Finite Group Databasebeta

← C24×C13×SD16 #15749417

Subgroups — C24×C13×SD16 #15749417

Order 3328.

13310 conjugacy classes of subgroups; only the 6878 normal subgroups are shown.

normal subgroups only

This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 6878 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
1C24×Q8×C13C211yesmaximal, characteristic, complemented
2C24×D4×C13C211yesmaximal, characteristic
3C23×C13×SD16C2160yesmaximal, direct product factor
4C24×C8×C13C211yesmaximal, characteristic, complemented
5C26×C13—21no—
6C23×Q8×C13—215no—
7C23×Q8×C13C22130yescomplemented
8C23×D4×C13—215no—
9C23×D4×C13C22130yes—
10C24×C4×C13—21no—
11C24×C4×C13C2211yescharacteristic
12C22×C13×SD16C221560yesdirect product factor
13C23×C8×C13C22130yescomplemented
14C25×C13—230no—
15C25×C13—416no—
16C25×C13D411yescharacteristic
17C22×Q8×C13—2210no—
18C22×Q8×C13C231140yescomplemented
19C22×D4×C13—2210no—
20C22×D4×C13C231140yes—
21C23×C4×C13—230no—
22C23×C4×C13D4115yes—
23C23×C4×C13C23115yes—
24C2×C13×SD16C231960yesdirect product factor
25C22×C8×C13C231140yescomplemented
26C24×SD16C1311yesmaximal, characteristic, direct product factor, Sylow
27C24×C13—2140no—
28C24×C13—4240no—
29C24×C13SD16116yesdirect product factor
30C24×C13C2×D4115yes—
31C2×Q8×C13—2420no—
32C2×Q8×C13C241120yescomplemented
33C2×D4×C13—2420no—
34C2×D4×C13C241120yes—
35C22×C4×C13—2140no—
36C22×C4×C13C2×D41105yes—
37C22×C4×C13C24135yes—
38C13×SD16C241256yesdirect product factor
39C2×C8×C13C241120yescomplemented
40C24×Q8C2×C1311yescharacteristic, complemented
41C24×D4C2×C1311yescharacteristic
42C23×SD16C2×C13160yesdirect product factor
43C24×C8C2×C1311yescharacteristic, complemented
44C23×C13—2120no—
45C23×C13—4560no—
46C23×C13C2×SD161120yesdirect product factor
47C23×C13C22×D4135yes—
48Q8×C13—2120no—
49Q8×C13C25116yescomplemented
50D4×C13—2120no—
51D4×C13C25116yes—
52C2×C4×C13—2120no—
53C2×C4×C13C22×D41105yes—
54C2×C4×C13C25115yes—
55C8×C13C25116yescomplemented
56C26—21no—
57C23×Q8—215no—
58C23×Q8C22×C13130yescomplemented
59C23×D4—215no—
60C23×D4C22×C13130yes—
61C24×C4—21no—
62C24×C4C22×C1311yescharacteristic
63C22×SD16C22×C131560yesdirect product factor
64C23×C8C22×C13130yescomplemented
65C22×C13—216no—
66C22×C13—4240no—
67C22×C13C22×SD161140yesdirect product factor
68C22×C13C23×D4115yes—
69C4×C13—216no—
70C4×C13C23×D4115yes—
71C4×C13C2611yescharacteristic
72C25—230no—
73C25—416no—
74C25D4×C1311yescharacteristic
75C22×Q8—2210no—
76C22×Q8C23×C131140yescomplemented
77C22×D4—2210no—
78C22×D4C23×C131140yes—
79C23×C4—230no—
80C23×C4D4×C13115yes—
81C23×C4C23×C13115yes—
82C2×SD16C23×C131960yesdirect product factor
83C22×C8C23×C131140yescomplemented
84C2×C13—416no—
85C2×C13C23×SD16130yesdirect product factor
86C2×C13C24×D411yescharacteristic
87C24—2140no—
88C24—4240no—
89C24C13×SD16116yesdirect product factor
90C24C2×D4×C13115yes—
91C2×Q8—2420no—
92C2×Q8C24×C131120yescomplemented
93C2×D4—2420no—
94C2×D4C24×C131120yes—
95C22×C4—2140no—
96C22×C4C2×D4×C131105yes—
97C22×C4C24×C13135yes—
98SD16C24×C131256yesdirect product factor
99C2×C8C24×C131120yescomplemented
100C13C24×SD1611yescharacteristic, direct product factor, Sylow
101C23—2120no—
102C23—4560no—
103C23C2×C13×SD161120yesdirect product factor
104C23C22×D4×C13135yes—
105Q8—2120no—
106Q8C25×C13116yescomplemented
107D4—2120no—
108D4C25×C13116yes—
109C2×C4—2120no—
110C2×C4C22×D4×C131105yes—
111C2×C4C25×C13115yes—
112C8C25×C13116yescomplemented
113C22—216no—
114C22—4240no—
115C22C22×C13×SD161140yesdirect product factor
116C22C23×D4×C13115yes—
117C4—216no—
118C4C23×D4×C13115yes—
119C4C26×C1311yescharacteristic
120C2—416no—
121C2C23×C13×SD16130yesdirect product factor
122C2C24×D4×C1311yescharacteristic
subgroupG/H
center, socleC25×C13D4
commutator, Frattini, cosocleC4C26×C13
prime radicalC24×D4×C13C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C25×C13 ◁ C24×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C24×Q8×C13C2semidirect
3. C23×C13×SD16C2direct (N × H)
4. C24×C8×C13C2semidirect
7. C23×Q8×C13C22semidirect
12. C22×C13×SD16C22direct (N × H)
13. C23×C8×C13C22semidirect
18. C22×Q8×C13C23semidirect
24. C2×C13×SD16C23direct (N × H)
25. C22×C8×C13C23semidirect
26. C24×SD16C13direct (N × H)
29. C24×C13SD16direct (N × H)
32. C2×Q8×C13C24semidirect
38. C13×SD16C24direct (N × H)
39. C2×C8×C13C24semidirect
40. C24×Q8C2×C13semidirect
42. C23×SD16C2×C13direct (N × H)
43. C24×C8C2×C13semidirect
46. C23×C13C2×SD16direct (N × H)
49. Q8×C13C25semidirect
55. C8×C13C25semidirect
58. C23×Q8C22×C13semidirect
63. C22×SD16C22×C13direct (N × H)
64. C23×C8C22×C13semidirect
67. C22×C13C22×SD16direct (N × H)
76. C22×Q8C23×C13semidirect
82. C2×SD16C23×C13direct (N × H)
83. C22×C8C23×C13semidirect
85. C2×C13C23×SD16direct (N × H)
89. C24C13×SD16direct (N × H)
92. C2×Q8C24×C13semidirect
98. SD16C24×C13direct (N × H)
99. C2×C8C24×C13semidirect
100. C13C24×SD16direct (N × H)
103. C23C2×C13×SD16direct (N × H)
106. Q8C25×C13semidirect
112. C8C25×C13semidirect
115. C22C22×C13×SD16direct (N × H)
121. C2C23×C13×SD16direct (N × H)

Maximal subgroups

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

subgroupindex
C24×Q8×C132
C24×D4×C132
C23×C13×SD162
C24×C8×C132
C24×SD1613