Finite Group Databasebeta

← #20268589

Subgroups — #20268589

Order 6592.

262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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, complemented
2#15693052C212yesmaximal, complemented
3#15693051C212yesmaximal, complemented
4#15693047C212yesmaximal, complemented
5#15693046C212yesmaximal, complemented
6#15693041C214yesmaximal, complemented
7C2×#13110089C211yesmaximal, characteristic, complemented
8C2×#41×C103C211yesmaximal, characteristic, complemented
9#13110105—21no—
10#13110105—21no—
11#13110105C2212yes—
12#13110105C2212yescomplemented
13C2×Dic206C2211yescharacteristic, complemented
14C2×D412C2211yescharacteristic, complemented
15C2×C22⋊D103—21no—
16C2×C4×D103—21no—
17#13110095C2214yescomplemented
18#13110093C2214yescomplemented
19#13110092C2214yescomplemented
20#13110090C2214yescomplemented
21#13110089C2212yescomplemented
22#13110089C2212yescomplemented
23C2×C103⋊C8C2212yescomplemented
24#41×C103—21no—
25#41×C103—21no—
26#41×C103C2212yes—
27#41×C103C2212yescomplemented
28C2×Q8×C103C2211yescharacteristic, complemented
29C2×D4×C103—21no—
30C2×D4×C103C2211yescharacteristic, complemented
31C22×C4×C103—21no—
32C22×C4×C103C2211yescharacteristic
33C23×C103—21no—
34C23×C103D411yescharacteristic
35C22×D103—21no—
36Q8×C103—21no—
37Q8×C103C2312yes—
38D4×C103—22no—
39D4×C103—22no—
40D4×C103—21no—
41D4×C103C2312yes—
42C2×C4×C103—21no—
43C2×C4×C103—22no—
44C2×C4×C103—22no—
45C2×C4×C103D411yescharacteristic
46C2×C4×C103D411yescharacteristic
47C2×C4×C103D411yescharacteristic
48C2×C4×C103C2311yescharacteristic
49C2×C4×C103C2311yescharacteristic
50C2×C4×C103C2311yescharacteristic
51C22⋊D103—22no—
52C22⋊D103—22no—
53C2×Dic103—21no—
54D412—21no—
55D412C2312yes—
56C4×D103—22no—
57C4×D103—22no—
58Dic206—21no—
59Dic206C2312yes—
60C103⋊C8C2314yes—
61C22×C103—22no—
62C22×C103—41no—
63C22×C103—42no—
64C22×C103C2×D411yescharacteristic
65C22×C103C2×D411yescharacteristic
66C22×C103C2×D411yescharacteristic
67C2×D103—22no—
68C2×D103—42no—
69C4×C103—22no—
70C4×C103C2×D411yescharacteristic
71C4×C103C2×D411yescharacteristic
72C4×C103C2×D411yescharacteristic
73C4×C103C2411yescharacteristic
74Dic103—22no—
75C2×C103—21no—
76C2×C103—21no—
77C2×C103—21no—
78C2×C103—42no—
79C2×C103C22×D411yescharacteristic
80D103—42no—
81C103#57511yescharacteristic, complemented, Sylow
82#575—1031nomaximal, Sylow
83C2×#41—1031no—
84C2×#41D10311yescharacteristic, complemented
85#137—1032no—
86#137—1032no—
87AGL(1,ℤ/8)—1032no—
88AGL(1,ℤ/8)—1032no—
89#135—1034no—
90C2×M16—1031no—
91#41—21no—
92#41—21no—
93#41—1032no—
94#41—1032no—
95#41—2061no—
96#41—2061no—
97#41C2×D10312yes—
98#41C2×D10312yescomplemented
99C2×Q8—1031no—
100C2×Q8C2×D10311yescharacteristic, complemented
101C2×D4—21no—
102C2×D4—1031no—
103C2×D4—2061no—
104C2×D4C2×D10311yescharacteristic, complemented
105C22×C4—21no—
106C22×C4—2061no—
107C22×C4C2×D10311yescharacteristic
108Q16—1034no—
109SD16—1034no—
110SD16—1034no—
111D8—1034no—
112M16—1032no—
113M16—1032no—
114C2×C8—1032no—
115C23—21no—
116C23—2061no—
117C23C22⋊D10311yescharacteristic
118Q8—21no—
119Q8—1032no—
120Q8—2061no—
121Q8C22×D10312yes—
122D4—22no—
123D4—22no—
124D4—21no—
125D4—1032no—
126D4—2062no—
127D4—2062no—
128D4—2061no—
129D4C22×D10312yes—
130C2×C4—21no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—2061no—
134C2×C4—2062no—
135C2×C4—2062no—
136C2×C4C22⋊D10311yescharacteristic
137C2×C4C22⋊D10311yescharacteristic
138C2×C4C22⋊D10311yescharacteristic
139C2×C4C22×D10311yescharacteristic
140C2×C4C22×D10311yescharacteristic
141C2×C4C22×D10311yescharacteristic
142C8—1034no—
143C22—22no—
144C22—41no—
145C22—42no—
146C22—4122no—
147C22—2062no—
148C22C2×C22⋊D10311yescharacteristic
149C22C2×C22⋊D10311yescharacteristic
150C22C2×C22⋊D10311yescharacteristic
151C4—22no—
152C4—2062no—
153C4C2×C22⋊D10311yescharacteristic
154C4C2×C22⋊D10311yescharacteristic
155C4C2×C22⋊D10311yescharacteristic
156C4C23×D10311yescharacteristic
157C2—21no—
158C2—21no—
159C2—21no—
160C2—42no—
161C2—4122no—
162C2C22×C22⋊D10311yescharacteristic
subgroupG/H
centerC4C2×C22⋊D103
commutatorC4×C103C24
FrattiniC4C23×D103
FittingC2×#41×C103C2
socleC2×C103C22×D4
hypercenterC2×#41D103
hypocenterC103#575
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13110105C2semidirect
2. #15693052C2semidirect
3. #15693051C2semidirect
4. #15693047C2semidirect
5. #15693046C2semidirect
6. #15693041C2semidirect
7. C2×#13110089C2semidirect
8. C2×#41×C103C2semidirect
12. #13110105C22semidirect
13. C2×Dic206C22semidirect
14. C2×D412C22semidirect
17. #13110095C22semidirect
18. #13110093C22semidirect
19. #13110092C22semidirect
20. #13110090C22semidirect
21. #13110089C22semidirect
22. #13110089C22semidirect
23. C2×C103⋊C8C22semidirect
27. #41×C103C22semidirect
28. C2×Q8×C103C22semidirect
30. C2×D4×C103C22semidirect
81. C103#575semidirect
84. C2×#41D103semidirect
98. #41C2×D103semidirect
100. C2×Q8C2×D103semidirect
104. C2×D4C2×D103semidirect