Finite Group Databasebeta

← C24×#6129 #16776801

Subgroups — C24×#6129 #16776801

Order 3328.

65470 conjugacy classes of subgroups; only the 32651 normal subgroups are shown.

normal subgroups only

This group has 65470 conjugacy classes of subgroups — too many to draw. Only its 32651 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
1C23×#6129C21120yesmaximal, direct product factor
2C24×Dic26C211yesmaximal, characteristic, complemented
3C24×C22⋊D13C212yesmaximal, complemented
4C25×Dic13C212yesmaximal, complemented
5C24×C4×D13C211yesmaximal, characteristic, complemented
6C24×D4×C13C211yesmaximal, characteristic, complemented
7C26×C13C2212yes—
8C25×D13C2211yescharacteristic
9C23×D4×C13C22160yescomplemented
10C24×C4×C13C2211yescharacteristic
11C23×C22⋊D13C221120yescomplemented
12C24×Dic13C2211yescharacteristic
13C24×Dic13C2212yes—
14C24×Dic13C221120yescomplemented
15C22×#6129C2212240yesdirect product factor
16C23×C4×D13C22160yescomplemented
17C23×Dic26C22160yescomplemented
18C25×C13—232no—
19C25×C13C23160yes—
20C25×C13C2311yescharacteristic
21C24×D13—216no—
22C24×D13C23130yes—
23C22×D4×C13C231560yescomplemented
24C23×C4×C13C23130yes—
25C22×C22⋊D13C2311120yescomplemented
26C23×Dic13C23160yes—
27C23×Dic13C23130yes—
28C23×Dic13C2311120yescomplemented
29C2×#6129C2317680yesdirect product factor
30C22×C4×D13C231560yescomplemented
31C22×Dic26C231560yescomplemented
32C24×#41—131nomaximal, Sylow
33C24×C13—2480no—
34C24×C13#41116yescomplemented
35C24×C13C241280yes—
36C24×C13C24115yes—
37C23×D13—2240no—
38C23×D13C241140yes—
39C2×D4×C13C241960yescomplemented
40C22×C4×C13C241140yes—
41C2×C22⋊D13C2411920yescomplemented
42C22×Dic13C241280yes—
43C22×Dic13C241140yes—
44C22×Dic13C2411920yescomplemented
45#6129C2414096yesdirect product factor
46C2×C4×D13C241960yescomplemented
47C2×Dic26C241960yescomplemented
48C23×#41—13120no—
49C24×Q8—131no—
50C24×D4—132no—
51C24×D4D1311yescharacteristic, complemented
52C25×C4—132no—
53C25×C4—131no—
54C23×C13—21120no—
55C23×C13C2×#411120yescomplemented
56C23×C13C251240yes—
57C23×C13C25135yes—
58C22×D13—2560no—
59C22×D13C251120yes—
60D4×C13C251256yescomplemented
61C2×C4×C13C251120yes—
62C22⋊D13C251512yescomplemented
63C2×Dic13C251240yes—
64C2×Dic13C251120yes—
65C2×Dic13C251512yescomplemented
66C4×D13C251256yescomplemented
67Dic26C251256yescomplemented
68C26—131no—
69C26C2×D1312yes—
70C22×#41—132240no—
71C23×Q8—1360no—
72C23×D4—13120no—
73C23×D4C2×D13160yescomplemented
74C24×C4—13120no—
75C24×C4—131no—
76C24×C4—132no—
77C24×C4—1360no—
78C24×C4C2×D1311yescharacteristic
79C22×C13—2480no—
80C22×C13C22×#411140yescomplemented
81C22×C13C26132yes—
82C22×C13C26115yes—
83C2×D13—2240no—
84C2×D13C26116yes—
85C4×C13C26116yes—
86Dic13C26132yes—
87Dic13C26116yes—
88C25—232no—
89C25—1330no—
90C25—2616no—
