Finite Group Databasebeta

← C3×C5×C7×C3⋊#1181 #49141554

Subgroups — C3×C5×C7×C3⋊#1181 #49141554

Order 36540.

112 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 56 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×C7×D29C211yesmaximal, characteristic
2C5×C7×C3⋊#1181C311yesmaximal, characteristic, direct product factor
3C3×C5×C7×#1181—31nomaximal
4C32×C5×C7×C29C411yescharacteristic, complemented, Hall
5C3×C7×C3⋊#1181C511yesmaximal, characteristic, direct product factor, Hall
6C3×C5×C7×D29—21no—
7C3×C5×C7×D29D311yescharacteristic
8C3×C5×C7×D29C2×C311yescharacteristic
9C3×C5×C3⋊#1181C711yesmaximal, characteristic, direct product factor, Hall
10C5×C7×#1181—31noHall
11C32×C7×D29C2×C511yescharacteristic
12C3×C5×C7×C29—21no—
13C3×C5×C7×C29Dic311yescharacteristic, complemented
14C3×C5×C7×C29C3×C411yescharacteristic, complemented
15C32×C5×D29C2×C711yescharacteristic
16C7×C3⋊#1181C3×C511yescharacteristic, direct product factor
17C3×C7×#1181—31no—
18C5×C7×D29C3×D311yescharacteristic
19C32×C7×C29C4×C511yescharacteristic, complemented, Hall
20C5×C3⋊#1181C3×C711yescharacteristic, direct product factor
21C3×C5×#1181—31no—
22C32×C5×C29C4×C711yescharacteristic, complemented, Hall
23C3×C5×C7×Dic3—291nomaximal, Hall
24C3×C7×D29—21no—
25C3×C7×D29C5×D311yescharacteristic
26C3×C7×D29C2×C3×C511yescharacteristic
27C3×C3⋊#1181C5×C711yescharacteristic, direct product factor, Hall
28C5×C7×C29C3×Dic311yescharacteristic, complemented, Hall
29C3×C5×D29—21no—
30C3×C5×D29D3×C711yescharacteristic
31C3×C5×D29C2×C3×C711yescharacteristic
32C7×#1181—31noHall
33C2×C32×C5×C7—291no—
34C3×C7×C29—21no—
35C3×C7×C29C5×Dic311yescharacteristic, complemented
36C3×C7×C29C3×C4×C511yescharacteristic, complemented
37C5×#1181—31noHall
38C32×D29C2×C5×C711yescharacteristic
39C3×C5×C29—21no—
40C3×C5×C29C7×Dic311yescharacteristic, complemented
41C3×C5×C29C3×C4×C711yescharacteristic, complemented
42C3×C4×C5×C7—871no—
43C5×C7×Dic3—291no—
44C7×D29C3×C5×D311yescharacteristic
45C3⋊#1181C3×C5×C711yescharacteristic, direct product factor
46C3×#1181—31no—
47C32×C5×C7#118111yescharacteristic, complemented, Hall
48C5×D29C3×D3×C711yescharacteristic
49C32×C29C4×C5×C711yescharacteristic, complemented, Hall
50C3×C7×Dic3—291noHall
51C2×C3×C5×C7—291no—
52C2×C3×C5×C7—291no—
53C2×C3×C5×C7—581no—
54C7×C29C3×C5×Dic311yescharacteristic, complemented, Hall
55C3×C5×Dic3—291noHall
56C3×D29—21no—
57C3×D29C5×D3×C711yescharacteristic
58C3×D29C2×C3×C5×C711yescharacteristic
59C5×C29C3×C7×Dic311yescharacteristic, complemented, Hall
60C4×C5×C7—871noHall
61C2×C32×C7—291no—
62#1181—31noHall
63C3×C5×C7—21no—
64C3×C5×C7C3×#118111yescharacteristic, complemented
65C3×C5×C7C3⋊#118111yescharacteristic, direct product factor
66C2×C32×C5—291no—
67C3×C29—21no—
68C3×C29C5×C7×Dic311yescharacteristic, complemented
69C3×C29C3×C4×C5×C711yescharacteristic, complemented
70C3×C4×C7—871no—
71C7×Dic3—291no—
72C2×C5×C7—291no—
73C32×C7C5×#118111yescharacteristic, complemented, Hall
74C3×C4×C5—871no—
75C5×Dic3—291no—
76D29C3×C5×D3×C711yescharacteristic
77C32×C5C7×#118111yescharacteristic, complemented, Hall
78C2×C3×C7—291no—
79C2×C3×C7—291no—
80C2×C3×C7—581no—
81C3×Dic3—291noHall
82C5×C7C3×C3⋊#118111yescharacteristic, direct product factor, Hall
83C2×C3×C5—291no—
84C2×C3×C5—291no—
85C2×C3×C5—581no—
86C29C3×C5×C7×Dic311yescharacteristic, complemented, Sylow
87C4×C7—871noHall
88C3×C7—21no—
89C3×C7C3×C5×#118111yescharacteristic, complemented
90C3×C7C5×C3⋊#118111yescharacteristic, direct product factor
91C4×C5—871noHall
92C2×C32—291no—
93C3×C5—21no—
94C3×C5C3×C7×#118111yescharacteristic, complemented
95C3×C5C7×C3⋊#118111yescharacteristic, direct product factor
96C2×C7—291no—
97C3×C4—871no—
98Dic3—291no—
99C2×C5—291no—
100C32C5×C7×#118111yescharacteristic, complemented, Sylow
101C7C3×C5×C3⋊#118111yescharacteristic, direct product factor, Sylow
102C2×C3—291no—
103C2×C3—291no—
104C2×C3—581no—
105C5C3×C7×C3⋊#118111yescharacteristic, direct product factor, Sylow
106C4—871noSylow
107C3—21no—
108C3C3×C5×C7×#118111yescharacteristic, complemented
109C3C5×C7×C3⋊#118111yescharacteristic, direct product factor
110C2—291no—
subgroupG/H
center, hypercenterC3×C5×C7C3⋊#1181
commutator, hypocenterC3×C29C3×C4×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C5×C7×D29C2
cosocleC3×D29C2×C3×C5×C7
LCSG ▷ C3×C29
UCSC1 ◁ C3×C5×C7

