Finite Group Databasebeta

← C2×#41×D317 #35204048

Subgroups — C2×#41×D317 #35204048

Order 20288.

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×#19099575C211yesmaximal, characteristic, complemented
2C2×#19099574C213yesmaximal, complemented
3C2×#19099573C213yesmaximal, complemented
4#41×D317C2116yesmaximal, direct product factor
5C2×Q8×D317C211yesmaximal, characteristic, complemented
6C2×D4×D317C213yesmaximal, complemented
7C22×C4×D317C213yesmaximal, complemented
8C2×#41×C317C211yesmaximal, characteristic, complemented
9C23×D317C2213yes—
10#19099575C2218yescomplemented
11#19099574C22124yescomplemented
12#19099573C22124yescomplemented
13C2×Dic634C2213yescomplemented
14Q8×D317C2218yescomplemented
15C2×D1268C2213yescomplemented
16C2×C22⋊D317C2216yescomplemented
17D4×D317C22124yescomplemented
18C22×Dic317C2213yescomplemented
19C2×C4×D317C2213yes—
20C2×C4×D317C2211yescharacteristic
21C2×C4×D317C2213yescomplemented
22C2×C4×D317C2213yescomplemented
23C2×C4×D317C22124yescomplemented
24#41×C317C2218yescomplemented
25C2×Q8×C317C2211yescharacteristic, complemented
26C2×D4×C317C2213yescomplemented
27C22×C4×C317C2213yescomplemented
28C22×D317—212no—
29C22×D317C23112yes—
30C22×D317C2313yes—
31C22×D317C2311yescharacteristic
32Dic634C23112yescomplemented
33D1268C23112yescomplemented
34C22⋊D317C23124yescomplemented
35C2×Dic317C2311yescharacteristic
36C2×Dic317C2313yes—
37C2×Dic317C23112yescomplemented
38C4×D317C2314yes—
39C4×D317C23112yes—
40C4×D317C23112yescomplemented
41C4×D317C23112yescomplemented
42C23×C317C2313yes—
43Q8×C317C2314yescomplemented
44D4×C317C23112yescomplemented
45C2×C4×C317C2313yes—
46C2×C4×C317C2311yescharacteristic
47C2×C4×C317C23112yescomplemented
48C22×C317—26no—
49C22×C317C2416yes—
50C22×C317C2411yescharacteristic
51C2×D317—26no—
52C2×D317—224no—
53C2×D317#4114yesdirect product factor
54C2×D317C2416yes—
55C2×D317C2412yes—
56C4×C317C2412yes—
57C4×C317C2416yes—
58Dic317C2412yes—
59Dic317C2416yes—
60C2×C317—26no—
61C2×C317C2×#4112yescomplemented
62C2×C317C2511yescharacteristic
63D317—26no—
64D317C2×#4114yesdirect product factor
65C317C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—3171nomaximal, Sylow
67C2×#41—31716no—
68C2×#41—3171no—
69C2×#41—3173no—
70C2×#41—3173no—
71C2×#41D31711yescharacteristic, direct product factor
72C22×Q8—3171no—
73C22×D4—3173no—
74C23×C4—3173no—
75C24—3173no—
76#41—3178no—
77#41—31724no—
78#41—31724no—
79#41C2×D31718yesdirect product factor
80C2×Q8—3178no—
81C2×Q8—3173no—
82C2×Q8C2×D31711yescharacteristic, complemented
83C2×D4—3176no—
84C2×D4—31724no—
85C2×D4—3173no—
86C2×D4C2×D31713yescomplemented
87C22×C4—3173no—
88C22×C4—3173no—
89C22×C4—3173no—
90C22×C4—3171no—
91C22×C4—3173no—
92C22×C4—31724no—
93C22×C4C2×D31713yescomplemented
94C23—3171no—
95C23—31712no—
96C23—3173no—
97C23—63412no—
98C23C22×D31713yes—
99Q8—31712no—
100Q8C22×D31714yescomplemented
101D4—31724no—
102D4—31712no—
103D4C22×D317112yescomplemented
104C2×C4—3171no—
105C2×C4—3173no—
106C2×C4—31712no—
107C2×C4—3174no—
108C2×C4—31712no—
109C2×C4—31712no—
110C2×C4—31712no—
111C2×C4C22×D31713yes—
112C2×C4C22×D31711yescharacteristic
113C2×C4C22×D317112yescomplemented
114C22—26no—
115C22—3174no—
116C22—3172no—
117C22—3176no—
118C22—63424no—
119C22—6346no—
120C22C23×D31716yes—
121C22C23×D31711yescharacteristic
122C4—3172no—
123C4—3176no—
124C4C23×D31712yes—
125C4C23×D31716yes—
126C2—26no—
127C2—3174no—
128C2—6346no—
129C2#41×D31712yesdirect product factor
130C2C24×D31711yescharacteristic
subgroupG/H
centerC2×C4C22×D317
commutator, cosocleC2×C317C25
FrattiniC2C24×D317
FittingC2×#41×C317C2
socleC22×C317C24
hypercenterC2×#41D317
hypocenterC317C22×#41
LCSG ▷ C2×C317 ▷ C317
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#19099575C2semidirect
2. C2×#19099574C2semidirect
3. C2×#19099573C2semidirect
4. #41×D317C2direct (N × H)
5. C2×Q8×D317C2semidirect
6. C2×D4×D317C2semidirect
7. C22×C4×D317C2semidirect
8. C2×#41×C317C2semidirect
10. #19099575C22semidirect
11. #19099574C22semidirect
12. #19099573C22semidirect
13. C2×Dic634C22semidirect
14. Q8×D317C22semidirect
15. C2×D1268C22semidirect
16. C2×C22⋊D317C22semidirect
17. D4×D317C22semidirect
18. C22×Dic317C22semidirect
21. C2×C4×D317C22semidirect
22. C2×C4×D317C22semidirect
23. C2×C4×D317C22semidirect
24. #41×C317C22semidirect
25. C2×Q8×C317C22semidirect
26. C2×D4×C317C22semidirect
27. C22×C4×C317C22semidirect
32. Dic634C23semidirect
33. D1268C23semidirect
34. C22⋊D317C23semidirect
37. C2×Dic317C23semidirect
40. C4×D317C23semidirect
41. C4×D317C23semidirect
43. Q8×C317C23semidirect
44. D4×C317C23semidirect
47. C2×C4×C317C23semidirect
53. C2×D317#41direct (N × H)
61. C2×C317C2×#41semidirect
64. D317C2×#41direct (N × H)
65. C317C22×#41semidirect
71. C2×#41D317direct (N × H)
79. #41C2×D317direct (N × H)
82. C2×Q8C2×D317semidirect
86. C2×D4C2×D317semidirect
93. C22×C4C2×D317semidirect
100. Q8C22×D317semidirect
103. D4C22×D317semidirect
113. C2×C4C22×D317semidirect
129. C2#41×D317direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190995752
C2×#190995742
C2×#190995732
#41×D3172
C2×Q8×D3172
C2×D4×D3172
C22×C4×D3172
C2×#41×C3172
C22×#41317