Finite Group Databasebeta

← #20268051

Subgroups — #20268051

Order 6592.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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#15693052C211yesmaximal, characteristic, complemented
2#15693047C211yesmaximal, characteristic
3#15693027C211yesmaximal, characteristic, complemented
4#15692957C211yesmaximal, characteristic, complemented
5#15692940C211yesmaximal, characteristic, complemented
6#15692938C211yesmaximal, characteristic, complemented
7C2×SD16×C103C211yesmaximal, characteristic, complemented
8#13110105C2211yescharacteristic
9#13110095—21no—
10#13110093—21no—
11#13110092—21no—
12#13110090—21no—
13#13110089C2211yescharacteristic
14#13110089C2211yescharacteristic
15#13110089C2211yescharacteristic
16#13110088—21no—
17C8×D103—21no—
18C2×Q8×C103C2211yescharacteristic
19C2×D4×C103C2211yescharacteristic
20SD16×C103—21no—
21SD16×C103—21no—
22C2×C8×C103C2211yescharacteristic
23C23×C103—21no—
24Q8×C103—21no—
25Q8×C103—21no—
26D4×C103—21no—
27D4×C103—21no—
28C2×C4×C103—21no—
29C2×C4×C103C2311yescharacteristic
30C22⋊D103—21no—
31D412D411yescharacteristic
32C4×D103—21no—
33Dic206D411yescharacteristic
34C8×C103D411yescharacteristic
35C8×C103D411yescharacteristic
36C103⋊C8—21no—
37C103⋊C8—21no—
38C103⋊C8—21no—
39C22×C103—41no—
40C22×C103—81no—
41C22×C103#4111yescharacteristic
42C2×D103—21no—
43C4×C103—41no—
44C4×C103C2×D411yescharacteristic
45C4×C103C2×D411yescharacteristic
46Dic103—21no—
47C2×C103—21no—
48C2×C103—81no—
49C2×C103#12111yescharacteristic
50D103—41no—
51C103#47111yescharacteristic, complemented, Sylow
52#471—1031nomaximal, Sylow
53#137—1031no—
54AGL(1,ℤ/8)—1031no—
55C2×SD16D10311yescharacteristic, complemented
56#131—1031no—
57#108—1031no—
58#101—1031no—
59#100—1031no—
60#41—1031no—
61C2×Q8C2×D10311yescharacteristic
62C2×D4C2×D10311yescharacteristic
63Q16—2061no—
64SD16—21no—
65SD16—21no—
66SD16—2061no—
67SD16—2061no—
68D8—2061no—
69M16—1031no—
70M16—1031no—
71M16—1031no—
72M16—2061no—
73C2×C8—2061no—
74C2×C8C2×D10311yescharacteristic
75C23—21no—
76Q8—21no—
77Q8—21no—
78Q8—1031no—
79D4—21no—
80D4—21no—
81D4—1031no—
82D4—2061no—
83C2×C4—21no—
84C2×C4—2061no—
85C2×C4C22×D10311yescharacteristic
86C8—2061no—
87C8—2061no—
88C8—2061no—
89C8C22⋊D10311yescharacteristic
90C8C22⋊D10311yescharacteristic
91C22—41no—
92C22—81no—
93C22—2061no—
94C22#1311010411yescharacteristic
95C4—41no—
96C4—2061no—
97C4D4×D10311yescharacteristic
98C4C2×C22⋊D10311yescharacteristic
99C2—21no—
100C2—81no—
101C2—4121no—
102C2#1569299211yescharacteristic
subgroupG/H
centerC2#15692992
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×SD16×C103C2
socleC2×C103#121
hypercenterC2×SD16D103
hypocenterC103#471
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #15693052C2semidirect
3. #15693027C2semidirect
4. #15692957C2semidirect
5. #15692940C2semidirect
6. #15692938C2semidirect
7. C2×SD16×C103C2semidirect
51. C103#471semidirect
55. C2×SD16D103semidirect