2061no—
67C2×Q8—2062no—
68C2×Q8C2×D10311yescharacteristic
69C22×C4—1031no—
70C22×C4—2061no—
71C22×C4—2061no—
72C2×C8—1031no—
73C2×C8—2062no—
74C2×C8C2×D10311yescharacteristic
75C4⋊C4—1031no—
76C4⋊C4—2061no—
77C4⋊C4C2×D10311yescharacteristic
78C23—1031no—
79Q8—21no—
80Q8—1032no—
81Q8—2064no—
82Q8—2061no—
83Q8C4×D10312yescomplemented
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—1031no—
87C2×C4—1032no—
88C2×C4—1032no—
89C2×C4—4122no—
90C2×C4—2064no—
91C2×C4—2061no—
92C2×C4—2061no—
93C2×C4C22×D10311yescharacteristic
94C8—21no—
95C8—2061no—
96C22—1032no—
97C22—1032no—
98C22—1032no—
99C22D4×D10311yescharacteristic
100C4—22no—
101C4—41no—
102C4—1032no—
103C4—4121no—
104C4—2062no—
105C4C2×C4×D10311yescharacteristic
106C4D4×D10311yescharacteristic
107C2—1034no—
108C2C22⋊C4×D10311yescharacteristic
109C2SD16×D10311yescharacteristic
110C2Q16×D10311yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#103×C103C2
socleC22×C103C2×D4
hypercenter#103D103
hypocenterC103C2×#103
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
24. Q8×C103C2×C4semidirect
37. Dic206C2×C4semidirect
54. D103#103direct (N × H)
55. C103C2×#103semidirect
63. #103D103direct (N × H)
83. Q8C4×D103semidirect