Finite Group Databasebeta

← #20268014

Subgroups — #20268014

Order 6592.

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

normal subgroups only

This group has 112 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×Dic412C211yesmaximal, characteristic, complemented
2C2×#13110094C211yesmaximal, characteristic
3#15693009C211yesmaximal, characteristic
4C4×Dic206C211yesmaximal, characteristic, complemented
5#15692946C211yesmaximal, characteristic, complemented
6#15692943C211yesmaximal, characteristic
7C4⋊C8×C103C211yesmaximal, characteristic, complemented
8C2×Dic206C2211yescharacteristic
9C2×Dic206C2211yescharacteristic
10C2×D412C2211yescharacteristic
11Dic412—22no—
12#13110094—22no—
13C4⋊Dic103C2211yescharacteristic
14Dic103⋊C4—21no—
15(C2×D103)⋊C4—21no—
16(C2×D103)⋊C4—21no—
17C4×Dic103—21no—
18C2×C8×C103C2211yescharacteristic
19C2×C8×C103C2211yescharacteristic
20C42×C103C2211yescharacteristic
21C22×D103—21no—
22C2×C4×C103D411yescharacteristic
23C2×C4×C103D411yescharacteristic
24C2×C4×C103C2311yescharacteristic
25C2×Dic103—21no—
26C2×Dic103—21no—
27C2×Dic103—21no—
28D412—21no—
29D412—21no—
30Dic206—21no—
31Dic206—21no—
32Dic206—21no—
33Dic206D412yes—
34C8×C103—21no—
35C8×C103—21no—
36C22×C103C2×D411yescharacteristic
37C2×D103—41no—
38C2×D103—41no—
39C2×D103—41no—
40C4×C103—21no—
41C4×C103—21no—
42C4×C103C2×D411yescharacteristic
43C4×C103#4111yescharacteristic
44Dic103—22no—
45Dic103—41no—
46Dic103—41no—
47C2×C103#12111yescharacteristic
48C2×C103#13511yescharacteristic
49C2×C103#13711yescharacteristic
50D103—81no—
51C103#46411yescharacteristic, complemented, Sylow
52#464—1031nomaximal, Sylow
53C2×Q16—1031no—
54C2×SD16—1031no—
55#124—1031no—
56C4×Q8—1031no—
57C4⋊C8D10311yescharacteristic, complemented
58#103—1031no—
59#102—1031no—
60C2×Q8—1031no—
61C2×Q8—1031no—
62C2×D4—1031no—
63Q16—2062no—
64SD16—2062no—
65C2×C8C2×D10311yescharacteristic
66C2×C8C2×D10311yescharacteristic
67C4⋊C4—1031no—
68C4⋊C4—2061no—
69C22⋊C4—2061no—
70C22⋊C4—2061no—
71C42—2061no—
72C42C2×D10311yescharacteristic
73C23—2061no—
74Q8—1032no—
75Q8—2061no—
76Q8—2061no—
77Q8—2061no—
78D4—2061no—
79D4—2061no—
80C2×C4—2061no—
81C2×C4—2061no—
82C2×C4—2061no—
83C2×C4D41211yescharacteristic
84C2×C4D41211yescharacteristic
85C2×C4C22×D10311yescharacteristic
86C8—21no—
87C8—21no—
88C22—4121no—
89C22—4121no—
90C22—4121no—
91C22C2×D41211yescharacteristic
92C4—21no—
93C4—21no—
94C4—4121no—
95C4—4121no—
96C4—2062no—
97C4D4×D10311yescharacteristic
98C4#1311010611yescharacteristic
99C2—8241no—
100C2#1569299611yescharacteristic
101C2#1569304311yescharacteristic
102C2#1569305411yescharacteristic
subgroupG/H
centerC22C2×D412
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC4⋊C8×C103C2
socleC22×C103C2×D4
hypercenterC4⋊C8D103
hypocenterC103#464
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×Dic412C2semidirect
4. C4×Dic206C2semidirect
5. #15692946C2semidirect
7. C4⋊C8×C103C2semidirect
51. C103#464semidirect
57. C4⋊C8D103semidirect