Finite Group Databasebeta

← C2×#41×D281 #31824288

Subgroups — C2×#41×D281 #31824288

Order 17984.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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×#17985139C211yesmaximal, characteristic, complemented
2C2×#17985138C213yesmaximal, complemented
3C2×#17985137C213yesmaximal, complemented
4#41×D281C2116yesmaximal, direct product factor
5C2×Q8×D281C211yesmaximal, characteristic, complemented
6C2×D4×D281C213yesmaximal, complemented
7C22×C4×D281C213yesmaximal, complemented
8C2×#41×C281C211yesmaximal, characteristic, complemented
9C23×D281C2213yes—
10#17985139C2218yescomplemented
11#17985138C22124yescomplemented
12#17985137C22124yescomplemented
13C2×Dic562C2213yescomplemented
14Q8×D281C2218yescomplemented
15C2×D1124C2213yescomplemented
16C2×C22⋊D281C2216yescomplemented
17D4×D281C22124yescomplemented
18C22×Dic281C2213yescomplemented
19C2×C4×D281C2211yescharacteristic
20C2×C4×D281C2213yes—
21C2×C4×D281C2213yescomplemented
22C2×C4×D281C2213yescomplemented
23C2×C4×D281C22124yescomplemented
24#41×C281C2218yescomplemented
25C2×Q8×C281C2211yescharacteristic, complemented
26C2×D4×C281C2213yescomplemented
27C22×C4×C281C2213yescomplemented
28C22×D281—212no—
29C22×D281C23112yes—
30C22×D281C2313yes—
31C22×D281C2311yescharacteristic
32Dic562C23112yescomplemented
33D1124C23112yescomplemented
34C22⋊D281C23124yescomplemented
35C2×Dic281C2311yescharacteristic
36C2×Dic281C2313yes—
37C2×Dic281C23112yescomplemented
38C4×D281C2314yes—
39C4×D281C23112yes—
40C4×D281C23112yescomplemented
41C4×D281C23112yescomplemented
42C23×C281C2313yes—
43Q8×C281C2314yescomplemented
44D4×C281C23112yescomplemented
45C2×C4×C281C2313yes—
46C2×C4×C281C2311yescharacteristic
47C2×C4×C281C23112yescomplemented
48C22×C281—26no—
49C22×C281C2416yes—
50C22×C281C2411yescharacteristic
51C2×D281—26no—
52C2×D281—224no—
53C2×D281#4114yesdirect product factor
54C2×D281C2416yes—
55C2×D281C2412yes—
56C4×C281C2412yes—
57C4×C281C2416yes—
58Dic281C2412yes—
59Dic281C2416yes—
60C2×C281—26no—
61C2×C281C2×#4112yescomplemented
62C2×C281C2511yescharacteristic
63D281—26no—
64D281C2×#4114yesdirect product factor
65C281C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—2811nomaximal, Sylow
67C2×#41—28116no—
68C2×#41—2811no—
69C2×#41—2813no—
70C2×#41—2813no—
71C2×#41D28111yescharacteristic, direct product factor
72C22×Q8—2811no—
73C22×D4—2813no—
74C23×C4—2813no—
75C24—2813no—
76#41—2818no—
77#41—28124no—
78#41—28124no—
79#41C2×D28118yesdirect product factor
80C2×Q8—2818no—
81C2×Q8—2813no—
82C2×Q8C2×D28111yescharacteristic, complemented
83C2×D4—2816no—
84C2×D4—28124no—
85C2×D4—2813no—
86C2×D4C2×D28113yescomplemented
87C22×C4—2813no—
88C22×C4—2813no—
89C22×C4—2813no—
90C22×C4—2811no—
91C22×C4—2813no—
92C22×C4—28124no—
93C22×C4C2×D28113yescomplemented
94C23—2811no—
95C23—28112no—
96C23—2813no—
97C23—56212no—
98C23C22×D28113yes—
99Q8—28112no—
100Q8C22×D28114yescomplemented
101D4—28124no—
102D4—28112no—
103D4C22×D281112yescomplemented
104C2×C4—2811no—
105C2×C4—2813no—
106C2×C4—28112no—
107C2×C4—2814no—
108C2×C4—28112no—
109C2×C4—28112no—
110C2×C4—28112no—
111C2×C4C22×D28113yes—
112C2×C4C22×D28111yescharacteristic
113C2×C4C22×D281112yescomplemented
114C22—26no—
115C22—2814no—
116C22—2812no—
117C22—2816no—
118C22—56224no—
119C22—5626no—
120C22C23×D28116yes—
121C22C23×D28111yescharacteristic
122C4—2812no—
123C4—2816no—
124C4C23×D28112yes—
125C4C23×D28116yes—
126C2—26no—
127C2—2814no—
128C2—5626no—
129C2#41×D28112yesdirect product factor
130C2C24×D28111yescharacteristic
subgroupG/H
centerC2×C4C22×D281
commutator, cosocleC2×C281C25
FrattiniC2C24×D281
FittingC2×#41×C281C2
socleC22×C281C24
hypercenterC2×#41D281
hypocenterC281C22×#41
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#17985139C2semidirect
2. C2×#17985138C2semidirect
3. C2×#17985137C2semidirect
4. #41×D281C2direct (N × H)
5. C2×Q8×D281C2semidirect
6. C2×D4×D281C2semidirect
7. C22×C4×D281C2semidirect
8. C2×#41×C281C2semidirect
10. #17985139C22semidirect
11. #17985138C22semidirect
12. #17985137C22semidirect
13. C2×Dic562C22semidirect
14. Q8×D281C22semidirect
15. C2×D1124C22semidirect
16. C2×C22⋊D281C22semidirect
17. D4×D281C22semidirect
18. C22×Dic281C22semidirect
21. C2×C4×D281C22semidirect
22. C2×C4×D281C22semidirect
23. C2×C4×D281C22semidirect
24. #41×C281C22semidirect
25. C2×Q8×C281C22semidirect
26. C2×D4×C281C22semidirect
27. C22×C4×C281C22semidirect
32. Dic562C23semidirect
33. D1124C23semidirect
34. C22⋊D281C23semidirect
37. C2×Dic281C23semidirect
40. C4×D281C23semidirect
41. C4×D281C23semidirect
43. Q8×C281C23semidirect
44. D4×C281C23semidirect
47. C2×C4×C281C23semidirect
53. C2×D281#41direct (N × H)
61. C2×C281C2×#41semidirect
64. D281C2×#41direct (N × H)
65. C281C22×#41semidirect
71. C2×#41D281direct (N × H)
79. #41C2×D281direct (N × H)
82. C2×Q8C2×D281semidirect
86. C2×D4C2×D281semidirect
93. C22×C4C2×D281semidirect
100. Q8C22×D281semidirect
103. D4C22×D281semidirect
113. C2×C4C22×D281semidirect
129. C2#41×D281direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179851392
C2×#179851382
C2×#179851372
#41×D2812
C2×Q8×D2812
C2×D4×D2812
C22×C4×D2812
C2×#41×C2812
C22×#41281