Finite Group Databasebeta

← C3×C3⋊(C11⋊#66772) #46778095

Subgroups — C3×C3⋊(C11⋊#66772) #46778095

Order 33660.

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×C11×D17C211yesmaximal, characteristic
2C3⋊(C11⋊#66772)C311yesmaximal, characteristic, direct product factor
3C3×C11⋊#66772—31nomaximal
4C32×C5×C11×C17C411yescharacteristic, complemented, Hall
5C3×C3⋊(C11⋊#595)—51nomaximal, Hall
6C3×C5×C11×D17—21no—
7C3×C5×C11×D17D311yescharacteristic
8C3×C5×C11×D17C2×C311yescharacteristic
9C11⋊#66772—31noHall
10C32×C11×D17D511yescharacteristic
11C3×C3⋊#66772—111nomaximal, Hall
12C3×C5×C11×C17—21no—
13C3×C5×C11×C17Dic311yescharacteristic, complemented
14C3×C5×C11×C17C3×C411yescharacteristic, complemented
15C3⋊(C11⋊#595)—51no—
16C3×C11⋊#595—151no—
17C3×Dic165—171nomaximal, Hall
18C5×C11×D17C3×D311yescharacteristic
19C32×C11×C17Dic511yescharacteristic, complemented, Hall
20C32×C5×D17D1111yescharacteristic
21C3×C11×D17—21no—
22C3×C11×D17C3×D511yescharacteristic
23C3×C11×D17D1511yescharacteristic
24C3⋊#66772—111no—
25C3×#66772—331no—
26C2×C32×C5×C11—171no—
27C5×C11×C17C3×Dic311yescharacteristic, complemented, Hall
28C32×C5×C17Dic1111yescharacteristic, complemented, Hall
29C11⋊#595—151noHall
30Dic165—171no—
31C3×Dic55—511no—
32C3×C3⋊#595—551noHall
33C3×C11×C17—21no—
34C3×C11×C17C3×Dic511yescharacteristic, complemented
35C3×C11×C17Dic1511yescharacteristic, complemented
36C3×C5×D17—21no—
37C3×C5×D17C3×D1111yescharacteristic
38C3×C5×D17D3311yescharacteristic
39C32×C5×C11#59511yescharacteristic, complemented, Hall
40C3×Dic33—851noHall
41C11×D17C3×D1511yescharacteristic
42#66772—331noHall
43C2×C3×C5×C11—171no—
44C2×C3×C5×C11—171no—
45C2×C3×C5×C11—341no—
46C32×D17D5511yescharacteristic
47C3×C5×C17—21no—
48C3×C5×C17C3×Dic1111yescharacteristic, complemented
49C3×C5×C17Dic3311yescharacteristic, complemented
50Dic55—511noHall
51C3⋊#595—551no—
52C3×#595—1651no—
53C2×C32×C11—171no—
54C11×C17C3×Dic1511yescharacteristic, complemented, Hall
55C3×Dic15—1871noHall
56C5×D17C3×D3311yescharacteristic
57C3×C5×C11—21no—
58C3×C5×C11C3×#59511yescharacteristic, complemented
59C3×C5×C11C3⋊#59511yescharacteristic, complemented
60C32×C17Dic5511yescharacteristic, complemented, Hall
61Dic33—851no—
62C3×Dic11—2551no—
63C2×C5×C11—171no—
64C3×D17—21no—
65C3×D17C3×D5511yescharacteristic
66C3×D17D16511yescharacteristic
67C32×C11#6677211yescharacteristic, complemented, Hall
68C2×C32×C5—171no—
69C5×C17C3×Dic3311yescharacteristic, complemented, Hall
70#595—1651noHall
71C2×C3×C11—171no—
72C2×C3×C11—171no—
73C2×C3×C11—341no—
74Dic15—1871no—
75C3×Dic5—5611no—
76C5×C11C3×C3⋊#59511yescharacteristic, complemented, Hall
77C3×C17—21no—
78C3×C17C3×Dic5511yescharacteristic, complemented
79C3×C17Dic16511yescharacteristic, complemented
80C32×C5C11⋊#59511yescharacteristic, complemented, Hall
81Dic11—2551noHall
82C3×Dic3—9351noHall
83D17C3×D16511yescharacteristic
84C3×C11—21no—
85C3×C11C3×#6677211yescharacteristic, complemented
86C3×C11C3⋊#6677211yescharacteristic, complemented
87C2×C3×C5—171no—
88C2×C3×C5—171no—
89C2×C3×C5—341no—
90C2×C11—171no—
91Dic5—5611noHall
92C2×C32—171no—
93C17C3×Dic16511yescharacteristic, complemented, Sylow
94C3×C5—21no—
95C3×C5C3×C11⋊#59511yescharacteristic, complemented
96C3×C5C3⋊(C11⋊#595)11yescharacteristic, complemented
97C3×C4—28051no—
98Dic3—9351no—
99C11C3×C3⋊#6677211yescharacteristic, complemented, Sylow
100C2×C5—171no—
101C32C11⋊#6677211yescharacteristic, complemented, Sylow
102C2×C3—171no—
103C2×C3—171no—
104C2×C3—341no—
105C5C3×C3⋊(C11⋊#595)11yescharacteristic, complemented, Sylow
106C4—28051noSylow
107C3—21no—
108C3C3×C11⋊#6677211yescharacteristic, complemented
109C3C3⋊(C11⋊#66772)11yescharacteristic, direct product factor
110C2—171no—
subgroupG/H
center, hypercenterC3C3⋊(C11⋊#66772)
commutator, hypocenterC3×C5×C11×C17C3×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×C5×C11×D17C2
cosocleC3×C5×C11×D17C2×C3
LCSG ▷ C3×C5×C11×C17
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3⋊(C11⋊#66772)C3direct (N × H)
4. C32×C5×C11×C17C4semidirect
13. C3×C5×C11×C17Dic3semidirect
14. C3×C5×C11×C17C3×C4semidirect
19. C32×C11×C17Dic5semidirect
27. C5×C11×C17C3×Dic3semidirect
28. C32×C5×C17Dic11semidirect
34. C3×C11×C17C3×Dic5semidirect
35. C3×C11×C17Dic15semidirect
39. C32×C5×C11#595semidirect
48. C3×C5×C17C3×Dic11semidirect
49. C3×C5×C17Dic33semidirect
54. C11×C17C3×Dic15semidirect
58. C3×C5×C11C3×#595semidirect
59. C3×C5×C11C3⋊#595semidirect
60. C32×C17Dic55semidirect
67. C32×C11#66772semidirect
69. C5×C17C3×Dic33semidirect
76. C5×C11C3×C3⋊#595semidirect
78. C3×C17C3×Dic55semidirect
79. C3×C17Dic165semidirect
80. C32×C5C11⋊#595semidirect
85. C3×C11C3×#66772semidirect
86. C3×C11C3⋊#66772semidirect
93. C17C3×Dic165semidirect
95. C3×C5C3×C11⋊#595semidirect
96. C3×C5C3⋊(C11⋊#595)semidirect
99. C11C3×C3⋊#66772semidirect
101. C32C11⋊#66772semidirect
105. C5C3×C3⋊(C11⋊#595)semidirect
108. C3C3×C11⋊#66772semidirect
109. C3C3⋊(C11⋊#66772)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×C11×D172
C3⋊(C11⋊#66772)3
C3×C11⋊#667723
C3×C3⋊(C11⋊#595)5
C3×C3⋊#6677211
C3×Dic16517