Finite Group Databasebeta

← C24×C22⋊#64408 #34032690

Subgroups — C24×C22⋊#64408 #34032690

Order 18688.

43678 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.

normal subgroups only

This group has 43678 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, complemented
2C23×C22⋊#64408C2160yesmaximal, direct product factor
3C26×D73C211yesmaximal, characteristic
4C24×#64408—232no—
5C24×#64408C22160yescomplemented
6C22×C22⋊#64408C221560yesdirect product factor
7C25×D73—232no—
8C25×D73C411yescharacteristic, complemented
9C25×D73C4130yescomplemented
10C25×D73C2211yescharacteristic
11C25×D73C22130yes—
12C26×C73C411yescharacteristic, complemented
13C23×#64408—2480no—
14C23×#64408C231280yescomplemented
15C2×C22⋊#64408C231960yesdirect product factor
16C24×D73—2480no—
17C24×D73—2480no—
18C24×D73—216no—
19C24×D73C2×C4115yes—
20C24×D73C2×C4130yescomplemented
21C24×D73C2×C41420yescomplemented
22C24×D73D4132yes—
23C24×D73C23115yes—
24C24×D73C231140yes—
25C25×C73—216no—
26C25×C73C2×C411yescharacteristic
27C25×C73C2×C4130yescomplemented
28C22×#64408—21120no—
29C22×#64408C241240yescomplemented
30C22⋊#64408C241256yesdirect product factor
31C23×D73—2240no—
32C23×D73—23360no—
33C23×D73—21120no—
34C23×D73C22⋊C41240yescomplemented
35C23×D73C22×C41105yes—
36C23×D73C22×C41840yescomplemented
37C23×D73C22×C41140yescomplemented
38C23×D73C2×D41240yes—
39C23×D73C241120yes—
40C23×D73C24135yes—
41C24×C73—2240no—
42C24×C73C22⋊C4116yescomplemented
43C24×C73C22×C4115yes—
44C24×C73C22×C41140yescomplemented
45C23×C73—2560no—
46C23×C73C2×C22⋊C41120yescomplemented
47C23×C73C23×C4135yes—
48C23×C73C23×C41120yescomplemented
49C22×D73—2560no—
50C22×D73—23360no—
51C22×D73—2480no—
52C22×D73C2×C22⋊C41840yescomplemented
53C22×D73C23×C41105yes—
54C22×D73C23×C41240yescomplemented
55C22×D73C23×C41120yescomplemented
56C22×D73C22×D41280yes—
57C22×D73C25116yes—
58C22×D73C25115yes—
59C2×#64408—2480no—
60C2×#64408C25132yescomplemented
61C22×C73—2240no—
62C22×C73C22×C22⋊C41140yescomplemented
63C22×C73C24×C4115yes—
64C22×C73C24×C4116yescomplemented
65C2×D73—2240no—
66C2×D73—232no—
67C2×D73—2480no—
68C2×D73C22×C22⋊C41420yescomplemented
69C2×D73C24×C4115yes—
70C2×D73C24×C4116yescomplemented
71C2×D73C23×D4160yes—
72C2×D73C2611yescharacteristic
73#64408—232no—
74C24×C22⋊C4—731nomaximal, Sylow
75C2×C73—216no—
76C2×C73C23×C22⋊C4130yescomplemented
77C2×C73C25×C411yescharacteristic
78D73—216no—
79D73C23×C22⋊C4130yescomplemented
80D73C24×D412yes—
81C27—731no—
82C25×C4—732no—
83C23×C22⋊C4—7360no—
84C73C24×C22⋊C411yescharacteristic, complemented, Sylow
85C26—731no—
86C26—731no—
87C26—7330no—
88C26—7330no—
89C26—14632no—
90C26#6440811yescharacteristic, complemented
91C24×C4—7360no—
92C24×C4—14632no—
93C22×C22⋊C4—73560no—
94C25—216no—
95C25—7332no—
96C25—7315no—
97C25—7315no—
98C25—7330no—
99C25—73140no—
100C25—73420no—
