Finite Group Databasebeta

← C2×#22582903 #31824248

Subgroups — C2×#22582903 #31824248

Order 17984.

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

normal subgroups only

This group has 298 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×#17985137C211yesmaximal, characteristic, complemented
2C2×D4×D281C211yesmaximal, characteristic, complemented
3#22582903C218yesmaximal, direct product factor
4C2×#17985127C211yesmaximal, characteristic, complemented
5C2×#17985126C211yesmaximal, characteristic, complemented
6C2×#17985123C211yesmaximal, characteristic, complemented
7C2×#17985121C211yesmaximal, characteristic, complemented
8C2×D8×C281C211yesmaximal, characteristic, complemented
9C23×D281—21no—
10#17985137—22no—
11#17985137C2214yescomplemented
12C2×Dic562C2211yescharacteristic, complemented
13C2×D1124C2211yescharacteristic
14C2×C22⋊D281—21no—
15C2×C22⋊D281—21no—
16D4×D281—22no—
17D4×D281C2214yescomplemented
18C22×Dic281—21no—
19C2×C4×D281C2211yescharacteristic
20#17985127C2214yescomplemented
21#17985126C2214yescomplemented
22#17985123C2214yescomplemented
23#17985121C2214yescomplemented
24C2×#14555886C2211yescharacteristic, complemented
25C2×D4×C281C2211yescharacteristic
26C2×D4×C281C2211yescharacteristic, complemented
27D8×C281C2214yescomplemented
28C2×C8×C281C2211yescharacteristic, complemented
29C22×D281—21no—
30C22×D281—24no—
31C22×D281—44no—
32C22×D281D411yescharacteristic
33Dic562—21no—
34Dic562C2312yescomplemented
35D1124—21no—
36D1124C2312yes—
37C22⋊D281—24no—
38C22⋊D281—24no—
39C2×Dic281—21no—
40C2×Dic281—24no—
41C2×Dic281D411yescharacteristic
42C4×D281D412yes—
43C4×D281C2312yes—
44#14555886C2312yescomplemented
45C23×C281—21no—
46C23×C281—21no—
47D4×C281—21no—
48D4×C281—21no—
49D4×C281C2312yes—
50D4×C281C2312yescomplemented
51C2×C4×C281C2311yescharacteristic
52C8×C281C2312yescomplemented
53C22×C281—22no—
54C22×C281—22no—
55C22×C281—42no—
56C22×C281—42no—
57C22×C281C2×D411yescharacteristic
58C2×D281—22no—
59C2×D281—22no—
60C2×D281—48no—
61C2×D281—42no—
62C2×D281C2×D412yes—
63C4×C281C2×D411yescharacteristic
64C4×C281C2411yescharacteristic
65Dic281—22no—
66Dic281C2×D412yes—
67C2×C281—42no—
68C2×C281—42no—
69C2×C281AGL(1,ℤ/8)12yescomplemented
70C2×C281C22×D411yescharacteristic
71D281—22no—
72D281—42no—
73C281C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
74C2×AGL(1,ℤ/8)—2811nomaximal, Sylow
75C2×#41—2811no—
76C22×D4—2811no—
77AGL(1,ℤ/8)—2818no—
78C2×SD16—2811no—
79C2×SD16—2811no—
80C2×D8—2811no—
81C2×D8D28111yescharacteristic, complemented
82C2×M16—2811no—
83C24—5621no—
84#41—2814no—
85#41—5622no—
86C2×Q8—2811no—
87C2×D4—2814no—
88C2×D4—2811no—
89C2×D4—5622no—
90C2×D4—5621no—
91C2×D4—5621no—
92C2×D4C2×D28111yescharacteristic
93C2×D4C2×D28111yescharacteristic, complemented
94C22×C4—2811no—
95C22×C4—5621no—
96SD16—2814no—
97SD16—2814no—
98D8—2814no—
99D8C2×D28114yescomplemented
100M16—2814no—
101C2×C8—2811no—
102C2×C8C2×D28111yescharacteristic, complemented
103C23—21no—
104C23—21no—
105C23—2811no—
106C23—5624no—
107C23—5621no—
108C23—11244no—
109Q8—2812no—
110Q8—5621no—
111D4—21no—
112D4—21no—
113D4—2812no—
114D4—5624no—
115D4—5624no—
116D4—5621no—
117D4C22×D28112yes—
118D4C22×D28112yescomplemented
119C2×C4—2811no—
120C2×C4—2812no—
121C2×C4—2812no—
122C2×C4—5624no—
123C2×C4—5621no—
124C2×C4C22×D28111yescharacteristic
125C8—2812no—
126C8C22×D28112yescomplemented
127C22—22no—
128C22—22no—
129C22—42no—
130C22—42no—
131C22—2812no—
132C22—5622no—
133C22—5622no—
134C22—11248no—
135C22—11242no—
136C22D4×D28111yescharacteristic
137C4—2812no—
138C4—5622no—
139C4D4×D28111yescharacteristic
140C4C23×D28111yescharacteristic
141C2—42no—
142C2—42no—
143C2—5622no—
144C2—11242no—
145C2#2258290312yesdirect product factor
146C2C2×D4×D28111yescharacteristic
subgroupG/H
centerC22D4×D281
commutator, cosocleC4×C281C24
FrattiniC4C23×D281
FittingC2×D8×C281C2
socleC22×C281C2×D4
hypercenterC2×D8D281
hypocenterC281C2×AGL(1,ℤ/8)
LCSG ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#17985137C2semidirect
2. C2×D4×D281C2semidirect
3. #22582903C2direct (N × H)
4. C2×#17985127C2semidirect
5. C2×#17985126C2semidirect
6. C2×#17985123C2semidirect
7. C2×#17985121C2semidirect
8. C2×D8×C281C2semidirect
11. #17985137C22semidirect
12. C2×Dic562C22semidirect
17. D4×D281C22semidirect
20. #17985127C22semidirect
21. #17985126C22semidirect
22. #17985123C22semidirect
23. #17985121C22semidirect
24. C2×#14555886C22semidirect
26. C2×D4×C281C22semidirect
27. D8×C281C22semidirect
28. C2×C8×C281C22semidirect
34. Dic562C23semidirect
44. #14555886C23semidirect
50. D4×C281C23semidirect
52. C8×C281C23semidirect
69. C2×C281AGL(1,ℤ/8)semidirect
73. C281C2×AGL(1,ℤ/8)semidirect
81. C2×D8D281semidirect
93. C2×D4C2×D281semidirect
99. D8C2×D281semidirect
102. C2×C8C2×D281semidirect
118. D4C22×D281semidirect
126. C8C22×D281semidirect
145. C2#22582903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179851372
C2×D4×D2812
#225829032
C2×#179851272
C2×#179851262
C2×#179851232
C2×#179851212
C2×D8×C2812
C2×AGL(1,ℤ/8)281