Finite Group Databasebeta

← C3×C3⋊(C7⋊#10596816) #49141569

Subgroups — C3×C3⋊(C7⋊#10596816) #49141569

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×C7×D5×C29C211yesmaximal, characteristic
2C3⋊(C7⋊#10596816)C311yesmaximal, characteristic, direct product factor
3C3×C7⋊#10596816—31nomaximal
4C32×C5×C7×C29C411yescharacteristic, complemented, Hall
5C3×Dic609—51nomaximal, Hall
6C3×C7×D5×C29—21no—
7C3×C7×D5×C29D311yescharacteristic
8C3×C7×D5×C29C2×C311yescharacteristic
9C3×C3⋊#10596816—71nomaximal, Hall
10C7⋊#10596816—31noHall
11C2×C32×C7×C29—51no—
12C3×C5×C7×C29—21no—
13C3×C5×C7×C29Dic311yescharacteristic, complemented
14C3×C5×C7×C29C3×C411yescharacteristic, complemented
15C32×D5×C29D711yescharacteristic
16Dic609—51no—
17C3×Dic203—151no—
18C7×D5×C29C3×D311yescharacteristic
19C32×C7×C29AGL(1,𝔽5)11yescharacteristic, complemented, Hall
20C3⋊#10596816—71no—
21C3×#10596816—211no—
22C32×C5×C29Dic711yescharacteristic, complemented, Hall
23C3×C3⋊(C7⋊AGL(1,𝔽5))—291nomaximal, Hall
24C2×C3×C7×C29—51no—
25C2×C3×C7×C29—51no—
26C2×C3×C7×C29—101no—
27C3×Dic87—351noHall
28C5×C7×C29C3×Dic311yescharacteristic, complemented, Hall
29C3×D5×C29—21no—
30C3×D5×C29C3×D711yescharacteristic
31C3×D5×C29D2111yescharacteristic
32Dic203—151noHall
33C32×C7×D5D2911yescharacteristic
34C3×C7×C29—21no—
35C3×C7×C29C3×AGL(1,𝔽5)11yescharacteristic, complemented
36C3×C7×C29ΓL(1,𝔽16)11yescharacteristic, complemented
37#10596816—211noHall
38C2×C32×C29—51no—
39C3×C5×C29—21no—
40C3×C5×C29C3×Dic711yescharacteristic, complemented
41C3×C5×C29Dic2111yescharacteristic, complemented
42C3⋊(C7⋊AGL(1,𝔽5))—291no—
43C3×C7⋊AGL(1,𝔽5)—871no—
44C2×C7×C29—51no—
45Dic87—351no—
46C3×Dic29—1051no—
47C32×C5×C7Dic2911yescharacteristic, complemented, Hall
48D5×C29C3×D2111yescharacteristic
49C32×C29C7⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
50C3×Dic21—1451noHall
51C3×C7×D5—21no—
52C3×C7×D5C3×D2911yescharacteristic
53C3×C7×D5D8711yescharacteristic
54C7×C29C3×ΓL(1,𝔽16)11yescharacteristic, complemented, Hall
55C3×ΓL(1,𝔽16)—2031noHall
56C2×C3×C29—51no—
57C2×C3×C29—51no—
58C2×C3×C29—101no—
59C5×C29C3×Dic2111yescharacteristic, complemented, Hall
60C7⋊AGL(1,𝔽5)—871noHall
61C2×C32×C7—51no—
62Dic29—1051noHall
63C3×C5×C7—21no—
64C3×C5×C7C3×Dic2911yescharacteristic, complemented
65C3×C5×C7Dic8711yescharacteristic, complemented
66C32×D5D20311yescharacteristic
67C3×C29—21no—
68C3×C29C3×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented
69C3×C29C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented
70Dic21—1451no—
71C3×Dic7—4351no—
72C7×D5C3×D8711yescharacteristic
