Finite Group Databasebeta

← #20268010

Subgroups — #20268010

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×#13110095C211yesmaximal, characteristic, complemented
2C2×#13110093C211yesmaximal, characteristic
3C4×Dic206C211yesmaximal, characteristic, complemented
4C4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
5#15692945C211yesmaximal, characteristic, complemented
6#15692942C211yesmaximal, characteristic
7#124×C103C211yesmaximal, characteristic
8C2×Dic206C2211yescharacteristic
9#13110095—22no—
10#13110093—22no—
11C2×C103⋊C8C2211yescharacteristic
12C2×C103⋊C8C2211yescharacteristic
13C4⋊Dic103C2211yescharacteristic
14Dic103⋊C4—21no—
15C4×Dic103—21no—
16C2×Q8×C103C2211yescharacteristic
17C2×D4×C103C2211yescharacteristic
18C22⋊C4×C103—21no—
19C22⋊C4×C103—21no—
20C42×C103C2211yescharacteristic
21C23×C103—21no—
22Q8×C103—21no—
23Q8×C103—21no—
24D4×C103—21no—
25D4×C103—21no—
26C2×C4×C103—21no—
27C2×C4×C103D411yescharacteristic
28C2×C4×C103D411yescharacteristic
29C2×C4×C103C2311yescharacteristic
30C2×Dic103—21no—
31C2×Dic103—21no—
32Dic206—21no—
33Dic206D412yes—
34C103⋊C8—21no—
35C103⋊C8—21no—
36C22×C103—41no—
37C22×C103—41no—
38C22×C103—41no—
39C22×C103C2×D411yescharacteristic
40C4×C103—21no—
41C4×C103—21no—
42C4×C103—41no—
43C4×C103C2×D411yescharacteristic
44C4×C103#4111yescharacteristic
45Dic103—22no—
46Dic103—41no—
47C2×C103—81no—
48C2×C103#12111yescharacteristic
49C2×C103#13511yescharacteristic
50C2×C103#13711yescharacteristic
51C103#46411yescharacteristic, complemented, Sylow
52#464—1031nomaximal, Sylow
53C2×Q16—1031no—
54C2×SD16—1031no—
55#124D10311yescharacteristic
56C4×Q8—1031no—
57C4⋊C8—1031no—
58#103—1031no—
59#102—1031no—
60C2×Q8—1031no—
61C2×Q8C2×D10311yescharacteristic
62C2×D4C2×D10311yescharacteristic
63Q16—2062no—
64SD16—2062no—
65C2×C8—1031no—
66C2×C8—1031no—
67C4⋊C4—1031no—
68C4⋊C4—2061no—
69C22⋊C4—21no—
70C22⋊C4—21no—
71C42—2061no—
72C42C2×D10311yescharacteristic
73C23—21no—
74Q8—21no—
75Q8—21no—
76Q8—1032no—
77Q8—2061no—
78D4—21no—
79D4—21no—
80C2×C4—21no—
81C2×C4—2061no—
82C2×C4—2061no—
83C2×C4C22⋊D10311yescharacteristic
84C2×C4C22⋊D10311yescharacteristic
85C2×C4C22×D10311yescharacteristic
86C8—2061no—
87C8—2061no—
88C22—41no—
89C22—41no—
90C22—41no—
91C22C2×C22⋊D10311yescharacteristic
92C4—21no—
93C4—21no—
94C4—41no—
95C4—4121no—
96C4—2062no—
97C4D4×D10311yescharacteristic
98C4#1311010411yescharacteristic
99C2—81no—
100C2#1569299211yescharacteristic
101C2#1569304111yescharacteristic
102C2#1569305111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#124×C103C2
socleC22×C103C2×D4
hypercenter#124D103
hypocenterC103#464
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#13110095C2semidirect
3. C4×Dic206C2semidirect
4. C4⋊(C103⋊C8)C2semidirect
5. #15692945C2semidirect
51. C103#464semidirect