Finite Group Databasebeta

← C2×SD16×D197 #27161850

Subgroups — C2×SD16×D197 #27161850

Order 12608.

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×D197C211yesmaximal, characteristic, complemented
2C2×D4×D197C211yesmaximal, characteristic
3C2×#15691347C211yesmaximal, characteristic, complemented
4C2×#15691346C211yesmaximal, characteristic, complemented
5C2×#15691345C211yesmaximal, characteristic, complemented
6SD16×D197C218yesmaximal, direct product factor
7C2×C8×D197C211yesmaximal, characteristic, complemented
8C2×SD16×C197C211yesmaximal, characteristic, complemented
9C23×D197—21no—
10C2×Dic394—21no—
11C2×Dic394C2211yescharacteristic, complemented
12Q8×D197—22no—
13Q8×D197C2214yescomplemented
14C2×D788C2211yescharacteristic
15C2×C22⋊D197—21no—
16D4×D197—22no—
17D4×D197C2214yes—
18C2×C4×D197—21no—
19C2×C4×D197C2211yescharacteristic
20#15691347C2214yescomplemented
21#15691346C2214yescomplemented
22#15691345C2214yescomplemented
23C2×#13096802C2211yescharacteristic, complemented
24C8×D197C2214yescomplemented
25C2×Q8×C197C2211yescharacteristic, complemented
26C2×D4×C197C2211yescharacteristic
27SD16×C197C2214yescomplemented
28C2×C8×C197C2211yescharacteristic, complemented
29C22×D197—21no—
30C22×D197—24no—
31C22×D197—44no—
32C22×D197D411yescharacteristic
33Dic394—21no—
34Dic394—24no—
35Dic394C2312yescomplemented
36D788—21no—
37D788C2312yes—
38C22⋊D197—24no—
39C2×Dic197—21no—
40C2×Dic197D411yescharacteristic
41C4×D197—24no—
42C4×D197D412yes—
43C4×D197C2312yes—
44#13096802C2312yescomplemented
45C23×C197—21no—
46Q8×C197—21no—
47Q8×C197C2312yescomplemented
48D4×C197—21no—
49D4×C197C2312yes—
50C2×C4×C197—21no—
51C2×C4×C197C2311yescharacteristic
52C8×C197C2312yescomplemented
53C22×C197—22no—
54C22×C197—42no—
55C22×C197C2×D411yescharacteristic
56C2×D197—22no—
57C2×D197—42no—
58C2×D197—48no—
59C2×D197SD1614yesdirect product factor
60C2×D197C2×D412yes—
61C4×C197—22no—
62C4×C197C2×D411yescharacteristic
63C4×C197C2411yescharacteristic
64Dic197—22no—
65Dic197C2×D412yes—
66C2×C197—42no—
67C2×C197C2×SD1612yescomplemented
68C2×C197C22×D411yescharacteristic
69D197—42no—
70D197C2×SD1614yesdirect product factor
71C197C22×SD1611yescharacteristic, complemented, Sylow
72C22×SD16—1971nomaximal, Sylow
73C22×Q8—1971no—
74C22×D4—1971no—
75C2×SD16—1971no—
76C2×SD16—1971no—
77C2×SD16—1978no—
78C2×SD16—1971no—
79C2×SD16D19711yescharacteristic, direct product factor
80C22×C8—1971no—
81C24—3941no—
82C2×Q8—3941no—
83C2×Q8—3942no—
84C2×Q8—1974no—
85C2×Q8—1971no—
86C2×Q8C2×D19711yescharacteristic, complemented
87C2×D4—3942no—
88C2×D4—3941no—
89C2×D4—1974no—
90C2×D4—1971no—
91C2×D4C2×D19711yescharacteristic
92C22×C4—3941no—
93C22×C4—1971no—
94SD16—1974no—
95SD16—1974no—
96SD16—1974no—
97SD16C2×D19714yesdirect product factor
98C2×C8—1971no—
99C2×C8—1974no—
100C2×C8C2×D19711yescharacteristic, complemented
101C23—21no—
102C23—7884no—
103C23—3944no—
104C23—3941no—
105C23—1971no—
106Q8—21no—
107Q8—3944no—
108Q8—3941no—
109Q8—1972no—
110Q8C22×D19712yescomplemented
111D4—21no—
112D4—3944no—
113D4—3941no—
114D4—1972no—
115D4C22×D19712yes—
116C2×C4—21no—
117C2×C4—3944no—
118C2×C4—3941no—
119C2×C4—1971no—
120C2×C4—1972no—
121C2×C4—1972no—
122C2×C4C22×D19711yescharacteristic
123C8—1972no—
124C8C22×D19712yescomplemented
125C22—22no—
126C22—42no—
127C22—7888no—
128C22—7882no—
129C22—3942no—
130C22—1974no—
131C22—1972no—
132C22D4×D19711yescharacteristic
133C4—22no—
134C4—3942no—
135C4—1972no—
136C4D4×D19711yescharacteristic
137C4C23×D19711yescharacteristic
138C2—42no—
139C2—7882no—
140C2—1974no—
141C2SD16×D19712yesdirect product factor
142C2C2×D4×D19711yescharacteristic
subgroupG/H
centerC22D4×D197
commutator, cosocleC4×C197C24
FrattiniC4C23×D197
FittingC2×SD16×C197C2
socleC22×C197C2×D4
prime radicalC2×D4×D197C2
hypercenterC2×SD16D197
hypocenterC197C22×SD16
LCSG ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D197C2semidirect
3. C2×#15691347C2semidirect
4. C2×#15691346C2semidirect
5. C2×#15691345C2semidirect
6. SD16×D197C2direct (N × H)
7. C2×C8×D197C2semidirect
8. C2×SD16×C197C2semidirect
11. C2×Dic394C22semidirect
13. Q8×D197C22semidirect
20. #15691347C22semidirect
21. #15691346C22semidirect
22. #15691345C22semidirect
23. C2×#13096802C22semidirect
24. C8×D197C22semidirect
25. C2×Q8×C197C22semidirect
27. SD16×C197C22semidirect
28. C2×C8×C197C22semidirect
35. Dic394C23semidirect
44. #13096802C23semidirect
47. Q8×C197C23semidirect
52. C8×C197C23semidirect
59. C2×D197SD16direct (N × H)
67. C2×C197C2×SD16semidirect
70. D197C2×SD16direct (N × H)
71. C197C22×SD16semidirect
79. C2×SD16D197direct (N × H)
86. C2×Q8C2×D197semidirect
97. SD16C2×D197direct (N × H)
100. C2×C8C2×D197semidirect
110. Q8C22×D197semidirect
124. C8C22×D197semidirect
141. C2SD16×D197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D1972
C2×D4×D1972
C2×#156913472
C2×#156913462
C2×#156913452
SD16×D1972
C2×C8×D1972
C2×SD16×C1972
C22×SD16197