Finite Group Databasebeta

← #20267980

Subgroups — #20267980

Order 6592.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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
1#15693066C211yesmaximal, characteristic
2#15693004C212yesmaximal, complemented
3#15692936C211yesmaximal, characteristic, complemented
4#15692935C212yesmaximal, complemented
5#123×C103C211yesmaximal, characteristic, complemented
6#13110105—21no—
7#13110104—22no—
8C2×C22⋊D103—21no—
9C2×C22⋊D103C2212yes—
10D4×D103—22no—
11Dic103⋊C4—22no—
12C22⋊Dic103C2212yescomplemented
13(C2×D103)⋊C4—22no—
14C2×D4×C103C2211yescharacteristic
15C22×C4×C103C2211yescharacteristic, complemented
16C4⋊C4×C103—21no—
17C22⋊C4×C103—21no—
18C22⋊C4×C103C2211yescharacteristic, complemented
19C23×C103D411yescharacteristic
20C23×C103C2311yescharacteristic
21C22×D103—21no—
22C22×D103D412yes—
23D4×C103—22no—
24C2×C4×C103—21no—
25C2×C4×C103—21no—
26C2×C4×C103—22no—
27C2×C4×C103D411yescharacteristic
28C22⋊D103—22no—
29C22⋊D103—22no—
30C22⋊D103—22no—
31C2×Dic103—21no—
32C2×Dic103—22no—
33C2×Dic103D412yes—
34D412—21no—
35C4×D103—22no—
36Dic206—21no—
37C22×C103—21no—
38C22×C103—41no—
39C22×C103—41no—
40C22×C103C2×D412yes—
41C22×C103C2×D411yescharacteristic
42C2×D103—22no—
43C2×D103—42no—
44C2×D103—81no—
45C4×C103—21no—
46C4×C103—41no—
47C4×C103—41no—
48Dic103—22no—
49Dic103—42no—
50C2×C103—22no—
51C2×C103—21no—
52C2×C103—41no—
53C2×C103#12011yescharacteristic
54D103—42no—
55C103#45811yescharacteristic, complemented, Sylow
56#458—1031nomaximal, Sylow
57H(5,𝔽2)—1031no—
58#123—1032no—
59#123D10311yescharacteristic, complemented
60#99—1031no—
61#99—1032no—
62#41—2062no—
63#41—2061no—
64C2×D4—1032no—
65C2×D4—2062no—
66C2×D4—2061no—
67C2×D4C2×D10311yescharacteristic
68C22×C4C2×D10311yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—2062no—
71C22⋊C4—21no—
72C22⋊C4—1032no—
73C22⋊C4—2062no—
74C22⋊C4C2×D10311yescharacteristic, complemented
75C23—1032no—
76C23—2061no—
77C23C22⋊D10311yescharacteristic
78C23C22×D10311yescharacteristic
79Q8—2061no—
80D4—22no—
81D4—2061no—
82D4—2062no—
83D4—2062no—
84D4—2062no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—1032no—
89C2×C4—2062no—
90C2×C4—2062no—
91C2×C4—2061no—
92C2×C4C22⋊D10311yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—8241no—
97C22—4122no—
98C22—2062no—
99C22D4×D10312yes—
100C22C2×C22⋊D10311yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—4122no—
105C4—2062no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—4122no—
110C2#1569298911yescharacteristic
subgroupG/H
centerC2#15692989
commutatorC23×C103C23
FrattiniC23C22×D103
Fitting#123×C103C2
socleC2×C103#120
hypercenter#123D103
hypocenterC103#458
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #15693004C2semidirect
3. #15692936C2semidirect
4. #15692935C2semidirect
5. #123×C103C2semidirect
12. C22⋊Dic103C22semidirect
15. C22×C4×C103C22semidirect
18. C22⋊C4×C103C22semidirect
55. C103#458semidirect
59. #123D103semidirect
68. C22×C4C2×D103semidirect
74. C22⋊C4C2×D103semidirect