Finite Group Databasebeta

← #120×D503 #44566765

Subgroups — #120×D503 #44566765

Order 32192.

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×D503C211yesmaximal, characteristic, complemented
2C2×D4×D503C213yesmaximal, complemented
3#30632834C213yesmaximal, complemented
4#30632833C211yesmaximal, characteristic, complemented
5#30632832C213yesmaximal, complemented
6C22⋊C4×D503C213yesmaximal, complemented
7#120×C503C211yesmaximal, characteristic, complemented
8C23×D503—212no—
9C23×D503C2213yes—
10C23×D503C2213yescomplemented
11C23×D503C2211yescharacteristic, complemented
12C2×D2012C2213yescomplemented
13C2×C22⋊D503C2213yescomplemented
14C2×C22⋊D503C2213yescomplemented
15D4×D503—212no—
16C2×C4×D503C2213yescomplemented
17C22⋊Dic503C2213yescomplemented
18(C2×D503)⋊C4C2216yescomplemented
19C24×C503C2211yescharacteristic, complemented
20C2×D4×C503C2213yescomplemented
21C22⋊C4×C503C2213yescomplemented
22C22×D503—232no—
23C22×D503—26no—
24C22×D503—212no—
25C22×D503—212no—
26C22×D503—26no—
27C22×D503D4112yescomplemented
28C22×D503C2313yes—
29C22×D503C2311yescharacteristic
30C22×D503C2311yescharacteristic, complemented
31D2012—26no—
32C22⋊D503—26no—
33C22⋊D503—26no—
34C2×Dic503C2313yescomplemented
35C4×D503—26no—
36C23×C503—26no—
37C23×C503C2313yes—
38C23×C503C2311yescharacteristic, complemented
39D4×C503—26no—
40C2×C4×C503C2313yescomplemented
41C22×C503—28no—
42C22×C503—26no—
43C22×C503—23no—
44C22×C503C2×D416yescomplemented
45C22×C503C2411yescharacteristic
46C2×D503—224no—
47C2×D503—26no—
48C2×D503—224no—
49C2×D503—23no—
50C2×D503—44no—
51C2×D503C2×D416yes—
52C2×D503C2×D416yescomplemented
53C4×C503—23no—
54Dic503—23no—
55C2×C503—26no—
56C2×C503—41no—
57C2×C503C22×D413yes—
58D503—26no—
59D503—41no—
60D503#12014yesdirect product factor
61C503C2×#12011yescharacteristic, complemented, Sylow
62C2×#120—5031nomaximal, Sylow
63C25—5031no—
64C22×D4—5033no—
65#120—5031no—
66#120—5033no—
67#120—5033no—
68#120D50311yescharacteristic, direct product factor
69C2×C22⋊C4—5033no—
70C24—100612no—
71C24—5033no—
72C24—5031no—
73C24—5033no—
74C24C2×D50311yescharacteristic, complemented
75C2×D4—100612no—
76C2×D4—5033no—
77C2×D4—5033no—
78C2×D4—5033no—
79C2×D4C2×D50313yescomplemented
80C22×C4—5033no—
81C22⋊C4—5033no—
82C22⋊C4—5036no—
83C22⋊C4C2×D50313yescomplemented
84C23—26no—
85C23—10066no—
86C23—100632no—
87C23—100612no—
88C23—100612no—
89C23—10066no—
90C23—5031no—
91C23—50312no—
92C23—5033no—
93C23—5031no—
94C23C22×D50313yes—
95C23C22×D50311yescharacteristic, complemented
96D4—26no—
97D4—10066no—
98D4—10066no—
99D4—10066no—
100C2×C4—10066no—
101C2×C4—5033no—
102C2×C4C22×D50313yescomplemented
103C22—28no—
104C22—26no—
105C22—23no—
106C22—20124no—
107C22—100624no—
108C22—100624no—
109C22—10063no—
110C22—10066no—
111C22—5036no—
112C22—5036no—
113C22D4×D50316yescomplemented
114C22C23×D50311yescharacteristic
115C4—23no—
116C4—10063no—
117C2—26no—
118C2—41no—
119C2—20121no—
120C2—10066no—
121C2—5034no—
122C2C2×D4×D50313yes—
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
Fitting#120×C503C2
hypercenter#120D503
hypocenterC503C2×#120
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×D503C2semidirect
2. C2×D4×D503C2semidirect
3. #30632834C2semidirect
4. #30632833C2semidirect
5. #30632832C2semidirect
6. C22⋊C4×D503C2semidirect
7. #120×C503C2semidirect
10. C23×D503C22semidirect
11. C23×D503C22semidirect
12. C2×D2012C22semidirect
13. C2×C22⋊D503C22semidirect
14. C2×C22⋊D503C22semidirect
16. C2×C4×D503C22semidirect
17. C22⋊Dic503C22semidirect
18. (C2×D503)⋊C4C22semidirect
19. C24×C503C22semidirect
20. C2×D4×C503C22semidirect
21. C22⋊C4×C503C22semidirect
27. C22×D503D4semidirect
30. C22×D503C23semidirect
34. C2×Dic503C23semidirect
38. C23×C503C23semidirect
40. C2×C4×C503C23semidirect
44. C22×C503C2×D4semidirect
52. C2×D503C2×D4semidirect
60. D503#120direct (N × H)
61. C503C2×#120semidirect
68. #120D503direct (N × H)
74. C24C2×D503semidirect
79. C2×D4C2×D503semidirect
83. C22⋊C4C2×D503semidirect
95. C23C22×D503semidirect
102. C2×C4C22×D503semidirect
113. C22D4×D503semidirect

Maximal subgroups

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

subgroupindex
C24×D5032
C2×D4×D5032
#306328342
#306328332
#306328322
C22⋊C4×D5032
#120×C5032
C2×#120503