Finite Group Databasebeta

← C24×D4×D13 #16776795

Subgroups — C24×D4×D13 #16776795

Order 3328.

111198 conjugacy classes of subgroups; only the 34795 normal subgroups are shown.

normal subgroups only

This group has 111198 conjugacy classes of subgroups — too many to draw. Only its 34795 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
1C26×D13C212yesmaximal, complemented
2C24×D52C211yesmaximal, characteristic, complemented
3C24×C22⋊D13C212yesmaximal, complemented
4C23×D4×D13C21120yesmaximal, direct product factor
5C24×C4×D13C211yesmaximal, characteristic, complemented
6C24×D4×C13C211yesmaximal, characteristic, complemented
7C26×C13C2212yescomplemented
8C25×D13—264no—
9C25×D13C2211yescharacteristic
10C25×D13C221120yescomplemented
11C25×D13C2212yescomplemented
12C23×D4×C13C22160yescomplemented
13C24×C4×C13C2211yescharacteristic, complemented
14C23×C22⋊D13C221120yescomplemented
15C24×Dic13C2211yescharacteristic, complemented
16C22×D4×D13C2212240yesdirect product factor
17C23×D52C22160yescomplemented
18C23×C4×D13C22160yescomplemented
19C25×C13—232no—
20C25×C13C2311yescharacteristic
21C25×C13C23160yescomplemented
22C24×D13—232no—
23C24×D13—21920no—
24C24×D13D4132yesdirect product factor
25C24×D13C23130yes—
26C24×D13C2311120yescomplemented
27C24×D13C23160yescomplemented
28C22×D4×C13C231560yescomplemented
29C23×C4×C13C23130yescomplemented
30C22×C22⋊D13C2311120yescomplemented
31C23×Dic13C23130yescomplemented
32C2×D4×D13C2317680yesdirect product factor
33C22×D52C231560yescomplemented
34C22×C4×D13C231560yescomplemented
35C25×D4—131nomaximal, Sylow
36C24×C13—2480no—
37C24×C13C2×D4116yescomplemented
38C24×C13C24115yes—
39C24×C13C241280yescomplemented
40C23×D13—2480no—
41C23×D13—28960no—
42C23×D13C2×D41480yesdirect product factor
43C23×D13C241140yes—
44C23×D13C2411920yescomplemented
45C23×D13C241280yescomplemented
46C2×D4×C13C241960yescomplemented
47C22×C4×C13C241140yescomplemented
48C2×C22⋊D13C2411920yescomplemented
49C22×Dic13C241140yescomplemented
50D4×D13C2414096yesdirect product factor
51C2×D52C241960yescomplemented
52C2×C4×D13C241960yescomplemented
53C27—132no—
54C24×D4—132no—
55C24×D4—13120no—
56C24×D4—131no—
57C24×D4D1311yescharacteristic, direct product factor
58C25×C4—131no—
59C23×C13—21120no—
60C23×C13C22×D41120yescomplemented
61C23×C13C25135yes—
62C23×C13C251240yescomplemented
63C22×D13—21120no—
64C22×D13—27680no—
65C22×D13C22×D411120yesdirect product factor
66C22×D13C251120yes—
67C22×D13C251512yescomplemented
68C22×D13C251240yescomplemented
69D4×C13C251256yescomplemented
70C2×C4×C13C251120yescomplemented
71C22⋊D13C251512yescomplemented
72C2×Dic13C251120yescomplemented
73D52C251256yescomplemented
74C4×D13C251256yescomplemented
75C26—131no—
76C26—132no—
77C26—13120no—
78C26—2664no—
79C26C2×D1312yescomplemented
80C23×D4—13120no—
81C23×D4—132240no—
82C23×D4—1360no—
83C23×D4C2×D13160yesdirect product factor
84C24×C4—131no—
85C24×C4—1360no—
86C24×C4C2×D1311yescharacteristic, complemented
87C22×C13—2480no—
88C22×C13C23×D41140yescomplemented
89C22×C13C26115yes—
90C22×C13C26132yescomplemented
91C2×D13—2480no—
92C2×D13—21024no—
93C2×D13C23×D41480yesdirect product factor
94C2×D13C26116yes—
95C2×D13C26132yescomplemented
96C4×C13C26116yescomplemented
97Dic13C26116yescomplemented
98C25—232no—
99C25—1332no—
100C25—1330no—
101C25—1360no—
102C25—131120no—
103C25—261920no—
104C25—2632no—
105C25C22×D1311yescharacteristic
106C25C22×D13160yescomplemented
107C22×D4—131120no—
108C22×D4—137680no—
109C22×D4—13560no—
110C22×D4C22×D131560yesdirect product factor
111C23×C4—1330no—
112C23×C4—13560no—
113C23×C4C22×D13130yescomplemented
114C2×C13—232no—
115C2×C13C24×D4130yescomplemented