91C25C22×D13160yes—
92C25C22×D1311yescharacteristic
93C2×#41—137680no—
94C22×Q8—13560no—
95C22×D4—131120no—
96C22×D4C22×D131560yescomplemented
97C23×C4—1330no—
98C23×C4—1360no—
99C23×C4—131120no—
100C23×C4—13560no—
101C23×C4C22×D13130yes—
102C2×C13—232no—
103C2×C13C23×#41130yescomplemented
104C2×C13C2711yescharacteristic
105D13—216no—
106C24—2480no—
107C24—13140no—
108C24—26240no—
109C24#6129116yesdirect product factor
110C24C23×D131280yes—
111C24C23×D13115yes—
112#41—134096no—
113C2×Q8—13960no—
114C2×D4—131920no—
115C2×D4C23×D131960yescomplemented
116C22×C4—13140no—
117C22×C4—13280no—
118C22×C4—131920no—
119C22×C4—13960no—
120C22×C4C23×D131140yes—
121C13C24×#4111yescharacteristic, complemented, Sylow
122C23—21120no—
123C23—13120no—
124C23—26560no—
125C23C2×#61291120yesdirect product factor
126C23C24×D131240yes—
127C23C24×D13135yes—
128Q8—13256no—
129D4—13512no—
130D4C24×D131256yescomplemented
131C2×C4—13120no—
132C2×C4—13240no—
133C2×C4—13512no—
134C2×C4—13256no—
135C2×C4C24×D131120yes—
136C22—2480no—
137C22—1316no—
138C22—26240no—
139C22C22×#61291140yesdirect product factor
140C22C25×D13132yes—
141C22C25×D13115yes—
142C4—1316no—
143C4—1332no—
144C4C25×D13116yes—
145C2—232no—
146C2—2616no—
147C2C23×#6129130yesdirect product factor
148C2C26×D1311yescharacteristic
subgroupG/H
centerC25C22×D13
commutator, cosocleC2×C13C27
FrattiniC2C26×D13
FittingC24×D4×C13C2
socleC25×C13C23
hypercenterC24×D4D13
hypocenterC13C24×#41
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C23×#6129C2direct (N × H)
2. C24×Dic26C2semidirect
3. C24×C22⋊D13C2semidirect
4. C25×Dic13C2semidirect
5. C24×C4×D13C2semidirect
6. C24×D4×C13C2semidirect
9. C23×D4×C13C22semidirect
11. C23×C22⋊D13C22semidirect
14. C24×Dic13C22semidirect
15. C22×#6129C22direct (N × H)
16. C23×C4×D13C22semidirect
17. C23×Dic26C22semidirect
23. C22×D4×C13C23semidirect
25. C22×C22⋊D13C23semidirect
28. C23×Dic13C23semidirect
29. C2×#6129C23direct (N × H)
30. C22×C4×D13C23semidirect
31. C22×Dic26C23semidirect
34. C24×C13#41semidirect
39. C2×D4×C13C24semidirect
41. C2×C22⋊D13C24semidirect
44. C22×Dic13C24semidirect
45. #6129C24direct (N × H)
46. C2×C4×D13C24semidirect
47. C2×Dic26C24semidirect
51. C24×D4D13semidirect
55. C23×C13C2×#41semidirect
60. D4×C13C25semidirect
62. C22⋊D13C25semidirect
65. C2×Dic13C25semidirect
66. C4×D13C25semidirect
67. Dic26C25semidirect
73. C23×D4C2×D13semidirect
80. C22×C13C22×#41semidirect
96. C22×D4C22×D13semidirect
103. C2×C13C23×#41semidirect
109. C24#6129direct (N × H)
115. C2×D4C23×D13semidirect
121. C13C24×#41semidirect
125. C23C2×#6129direct (N × H)
130. D4C24×D13semidirect
139. C22C22×#6129direct (N × H)
147. C2C23×#6129direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#61292
C24×Dic262
C24×C22⋊D132
C25×Dic132
C24×C4×D132
C24×D4×C132
C24×#4113