Finite Group Databasebeta

← C24×C4⋊#64408 #34032691

Subgroups — C24×C4⋊#64408 #34032691

Order 18688.

19742 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.

normal subgroups only

This group has 19742 conjugacy classes of subgroups — too many to draw. Only its 8408 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
1C25×#64408C212yesmaximal
2C23×C4⋊#64408C2160yesmaximal, direct product factor
3C24×C4×D73C211yesmaximal, characteristic
4C24×#64408—232no—
5C24×#64408C22160yes—
6C22×C4⋊#64408C221560yesdirect product factor
7C25×D73C2211yescharacteristic
8C24×Dic73C411yescharacteristic, complemented
9C23×C4×D73C4130yescomplemented
10C23×C4×D73C22130yes—
11C24×C4×C73C411yescharacteristic, complemented
12C23×#64408—2480no—
13C23×#64408C231280yes—
14C2×C4⋊#64408C231960yesdirect product factor
15C24×D73C2×C4115yes—
16C24×D73D4116yes—
17C24×D73Q8116yes—
18C24×D73C23115yes—
19C23×Dic73C2×C4130yescomplemented
20C22×C4×D73C2×C41420yescomplemented
21C22×C4×D73C231140yes—
22C25×C73C2×C411yescharacteristic
23C23×C4×C73C2×C4130yescomplemented
24C22×#64408—21120no—
25C22×#64408C241240yes—
26C4⋊#64408C241256yesdirect product factor
27C23×D73C4⋊C41240yescomplemented
28C23×D73C22×C41105yes—
29C23×D73C2×D41120yes—
30C23×D73C2×Q81120yes—
31C23×D73C24135yes—
32C22×Dic73C22×C41140yescomplemented
33C2×C4×D73C22×C41840yescomplemented
34C2×C4×D73C241120yes—
35C24×C73C4⋊C4116yescomplemented
36C24×C73C22×C4115yes—
37C22×C4×C73C22×C41140yescomplemented
38C23×C73C2×C4⋊C41120yescomplemented
39C23×C73C23×C4135yes—
40C22×D73C2×C4⋊C41840yescomplemented
41C22×D73C23×C41105yes—
42C22×D73C22×D41140yes—
43C22×D73C22×Q81140yes—
44C22×D73C25115yes—
45C2×#64408—2480no—
46C2×#64408C25132yes—
47C2×C4×C73C23×C41120yescomplemented
48C2×Dic73C23×C41120yescomplemented
49C4×D73C23×C41240yescomplemented
50C4×D73C25116yes—
51C22×C73C22×C4⋊C41140yescomplemented
52C22×C73C24×C4115yes—
53C2×D73C22×C4⋊C41420yescomplemented
54C2×D73C24×C4115yes—
55C2×D73C23×D4130yes—
56C2×D73C23×Q8130yes—
57C2×D73C2611yescharacteristic
58#64408—232no—
59C4×C73C24×C4116yescomplemented
60Dic73C24×C4116yescomplemented
61C24×C4⋊C4—731nomaximal, Sylow
62C2×C73C23×C4⋊C4130yescomplemented
63C2×C73C25×C411yescharacteristic
64D73C23×C4⋊C4130yescomplemented
65D73C24×D411yescharacteristic
66D73C24×Q811yescharacteristic
67C25×C4—731no—
68C25×C4—732no—
69C23×C4⋊C4—7360no—
70C73C24×C4⋊C411yescharacteristic, complemented, Sylow
71C26—731no—
72C24×C4—731no—
73C24×C4—7330no—
74C24×C4—7330no—
75C24×C4—7360no—
76C24×C4—14632no—
77C24×C4#6440811yescharacteristic, complemented
78C22×C4⋊C4—73560no—
79C25—7316no—
80C25—7316no—
81C25—7315no—
82C25—7315no—
83C25C2×#6440811yescharacteristic
84C23×C4—7330no—
85C23×C4—73140no—
86C23×C4—73420no—
87C23×C4—73280no—
88C23×C4—146480no—
89C23×C4C2×#64408130yescomplemented
90C2×C4⋊C4—73960no—
91C24—73105no—
92C24—7335no—
93C24—73240no—
94C24—73120no—
95C24—73120no—
96C24C4⋊#64408116yesdirect product factor
97C24C22×#64408115yes—
98C22×C4—73140no—
99C22×C4—73840no—
100C22×C4—73120no—
101C22×C4—73240no—
102C22×C4—1461120no—
103C22×C4C22×#644081140yescomplemented
104C4⋊C4—73256no—
105C23—73140no—
106C23—73840no—
107C23—73140no—
108C23—7315no—
109C23—73105no—
110C23C2×C4⋊#644081120yesdirect product factor
111C23C23×#64408135yes—
112C2×C4—73120no—
113C2×C4—7316no—
114C2×C4—73240no—
115C2×C4—7332no—
116C2×C4—146480no—
117C2×C4C23×#644081120yescomplemented
118C22—7330no—
119C22—73420no—
120C22—7330no—
121C22—731no—
122C22—7315no—
123C22C22×C4⋊#644081140yesdirect product factor
124C22C24×#64408115yes—
125C4—7316no—
126C4—14632no—
127C4C24×#64408116yescomplemented
128C2—731no—
129C2—731no—
130C2—7330no—
131C2C23×C4⋊#64408130yesdirect product factor
132C2C25×#6440811yescharacteristic
subgroupG/H
centerC25C2×#64408
commutatorC2×C73C25×C4
FrattiniC2C25×#64408
FittingC24×C4×C73C4
socleC25×C73C2×C4
prime radicalC25×D73C22
cosocleC2×D73C26
hypercenterC24×C4#64408
hypocenterC73C24×C4⋊C4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊#64408C2direct (N × H)
6. C22×C4⋊#64408C22direct (N × H)
8. C24×Dic73C4semidirect
9. C23×C4×D73C4semidirect
11. C24×C4×C73C4semidirect
14. C2×C4⋊#64408C23direct (N × H)
19. C23×Dic73C2×C4semidirect
20. C22×C4×D73C2×C4semidirect
23. C23×C4×C73C2×C4semidirect
26. C4⋊#64408C24direct (N × H)
27. C23×D73C4⋊C4semidirect
32. C22×Dic73C22×C4semidirect
33. C2×C4×D73C22×C4semidirect
35. C24×C73C4⋊C4semidirect
37. C22×C4×C73C22×C4semidirect
38. C23×C73C2×C4⋊C4semidirect
40. C22×D73C2×C4⋊C4semidirect
47. C2×C4×C73C23×C4semidirect
48. C2×Dic73C23×C4semidirect
49. C4×D73C23×C4semidirect
51. C22×C73C22×C4⋊C4semidirect
53. C2×D73C22×C4⋊C4semidirect
59. C4×C73C24×C4semidirect
60. Dic73C24×C4semidirect
62. C2×C73C23×C4⋊C4semidirect
64. D73C23×C4⋊C4semidirect
70. C73C24×C4⋊C4semidirect
77. C24×C4#64408semidirect
89. C23×C4C2×#64408semidirect
96. C24C4⋊#64408direct (N × H)
103. C22×C4C22×#64408semidirect
110. C23C2×C4⋊#64408direct (N × H)
117. C2×C4C23×#64408semidirect
123. C22C22×C4⋊#64408direct (N × H)
127. C4C24×#64408semidirect
131. C2C23×C4⋊#64408direct (N × H)

Maximal subgroups

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

subgroupindex
C25×#644082
C23×C4⋊#644082
C24×C4×D732
C24×C4⋊C473