Finite Group Databasebeta

← C3×C3⋊(C7⋊#10596817) #49141572

Subgroups — C3×C3⋊(C7⋊#10596817) #49141572

Order 36540.

112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 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
2C3⋊(C7⋊#10596817)C311yesmaximal, characteristic, direct product factor
3C3×C7⋊#10596817—31nomaximal
4C32×C5×C7×C29C411yescharacteristic, complemented, Hall
5C3×C3⋊(C7⋊#1181)—51nomaximal, Hall
6C3×C5×C7×D29—21no—
7C3×C5×C7×D29D311yescharacteristic
8C3×C5×C7×D29C2×C311yescharacteristic
9C3×C3⋊#10596817—71nomaximal, Hall
10C7⋊#10596817—31noHall
11C32×C7×D29D511yescharacteristic
12C3×C5×C7×C29—21no—
13C3×C5×C7×C29Dic311yescharacteristic, complemented
14C3×C5×C7×C29C3×C411yescharacteristic, complemented
15C32×C5×D29D711yescharacteristic
16C3⋊(C7⋊#1181)—51no—
17C3×C7⋊#1181—151no—
18C5×C7×D29C3×D311yescharacteristic
19C32×C7×C29Dic511yescharacteristic, complemented, Hall
20C3⋊#10596817—71no—
21C3×#10596817—211no—
22C32×C5×C29Dic711yescharacteristic, complemented, Hall
23C3×Dic105—291nomaximal, Hall
24C3×C7×D29—21no—
25C3×C7×D29C3×D511yescharacteristic
26C3×C7×D29D1511yescharacteristic
27C3×C3⋊#1181—351noHall
28C5×C7×C29C3×Dic311yescharacteristic, complemented, Hall
29C3×C5×D29—21no—
30C3×C5×D29C3×D711yescharacteristic
31C3×C5×D29D2111yescharacteristic
32C7⋊#1181—151noHall
33C2×C32×C5×C7—291no—
34C3×C7×C29—21no—
35C3×C7×C29C3×Dic511yescharacteristic, complemented
36C3×C7×C29Dic1511yescharacteristic, complemented
37#10596817—211noHall
38C32×D29D3511yescharacteristic
39C3×C5×C29—21no—
40C3×C5×C29C3×Dic711yescharacteristic, complemented
41C3×C5×C29Dic2111yescharacteristic, complemented
42Dic105—291no—
43C3×Dic35—871no—
44C7×D29C3×D1511yescharacteristic
45C3⋊#1181—351no—
46C3×#1181—1051no—
47C32×C5×C7#118111yescharacteristic, complemented, Hall
48C5×D29C3×D2111yescharacteristic
49C32×C29Dic3511yescharacteristic, complemented, Hall
50C3×Dic21—1451noHall
51C2×C3×C5×C7—291no—
52C2×C3×C5×C7—291no—
53C2×C3×C5×C7—581no—
54C7×C29C3×Dic1511yescharacteristic, complemented, Hall
55C3×Dic15—2031noHall
56C3×D29—21no—
57C3×D29C3×D3511yescharacteristic
58C3×D29D10511yescharacteristic
59C5×C29C3×Dic2111yescharacteristic, complemented, Hall
60Dic35—871noHall
61C2×C32×C7—291no—
62#1181—1051noHall
63C3×C5×C7—21no—
64C3×C5×C7C3×#118111yescharacteristic, complemented
65C3×C5×C7C3⋊#118111yescharacteristic, complemented
66C2×C32×C5—291no—
67C3×C29—21no—
68C3×C29C3×Dic3511yescharacteristic, complemented
69C3×C29Dic10511yescharacteristic, complemented
70Dic21—1451no—
71C3×Dic7—4351no—
72C2×C5×C7—291no—
73C32×C7#1059681711yescharacteristic, complemented, Hall
74Dic15—2031no—
75C3×Dic5—6091no—
76D29C3×D10511yescharacteristic
77C32×C5C7⋊#118111yescharacteristic, complemented, Hall
78C2×C3×C7—291no—
79C2×C3×C7—291no—
80C2×C3×C7—581no—
81C3×Dic3—10151noHall
82C5×C7C3×C3⋊#118111yescharacteristic, complemented, Hall
83C2×C3×C5—291no—
84C2×C3×C5—291no—
85C2×C3×C5—581no—
86C29C3×Dic10511yescharacteristic, complemented, Sylow
87Dic7—4351noHall
88C3×C7—21no—
89C3×C7C3×#1059681711yescharacteristic, complemented
90C3×C7C3⋊#1059681711yescharacteristic, complemented
91Dic5—6091noHall
92C2×C32—291no—
93C3×C5—21no—
94C3×C5C3×C7⋊#118111yescharacteristic, complemented
95C3×C5C3⋊(C7⋊#1181)11yescharacteristic, complemented
96C2×C7—291no—
97C3×C4—30451no—
98Dic3—10151no—
99C2×C5—291no—
100C32C7⋊#1059681711yescharacteristic, complemented, Sylow
101C7C3×C3⋊#1059681711yescharacteristic, complemented, Sylow
102C2×C3—291no—
103C2×C3—291no—
104C2×C3—581no—
105C5C3×C3⋊(C7⋊#1181)11yescharacteristic, complemented, Sylow
106C4—30451noSylow
107C3—21no—
108C3C3×C7⋊#1059681711yescharacteristic, complemented
109C3C3⋊(C7⋊#10596817)11yescharacteristic, direct product factor
110C2—291no—
subgroupG/H
center, hypercenterC3C3⋊(C7⋊#10596817)
commutator, hypocenterC3×C5×C7×C29C3×C4
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C5×C7×D29C2
cosocleC3×C5×C7×D29C2×C3
LCSG ▷ C3×C5×C7×C29
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3⋊(C7⋊#10596817)C3direct (N × H)
4. C32×C5×C7×C29C4semidirect
13. C3×C5×C7×C29Dic3semidirect
14. C3×C5×C7×C29C3×C4semidirect
19. C32×C7×C29Dic5semidirect
22. C32×C5×C29Dic7semidirect
28. C5×C7×C29C3×Dic3semidirect
35. C3×C7×C29C3×Dic5semidirect
36. C3×C7×C29Dic15semidirect
40. C3×C5×C29C3×Dic7semidirect
41. C3×C5×C29Dic21semidirect
47. C32×C5×C7#1181semidirect
49. C32×C29Dic35semidirect
54. C7×C29C3×Dic15semidirect
59. C5×C29C3×Dic21semidirect
64. C3×C5×C7C3×#1181semidirect
65. C3×C5×C7C3⋊#1181semidirect
68. C3×C29C3×Dic35semidirect
69. C3×C29Dic105semidirect
73. C32×C7#10596817semidirect
77. C32×C5C7⋊#1181semidirect
82. C5×C7C3×C3⋊#1181semidirect
86. C29C3×Dic105semidirect
89. C3×C7C3×#10596817semidirect
90. C3×C7C3⋊#10596817semidirect
94. C3×C5C3×C7⋊#1181semidirect
95. C3×C5C3⋊(C7⋊#1181)semidirect
100. C32C7⋊#10596817semidirect
101. C7C3×C3⋊#10596817semidirect
105. C5C3×C3⋊(C7⋊#1181)semidirect
108. C3C3×C7⋊#10596817semidirect
109. C3C3⋊(C7⋊#10596817)direct (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
C3⋊(C7⋊#10596817)3
C3×C7⋊#105968173
C3×C3⋊(C7⋊#1181)5
C3×C3⋊#105968177
C3×Dic10529