101C25—146480no—
102C25—146480no—
103C25—14616no—
104C25C2×#6440811yescharacteristic
105C25C2×#64408130yescomplemented
106C23×C4—73280no—
107C23×C4—146480no—
108C2×C22⋊C4—73960no—
109C24—2240no—
110C24—73105no—
111C24—7335no—
112C24—73240no—
113C24—73240no—
114C24—73140no—
115C24—73840no—
116C24—73120no—
117C24—1461120no—
118C24—1463360no—
119C24—146240no—
120C24C22⋊#64408116yesdirect product factor
121C24C22×#64408115yes—
122C24C22×#644081140yescomplemented
123C22×C4—73240no—
124C22×C4—1461120no—
125C22⋊C4—73256no—
126C23—2560no—
127C23—73280no—
128C23—73840no—
129C23—7315no—
130C23—73105no—
131C23—73120no—
132C23—7316no—
133C23—73240no—
134C23—146480no—
135C23—1463360no—
136C23—146560no—
137C23C2×C22⋊#644081120yesdirect product factor
138C23C23×#64408135yes—
139C23C23×#644081120yescomplemented
140C2×C4—7332no—
141C2×C4—146480no—
142C22—2240no—
143C22—7360no—
144C22—73420no—
145C22—731no—
146C22—7315no—
147C22—7316no—
148C22—14632no—
149C22—146480no—
150C22—146240no—
151C22C22×C22⋊#644081140yesdirect product factor
152C22C24×#64408115yes—
153C22C24×#64408116yescomplemented
154C4—14632no—
155C2—216no—
156C2—732no—
157C2—7330no—
158C2—14616no—
159C2C23×C22⋊#64408130yesdirect product factor
160C2C25×#6440811yescharacteristic
subgroupG/H
centerC25C2×#64408
commutatorC2×C73C25×C4
FrattiniC2C25×#64408
FittingC26×C73C4
socleC25×C73C2×C4
prime radicalC26×D73C2
cosocleC2×D73C26
hypercenterC26#64408
hypocenterC73C24×C22⋊C4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C25 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C25×#64408C2semidirect
2. C23×C22⋊#64408C2direct (N × H)
5. C24×#64408C22semidirect
6. C22×C22⋊#64408C22direct (N × H)
8. C25×D73C4semidirect
9. C25×D73C4semidirect
12. C26×C73C4semidirect
14. C23×#64408C23semidirect
15. C2×C22⋊#64408C23direct (N × H)
20. C24×D73C2×C4semidirect
21. C24×D73C2×C4semidirect
27. C25×C73C2×C4semidirect
29. C22×#64408C24semidirect
30. C22⋊#64408C24direct (N × H)
34. C23×D73C22⋊C4semidirect
36. C23×D73C22×C4semidirect
37. C23×D73C22×C4semidirect
42. C24×C73C22⋊C4semidirect
44. C24×C73C22×C4semidirect
46. C23×C73C2×C22⋊C4semidirect
48. C23×C73C23×C4semidirect
52. C22×D73C2×C22⋊C4semidirect
54. C22×D73C23×C4semidirect
55. C22×D73C23×C4semidirect
60. C2×#64408C25semidirect
62. C22×C73C22×C22⋊C4semidirect
64. C22×C73C24×C4semidirect
68. C2×D73C22×C22⋊C4semidirect
70. C2×D73C24×C4semidirect
76. C2×C73C23×C22⋊C4semidirect
79. D73C23×C22⋊C4semidirect
84. C73C24×C22⋊C4semidirect
90. C26#64408semidirect
105. C25C2×#64408semidirect
120. C24C22⋊#64408direct (N × H)
122. C24C22×#64408semidirect
137. C23C2×C22⋊#64408direct (N × H)
139. C23C23×#64408semidirect
151. C22C22×C22⋊#64408direct (N × H)
153. C22C24×#64408semidirect
159. C2C23×C22⋊#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×C22⋊#644082
C26×D732
C24×C22⋊C473