Finite Group Databasebeta

← D3×C13×#41 #11929295

Subgroups — D3×C13×#41 #11929295

Order 1248.

328 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 174 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
1C3×C13×#41C211yesmaximal, characteristic, complemented
2C13×#239C211yesmaximal, characteristic, complemented
3D3×Q8×C13C211yesmaximal, characteristic, complemented
4C13×#237C213yesmaximal, complemented
5D3×D4×C13C213yesmaximal, complemented
6C13×#235C213yesmaximal, complemented
7C2×C4×D3×C13C213yesmaximal, complemented
8C2×C13×#41—31nomaximal, Hall
9C22×D3×C13C2213yes—
10C3×Q8×C13C2211yescharacteristic, complemented
11C3×D4×C13C2213yescomplemented
12C2×C3×C4×C13C2213yescomplemented
13C13×#67C2216yescomplemented
14C2×Dic3×C13C2213yescomplemented
15C13×D12C2213yescomplemented
16C4×D3×C13C2211yescharacteristic
17C4×D3×C13C2213yes—
18C4×D3×C13C2213yescomplemented
19C4×D3×C13C2213yescomplemented
20C13×Dic6C2213yescomplemented
21C13×#41—31no—
22C13×#41—33no—
23C13×#41—33no—
24C13×#41D311yescharacteristic, direct product factor
25C2×Q8×C13—31no—
26C2×D4×C13—33no—
27C22×C4×C13—33no—
28C22×C3×C13C2313yes—
29C2×D3×C13—26no—
30C2×D3×C13C2313yes—
31C2×D3×C13C2311yescharacteristic
32C3×C4×C13C2313yes—
33C3×C4×C13C2311yescharacteristic
34Dic3×C13C2313yes—
35Dic3×C13C2311yescharacteristic
36C23×C13—33no—
37Q8×C13—33no—
38Q8×C13C2×D311yescharacteristic, complemented
39D4×C13—36no—
40D4×C13—33no—
41D4×C13C2×D313yescomplemented
42C2×C4×C13—33no—
43C2×C4×C13—33no—
44C2×C4×C13—33no—
45C2×C4×C13—31no—
46C2×C4×C13—33no—
47C2×C4×C13C2×D313yescomplemented
48D3×#41C1311yesmaximal, characteristic, direct product factor, Hall
49C2×C3×C13—23no—
50C2×C3×C13C2411yescharacteristic
51D3×C13—23no—
52D3×C13#4112yesdirect product factor
53C22×C13—31no—
54C22×C13—33no—
55C22×C13—66no—
56C22×C13C22×D313yes—
57C4×C13—31no—
58C4×C13—33no—
59C4×C13C22×D313yes—
60C4×C13C22×D311yescharacteristic
61C3×#41C2×C1311yescharacteristic, complemented
62#239C2×C1311yescharacteristic, complemented
63D3×Q8C2×C1311yescharacteristic, complemented
64#237C2×C1313yescomplemented
65D3×D4C2×C1313yescomplemented
66#235C2×C1313yescomplemented
67C2×C4×D3C2×C1313yescomplemented
68C3×C13C2×#4111yescharacteristic, complemented, Hall
69C2×#41—31noSylow
70C2×C13—23no—
71C2×C13—32no—
72C2×C13—63no—
73C2×C13C23×D311yescharacteristic
74C22×D3C22×C1313yes—
75C3×Q8C22×C1311yescharacteristic, complemented
76C3×D4C22×C1313yescomplemented
77C2×C3×C4C22×C1313yescomplemented
78#67C22×C1316yescomplemented
79C2×Dic3C22×C1313yescomplemented
80D12C22×C1313yescomplemented
81C4×D3C22×C1311yescharacteristic
82C4×D3C22×C1313yes—
83C4×D3C22×C1313yescomplemented
84C4×D3C22×C1313yescomplemented
85Dic6C22×C1313yescomplemented
86#41—31no—
87#41—33no—
88#41—33no—
89#41D3×C1311yescharacteristic, direct product factor
90C2×Q8—31no—
91C2×D4—33no—
92C22×C4—33no—
93C13D3×#4111yescharacteristic, direct product factor, Sylow
94C22×C3C23×C1313yes—
95C2×D3—26no—
96C2×D3C23×C1313yes—
97C2×D3C23×C1311yescharacteristic
98C3×C4C23×C1313yes—
99C3×C4C23×C1311yescharacteristic
100Dic3C23×C1313yes—
101Dic3C23×C1311yescharacteristic
102C23—33no—
103Q8—33no—
104Q8C2×D3×C1311yescharacteristic, complemented
105D4—36no—
106D4—33no—
107D4C2×D3×C1313yescomplemented
108C2×C4—33no—
109C2×C4—31no—
110C2×C4—33no—
111C2×C4—33no—
112C2×C4—33no—
113C2×C4C2×D3×C1313yescomplemented
114C2×C3—23no—
115C2×C3C24×C1311yescharacteristic
116D3—23no—
117D3C13×#4112yesdirect product factor
118C22—31no—
119C22—33no—
120C22—66no—
121C22C22×D3×C1313yes—
122C4—31no—
123C4—33no—
124C4C22×D3×C1313yes—
125C4C22×D3×C1311yescharacteristic
126C3C2×C13×#4111yescharacteristic, complemented, Sylow
127C2—23no—
128C2—32no—
129C2—63no—
130C2C23×D3×C1311yescharacteristic
subgroupG/H
centerC4×C13C22×D3
commutator, cosocleC2×C3C24×C13
FrattiniC2C23×D3×C13
FittingC3×C13×#41C2
socleC2×C3×C13C24
hypercenterC13×#41D3
hypocenterC3C2×C13×#41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C13 ◁ C13×#41

