Finite Group Databasebeta

← #20268017

Subgroups — #20268017

Order 6592.

124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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×C8×D103C211yesmaximal, characteristic, complemented
2#15692997C211yesmaximal, characteristic, complemented
3#15692992C211yesmaximal, characteristic
4#15692953C211yesmaximal, characteristic, complemented
5#15692945C211yesmaximal, characteristic, complemented
6#15692942C211yesmaximal, characteristic, complemented
7C2×SD16×C103C211yesmaximal, characteristic, complemented
8C2×C22⋊D103—21no—
9C2×C4×D103C2211yescharacteristic
10C2×C103⋊C8C2211yescharacteristic
11C8×D103—22no—
12C4⋊Dic103C2211yescharacteristic
13C4⋊Dic103C2211yescharacteristic
14Dic103⋊C4—21no—
15C22⋊Dic103—21no—
16(C2×D103)⋊C4—21no—
17C2×Q8×C103C2211yescharacteristic
18C2×D4×C103C2211yescharacteristic
19SD16×C103—22no—
20C2×C8×C103C2211yescharacteristic
21C23×C103—21no—
22C22×D103D411yescharacteristic
23Q8×C103—21no—
24Q8×C103—21no—
25D4×C103—21no—
26D4×C103—21no—
27C2×C4×C103—21no—
28C2×C4×C103C2311yescharacteristic
29C22⋊D103—42no—
30C2×Dic103—21no—
31C2×Dic103—21no—
32C2×Dic103D411yescharacteristic
33C4×D103—21no—
34C4×D103—21no—
35C8×C103D412yescomplemented
36C103⋊C8—21no—
37C22×C103—41no—
38C22×C103—41no—
39C22×C103—41no—
40C22×C103C2×D411yescharacteristic
41C2×D103—21no—
42C2×D103—21no—
43C2×D103SD1612yescomplemented
44C4×C103—41no—
45C4×C103C2×D411yescharacteristic
46C4×C103#4111yescharacteristic
47Dic103—21no—
48Dic103—41no—
49Dic103—41no—
50C2×C103—81no—
51C2×C103#12111yescharacteristic
52C2×C103C2×SD1611yescharacteristic
53C2×C103#13511yescharacteristic
54D103—22no—
55C103#46511yescharacteristic, complemented, Sylow
56#465—1031nomaximal, Sylow
57C2×SD16D10311yescharacteristic, complemented
58C22×C8—1031no—
59C22⋊Q8—1031no—
60#121—1031no—
61#106—1031no—
62#103—1031no—
63#102—1031no—
64C2×Q8C2×D10311yescharacteristic
65C2×D4—2061no—
66C2×D4C2×D10311yescharacteristic
67C22×C4—1031no—
68SD16—22no—
69C2×C8—1031no—
70C2×C8—2062no—
71C2×C8C2×D10311yescharacteristic
72C4⋊C4—1031no—
73C4⋊C4—1031no—
74C4⋊C4—2061no—
75C22⋊C4—2061no—
76C22⋊C4—2061no—
77C23—21no—
78C23—1031no—
79Q8—21no—
80Q8—21no—
81D4—21no—
82D4—21no—
83D4—4122no—
84C2×C4—21no—
85C2×C4—1031no—
86C2×C4—2061no—
87C2×C4—2061no—
88C2×C4—2061no—
89C2×C4—2061no—
90C2×C4C22×D10311yescharacteristic
91C8—2061no—
92C8C22⋊D10312yescomplemented
93C22—41no—
94C22—41no—
95C22—41no—
96C22—1032no—
97C22—2061no—
98C22—2061no—
99C22D4×D10311yescharacteristic
100C4—41no—
101C4—4121no—
102C4—4121no—
103C4—2061no—
104C4C2×C22⋊D10311yescharacteristic
105C4#1311010411yescharacteristic
106C2—81no—
107C2—2062no—
108C2#1569299211yescharacteristic
109C2SD16×D10311yescharacteristic
110C2#1569304211yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×SD16×C103C2
socleC22×C103C2×D4
hypercenterC2×SD16D103
hypocenterC103#465
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C8×D103C2semidirect
2. #15692997C2semidirect
4. #15692953C2semidirect
5. #15692945C2semidirect
6. #15692942C2semidirect
7. C2×SD16×C103C2semidirect
35. C8×C103D4semidirect
43. C2×D103SD16semidirect
55. C103#465semidirect
57. C2×SD16D103semidirect
92. C8C22⋊D103semidirect