Finite Group Databasebeta

← C3×C11⋊C5×C3⋊#595 #46778005

Subgroups — C3×C11⋊C5×C3⋊#595 #46778005

Order 33660.

112 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 42 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×D17×C11⋊C5C211yesmaximal, characteristic
2C11⋊C5×C3⋊#595C311yesmaximal, characteristic, direct product factor
3C3×C11⋊C5×#595—31nomaximal
4C32×C17×C11⋊C5C411yescharacteristic, complemented, Hall
5C3×C11×C3⋊#595C511yesmaximal, characteristic, complemented, Hall
6C3×D17×C11⋊C5—21no—
7C3×D17×C11⋊C5D311yescharacteristic
8C3×D17×C11⋊C5C2×C311yescharacteristic
9C11⋊C5×#595—31noHall
10C32×C11×D17C2×C511yescharacteristic
11C3×C5×C3⋊#595—111nomaximal, Hall
12C3×C17×C11⋊C5—21no—
13C3×C17×C11⋊C5Dic311yescharacteristic, complemented
14C3×C17×C11⋊C5C3×C411yescharacteristic, complemented
15C11×C3⋊#595C3×C511yescharacteristic, complemented
16C3×C11×#595—31no—
17C3×Dic3×C11⋊C5—171nomaximal, Hall
18D17×C11⋊C5C3×D311yescharacteristic
19C32×C11×C17C4×C511yescharacteristic, complemented, Hall
20C32×C5×D17—111no—
21C3×C11×D17—21no—
22C3×C11×D17C5×D311yescharacteristic
23C3×C11×D17C2×C3×C511yescharacteristic
24C5×C3⋊#595—111no—
25C3×C5×#595—331no—
26C2×C32×C11⋊C5—171no—
27C17×C11⋊C5C3×Dic311yescharacteristic, complemented, Hall
28C32×C5×C17—111noHall
29C11×#595—31noHall
30C3×C4×C11⋊C5—511no—
31Dic3×C11⋊C5—171no—
32C3×C3⋊#595C11⋊C511yescharacteristic, direct product factor, Hall
33C3×C11×C17—21no—
34C3×C11×C17C5×Dic311yescharacteristic, complemented
35C3×C11×C17C3×C4×C511yescharacteristic, complemented
36C3×C5×D17—111no—
37C3×C5×D17—111no—
38C3×C5×D17—221no—
39C32×C11⋊C5#59511yescharacteristic, complemented, Hall
40C3×C11×Dic3—171noHall
41C11×D17C3×C5×D311yescharacteristic
42C5×#595—331noHall
43C2×C3×C11⋊C5—171no—
44C2×C3×C11⋊C5—171no—
45C2×C3×C11⋊C5—341no—
46C32×D17C2×C11⋊C511yescharacteristic
47C3×C5×C17—111no—
48C3×C5×C17—111no—
49C3×C5×C17—221no—
50C4×C11⋊C5—511noHall
51C3⋊#595C3×C11⋊C511yescharacteristic, direct product factor
52C3×#595—31no—
53C2×C32×C11—171no—
54C11×C17C3×C5×Dic311yescharacteristic, complemented, Hall
55C3×C5×Dic3—1871noHall
56C5×D17—111no—
57C3×C11⋊C5—21no—
58C3×C11⋊C5C3×#59511yescharacteristic, complemented
59C3×C11⋊C5C3⋊#59511yescharacteristic, direct product factor
60C32×C17C4×C11⋊C511yescharacteristic, complemented, Hall
61C3×C4×C11—511no—
62C11×Dic3—171no—
63C2×C11⋊C5—171no—
64C3×D17—21no—
65C3×D17D3×C11⋊C511yescharacteristic
66C3×D17C2×C3×C11⋊C511yescharacteristic
67C32×C11C5×#59511yescharacteristic, complemented, Hall
