Finite Group Databasebeta

← C2×#29506350 #44500880

Subgroups — C2×#29506350 #44500880

Order 30656.

662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 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×D479C211yesmaximal, characteristic, complemented
2C22×C22⋊D479C212yesmaximal, complemented
3#29506350C218yesmaximal, direct product factor
4C2×C22⋊Dic479C211yesmaximal, characteristic, complemented
5C2×(C2×D479)⋊C4C212yesmaximal, complemented
6C22×D4×C479C211yesmaximal, characteristic, complemented
7C23×D479—28no—
8C23×D479—24no—
9C23×D479C2212yes—
10C23×D479C2214yescomplemented
11C2×C22⋊D479—28no—
12C2×C22⋊D479C2218yescomplemented
13C22×Dic479C2212yescomplemented
14C22⋊Dic479C2214yescomplemented
15(C2×D479)⋊C4C2218yescomplemented
16C24×C479C2211yescharacteristic
17C24×C479C2211yescharacteristic, complemented
18C2×D4×C479—24no—
19C2×D4×C479C2214yescomplemented
20C22×C4×C479C2211yescharacteristic, complemented
21C22×D479—232no—
22C22×D479—24no—
23C22×D479—24no—
24C22×D479—28no—
25C22×D479—216no—
26C22×D479D418yescomplemented
27C22×D479C2314yes—
28C22⋊D479—216no—
29C2×Dic479—24no—
30C2×Dic479C2314yescomplemented
31C23×C479—24no—
32C23×C479—22no—
33C23×C479—24no—
34C23×C479D414yescomplemented
35C23×C479C2312yes—
36C23×C479C2311yescharacteristic
37C23×C479C2312yescomplemented
38D4×C479—28no—
39C2×C4×C479—22no—
40C2×C4×C479C2312yescomplemented
41C22×C479—28no—
42C22×C479—24no—
43C22×C479—22no—
44C22×C479—24no—
45C22×C479—44no—
46C22×C479C2×D414yes—
47C22×C479C2×D412yes—
48C22×C479C2×D414yescomplemented
49C22×C479C2411yescharacteristic
50C2×D479—232no—
51C2×D479—216no—
52C2×D479—24no—
53C2×D479—24no—
54C2×D479C2×D418yescomplemented
55C4×C479—22no—
56Dic479—24no—
57C2×C479—24no—
58C2×C479—42no—
59C2×C479#12014yescomplemented
60C2×C479C22×D412yes—
61C2×C479C22×D411yescharacteristic
62D479—28no—
63C479C2×#12011yescharacteristic, complemented, Sylow
64C2×#120—4791nomaximal, Sylow
65C25—4791no—
66C22×D4—4792no—
67C22×D4D47911yescharacteristic, complemented
68#120—4798no—
69C2×C22⋊C4—4791no—
70C2×C22⋊C4—4792no—
71C24—9588no—
72C24—9584no—
73C24—4794no—
74C24—4792no—
75C24C2×D47911yescharacteristic
76C24C2×D47911yescharacteristic, complemented
77C2×D4—24no—
78C2×D4—9588no—
79C2×D4—4798no—
80C2×D4C2×D47914yescomplemented
81C22×C4—4792no—
82C22×C4C2×D47911yescharacteristic, complemented
83C22⋊C4—4794no—
84C22⋊C4—4798no—
85C23—24no—
86C23—24no—
87C23—22no—
88C23—95832no—
89C23—95816no—
90C23—9584no—
91C23—9584no—
92C23—9588no—
93C23—4798no—
94C23—4794no—
95C23C22⋊D47914yescomplemented
96C23C22×D47912yes—
97C23C22×D47911yescharacteristic
98C23C22×D47912yescomplemented
99D4—28no—
100D4—95816no—
101C2×C4—22no—
102C2×C4—9584no—
103C2×C4—4794no—
104C2×C4C22×D47912yescomplemented
105C22—28no—
106C22—24no—
107C22—24no—
108C22—22no—
109C22—44no—
110C22—95832no—
111C22—95816no—
112C22—9584no—
113C22—9584no—
114C22—4798no—
115C22D4×D47914yes—
116C22C2×C22⋊D47912yes—
117C22C2×C22⋊D47914yescomplemented
118C22C23×D47911yescharacteristic
119C4—22no—
120C4—9584no—
121C2—24no—
122C2—42no—
123C2—9588no—
124C2#2950635014yesdirect product factor
125C2C2×D4×D47912yes—
126C2C22×C22⋊D47911yescharacteristic
subgroupG/H
centerC23C22×D479
commutator, cosocleC22×C479C24
FrattiniC22C23×D479
FittingC22×D4×C479C2
socleC23×C479C23
hypercenterC22×D4D479
hypocenterC479C2×#120
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×D479C2semidirect
2. C22×C22⋊D479C2semidirect
3. #29506350C2direct (N × H)
4. C2×C22⋊Dic479C2semidirect
5. C2×(C2×D479)⋊C4C2semidirect
6. C22×D4×C479C2semidirect
10. C23×D479C22semidirect
12. C2×C22⋊D479C22semidirect
13. C22×Dic479C22semidirect
14. C22⋊Dic479C22semidirect
15. (C2×D479)⋊C4C22semidirect
17. C24×C479C22semidirect
19. C2×D4×C479C22semidirect
20. C22×C4×C479C22semidirect
26. C22×D479D4semidirect
30. C2×Dic479C23semidirect
34. C23×C479D4semidirect
37. C23×C479C23semidirect
40. C2×C4×C479C23semidirect
48. C22×C479C2×D4semidirect
54. C2×D479C2×D4semidirect
59. C2×C479#120semidirect
63. C479C2×#120semidirect
67. C22×D4D479semidirect
76. C24C2×D479semidirect
80. C2×D4C2×D479semidirect
82. C22×C4C2×D479semidirect
95. C23C22⋊D479semidirect
98. C23C22×D479semidirect
104. C2×C4C22×D479semidirect
117. C22C2×C22⋊D479semidirect
124. C2#29506350direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D4792
C22×C22⋊D4792
#295063502
C2×C22⋊Dic4792
C2×(C2×D479)⋊C42
C22×D4×C4792
C2×#120479