Finite Group Databasebeta

← #20268031

Subgroups — #20268031

Order 6592.

114 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 41 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×C8×D103C211yesmaximal, characteristic
3#15693001C211yesmaximal, characteristic
4#15692997C211yesmaximal, characteristic
5#15692954C211yesmaximal, characteristic, complemented
6#15692946C211yesmaximal, characteristic, complemented
7#103×C103C211yesmaximal, characteristic, complemented
8C2×Dic206C2211yescharacteristic
9C2×C4×D103C2211yescharacteristic
10#13110095—22no—
11C2×C103⋊C8C2211yescharacteristic
12C8×D103—22no—
13C4⋊Dic103—21no—
14C4⋊Dic103C2211yescharacteristic
15Dic103⋊C4—21no—
16(C2×D103)⋊C4—21no—
17(C2×D103)⋊C4—21no—
18C2×Q8×C103C2211yescharacteristic
19C2×C8×C103C2211yescharacteristic
20C4⋊C4×C103C2211yescharacteristic
21C22×D103D411yescharacteristic
22Q8×C103—21no—
23Q8×C103—21no—
24C2×C4×C103—21no—
25C2×C4×C103—21no—
26C2×C4×C103C2311yescharacteristic
27C2×Dic103—21no—
28C2×Dic103—21no—
29C2×Dic103D411yescharacteristic
30C4×D103—21no—
31C4×D103—21no—
32Dic206—21no—
33Dic206—21no—
34C8×C103—21no—
35C103⋊C8D412yes—
36C22×C103C2×D411yescharacteristic
37C2×D103—21no—
38C2×D103—21no—
39C2×D103Q1612yescomplemented
40C4×C103—41no—
41C4×C103—41no—
42C4×C103C2×D411yescharacteristic
43C4×C103#4111yescharacteristic
44Dic103—21no—
45Dic103—41no—
46Dic103—41no—
47C2×C103#12111yescharacteristic
48C2×C103C2×Q1611yescharacteristic
49C2×C103#13511yescharacteristic
50D103—22no—
51C103#46711yescharacteristic, complemented, Sylow
52#467—1031nomaximal, Sylow
53C2×Q16—1031no—
54C22×C8—1031no—
55C22⋊Q8—1031no—
56C22⋊Q8—1031no—
57#107—1031no—
58#103—1031no—
59#103D10311yescharacteristic, complemented
60C2×Q8—1031no—
61C2×Q8C2×D10311yescharacteristic
62C22×C4—1031no—
63Q16—2062no—
64C2×C8—1031no—
65C2×C8—2062no—
66C2×C8C2×D10311yescharacteristic
67C4⋊C4—1031no—
68C4⋊C4—2061no—
69C4⋊C4—2061no—
70C4⋊C4C2×D10311yescharacteristic
71C22⋊C4—2061no—
72C22⋊C4—2061no—
73C23—1031no—
74Q8—21no—
75Q8—21no—
76Q8—2061no—
77Q8—2061no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—1031no—
81C2×C4—2061no—
82C2×C4—2061no—
83C2×C4—2061no—
84C2×C4—2061no—
85C2×C4C22×D10311yescharacteristic
86C8—21no—
87C8—1032no—
88C22—1032no—
89C22—2061no—
90C22—2061no—
91C22D4×D10311yescharacteristic
92C4—41no—
93C4—41no—
94C4—4121no—
95C4—4121no—
96C4—2061no—
97C4D4×D10311yescharacteristic
98C4#1311010511yescharacteristic
99C2—2062no—
100C2#1569299411yescharacteristic
101C2Q16×D10311yescharacteristic
102C2#1569304211yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#103×C103C2
socleC22×C103C2×D4
hypercenter#103D103
hypocenterC103#467
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#13110095C2semidirect
5. #15692954C2semidirect
6. #15692946C2semidirect
7. #103×C103C2semidirect
39. C2×D103Q16semidirect
51. C103#467semidirect
59. #103D103semidirect