Finite Group Databasebeta

← #20267794

Subgroups — #20267794

Order 6592.

190 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 55 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×D4×D103C211yesmaximal, characteristic
2C2×#13110088C211yesmaximal, characteristic, complemented
3#15692979C211yesmaximal, characteristic, complemented
4#15692943C211yesmaximal, characteristic, complemented
5#15692942C211yesmaximal, characteristic, complemented
6#15692941C211yesmaximal, characteristic, complemented
7#102×C103C211yesmaximal, characteristic, complemented
8C23×D103—21no—
9C2×D412C2211yescharacteristic
10C2×C22⋊D103—21no—
11D4×D103—22no—
12D4×D103C414yescomplemented
13C2×C4×D103C2211yescharacteristic
14#13110088—22no—
15C2×C103⋊C8C2211yescharacteristic, complemented
16C4⋊Dic103C2211yescharacteristic, complemented
17(C2×D103)⋊C4—21no—
18C4×Dic103—21no—
19C2×D4×C103C2211yescharacteristic
20C2×C8×C103C2211yescharacteristic, complemented
21C4⋊C4×C103C2211yescharacteristic, complemented
22C23×C103—21no—
23C22×D103—21no—
24C22×D103—24no—
25C22×D103—42no—
26C22×D103—42no—
27C22×D103D411yescharacteristic
28D4×C103—21no—
29D4×C103C2×C412yes—
30C2×C4×C103—21no—
31C2×C4×C103C2311yescharacteristic
32C22⋊D103—24no—
33C2×Dic103—21no—
34C2×Dic103D411yescharacteristic
35D412—21no—
36D412C2×C412yes—
37C4×D103C2×C412yes—
38C4×D103D412yes—
39C8×C103—21no—
40C103⋊C8—21no—
41C22×C103—22no—
42C22×C103—41no—
43C22×C103—41no—
44C22×C103C2×D411yescharacteristic
45C2×D103—21no—
46C2×D103—21no—
47C2×D103—22no—
48C2×D103—48no—
49C2×D103—41no—
50C2×D103—41no—
51C2×D103C22⋊C412yes—
52C4×C103—41no—
53C4×C103C22×C411yescharacteristic
54C4×C103C2×D411yescharacteristic
55Dic103—41no—
56Dic103C22⋊C412yes—
57C2×C103—42no—
58C2×C103C2×C22⋊C411yescharacteristic
59C2×C103AGL(1,ℤ/8)11yescharacteristic
60C2×C103AGL(1,ℤ/8)11yescharacteristic
61D103—22no—
62D103—42no—
63C103#41811yescharacteristic, complemented, Sylow
64#418—1031nomaximal, Sylow
65C22×D4—1031no—
66C2×M16—1031no—
67#117—1031no—
68#102—1031no—
69#102—1031no—
70#102—1031no—
71#102D10311yescharacteristic, complemented
72C24—2061no—
73C2×D4—1034no—
74C2×D4—1031no—
75C2×D4—2062no—
76C2×D4—2061no—
77C2×D4C2×D10311yescharacteristic
78C22×C4—1031no—
79M16—2062no—
80C2×C8—1031no—
81C2×C8C2×D10311yescharacteristic, complemented
82C4⋊C4—1031no—
83C4⋊C4C2×D10311yescharacteristic, complemented
84C22⋊C4—2061no—
85C42—2061no—
86C23—21no—
87C23—1031no—
88C23—4122no—
89C23—4122no—
90C23—2064no—
91C23—2061no—
92D4—21no—
93D4—1032no—
94D4—2064no—
95D4—2061no—
96D4C4×D10312yes—
97C2×C4—21no—
98C2×C4—1031no—
99C2×C4—1032no—
100C2×C4—1032no—
101C2×C4—2061no—
102C2×C4C22×D10311yescharacteristic
103C8—21no—
104C8—2061no—
105C22—22no—
106C22—41no—
107C22—41no—
108C22—1032no—
109C22—4128no—
110C22—4121no—
111C22—4121no—
112C22—2062no—
113C22—2061no—
114C22—2061no—
115C22D4×D10311yescharacteristic
116C4—41no—
117C4—1032no—
118C4—4121no—
119C4C2×C4×D10311yescharacteristic
120C4D4×D10311yescharacteristic
121C2—42no—
122C2—4122no—
123C2—2062no—
124C2C22⋊C4×D10311yescharacteristic
125C2#1569304511yescharacteristic
126C2#1569304811yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#102×C103C2
socleC22×C103C2×D4
hypercenter#102D103
hypocenterC103#418
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#13110088C2semidirect
3. #15692979C2semidirect
4. #15692943C2semidirect
5. #15692942C2semidirect
6. #15692941C2semidirect
7. #102×C103C2semidirect
12. D4×D103C4semidirect
15. C2×C103⋊C8C22semidirect
16. C4⋊Dic103C22semidirect
20. C2×C8×C103C22semidirect
21. C4⋊C4×C103C22semidirect
63. C103#418semidirect
71. #102D103semidirect
81. C2×C8C2×D103semidirect
83. C4⋊C4C2×D103semidirect