Finite Group Databasebeta

← C2×#15693050 #20268582

Subgroups — C2×#15693050 #20268582

Order 6592.

258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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×#13110104C211yesmaximal, characteristic
2C2×Q8×D103C211yesmaximal, characteristic, complemented
3#15693050C218yesmaximal, direct product factor
4C2×Dic412C211yesmaximal, characteristic, complemented
5C2×#13110095C211yesmaximal, characteristic, complemented
6C2×#13110093C211yesmaximal, characteristic, complemented
7C2×#13110088C211yesmaximal, characteristic, complemented
8C2×SD16×C103C211yesmaximal, characteristic, complemented
9#13110104—22no—
10#13110104C2214yes—
11C2×Dic206—21no—
12C2×Dic206C2211yescharacteristic
13C2×Dic206C2211yescharacteristic
14Q8×D103—22no—
15Q8×D103C2214yescomplemented
16C2×C22⋊D103—21no—
17C22×Dic103—21no—
18C2×C4×D103—21no—
19C2×C4×D103C2211yescharacteristic
20Dic412C2214yescomplemented
21#13110095C2214yescomplemented
22#13110093C2214yescomplemented
23#13110088C2214yescomplemented
24C2×C103⋊C8C2211yescharacteristic
25C2×Q8×C103C2211yescharacteristic
26C2×D4×C103C2211yescharacteristic
27SD16×C103C2214yescomplemented
28C2×C8×C103C2211yescharacteristic
29C23×C103—21no—
30C22×D103D411yescharacteristic
31Q8×C103—21no—
32Q8×C103C2312yes—
33D4×C103—21no—
34D4×C103C2312yes—
35C2×C4×C103—21no—
36C2×C4×C103C2311yescharacteristic
37C22⋊D103—24no—
38C2×Dic103—21no—
39C2×Dic103—21no—
40C2×Dic103—24no—
41C2×Dic103D411yescharacteristic
42C4×D103—24no—
43C4×D103D412yes—
44C4×D103C2312yes—
45Dic206—21no—
46Dic206—21no—
47Dic206—24no—
48Dic206C2312yes—
49Dic206C2312yes—
50C8×C103C2312yes—
51C103⋊C8C2312yes—
52C22×C103—22no—
53C22×C103—42no—
54C22×C103C2×D411yescharacteristic
55C2×D103—22no—
56C2×D103C2×D412yes—
57C4×C103—22no—
58C4×C103C2×D411yescharacteristic
59C4×C103C2411yescharacteristic
60Dic103—22no—
61Dic103—22no—
62Dic103C2×D412yes—
63C2×C103—42no—
64C2×C103#13712yescomplemented
65C2×C103C22×D411yescharacteristic
66D103—22no—
67C103C2×#13711yescharacteristic, complemented, Sylow
68C2×#137—1031nomaximal, Sylow
69C2×#41—1031no—
70C22×Q8—1031no—
71#137—1038no—
72C2×Q16—1031no—
73C2×Q16—1031no—
74C2×SD16—1031no—
75C2×SD16D10311yescharacteristic, complemented
76C2×M16—1031no—
77#41—1034no—
78#41—2062no—
79C2×Q8—1034no—
80C2×Q8—1031no—
81C2×Q8—1031no—
82C2×Q8—2061no—
83C2×Q8—2062no—
84C2×Q8C2×D10311yescharacteristic
85C2×D4—2061no—
86C2×D4C2×D10311yescharacteristic
87C22×C4—1031no—
88C22×C4—2061no—
89C22×C4—2061no—
90Q16—1034no—
91Q16—1034no—
92SD16—1034no—
93SD16C2×D10314yescomplemented
94M16—1034no—
95C2×C8—1031no—
96C2×C8C2×D10311yescharacteristic
97C23—21no—
98C23—1031no—
99Q8—21no—
100Q8—1032no—
101Q8—1032no—
102Q8—2064no—
103Q8—2061no—
104Q8—2061no—
105Q8C22×D10312yes—
106D4—21no—
107D4—2064no—
108D4C22×D10312yes—
109C2×C4—21no—
110C2×C4—1031no—
111C2×C4—1032no—
112C2×C4—1032no—
113C2×C4—2064no—
114C2×C4—2064no—
115C2×C4—2061no—
116C2×C4—2061no—
117C2×C4C22×D10311yescharacteristic
118C8—1032no—
119C8C22×D10312yes—
120C22—22no—
121C22—42no—
122C22—1032no—
123C22—2062no—
124C22D4×D10311yescharacteristic
125C4—22no—
126C4—1032no—
127C4—2062no—
128C4—2062no—
129C4D4×D10311yescharacteristic
130C4C23×D10311yescharacteristic
131C2—42no—
132C2—2062no—
133C2#1569305012yesdirect product factor
134C2C2×D4×D10311yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C24
FrattiniC4C23×D103
FittingC2×SD16×C103C2
socleC22×C103C2×D4
hypercenterC2×SD16D103
hypocenterC103C2×#137
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×Q8×D103C2semidirect
3. #15693050C2direct (N × H)
4. C2×Dic412C2semidirect
5. C2×#13110095C2semidirect
6. C2×#13110093C2semidirect
7. C2×#13110088C2semidirect
8. C2×SD16×C103C2semidirect
15. Q8×D103C22semidirect
20. Dic412C22semidirect
21. #13110095C22semidirect
22. #13110093C22semidirect
23. #13110088C22semidirect
27. SD16×C103C22semidirect
64. C2×C103#137semidirect
67. C103C2×#137semidirect
75. C2×SD16D103semidirect
93. SD16C2×D103semidirect
133. C2#15693050direct (N × H)