Complements

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

NH ≅ G/Ntype
2. C5×C7×C3⋊#1181C3direct (N × H)
4. C32×C5×C7×C29C4semidirect
5. C3×C7×C3⋊#1181C5direct (N × H)
9. C3×C5×C3⋊#1181C7direct (N × H)
13. C3×C5×C7×C29Dic3semidirect
14. C3×C5×C7×C29C3×C4semidirect
16. C7×C3⋊#1181C3×C5direct (N × H)
19. C32×C7×C29C4×C5semidirect
20. C5×C3⋊#1181C3×C7direct (N × H)
22. C32×C5×C29C4×C7semidirect
27. C3×C3⋊#1181C5×C7direct (N × H)
28. C5×C7×C29C3×Dic3semidirect
35. C3×C7×C29C5×Dic3semidirect
36. C3×C7×C29C3×C4×C5semidirect
40. C3×C5×C29C7×Dic3semidirect
41. C3×C5×C29C3×C4×C7semidirect
45. C3⋊#1181C3×C5×C7direct (N × H)
47. C32×C5×C7#1181semidirect
49. C32×C29C4×C5×C7semidirect
54. C7×C29C3×C5×Dic3semidirect
59. C5×C29C3×C7×Dic3semidirect
64. C3×C5×C7C3×#1181semidirect
65. C3×C5×C7C3⋊#1181direct (N × H)
68. C3×C29C5×C7×Dic3semidirect
69. C3×C29C3×C4×C5×C7semidirect
73. C32×C7C5×#1181semidirect
77. C32×C5C7×#1181semidirect
82. C5×C7C3×C3⋊#1181direct (N × H)
86. C29C3×C5×C7×Dic3semidirect
89. C3×C7C3×C5×#1181semidirect
90. C3×C7C5×C3⋊#1181direct (N × H)
94. C3×C5C3×C7×#1181semidirect
95. C3×C5C7×C3⋊#1181direct (N × H)
100. C32C5×C7×#1181semidirect
101. C7C3×C5×C3⋊#1181direct (N × H)
105. C5C3×C7×C3⋊#1181direct (N × H)
108. C3C3×C5×C7×#1181semidirect
109. C3C5×C7×C3⋊#1181direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C7×D292
C5×C7×C3⋊#11813
C3×C5×C7×#11813
C3×C7×C3⋊#11815
C3×C5×C3⋊#11817
C3×C5×C7×Dic329