Finite Group Databasebeta

← #20268008

Subgroups — #20268008

Order 6592.

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

normal subgroups only

This group has 124 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×#13110090C211yesmaximal, characteristic
2#15693010C211yesmaximal, characteristic, complemented
3D4×Dic103C211yesmaximal, characteristic, complemented
4Dic103⋊C8C211yesmaximal, characteristic, complemented
5#15692945C211yesmaximal, characteristic, complemented
6#15692943C211yesmaximal, characteristic, complemented
7C2×SD16×C103C211yesmaximal, characteristic, complemented
8C2×D412C2211yescharacteristic
9C22×Dic103—21no—
10#13110090—22no—
11C2×C103⋊C8C2211yescharacteristic
12C4⋊Dic103C2211yescharacteristic
13C22⋊Dic103—21no—
14(C2×D103)⋊C4—21no—
15(C2×D103)⋊C4—21no—
16C4×Dic103C2211yescharacteristic
17C2×Q8×C103C2211yescharacteristic
18C2×D4×C103C2211yescharacteristic
19SD16×C103—22no—
20C2×C8×C103C2211yescharacteristic
21C23×C103—21no—
22C22×D103—21no—
23Q8×C103—21no—
24Q8×C103—21no—
25D4×C103—21no—
26D4×C103D412yes—
27C2×C4×C103—21no—
28C2×C4×C103C2311yescharacteristic
29C2×Dic103—21no—
30C2×Dic103—42no—
31C2×Dic103D411yescharacteristic
32C2×Dic103D411yescharacteristic
33D412—21no—
34D412—21no—
35C8×C103—21no—
36C103⋊C8—21no—
37C22×C103—22no—
38C22×C103—41no—
39C22×C103—41no—
40C22×C103C2×D411yescharacteristic
41C2×D103—41no—
42C2×D103—41no—
43C2×D103—41no—
44C4×C103—41no—
45C4×C103C2×D411yescharacteristic
46C4×C103#4111yescharacteristic
47Dic103—21no—
48Dic103—21no—
49Dic103—41no—
50C2×C103—42no—
51C2×C103#12111yescharacteristic
52C2×C103#13511yescharacteristic
53C2×C103AGL(1,ℤ/8)11yescharacteristic
54D103—81no—
55C103#46311yescharacteristic, complemented, Sylow
56#463—1031nomaximal, Sylow
57C2×SD16D10311yescharacteristic, complemented
58C2×D8—1031no—
59#124—1031no—
60C4×D4—1031no—
61C4⋊C8—1031no—
62#103—1031no—
63#102—1031no—
64C2×Q8C2×D10311yescharacteristic
65C2×D4—1031no—
66C2×D4C2×D10311yescharacteristic
67C22×C4—2061no—
68SD16—22no—
69D8—2062no—
70C2×C8—1031no—
71C2×C8C2×D10311yescharacteristic
72C4⋊C4—1031no—
73C22⋊C4—2061no—
74C22⋊C4—2061no—
75C22⋊C4—2061no—
76C42—1031no—
77C23—21no—
78C23—2061no—
79Q8—21no—
80Q8—21no—
81D4—21no—
82D4—2061no—
83D4—2061no—
84D4C22⋊D10312yes—
85C2×C4—21no—
86C2×C4—1031no—
87C2×C4—1031no—
88C2×C4—4122no—
89C2×C4—2061no—
90C2×C4C22×D10311yescharacteristic
91C8—21no—
92C8—2061no—
93C22—22no—
94C22—41no—
95C22—41no—
96C22—4121no—
97C22—4121no—
98C22—4121no—
99C22D4×D10311yescharacteristic
100C4—41no—
101C4—4121no—
102C4—2061no—
103C4—2061no—
104C4C2×C22⋊D10311yescharacteristic
105C4#1311010411yescharacteristic
106C2—42no—
107C2—8241no—
108C2#1569299311yescharacteristic
109C2#1569304211yescharacteristic
110C2#1569304811yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×SD16×C103C2
socleC22×C103C2×D4
hypercenterC2×SD16D103
hypocenterC103#463
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
2. #15693010C2semidirect
3. D4×Dic103C2semidirect
4. Dic103⋊C8C2semidirect
5. #15692945C2semidirect
6. #15692943C2semidirect
7. C2×SD16×C103C2semidirect
55. C103#463semidirect
57. C2×SD16D103semidirect