Finite Group Databasebeta

← C2×SD16×D193 #27136030

Subgroups — C2×SD16×D193 #27136030

Order 12352.

298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×Q8×D193C211yesmaximal, characteristic, complemented
2C2×D4×D193C211yesmaximal, characteristic
3C2×#15690544C211yesmaximal, characteristic, complemented
4C2×#15690543C211yesmaximal, characteristic, complemented
5C2×#15690542C211yesmaximal, characteristic, complemented
6SD16×D193C218yesmaximal, direct product factor
7C2×C8×D193C211yesmaximal, characteristic, complemented
8C2×SD16×C193C211yesmaximal, characteristic, complemented
9C23×D193—21no—
10C2×Dic386—21no—
11C2×Dic386C2211yescharacteristic, complemented
12Q8×D193—22no—
13Q8×D193C2214yescomplemented
14C2×D772C2211yescharacteristic
15C2×C22⋊D193—21no—
16D4×D193—22no—
17D4×D193C2214yes—
18C2×C4×D193—21no—
19C2×C4×D193C2211yescharacteristic
20#15690544C2214yescomplemented
21#15690543C2214yescomplemented
22#15690542C2214yescomplemented
23C2×#13095393C2211yescharacteristic, complemented
24C8×D193C2214yescomplemented
25C2×Q8×C193C2211yescharacteristic, complemented
26C2×D4×C193C2211yescharacteristic
27SD16×C193C2214yescomplemented
28C2×C8×C193C2211yescharacteristic, complemented
29C22×D193—21no—
30C22×D193—24no—
31C22×D193—44no—
32C22×D193D411yescharacteristic
33Dic386—21no—
34Dic386—24no—
35Dic386C2312yescomplemented
36D772—21no—
37D772C2312yes—
38C22⋊D193—24no—
39C2×Dic193—21no—
40C2×Dic193D411yescharacteristic
41C4×D193—24no—
42C4×D193D412yes—
43C4×D193C2312yes—
44#13095393C2312yescomplemented
45C23×C193—21no—
46Q8×C193—21no—
47Q8×C193C2312yescomplemented
48D4×C193—21no—
49D4×C193C2312yes—
50C2×C4×C193—21no—
51C2×C4×C193C2311yescharacteristic
52C8×C193C2312yescomplemented
53C22×C193—22no—
54C22×C193—42no—
55C22×C193C2×D411yescharacteristic
56C2×D193—22no—
57C2×D193—42no—
58C2×D193—48no—
59C2×D193SD1614yesdirect product factor
60C2×D193C2×D412yes—
61C4×C193—22no—
62C4×C193C2×D411yescharacteristic
63C4×C193C2411yescharacteristic
64Dic193—22no—
65Dic193C2×D412yes—
66C2×C193—42no—
67C2×C193C2×SD1612yescomplemented
68C2×C193C22×D411yescharacteristic
69D193—42no—
70D193C2×SD1614yesdirect product factor
71C193C22×SD1611yescharacteristic, complemented, Sylow
72C22×SD16—1931nomaximal, Sylow
73C22×Q8—1931no—
74C22×D4—1931no—
75C2×SD16—1931no—
76C2×SD16—1931no—
77C2×SD16—1938no—
78C2×SD16—1931no—
79C2×SD16D19311yescharacteristic, direct product factor
80C22×C8—1931no—
81C24—3861no—
82C2×Q8—3861no—
83C2×Q8—3862no—
84C2×Q8—1934no—
85C2×Q8—1931no—
86C2×Q8C2×D19311yescharacteristic, complemented
87C2×D4—3862no—
88C2×D4—3861no—
89C2×D4—1934no—
90C2×D4—1931no—
91C2×D4C2×D19311yescharacteristic
92C22×C4—3861no—
93C22×C4—1931no—
94SD16—1934no—
95SD16—1934no—
96SD16—1934no—
97SD16C2×D19314yesdirect product factor
98C2×C8—1931no—
99C2×C8—1934no—
100C2×C8C2×D19311yescharacteristic, complemented
101C23—21no—
102C23—7724no—
103C23—3864no—
104C23—3861no—
105C23—1931no—
106Q8—21no—
107Q8—3864no—
108Q8—3861no—
109Q8—1932no—
110Q8C22×D19312yescomplemented
111D4—21no—
112D4—3864no—
113D4—3861no—
114D4—1932no—
115D4C22×D19312yes—
116C2×C4—21no—
117C2×C4—3864no—
118C2×C4—3861no—
119C2×C4—1931no—
120C2×C4—1932no—
121C2×C4—1932no—
122C2×C4C22×D19311yescharacteristic
123C8—1932no—
124C8C22×D19312yescomplemented
125C22—22no—
126C22—42no—
127C22—7728no—
128C22—7722no—
129C22—3862no—
130C22—1934no—
131C22—1932no—
132C22D4×D19311yescharacteristic
133C4—22no—
134C4—3862no—
135C4—1932no—
136C4D4×D19311yescharacteristic
137C4C23×D19311yescharacteristic
138C2—42no—
139C2—7722no—
140C2—1934no—
141C2SD16×D19312yesdirect product factor
142C2C2×D4×D19311yescharacteristic
subgroupG/H
centerC22D4×D193
commutator, cosocleC4×C193C24
FrattiniC4C23×D193
FittingC2×SD16×C193C2
socleC22×C193C2×D4
prime radicalC2×D4×D193C2
hypercenterC2×SD16D193
hypocenterC193C22×SD16
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D193C2semidirect
3. C2×#15690544C2semidirect
4. C2×#15690543C2semidirect
5. C2×#15690542C2semidirect
6. SD16×D193C2direct (N × H)
7. C2×C8×D193C2semidirect
8. C2×SD16×C193C2semidirect
11. C2×Dic386C22semidirect
13. Q8×D193C22semidirect
20. #15690544C22semidirect
21. #15690543C22semidirect
22. #15690542C22semidirect
23. C2×#13095393C22semidirect
24. C8×D193C22semidirect
25. C2×Q8×C193C22semidirect
27. SD16×C193C22semidirect
28. C2×C8×C193C22semidirect
35. Dic386C23semidirect
44. #13095393C23semidirect
47. Q8×C193C23semidirect
52. C8×C193C23semidirect
59. C2×D193SD16direct (N × H)
67. C2×C193C2×SD16semidirect
70. D193C2×SD16direct (N × H)
71. C193C22×SD16semidirect
79. C2×SD16D193direct (N × H)
86. C2×Q8C2×D193semidirect
97. SD16C2×D193direct (N × H)
100. C2×C8C2×D193semidirect
110. Q8C22×D193semidirect
124. C8C22×D193semidirect
141. C2SD16×D193direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×Q8×D1932
C2×D4×D1932
C2×#156905442
C2×#156905432
C2×#156905422
SD16×D1932
C2×C8×D1932
C2×SD16×C1932
C22×SD16193