Finite Group Databasebeta

← C2×#41×D389 #38734924

Subgroups — C2×#41×D389 #38734924

Order 24896.

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×#20261967C211yesmaximal, characteristic, complemented
2C2×#20261966C213yesmaximal, complemented
3C2×#20261965C213yesmaximal, complemented
4#41×D389C2116yesmaximal, direct product factor
5C2×Q8×D389C211yesmaximal, characteristic, complemented
6C2×D4×D389C213yesmaximal, complemented
7C22×C4×D389C213yesmaximal, complemented
8C2×#41×C389C211yesmaximal, characteristic, complemented
9C23×D389C2213yes—
10#20261967C2218yescomplemented
11#20261966C22124yescomplemented
12#20261965C22124yescomplemented
13C2×Dic778C2213yescomplemented
14Q8×D389C2218yescomplemented
15C2×D1556C2213yescomplemented
16C2×C22⋊D389C2216yescomplemented
17D4×D389C22124yescomplemented
18C22×Dic389C2213yescomplemented
19C2×C4×D389C2211yescharacteristic
20C2×C4×D389C2213yes—
21C2×C4×D389C2213yescomplemented
22C2×C4×D389C2213yescomplemented
23C2×C4×D389C22124yescomplemented
24#41×C389C2218yescomplemented
25C2×Q8×C389C2211yescharacteristic, complemented
26C2×D4×C389C2213yescomplemented
27C22×C4×C389C2213yescomplemented
28C22×D389—212no—
29C22×D389C23112yes—
30C22×D389C2313yes—
31C22×D389C2311yescharacteristic
32Dic778C23112yescomplemented
33D1556C23112yescomplemented
34C22⋊D389C23124yescomplemented
35C2×Dic389C2311yescharacteristic
36C2×Dic389C2313yes—
37C2×Dic389C23112yescomplemented
38C4×D389C2314yes—
39C4×D389C23112yes—
40C4×D389C23112yescomplemented
41C4×D389C23112yescomplemented
42C23×C389C2313yes—
43Q8×C389C2314yescomplemented
44D4×C389C23112yescomplemented
45C2×C4×C389C2313yes—
46C2×C4×C389C2311yescharacteristic
47C2×C4×C389C23112yescomplemented
48C22×C389—26no—
49C22×C389C2416yes—
50C22×C389C2411yescharacteristic
51C2×D389—26no—
52C2×D389—224no—
53C2×D389#4114yesdirect product factor
54C2×D389C2416yes—
55C2×D389C2412yes—
56C4×C389C2416yes—
57C4×C389C2412yes—
58Dic389C2416yes—
59Dic389C2412yes—
60C2×C389—26no—
61C2×C389C2×#4112yescomplemented
62C2×C389C2511yescharacteristic
63D389—26no—
64D389C2×#4114yesdirect product factor
65C389C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—3891nomaximal, Sylow
67C2×#41—38916no—
68C2×#41—3891no—
69C2×#41—3893no—
70C2×#41—3893no—
71C2×#41D38911yescharacteristic, direct product factor
72C22×Q8—3891no—
73C22×D4—3893no—
74C23×C4—3893no—
75C24—3893no—
76#41—3898no—
77#41—38924no—
78#41—38924no—
79#41C2×D38918yesdirect product factor
80C2×Q8—3898no—
81C2×Q8—3893no—
82C2×Q8C2×D38911yescharacteristic, complemented
83C2×D4—3896no—
84C2×D4—38924no—
85C2×D4—3893no—
86C2×D4C2×D38913yescomplemented
87C22×C4—3893no—
88C22×C4—3893no—
89C22×C4—3893no—
90C22×C4—3891no—
91C22×C4—3893no—
92C22×C4—38924no—
93C22×C4C2×D38913yescomplemented
94C23—77812no—
95C23—38912no—
96C23—3893no—
97C23—3891no—
98C23C22×D38913yes—
99Q8—38912no—
100Q8C22×D38914yescomplemented
101D4—38924no—
102D4—38912no—
103D4C22×D389112yescomplemented
104C2×C4—3891no—
105C2×C4—3893no—
106C2×C4—38912no—
107C2×C4—3894no—
108C2×C4—38912no—
109C2×C4—38912no—
110C2×C4—38912no—
111C2×C4C22×D38913yes—
112C2×C4C22×D38911yescharacteristic
113C2×C4C22×D389112yescomplemented
114C22—26no—
115C22—77824no—
116C22—7786no—
117C22—3896no—
118C22—3894no—
119C22—3892no—
120C22C23×D38916yes—
121C22C23×D38911yescharacteristic
122C4—3892no—
123C4—3896no—
124C4C23×D38912yes—
125C4C23×D38916yes—
126C2—26no—
127C2—7786no—
128C2—3894no—
129C2#41×D38912yesdirect product factor
130C2C24×D38911yescharacteristic
subgroupG/H
centerC2×C4C22×D389
commutator, cosocleC2×C389C25
FrattiniC2C24×D389
FittingC2×#41×C389C2
socleC22×C389C24
hypercenterC2×#41D389
hypocenterC389C22×#41
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20261967C2semidirect
2. C2×#20261966C2semidirect
3. C2×#20261965C2semidirect
4. #41×D389C2direct (N × H)
5. C2×Q8×D389C2semidirect
6. C2×D4×D389C2semidirect
7. C22×C4×D389C2semidirect
8. C2×#41×C389C2semidirect
10. #20261967C22semidirect
11. #20261966C22semidirect
12. #20261965C22semidirect
13. C2×Dic778C22semidirect
14. Q8×D389C22semidirect
15. C2×D1556C22semidirect
16. C2×C22⋊D389C22semidirect
17. D4×D389C22semidirect
18. C22×Dic389C22semidirect
21. C2×C4×D389C22semidirect
22. C2×C4×D389C22semidirect
23. C2×C4×D389C22semidirect
24. #41×C389C22semidirect
25. C2×Q8×C389C22semidirect
26. C2×D4×C389C22semidirect
27. C22×C4×C389C22semidirect
32. Dic778C23semidirect
33. D1556C23semidirect
34. C22⋊D389C23semidirect
37. C2×Dic389C23semidirect
40. C4×D389C23semidirect
41. C4×D389C23semidirect
43. Q8×C389C23semidirect
44. D4×C389C23semidirect
47. C2×C4×C389C23semidirect
53. C2×D389#41direct (N × H)
61. C2×C389C2×#41semidirect
64. D389C2×#41direct (N × H)
65. C389C22×#41semidirect
71. C2×#41D389direct (N × H)
79. #41C2×D389direct (N × H)
82. C2×Q8C2×D389semidirect
86. C2×D4C2×D389semidirect
93. C22×C4C2×D389semidirect
100. Q8C22×D389semidirect
103. D4C22×D389semidirect
113. C2×C4C22×D389semidirect
129. C2#41×D389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202619672
C2×#202619662
C2×#202619652
#41×D3892
C2×Q8×D3892
C2×D4×D3892
C22×C4×D3892
C2×#41×C3892
C22×#41389