Finite Group Databasebeta

← #120×D479 #44500879

Subgroups — #120×D479 #44500879

Order 30656.

662 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 131 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
2C2×D4×D479C213yesmaximal, complemented
3#29506352C213yesmaximal, complemented
4#29506351C211yesmaximal, characteristic, complemented
5#29506350C213yesmaximal, complemented
6C22⋊C4×D479C213yesmaximal, complemented
7#120×C479C211yesmaximal, characteristic, complemented
8C23×D479—212no—
9C23×D479C2213yes—
10C23×D479C2213yescomplemented
11C23×D479C2211yescharacteristic, complemented
12C2×D1916C2213yescomplemented
13C2×C22⋊D479C2213yescomplemented
14C2×C22⋊D479C2213yescomplemented
15D4×D479—212no—
16C2×C4×D479C2213yescomplemented
17C22⋊Dic479C2213yescomplemented
18(C2×D479)⋊C4C2216yescomplemented
19C24×C479C2211yescharacteristic, complemented
20C2×D4×C479C2213yescomplemented
21C22⋊C4×C479C2213yescomplemented
22C22×D479—232no—
23C22×D479—26no—
24C22×D479—212no—
25C22×D479—212no—
26C22×D479—26no—
27C22×D479D4112yescomplemented
28C22×D479C2313yes—
29C22×D479C2311yescharacteristic
30C22×D479C2311yescharacteristic, complemented
31D1916—26no—
32C22⋊D479—26no—
33C22⋊D479—26no—
34C2×Dic479C2313yescomplemented
35C4×D479—26no—
36C23×C479—26no—
37C23×C479C2313yes—
38C23×C479C2311yescharacteristic, complemented
39D4×C479—26no—
40C2×C4×C479C2313yescomplemented
41C22×C479—28no—
42C22×C479—26no—
43C22×C479—23no—
44C22×C479C2×D416yescomplemented
45C22×C479C2411yescharacteristic
46C2×D479—224no—
47C2×D479—26no—
48C2×D479—224no—
49C2×D479—23no—
50C2×D479—44no—
51C2×D479C2×D416yes—
52C2×D479C2×D416yescomplemented
53C4×C479—23no—
54Dic479—23no—
55C2×C479—26no—
56C2×C479—41no—
57C2×C479C22×D413yes—
58D479—26no—
59D479—41no—
60D479#12014yesdirect product factor
61C479C2×#12011yescharacteristic, complemented, Sylow
62C2×#120—4791nomaximal, Sylow
63C25—4791no—
64C22×D4—4793no—
65#120—4791no—
66#120—4793no—
67#120—4793no—
68#120D47911yescharacteristic, direct product factor
69C2×C22⋊C4—4793no—
70C24—95812no—
71C24—4793no—
72C24—4791no—
73C24—4793no—
74C24C2×D47911yescharacteristic, complemented
75C2×D4—95812no—
76C2×D4—4793no—
77C2×D4—4793no—
78C2×D4—4793no—
79C2×D4C2×D47913yescomplemented
80C22×C4—4793no—
81C22⋊C4—4793no—
82C22⋊C4—4796no—
83C22⋊C4C2×D47913yescomplemented
84C23—26no—
85C23—9586no—
86C23—95832no—
87C23—95812no—
88C23—95812no—
89C23—9586no—
90C23—4791no—
91C23—47912no—
92C23—4793no—
93C23—4791no—
94C23C22×D47913yes—
95C23C22×D47911yescharacteristic, complemented
96D4—26no—
97D4—9586no—
98D4—9586no—
99D4—9586no—
100C2×C4—9586no—
101C2×C4—4793no—
102C2×C4C22×D47913yescomplemented
103C22—28no—
104C22—26no—
105C22—23no—
106C22—19164no—
107C22—95824no—
108C22—95824no—
109C22—9583no—
110C22—9586no—
111C22—4796no—
112C22—4796no—
113C22D4×D47916yescomplemented
114C22C23×D47911yescharacteristic
115C4—23no—
116C4—9583no—
117C2—26no—
118C2—41no—
119C2—19161no—
120C2—9586no—
121C2—4794no—
122C2C2×D4×D47913yes—
subgroupG/H
center, FrattiniC22C23×D479
commutator, socle, cosocleC22×C479C24
Fitting#120×C479C2
hypercenter#120D479
hypocenterC479C2×#120
LCSG ▷ C22×C479 ▷ C479
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×D479C2semidirect
2. C2×D4×D479C2semidirect
3. #29506352C2semidirect
4. #29506351C2semidirect
5. #29506350C2semidirect
6. C22⋊C4×D479C2semidirect
7. #120×C479C2semidirect
10. C23×D479C22semidirect
11. C23×D479C22semidirect
12. C2×D1916C22semidirect
13. C2×C22⋊D479C22semidirect
14. C2×C22⋊D479C22semidirect
16. C2×C4×D479C22semidirect
17. C22⋊Dic479C22semidirect
18. (C2×D479)⋊C4C22semidirect
19. C24×C479C22semidirect
20. C2×D4×C479C22semidirect
21. C22⋊C4×C479C22semidirect
27. C22×D479D4semidirect
30. C22×D479C23semidirect
34. C2×Dic479C23semidirect
38. C23×C479C23semidirect
40. C2×C4×C479C23semidirect
44. C22×C479C2×D4semidirect
52. C2×D479C2×D4semidirect
60. D479#120direct (N × H)
61. C479C2×#120semidirect
68. #120D479direct (N × H)
74. C24C2×D479semidirect
79. C2×D4C2×D479semidirect
83. C22⋊C4C2×D479semidirect
95. C23C22×D479semidirect
102. C2×C4C22×D479semidirect
113. C22D4×D479semidirect

Maximal subgroups

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

subgroupindex
C24×D4792
C2×D4×D4792
#295063522
#295063512
#295063502
C22⋊C4×D4792
#120×C4792
C2×#120479