Finite Group Databasebeta

← #20267773

Subgroups — #20267773

Order 6592.

150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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×#13110105C211yesmaximal, characteristic
2C2×#13110089C211yesmaximal, characteristic, complemented
3#15692939C212yesmaximal, complemented
4#15692937C212yesmaximal, complemented
5C2×M16×C103C211yesmaximal, characteristic, complemented
6#13110105—21no—
7#13110105—21no—
8#13110105—21no—
9#13110105—21no—
10C2×Dic206C2211yescharacteristic
11C2×D412C2211yescharacteristic
12C2×C22⋊D103C412yes—
13C2×C4×D103C412yes—
14#13110089—21no—
15#13110089C2212yes—
16C2×C103⋊C8—21no—
17C22×C4×C103C2211yescharacteristic
18M16×C103—21no—
19M16×C103C2212yes—
20C2×C8×C103—21no—
21C23×C103C2×C411yescharacteristic
22C22×D103C2×C412yes—
23C2×C4×C103C2×C411yescharacteristic
24C2×C4×C103D411yescharacteristic
25C2×C4×C103D411yescharacteristic
26C2×C4×C103D411yescharacteristic
27C2×C4×C103D411yescharacteristic
28C2×C4×C103C2311yescharacteristic
29C22⋊D103—22no—
30C22⋊D103—22no—
31C2×Dic103C2×C412yes—
32D412—21no—
33D412—21no—
34C4×D103—22no—
35C4×D103—22no—
36Dic206—21no—
37Dic206—21no—
38C8×C103—22no—
39C103⋊C8—22no—
40C22×C103—41no—
41C22×C103C22⋊C411yescharacteristic
42C22×C103C22⋊C411yescharacteristic
43C22×C103C22×C411yescharacteristic
44C2×D103—22no—
45C2×D103—42no—
46C4×C103C22⋊C411yescharacteristic
47C4×C103C22⋊C411yescharacteristic
48C4×C103C2×D411yescharacteristic
49C4×C103C2×D411yescharacteristic
50Dic103—22no—
51C2×C103—21no—
52C2×C103—21no—
53C2×C103—21no—
54C2×C103C2×C22⋊C411yescharacteristic
55D103—42no—
56C103#41311yescharacteristic, complemented, Sylow
57#413—1031nomaximal, Sylow
58C2×#41—1031no—
59C2×M16—1031no—
60C2×M16D10311yescharacteristic, complemented
61#101—1032no—
62#100—1032no—
63#41—2061no—
64#41—2061no—
65#41—2061no—
66#41—2061no—
67C2×Q8—1031no—
68C2×D4—1032no—
69C2×D4—1031no—
70C22×C4—1032no—
71C22×C4C2×D10311yescharacteristic
72M16—21no—
73M16—1032no—
74M16—2061no—
75M16C2×D10312yes—
76C2×C8—21no—
77C2×C8—2061no—
78C23—1032no—
79C23C4×D10311yescharacteristic
80Q8—2061no—
81Q8—2061no—
82D4—2062no—
83D4—2062no—
84D4—2061no—
85D4—2061no—
86C2×C4—1032no—
87C2×C4—2062no—
88C2×C4—2062no—
89C2×C4C4×D10311yescharacteristic
90C2×C4D41211yescharacteristic
91C2×C4D41211yescharacteristic
92C2×C4C22⋊D10311yescharacteristic
93C2×C4C22⋊D10311yescharacteristic
94C2×C4C22×D10311yescharacteristic
95C8—22no—
96C8—2062no—
97C22—41no—
98C22—4122no—
99C22—2062no—
100C22(C2×D103)⋊C411yescharacteristic
101C22(C2×D103)⋊C411yescharacteristic
102C22C2×C4×D10311yescharacteristic
103C4—2062no—
104C4(C2×D103)⋊C411yescharacteristic
105C4(C2×D103)⋊C411yescharacteristic
106C4C2×C22⋊D10311yescharacteristic
107C4C2×D41211yescharacteristic
108C2—21no—
109C2—21no—
110C2—21no—
111C2—4122no—
112C2C2×(C2×D103)⋊C411yescharacteristic
subgroupG/H
centerC4(C2×D103)⋊C4
commutatorC22×C103C22×C4
FrattiniC2×C4C22×D103
FittingC2×M16×C103C2
socleC2×C103C2×C22⋊C4
hypercenterC2×M16D103
hypocenterC103#413
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#13110089C2semidirect
3. #15692939C2semidirect
4. #15692937C2semidirect
5. C2×M16×C103C2semidirect
56. C103#413semidirect
60. C2×M16D103semidirect