Finite Group Databasebeta

← C2×D16×D97 #27154840

Subgroups — C2×D16×D97 #27154840

Order 12416.

440 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 125 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×D8×D97C212yesmaximal, complemented
2C2×D1552C211yesmaximal, characteristic, complemented
3C2×#15690751C212yesmaximal, complemented
4D16×D97C218yesmaximal, direct product factor
5C2×C16×D97C211yesmaximal, characteristic, complemented
6C2×D16×C97C211yesmaximal, characteristic, complemented
7C2×D4×D97—22no—
8C2×D776C2212yescomplemented
9C2×#13095496—22no—
10D8×D97—24no—
11D8×D97C2218yescomplemented
12C2×C8×D97C2211yescharacteristic
13D1552C2214yescomplemented
14#15690751C2218yescomplemented
15C2×#13095486C2211yescharacteristic, complemented
16C16×D97C2214yescomplemented
17C2×D8×C97C2212yescomplemented
18D16×C97C2214yescomplemented
19C2×C16×C97C2211yescharacteristic, complemented
20C23×D97—42no—
21C2×D388—22no—
22C2×C22⋊D97—42no—
23D4×D97—28no—
24D4×D97—44no—
25C2×C4×D97D411yescharacteristic
26D776—22no—
27D776C2314yescomplemented
28#13095496—28no—
29C2×#11715895D411yescharacteristic
30C8×D97D412yes—
31C8×D97C2312yes—
32#13095486C2312yescomplemented
33C2×D4×C97—22no—
34D8×C97—22no—
35D8×C97C2314yescomplemented
36C2×C8×C97C2311yescharacteristic
37C16×C97C2312yescomplemented
38C23×C97—42no—
39C22×D97—42no—
40C22×D97—48no—
41C22×D97—88no—
42C22×D97D811yescharacteristic
43D4×C97—24no—
44D4×C97—42no—
45C2×C4×C97C2×D411yescharacteristic
46C22⋊D97—48no—
47C2×Dic97D811yescharacteristic
48D388—24no—
49D388—42no—
50C4×D97D812yes—
51C4×D97C2×D412yes—
52C8×C97C2×D411yescharacteristic
53C8×C97C2411yescharacteristic
54#11715895C2×D412yes—
55C22×C97—44no—
56C22×C97—84no—
57C22×C97C2×D811yescharacteristic
58C2×D97—44no—
59C2×D97—84no—
60C2×D97—816no—
61C2×D97D1614yesdirect product factor
62C2×D97C2×D812yes—
63C4×C97C2×D811yescharacteristic
64C4×C97C22×D411yescharacteristic
65Dic97C2×D812yes—
66C2×C97—84no—
67C2×C97C2×D1612yescomplemented
68C2×C97C22×D811yescharacteristic
69D97—84no—
70D97C2×D1614yesdirect product factor
71C22×D16—971nomaximal, Sylow
72C97C22×D1611yescharacteristic, complemented, Sylow
73C22×D8—972no—
74C2×D16—972no—
75C2×D16—978no—
76C2×D16—971no—
77C2×D16D9711yescharacteristic, direct product factor
78C22×C16—971no—
79C22×D4—1942no—
80C2×D8—978no—
81C2×D8—972no—
82C2×D8—1944no—
83C2×D8—1942no—
84C2×D8C2×D9712yescomplemented
85C22×C8—971no—
86D16—978no—
87D16—974no—
88D16C2×D9714yesdirect product factor
89C2×C16—971no—
90C2×C16—974no—
91C2×C16C2×D9711yescharacteristic, complemented
92C24—3882no—
93C2×D4—22no—
94C2×D4—3884no—
95C2×D4—3882no—
96C2×D4—1948no—
97C2×D4—1942no—
98C22×C4—971no—
99D8—22no—
100D8—974no—
101D8—1948no—
102D8—1942no—
103D8C22×D9714yescomplemented
104C2×C8—971no—
105C2×C8—972no—
106C2×C8—972no—
107C2×C8C22×D9711yescharacteristic
108C16—972no—
109C16C22×D9712yescomplemented
110C23—42no—
111C23—7768no—
112C23—971no—
113C23—3888no—
114C23—3882no—
115D4—24no—
116D4—42no—
117D4—3888no—
118D4—3882no—
119D4—1944no—
120C2×C4—971no—
121C2×C4—972no—
122C2×C4—972no—
123C2×C4D4×D9711yescharacteristic
124C8—972no—
125C8D4×D9711yescharacteristic
126C8C23×D9711yescharacteristic
127C22—44no—
128C22—84no—
129C22—77616no—
130C22—7764no—
131C22—974no—
132C22—972no—
133C22—3884no—
134C22D8×D9711yescharacteristic
135C4—972no—
136C4D8×D9711yescharacteristic
137C4C2×D4×D9711yescharacteristic
138C2—84no—
139C2—7764no—
140C2—974no—
141C2D16×D9712yesdirect product factor
142C2C2×D8×D9711yescharacteristic
subgroupG/H
centerC22D8×D97
commutator, cosocleC8×C97C24
FrattiniC8C23×D97
FittingC2×D16×C97C2
socleC22×C97C2×D8
hypercenterC2×D16D97
hypocenterC97C22×D16
LCSG ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×D97C2semidirect
2. C2×D1552C2semidirect
3. C2×#15690751C2semidirect
4. D16×D97C2direct (N × H)
5. C2×C16×D97C2semidirect
6. C2×D16×C97C2semidirect
8. C2×D776C22semidirect
11. D8×D97C22semidirect
13. D1552C22semidirect
14. #15690751C22semidirect
15. C2×#13095486C22semidirect
16. C16×D97C22semidirect
17. C2×D8×C97C22semidirect
18. D16×C97C22semidirect
19. C2×C16×C97C22semidirect
27. D776C23semidirect
32. #13095486C23semidirect
35. D8×C97C23semidirect
37. C16×C97C23semidirect
61. C2×D97D16direct (N × H)
67. C2×C97C2×D16semidirect
70. D97C2×D16direct (N × H)
72. C97C22×D16semidirect
77. C2×D16D97direct (N × H)
84. C2×D8C2×D97semidirect
88. D16C2×D97direct (N × H)
91. C2×C16C2×D97semidirect
103. D8C22×D97semidirect
109. C16C22×D97semidirect
141. C2D16×D97direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×D972
C2×D15522
C2×#156907512
D16×D972
C2×C16×D972
C2×D16×C972
C22×D1697