116C2×C13C2711yescharacteristic
117D13—232no—
118D13C24×D4132yesdirect product factor
119C24—2480no—
120C24—13480no—
121C24—13140no—
122C24—13280no—
123C24—131920no—
124C24—268960no—
125C24—26480no—
126C24D4×D13116yesdirect product factor
127C24C23×D13115yes—
128C24C23×D131280yescomplemented
129C2×D4—131920no—
130C2×D4—134096no—
131C2×D4—13960no—
132C2×D4C23×D131960yesdirect product factor
133C22×C4—13140no—
134C22×C4—13960no—
135C22×C4C23×D131140yescomplemented
136C13C25×D411yescharacteristic, complemented, Sylow
137C23—21120no—
138C23—131120no—
139C23—13120no—
140C23—13240no—
141C23—13512no—
142C23—267680no—
143C23—261120no—
144C23C2×D4×D131120yesdirect product factor
145C23C24×D13135yes—
146C23C24×D131240yescomplemented
147D4—13512no—
148D4—13256no—
149D4C24×D131256yesdirect product factor
150C2×C4—13120no—
151C2×C4—13256no—
152C2×C4C24×D131120yescomplemented
153C22—2480no—
154C22—13480no—
155C22—1316no—
156C22—1332no—
157C22—261024no—
158C22—26480no—
159C22C22×D4×D131140yesdirect product factor
160C22C25×D13115yes—
161C22C25×D13132yescomplemented
162C4—1316no—
163C4C25×D13116yescomplemented
164C2—232no—
165C2—1332no—
166C2—2632no—
167C2C23×D4×D13130yesdirect product factor
168C2C26×D1311yescharacteristic
subgroupG/H
centerC25C22×D13
commutator, cosocleC2×C13C27
FrattiniC2C26×D13
FittingC24×D4×C13C2
socleC25×C13C23
hypercenterC24×D4D13
hypocenterC13C25×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C26×D13C2semidirect
2. C24×D52C2semidirect
3. C24×C22⋊D13C2semidirect
4. C23×D4×D13C2direct (N × H)
5. C24×C4×D13C2semidirect
6. C24×D4×C13C2semidirect
7. C26×C13C22semidirect
10. C25×D13C22semidirect
11. C25×D13C22semidirect
12. C23×D4×C13C22semidirect
13. C24×C4×C13C22semidirect
14. C23×C22⋊D13C22semidirect
15. C24×Dic13C22semidirect
16. C22×D4×D13C22direct (N × H)
17. C23×D52C22semidirect
18. C23×C4×D13C22semidirect
21. C25×C13C23semidirect
24. C24×D13D4direct (N × H)
26. C24×D13C23semidirect
27. C24×D13C23semidirect
28. C22×D4×C13C23semidirect
29. C23×C4×C13C23semidirect
30. C22×C22⋊D13C23semidirect
31. C23×Dic13C23semidirect
32. C2×D4×D13C23direct (N × H)
33. C22×D52C23semidirect
34. C22×C4×D13C23semidirect
37. C24×C13C2×D4semidirect
39. C24×C13C24semidirect
42. C23×D13C2×D4direct (N × H)
44. C23×D13C24semidirect
45. C23×D13C24semidirect
46. C2×D4×C13C24semidirect
47. C22×C4×C13C24semidirect
48. C2×C22⋊D13C24semidirect
49. C22×Dic13C24semidirect
50. D4×D13C24direct (N × H)
51. C2×D52C24semidirect
52. C2×C4×D13C24semidirect
57. C24×D4D13direct (N × H)
60. C23×C13C22×D4semidirect
62. C23×C13C25semidirect
65. C22×D13C22×D4direct (N × H)
67. C22×D13C25semidirect
68. C22×D13C25semidirect
69. D4×C13C25semidirect
70. C2×C4×C13C25semidirect
71. C22⋊D13C25semidirect
72. C2×Dic13C25semidirect
73. D52C25semidirect
74. C4×D13C25semidirect
79. C26C2×D13semidirect
83. C23×D4C2×D13direct (N × H)
86. C24×C4C2×D13semidirect
88. C22×C13C23×D4semidirect
90. C22×C13C26semidirect
93. C2×D13C23×D4direct (N × H)
95. C2×D13C26semidirect
96. C4×C13C26semidirect
97. Dic13C26semidirect
106. C25C22×D13semidirect
110. C22×D4C22×D13direct (N × H)
113. C23×C4C22×D13semidirect
115. C2×C13C24×D4semidirect
118. D13C24×D4direct (N × H)
126. C24D4×D13direct (N × H)
128. C24C23×D13semidirect
132. C2×D4C23×D13direct (N × H)
135. C22×C4C23×D13semidirect
136. C13C25×D4semidirect
144. C23C2×D4×D13direct (N × H)
146. C23C24×D13semidirect
149. D4C24×D13direct (N × H)
152. C2×C4C24×D13semidirect
159. C22C22×D4×D13direct (N × H)
161. C22C25×D13semidirect
163. C4C25×D13semidirect
167. C2C23×D4×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C26×D132
C24×D522
C24×C22⋊D132
C23×D4×D132
C24×C4×D132
C24×D4×C132
C25×D413