68C2×C32×C5—1871no—
69C5×C17—111noHall
70#595—31noHall
71C2×C3×C11—171no—
72C2×C3×C11—171no—
73C2×C3×C11—341no—
74C3×C4×C5—5611no—
75C5×Dic3—1871no—
76C11⋊C5C3×C3⋊#59511yescharacteristic, direct product factor, Hall
77C3×C17—21no—
78C3×C17Dic3×C11⋊C511yescharacteristic, complemented
79C3×C17C3×C4×C11⋊C511yescharacteristic, complemented
80C32×C5—111noHall
81C4×C11—511noHall
82C3×Dic3—171noHall
83D17C3×D3×C11⋊C511yescharacteristic
84C3×C11—21no—
85C3×C11C3×C5×#59511yescharacteristic, complemented
86C3×C11C5×C3⋊#59511yescharacteristic, complemented
87C2×C3×C5—3741no—
88C2×C3×C5—1871no—
89C2×C3×C5—1871no—
90C2×C11—171no—
91C4×C5—5611noHall
92C2×C32—171no—
93C17C3×Dic3×C11⋊C511yescharacteristic, complemented, Sylow
94C3×C5—111no—
95C3×C5—111no—
96C3×C5—221no—
97C3×C4—511no—
98Dic3—171no—
99C11C3×C5×C3⋊#59511yescharacteristic, complemented, Sylow
100C2×C5—1871no—
101C32C11⋊C5×#59511yescharacteristic, complemented, Sylow
102C2×C3—171no—
103C2×C3—171no—
104C2×C3—341no—
105C5—111noSylow
106C4—511noSylow
107C3—21no—
108C3C3×C11⋊C5×#59511yescharacteristic, complemented
109C3C11⋊C5×C3⋊#59511yescharacteristic, direct product factor
110C2—171no—
subgroupG/H
center, hypercenterC3C11⋊C5×C3⋊#595
commutator, hypocenterC3×C11×C17C3×C4×C5
FrattiniC1G
Fitting, socleC32×C11×C17C4×C5
prime radicalC32×D17×C11⋊C5C2
cosocleC3×C11×D17C2×C3×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C11⋊C5×C3⋊#595C3direct (N × H)
4. C32×C17×C11⋊C5C4semidirect
5. C3×C11×C3⋊#595C5semidirect
13. C3×C17×C11⋊C5Dic3semidirect
14. C3×C17×C11⋊C5C3×C4semidirect
15. C11×C3⋊#595C3×C5semidirect
19. C32×C11×C17C4×C5semidirect
27. C17×C11⋊C5C3×Dic3semidirect
32. C3×C3⋊#595C11⋊C5direct (N × H)
34. C3×C11×C17C5×Dic3semidirect
35. C3×C11×C17C3×C4×C5semidirect
39. C32×C11⋊C5#595semidirect
51. C3⋊#595C3×C11⋊C5direct (N × H)
54. C11×C17C3×C5×Dic3semidirect
58. C3×C11⋊C5C3×#595semidirect
59. C3×C11⋊C5C3⋊#595direct (N × H)
60. C32×C17C4×C11⋊C5semidirect
67. C32×C11C5×#595semidirect
76. C11⋊C5C3×C3⋊#595direct (N × H)
78. C3×C17Dic3×C11⋊C5semidirect
79. C3×C17C3×C4×C11⋊C5semidirect
85. C3×C11C3×C5×#595semidirect
86. C3×C11C5×C3⋊#595semidirect
93. C17C3×Dic3×C11⋊C5semidirect
99. C11C3×C5×C3⋊#595semidirect
101. C32C11⋊C5×#595semidirect
108. C3C3×C11⋊C5×#595semidirect
109. C3C11⋊C5×C3⋊#595direct (N × H)

Maximal subgroups

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

subgroupindex
C32×D17×C11⋊C52
C11⋊C5×C3⋊#5953
C3×C11⋊C5×#5953
C3×C11×C3⋊#5955
C3×C5×C3⋊#59511
C3×Dic3×C11⋊C517