Finite Group Databasebeta

← C2×#22582847 #31823948

Subgroups — C2×#22582847 #31823948

Order 17984.

662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C24×D281C211yesmaximal, characteristic, complemented
2C22×C22⋊D281C212yesmaximal, complemented
3#22582847C218yesmaximal, direct product factor
4C2×C22⋊Dic281C211yesmaximal, characteristic, complemented
5C2×#17985115C212yesmaximal, complemented
6C22×D4×C281C211yesmaximal, characteristic, complemented
7C23×D281—28no—
8C23×D281—24no—
9C23×D281C2212yes—
10C23×D281C2214yescomplemented
11C2×C22⋊D281—28no—
12C2×C22⋊D281C2218yescomplemented
13C22×Dic281C2212yescomplemented
14C22⋊Dic281C2214yescomplemented
15#17985115C2218yescomplemented
16C24×C281C2211yescharacteristic
17C24×C281C2211yescharacteristic, complemented
18C2×D4×C281—24no—
19C2×D4×C281C2214yescomplemented
20C22×C4×C281C2211yescharacteristic, complemented
21C22×D281—232no—
22C22×D281—24no—
23C22×D281—24no—
24C22×D281—28no—
25C22×D281—216no—
26C22×D281D418yescomplemented
27C22×D281C2314yes—
28C22⋊D281—216no—
29C2×Dic281—24no—
30C2×Dic281C2314yescomplemented
31C23×C281—24no—
32C23×C281—22no—
33C23×C281—24no—
34C23×C281D414yescomplemented
35C23×C281C2312yes—
36C23×C281C2311yescharacteristic
37C23×C281C2312yescomplemented
38D4×C281—28no—
39C2×C4×C281—22no—
40C2×C4×C281C2312yescomplemented
41C22×C281—28no—
42C22×C281—24no—
43C22×C281—22no—
44C22×C281—24no—
45C22×C281—44no—
46C22×C281C2×D414yes—
47C22×C281C2×D412yes—
48C22×C281C2×D414yescomplemented
49C22×C281C2411yescharacteristic
50C2×D281—232no—
51C2×D281—216no—
52C2×D281—24no—
53C2×D281—24no—
54C2×D281C2×D418yescomplemented
55C4×C281—22no—
56Dic281—24no—
57C2×C281—24no—
58C2×C281—42no—
59C2×C281#12014yescomplemented
60C2×C281C22×D412yes—
61C2×C281C22×D411yescharacteristic
62D281—28no—
63C281C2×#12011yescharacteristic, complemented, Sylow
64C2×#120—2811nomaximal, Sylow
65C25—2811no—
66C22×D4—2812no—
67C22×D4D28111yescharacteristic, complemented
68#120—2818no—
69C2×C22⋊C4—2811no—
70C2×C22⋊C4—2812no—
71C24—2812no—
72C24—2814no—
73C24—5628no—
74C24—5624no—
75C24C2×D28111yescharacteristic
76C24C2×D28111yescharacteristic, complemented
77C2×D4—24no—
78C2×D4—2818no—
79C2×D4—5628no—
80C2×D4C2×D28114yescomplemented
81C22×C4—2812no—
82C22×C4C2×D28111yescharacteristic, complemented
83C22⋊C4—2814no—
84C22⋊C4—2818no—
85C23—24no—
86C23—24no—
87C23—22no—
88C23—2818no—
89C23—2814no—
90C23—56216no—
91C23—56232no—
92C23—5624no—
93C23—5624no—
94C23—5628no—
95C23C22⋊D28114yescomplemented
96C23C22×D28112yes—
97C23C22×D28111yescharacteristic
98C23C22×D28112yescomplemented
99D4—28no—
100D4—56216no—
101C2×C4—22no—
102C2×C4—2814no—
103C2×C4—5624no—
104C2×C4C22×D28112yescomplemented
105C22—28no—
106C22—24no—
107C22—24no—
108C22—22no—
109C22—44no—
110C22—2818no—
111C22—56232no—
112C22—56216no—
113C22—5624no—
114C22—5624no—
115C22D4×D28114yes—
116C22C2×C22⋊D28112yes—
117C22C2×C22⋊D28114yescomplemented
118C22C23×D28111yescharacteristic
119C4—22no—
120C4—5624no—
121C2—24no—
122C2—42no—
123C2—5628no—
124C2#2258284714yesdirect product factor
125C2C2×D4×D28112yes—
126C2C22×C22⋊D28111yescharacteristic
subgroupG/H
centerC23C22×D281
commutator, cosocleC22×C281C24
FrattiniC22C23×D281
FittingC22×D4×C281C2
socleC23×C281C23
hypercenterC22×D4D281
hypocenterC281C2×#120
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D281C2semidirect
2. C22×C22⋊D281C2semidirect
3. #22582847C2direct (N × H)
4. C2×C22⋊Dic281C2semidirect
5. C2×#17985115C2semidirect
6. C22×D4×C281C2semidirect
10. C23×D281C22semidirect
12. C2×C22⋊D281C22semidirect
13. C22×Dic281C22semidirect
14. C22⋊Dic281C22semidirect
15. #17985115C22semidirect
17. C24×C281C22semidirect
19. C2×D4×C281C22semidirect
20. C22×C4×C281C22semidirect
26. C22×D281D4semidirect
30. C2×Dic281C23semidirect
34. C23×C281D4semidirect
37. C23×C281C23semidirect
40. C2×C4×C281C23semidirect
48. C22×C281C2×D4semidirect
54. C2×D281C2×D4semidirect
59. C2×C281#120semidirect
63. C281C2×#120semidirect
67. C22×D4D281semidirect
76. C24C2×D281semidirect
80. C2×D4C2×D281semidirect
82. C22×C4C2×D281semidirect
95. C23C22⋊D281semidirect
98. C23C22×D281semidirect
104. C2×C4C22×D281semidirect
117. C22C2×C22⋊D281semidirect
124. C2#22582847direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D2812
C22×C22⋊D2812
#225828472
C2×C22⋊Dic2812
C2×#179851152
C22×D4×C2812
C2×#120281