Complements

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

NH ≅ G/Ntype
1. C3×C13×#41C2semidirect
2. C13×#239C2semidirect
3. D3×Q8×C13C2semidirect
4. C13×#237C2semidirect
5. D3×D4×C13C2semidirect
6. C13×#235C2semidirect
7. C2×C4×D3×C13C2semidirect
10. C3×Q8×C13C22semidirect
11. C3×D4×C13C22semidirect
12. C2×C3×C4×C13C22semidirect
13. C13×#67C22semidirect
14. C2×Dic3×C13C22semidirect
15. C13×D12C22semidirect
18. C4×D3×C13C22semidirect
19. C4×D3×C13C22semidirect
20. C13×Dic6C22semidirect
24. C13×#41D3direct (N × H)
38. Q8×C13C2×D3semidirect
41. D4×C13C2×D3semidirect
47. C2×C4×C13C2×D3semidirect
48. D3×#41C13direct (N × H)
52. D3×C13#41direct (N × H)
61. C3×#41C2×C13semidirect
62. #239C2×C13semidirect
63. D3×Q8C2×C13semidirect
64. #237C2×C13semidirect
65. D3×D4C2×C13semidirect
66. #235C2×C13semidirect
67. C2×C4×D3C2×C13semidirect
68. C3×C13C2×#41semidirect
75. C3×Q8C22×C13semidirect
76. C3×D4C22×C13semidirect
77. C2×C3×C4C22×C13semidirect
78. #67C22×C13semidirect
79. C2×Dic3C22×C13semidirect
80. D12C22×C13semidirect
83. C4×D3C22×C13semidirect
84. C4×D3C22×C13semidirect
85. Dic6C22×C13semidirect
89. #41D3×C13direct (N × H)
93. C13D3×#41direct (N × H)
104. Q8C2×D3×C13semidirect
107. D4C2×D3×C13semidirect
113. C2×C4C2×D3×C13semidirect
117. D3C13×#41direct (N × H)
126. C3C2×C13×#41semidirect

Maximal subgroups

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

subgroupindex
C3×C13×#412
C13×#2392
D3×Q8×C132
C13×#2372
D3×D4×C132
C13×#2352
C2×C4×D3×C132
C2×C13×#413
D3×#4113