Finite Group Databasebeta

← C32×D35⋊D17 #36339451

Subgroups — C32×D35⋊D17 #36339451

Order 21420.

240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C32×C5×D119C211yesmaximal, characteristic, complemented
2C32×C7×D85C211yesmaximal, characteristic, complemented
3C32×C17×D35C211yesmaximal, characteristic, complemented
4C3×D35⋊D17C314yesmaximal, direct product factor
5C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
6C32×D7×D17—51nomaximal, Hall
7C3×C17×D35C2×C314yescomplemented
8C3×C7×D85C2×C314yescomplemented
9C3×C5×D119C2×C314yescomplemented
10C32×D5×D17—71nomaximal, Hall
11D35⋊D17C3211yescharacteristic, direct product factor, Hall
12C32×D119D511yescharacteristic, complemented
13C32×D7×C17—51no—
14C32×C7×D17—51no—
15C3×C5×C7×C17C22×C314yescomplemented
16C32×D85D711yescharacteristic, complemented
17C32×D5×C17—71no—
18C32×C5×D17—71no—
19C3×D7×D17—54no—
20C32×D5×D7—171nomaximal, Hall
21C17×D35C2×C3211yescharacteristic, complemented
22C7×D85C2×C3211yescharacteristic, complemented
23C5×D119C2×C3211yescharacteristic, complemented
24C32×C7×C17C2×D511yescharacteristic, complemented, Hall
25C3×D5×D17—74no—
26C32×C5×C17C2×D711yescharacteristic, complemented, Hall
27C3×D119C3×D514yescomplemented
28C3×D7×C17—54no—
29C3×C7×D17—54no—
30C32×D35D1711yescharacteristic, complemented
31C32×C7×D5—171no—
32C32×C5×D7—171no—
33C2×C32×D17—351noHall
34C5×C7×C17C22×C3211yescharacteristic, complemented, Hall
35C3×D85C3×D714yescomplemented
36C3×D5×C17—74no—
37C3×C5×D17—74no—
38D7×D17—51noHall
39C3×D5×D7—174no—
40C3×C7×C17C2×C3×D514yescomplemented
41D5×D17—71noHall
42C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
43C2×C32×C17—351no—
44C32×D17—51no—
45C32×D17—71no—
46C3×C5×C17C2×C3×D714yescomplemented
47C2×C32×D7—851noHall
48D119C32×D511yescharacteristic, complemented
49C7×D17—51no—
50D7×C17—51no—
51C3×D35C3×D1714yescomplemented
52C3×C7×D5—174no—
53C3×C5×D7—174no—
54C2×C3×D17—354no—
55C2×C32×D5—1191noHall
56D85C32×D711yescharacteristic, complemented
57C5×D17—71no—
58D5×C17—71no—
59C32×C17D5×D711yescharacteristic, complemented, Hall
60D5×D7—171noHall
61C2×C32×C7—851no—
62C32×D7—51no—
63C32×D7—171no—
64C7×C17C2×C32×D511yescharacteristic, complemented, Hall
65C3×C5×C7C2×C3×D1714yescomplemented
66C2×C3×C17—354no—
67C3×D17—54no—
68C3×D17—74no—
69C2×C32×C5—1191no—
70C32×D5—71no—
71C32×D5—171no—
72C5×C17C2×C32×D711yescharacteristic, complemented, Hall
73C2×C3×D7—854no—
74D35C32×D1711yescharacteristic, complemented
75C5×D7—171no—
76C7×D5—171no—
77C2×D17—351noHall
78C32×C7D5×D1711yescharacteristic, complemented, Hall
79C2×C3×D5—1194no—
80C3×C17C3×D5×D714yescomplemented
81C32×C5D7×D1711yescharacteristic, complemented, Hall
82C2×C3×C7—854no—
83C3×D7—54no—
84C3×D7—174no—
85C22×C32—5951noHall
86C5×C7C2×C32×D1711yescharacteristic, complemented, Hall
87C2×C17—351no—
88D17—51no—
89D17—71no—
90C2×C3×C5—1194no—
91C3×D5—74no—
92C3×D5—174no—
93C2×D7—851noHall
94C3×C7C3×D5×D1714yescomplemented
95C2×D5—1191noHall
96C2×C32—351no—
97C2×C32—851no—
98C2×C32—1191no—
99C17C32×D5×D711yescharacteristic, complemented, Sylow
100C3×C5C3×D7×D1714yescomplemented
101C2×C7—851no—
102D7—51no—
103D7—171no—
104C22×C3—5954no—
105C2×C5—1191no—
106D5—71no—
107D5—171no—
108C32D35⋊D1711yescharacteristic, direct product factor, Sylow
109C7C32×D5×D1711yescharacteristic, complemented, Sylow
110C2×C3—354no—
111C2×C3—854no—
112C2×C3—1194no—
113C5C32×D7×D1711yescharacteristic, complemented, Sylow
114C22—5951noSylow
115C3C3×D35⋊D1714yesdirect product factor
116C2—351no—
117C2—851no—
118C2—1191no—
subgroupG/H
center, hypercenterC32D35⋊D17
commutator, cosocle, hypocenterC5×C7×C17C22×C32
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C5×C7×C17
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C5×D119C2semidirect
2. C32×C7×D85C2semidirect
3. C32×C17×D35C2semidirect
4. C3×D35⋊D17C3direct (N × H)
5. C32×C5×C7×C17C22semidirect
7. C3×C17×D35C2×C3semidirect
8. C3×C7×D85C2×C3semidirect
9. C3×C5×D119C2×C3semidirect
11. D35⋊D17C32direct (N × H)
12. C32×D119D5semidirect
15. C3×C5×C7×C17C22×C3semidirect
16. C32×D85D7semidirect
21. C17×D35C2×C32semidirect
22. C7×D85C2×C32semidirect
23. C5×D119C2×C32semidirect
24. C32×C7×C17C2×D5semidirect
26. C32×C5×C17C2×D7semidirect
27. C3×D119C3×D5semidirect
30. C32×D35D17semidirect
34. C5×C7×C17C22×C32semidirect
35. C3×D85C3×D7semidirect
40. C3×C7×C17C2×C3×D5semidirect
42. C32×C5×C7C2×D17semidirect
46. C3×C5×C17C2×C3×D7semidirect
48. D119C32×D5semidirect
51. C3×D35C3×D17semidirect
56. D85C32×D7semidirect
59. C32×C17D5×D7semidirect
64. C7×C17C2×C32×D5semidirect
65. C3×C5×C7C2×C3×D17semidirect
72. C5×C17C2×C32×D7semidirect
74. D35C32×D17semidirect
78. C32×C7D5×D17semidirect
80. C3×C17C3×D5×D7semidirect
81. C32×C5D7×D17semidirect
86. C5×C7C2×C32×D17semidirect
94. C3×C7C3×D5×D17semidirect
99. C17C32×D5×D7semidirect
100. C3×C5C3×D7×D17semidirect
108. C32D35⋊D17direct (N × H)
109. C7C32×D5×D17semidirect
113. C5C32×D7×D17semidirect
115. C3C3×D35⋊D17direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D1192
C32×C7×D852
C32×C17×D352
C3×D35⋊D173
C32×D7×D175
C32×D5×D177
C32×D5×D717