Finite Group Databasebeta

← #20267970

Subgroups — #20267970

Order 6592.

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

normal subgroups only

This group has 152 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#15693067C211yesmaximal, characteristic
2#15693054C211yesmaximal, characteristic, complemented
3#15693051C211yesmaximal, characteristic, complemented
4#15693009C211yesmaximal, characteristic, complemented
5#15692949C211yesmaximal, characteristic, complemented
6#15692937C211yesmaximal, characteristic, complemented
7#104×C103C211yesmaximal, characteristic, complemented
8#13110106—21no—
9#13110105—21no—
10#13110105C2211yescharacteristic
11C2×Dic206C2211yescharacteristic, complemented
12C2×D412—21no—
13C2×D412C2211yescharacteristic
14D4×D103—22no—
15D4×D103—21no—
16Dic412—21no—
17#13110095—21no—
18#13110094—21no—
19#13110093—21no—
20#13110089C2211yescharacteristic, complemented
21(C2×D103)⋊C4—22no—
22#41×C103C2211yescharacteristic
23M16×C103C2211yescharacteristic, complemented
24C42×C103C2211yescharacteristic, complemented
25C22×D103—22no—
26C22×D103D412yes—
27Q8×C103D411yescharacteristic
28D4×C103—21no—
29D4×C103D411yescharacteristic
30C2×C4×C103—21no—
31C2×C4×C103—21no—
32C2×C4×C103C2311yescharacteristic
33C22⋊D103—22no—
34C22⋊D103—21no—
35C2×Dic103—21no—
36D412—22no—
37D412—21no—
38D412—21no—
39D412D411yescharacteristic
40C4×D103—22no—
41C4×D103—21no—
42Dic206—21no—
43Dic206—21no—
44Dic206D411yescharacteristic
45C8×C103—21no—
46C103⋊C8—21no—
47C22×C103—21no—
48C22×C103C2×D411yescharacteristic
49C2×D103—22no—
50C2×D103—21no—
51C2×D103—42no—
52C2×D103—82no—
53C4×C103—21no—
54C4×C103—41no—
55C4×C103C2×D411yescharacteristic
56C4×C103C2×D411yescharacteristic
57Dic103—21no—
58Dic103—41no—
59C2×C103—21no—
60C2×C103—41no—
61C2×C103#12011yescharacteristic
62D103—42no—
63D103—41no—
64C103#45511yescharacteristic, complemented, Sylow
65#455—1031nomaximal, Sylow
66H(5,𝔽2)—1031no—
67#137—1031no—
68#137—1031no—
69#124—1031no—
70#104—1031no—
71#104D10311yescharacteristic, complemented
72#100—1031no—
73#41—1031no—
74#41—2061no—
75#41—2061no—
76#41C2×D10311yescharacteristic
77C2×Q8—1031no—
78C2×D4—1031no—
79C2×D4—2061no—
80C2×D4—2062no—
81C2×D4—2061no—
82Q16—2061no—
83Q16—2061no—
84SD16—2061no—
85SD16—2061no—
86M16—1031no—
87M16C2×D10311yescharacteristic, complemented
88C22⋊C4—2062no—
89C42C2×D10311yescharacteristic, complemented
90C23—1032no—
91C23—2062no—
92Q8—1031no—
93Q8—2061no—
94Q8—2061no—
95Q8D41211yescharacteristic
96D4—21no—
97D4—1031no—
98D4—2062no—
99D4—2062no—
100D4—2061no—
101D4—2061no—
102D4—2061no—
103D4D41211yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—2062no—
107C2×C4—2061no—
108C2×C4—2061no—
109C2×C4C22×D10311yescharacteristic
110C8—21no—
111C8—2061no—
112C22—21no—
113C22—8242no—
114C22—4122no—
115C22—2061no—
116C22—2062no—
117C22D4×D10311yescharacteristic
118C4—21no—
119C4—41no—
120C4—4121no—
121C4—2061no—
122C4D4×D10311yescharacteristic
123C4C2×D41211yescharacteristic
124C2—21no—
125C2—41no—
126C2—4121no—
127C2—4122no—
128C2#1569299111yescharacteristic
subgroupG/H
centerC2#15692991
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#104×C103C2
socleC2×C103#120
hypercenter#104D103
hypocenterC103#455
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #15693054C2semidirect
3. #15693051C2semidirect
4. #15693009C2semidirect
5. #15692949C2semidirect
6. #15692937C2semidirect
7. #104×C103C2semidirect
11. C2×Dic206C22semidirect
20. #13110089C22semidirect
23. M16×C103C22semidirect
24. C42×C103C22semidirect
64. C103#455semidirect
71. #104D103semidirect
87. M16C2×D103semidirect
89. C42C2×D103semidirect