73C32×C7#1059681611yescharacteristic, complemented, Hall
74ΓL(1,𝔽16)—2031no—
75C3×AGL(1,𝔽5)—6091no—
76C2×C29—51no—
77C32×C5Dic20311yescharacteristic, complemented, Hall
78C2×C3×C7—51no—
79C2×C3×C7—51no—
80C2×C3×C7—101no—
81C3×Dic3—10151noHall
82C5×C7C3×Dic8711yescharacteristic, complemented, Hall
83C3×D5—21no—
84C3×D5C3×D20311yescharacteristic
85C3×D5D60911yescharacteristic
86C29C3×C3⋊(C7⋊AGL(1,𝔽5))11yescharacteristic, complemented, Sylow
87Dic7—4351noHall
88C3×C7—21no—
89C3×C7C3×#1059681611yescharacteristic, complemented
90C3×C7C3⋊#1059681611yescharacteristic, complemented
91AGL(1,𝔽5)—6091noHall
92C2×C32—51no—
93C3×C5—21no—
94C3×C5C3×Dic20311yescharacteristic, complemented
95C3×C5Dic60911yescharacteristic, complemented
96C2×C7—51no—
97C3×C4—30451no—
98Dic3—10151no—
99D5C3×D60911yescharacteristic
100C32C7⋊#1059681611yescharacteristic, complemented, Sylow
101C7C3×C3⋊#1059681611yescharacteristic, complemented, Sylow
102C2×C3—51no—
103C2×C3—51no—
104C2×C3—101no—
105C5C3×Dic60911yescharacteristic, complemented, Sylow
106C4—30451noSylow
107C3—21no—
108C3C3×C7⋊#1059681611yescharacteristic, complemented
109C3C3⋊(C7⋊#10596816)11yescharacteristic, direct product factor
110C2—51no—
subgroupG/H
center, hypercenterC3C3⋊(C7⋊#10596816)
commutator, hypocenterC3×C5×C7×C29C3×C4
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C7×D5×C29C2
cosocleC3×C7×D5×C29C2×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⋊#10596816)C3direct (N × H)
4. C32×C5×C7×C29C4semidirect
13. C3×C5×C7×C29Dic3semidirect
14. C3×C5×C7×C29C3×C4semidirect
19. C32×C7×C29AGL(1,𝔽5)semidirect
22. C32×C5×C29Dic7semidirect
28. C5×C7×C29C3×Dic3semidirect
35. C3×C7×C29C3×AGL(1,𝔽5)semidirect
36. C3×C7×C29ΓL(1,𝔽16)semidirect
40. C3×C5×C29C3×Dic7semidirect
41. C3×C5×C29Dic21semidirect
47. C32×C5×C7Dic29semidirect
49. C32×C29C7⋊AGL(1,𝔽5)semidirect
54. C7×C29C3×ΓL(1,𝔽16)semidirect
59. C5×C29C3×Dic21semidirect
64. C3×C5×C7C3×Dic29semidirect
65. C3×C5×C7Dic87semidirect
68. C3×C29C3×C7⋊AGL(1,𝔽5)semidirect
69. C3×C29C3⋊(C7⋊AGL(1,𝔽5))semidirect
73. C32×C7#10596816semidirect
77. C32×C5Dic203semidirect
82. C5×C7C3×Dic87semidirect
86. C29C3×C3⋊(C7⋊AGL(1,𝔽5))semidirect
89. C3×C7C3×#10596816semidirect
90. C3×C7C3⋊#10596816semidirect
94. C3×C5C3×Dic203semidirect
95. C3×C5Dic609semidirect
100. C32C7⋊#10596816semidirect
101. C7C3×C3⋊#10596816semidirect
105. C5C3×Dic609semidirect
108. C3C3×C7⋊#10596816semidirect
109. C3C3⋊(C7⋊#10596816)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×D5×C292
C3⋊(C7⋊#10596816)3
C3×C7⋊#105968163
C3×Dic6095
C3×C3⋊#105968167
C3×C3⋊(C7⋊AGL(1,𝔽5))29