Finite Group Databasebeta

← C24×SD16×C61 #29566511

Subgroups — C24×SD16×C61 #29566511

Order 15616.

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×C61C211yesmaximal, characteristic, complemented
2C24×D4×C61C211yesmaximal, characteristic
3C23×SD16×C61C2160yesmaximal, direct product factor
4C24×C8×C61C211yesmaximal, characteristic, complemented
5C26×C61—21no—
6C23×Q8×C61—215no—
7C23×Q8×C61C22130yescomplemented
8C23×D4×C61—215no—
9C23×D4×C61C22130yes—
10C24×C4×C61—21no—
11C24×C4×C61C2211yescharacteristic
12C22×SD16×C61C221560yesdirect product factor
13C23×C8×C61C22130yescomplemented
14C25×C61—230no—
15C25×C61—416no—
16C25×C61D411yescharacteristic
17C22×Q8×C61—2210no—
18C22×Q8×C61C231140yescomplemented
19C22×D4×C61—2210no—
20C22×D4×C61C231140yes—
21C23×C4×C61—230no—
22C23×C4×C61D4115yes—
23C23×C4×C61C23115yes—
24C2×SD16×C61C231960yesdirect product factor
25C22×C8×C61C231140yescomplemented
26C24×C61—2140no—
27C24×C61—4240no—
28C24×C61SD16116yesdirect product factor
29C24×C61C2×D4115yes—
30C2×Q8×C61—2420no—
31C2×Q8×C61C241120yescomplemented
32C2×D4×C61—2420no—
33C2×D4×C61C241120yes—
34C22×C4×C61—2140no—
35C22×C4×C61C2×D41105yes—
36C22×C4×C61C24135yes—
37SD16×C61C241256yesdirect product factor
38C2×C8×C61C241120yescomplemented
39C23×C61—2120no—
40C23×C61—4560no—
41C23×C61C2×SD161120yesdirect product factor
42C23×C61C22×D4135yes—
43Q8×C61—2120no—
44Q8×C61C25116yescomplemented
45D4×C61—2120no—
46D4×C61C25116yes—
47C2×C4×C61—2120no—
48C2×C4×C61C22×D41105yes—
49C2×C4×C61C25115yes—
50C8×C61C25116yescomplemented
51C24×SD16C6111yesmaximal, characteristic, direct product factor, Sylow
52C22×C61—216no—
53C22×C61—4240no—
54C22×C61C22×SD161140yesdirect product factor
55C22×C61C23×D4115yes—
56C4×C61—216no—
57C4×C61C23×D4115yes—
58C4×C61C2611yescharacteristic
59C24×Q8C2×C6111yescharacteristic, complemented
60C24×D4C2×C6111yescharacteristic
61C23×SD16C2×C61160yesdirect product factor
62C24×C8C2×C6111yescharacteristic, complemented
63C2×C61—416no—
64C2×C61C23×SD16130yesdirect product factor
65C2×C61C24×D411yescharacteristic
66C26—21no—
67C23×Q8—215no—
68C23×Q8C22×C61130yescomplemented
69C23×D4—215no—
70C23×D4C22×C61130yes—
71C24×C4—21no—
72C24×C4C22×C6111yescharacteristic
73C22×SD16C22×C611560yesdirect product factor
74C23×C8C22×C61130yescomplemented
75C61C24×SD1611yescharacteristic, direct product factor, Sylow
76C25—230no—
77C25—416no—
78C25D4×C6111yescharacteristic
79C22×Q8—2210no—
80C22×Q8C23×C611140yescomplemented
81C22×D4—2210no—
82C22×D4C23×C611140yes—
83C23×C4—230no—
84C23×C4D4×C61115yes—
85C23×C4C23×C61115yes—
86C2×SD16C23×C611960yesdirect product factor
87C22×C8C23×C611140yescomplemented
88C24—2140no—
89C24—4240no—
90C24SD16×C61116yesdirect product factor
91C24C2×D4×C61115yes—
92C2×Q8—2420no—
93C2×Q8C24×C611120yescomplemented
94C2×D4—2420no—
95C2×D4C24×C611120yes—
96C22×C4—2140no—
97C22×C4C2×D4×C611105yes—
98C22×C4C24×C61135yes—
99SD16C24×C611256yesdirect product factor
100C2×C8C24×C611120yescomplemented
101C23—2120no—
102C23—4560no—
103C23C2×SD16×C611120yesdirect product factor
104C23C22×D4×C61135yes—
105Q8—2120no—
106Q8C25×C61116yescomplemented
107D4—2120no—
108D4C25×C61116yes—
109C2×C4—2120no—
110C2×C4C22×D4×C611105yes—
111C2×C4C25×C61115yes—
112C8C25×C61116yescomplemented
113C22—216no—
114C22—4240no—
115C22C22×SD16×C611140yesdirect product factor
116C22C23×D4×C61115yes—
117C4—216no—
118C4C23×D4×C61115yes—
119C4C26×C6111yescharacteristic
120C2—416no—
121C2C23×SD16×C61130yesdirect product factor
122C2C24×D4×C6111yescharacteristic
subgroupG/H
center, socleC25×C61D4
commutator, Frattini, cosocleC4C26×C61
prime radicalC24×D4×C61C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C25×C61 ◁ C24×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C24×Q8×C61C2semidirect
3. C23×SD16×C61C2direct (N × H)
4. C24×C8×C61C2semidirect
7. C23×Q8×C61C22semidirect
12. C22×SD16×C61C22direct (N × H)
13. C23×C8×C61C22semidirect
18. C22×Q8×C61C23semidirect
24. C2×SD16×C61C23direct (N × H)
25. C22×C8×C61C23semidirect
28. C24×C61SD16direct (N × H)
31. C2×Q8×C61C24semidirect
37. SD16×C61C24direct (N × H)
38. C2×C8×C61C24semidirect
41. C23×C61C2×SD16direct (N × H)
44. Q8×C61C25semidirect
50. C8×C61C25semidirect
51. C24×SD16C61direct (N × H)
54. C22×C61C22×SD16direct (N × H)
59. C24×Q8C2×C61semidirect
61. C23×SD16C2×C61direct (N × H)
62. C24×C8C2×C61semidirect
64. C2×C61C23×SD16direct (N × H)
68. C23×Q8C22×C61semidirect
73. C22×SD16C22×C61direct (N × H)
74. C23×C8C22×C61semidirect
75. C61C24×SD16direct (N × H)
80. C22×Q8C23×C61semidirect
86. C2×SD16C23×C61direct (N × H)
87. C22×C8C23×C61semidirect
90. C24SD16×C61direct (N × H)
93. C2×Q8C24×C61semidirect
99. SD16C24×C61direct (N × H)
100. C2×C8C24×C61semidirect
103. C23C2×SD16×C61direct (N × H)
106. Q8C25×C61semidirect
112. C8C25×C61semidirect
115. C22C22×SD16×C61direct (N × H)
121. C2C23×SD16×C61direct (N × H)

Maximal subgroups

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

subgroupindex
C24×Q8×C612
C24×D4×C612
C23×SD16×C612
C24×C8×C612
C24×SD1661