Finite Group Databasebeta

← D3×C37×D75 #45685906

Subgroups — D3×C37×D75 #45685906

Order 33300.

132 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C37×C3⋊D75C211yesmaximal, characteristic, complemented
2C3×C37×D75C211yesmaximal, characteristic, complemented
3C3×D3×C25×C37C211yesmaximal, characteristic, complemented
4C2×C37×D75—31nomaximal
5D3×C37×D25—31nomaximal
6C32×C25×C37C2211yescharacteristic, complemented, Hall
7D3×D15×C37—51nomaximal
8C37×D75—31no—
9C37×D75—31no—
10C37×D75—61no—
11C37×D75D311yescharacteristic, direct product factor
12D3×C25×C37D311yescharacteristic, complemented
13C3×C37×D25—31no—
14C2×C3×C25×C37—31no—
15C2×C37×D25—91noHall
16C37×C3⋊D15—51no—
17C3×D15×C37—51no—
18C3×C5×D3×C37D511yescharacteristic
19C3×C25×C37—21no—
20C3×C25×C37C2×D311yescharacteristic, complemented
21C3×C25×C37C2×D311yescharacteristic, complemented
22C2×D15×C37—151no—
23D3×D5×C37—151no—
24C2×C25×C37—31no—
25C37×D25—31no—
26C37×D25—91no—
27C32×C5×C37C2×D511yescharacteristic
28D32×C37—251noHall
29C2×C3×C5×C37—31no—
30D15×C37—51no—
31D15×C37—151no—
32D15×C37—151no—
33D15×C37—301no—
34C5×D3×C37D1511yescharacteristic
35C3×D5×C37—151no—
36C25×C37D3211yescharacteristic, complemented, Hall
37D3×D75C3711yesmaximal, characteristic, direct product factor, Hall
38C2×D5×C37—451no—
39C3⋊D3×C37—251no—
40C3×D3×C37—251no—
41C3×D3×C37D2511yescharacteristic, complemented
42C3×C5×C37—21no—
43C3×C5×C37D3×D511yescharacteristic
44C3×C5×C37C2×D1511yescharacteristic
45C3⋊D75C2×C3711yescharacteristic, complemented
46C3×D75C2×C3711yescharacteristic, complemented
47C3×D3×C25C2×C3711yescharacteristic, complemented
48C2×D3×C37—751no—
49C2×D3×C37—751no—
50C2×C5×C37—31no—
51D5×C37—151no—
52D5×C37—451no—
53C32×C37C2×D2511yescharacteristic, complemented, Hall
54C2×D75—31no—
55D3×D25—31no—
56C32×C25C22×C3711yescharacteristic, complemented, Hall
57C2×C3×C37—31no—
58C2×C3×C37—751no—
59D3×C37—251no—
60D3×C37—751no—
61D3×C37—751no—
62D3×C37—1501no—
63D3×C37D7511yescharacteristic, direct product factor
64C5×C37D3×D1511yescharacteristic
65D3×D15—51no—
66C2×C3×C25—31no—
67D75—31no—
68D75—31no—
69D75—61no—
70D75D3×C3711yescharacteristic, direct product factor
71C3×D25—31no—
72D3×C25D3×C3711yescharacteristic, complemented
73C22×C37—2251noHall
74C3×C37—21no—
75C3×C37D3×D2511yescharacteristic, complemented
76C3×C37C2×D7511yescharacteristic, complemented
77C2×D25—91noHall
78C3⋊D15—51no—
79C3×D15—51no—
80C3×C5×D3D5×C3711yescharacteristic
81C3×C25—21no—
82C3×C25C2×D3×C3711yescharacteristic, complemented
83C3×C25C2×D3×C3711yescharacteristic, complemented
84C2×C37—31no—
85C2×C37—751no—
86C2×C37—2251no—
87C2×D15—151no—
88D3×D5—151no—
89C2×C25—31no—
90D25—31no—
91D25—91no—
92C32×C5C2×D5×C3711yescharacteristic
93C37D3×D7511yescharacteristic, direct product factor, Sylow
94D32—251noHall
95C2×C3×C5—31no—
96D15—51no—
97D15—151no—
98D15—151no—
99D15—301no—
100C3×D5—151no—
101C5×D3D15×C3711yescharacteristic
102C25D32×C3711yescharacteristic, complemented, Sylow
103C2×D5—451no—
104C3⋊D3—251no—
105C3×D3—251no—
106C3×D3C37×D2511yescharacteristic, complemented
107C3×C5—21no—
108C3×C5D3×D5×C3711yescharacteristic
109C3×C5C2×D15×C3711yescharacteristic
110C2×D3—751no—
111C2×D3—751no—
112C2×C5—31no—
113D5—151no—
114D5—451no—
115C32C2×C37×D2511yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—751no—
118D3—251no—
119D3—751no—
120D3—751no—
121D3—1501no—
122D3C37×D7511yescharacteristic, direct product factor
123C5D3×D15×C3711yescharacteristic
124C22—2251noSylow
125C3—21no—
126C3D3×C37×D2511yescharacteristic, complemented
127C3C2×C37×D7511yescharacteristic, complemented
128C2—31no—
129C2—751no—
130C2—2251no—
subgroupG/H
center, hypercenterC37D3×D75
commutator, cosocle, hypocenterC32×C25C22×C37
FrattiniC5D3×D15×C37
FittingC32×C25×C37C22
socleC32×C5×C37C2×D5
LCSG ▷ C32×C25
UCSC1 ◁ C37

Complements

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

NH ≅ G/Ntype
1. C37×C3⋊D75C2semidirect
2. C3×C37×D75C2semidirect
3. C3×D3×C25×C37C2semidirect
6. C32×C25×C37C22semidirect
11. C37×D75D3direct (N × H)
12. D3×C25×C37D3semidirect
20. C3×C25×C37C2×D3semidirect
21. C3×C25×C37C2×D3semidirect
36. C25×C37D32semidirect
37. D3×D75C37direct (N × H)
41. C3×D3×C37D25semidirect
45. C3⋊D75C2×C37semidirect
46. C3×D75C2×C37semidirect
47. C3×D3×C25C2×C37semidirect
53. C32×C37C2×D25semidirect
56. C32×C25C22×C37semidirect
63. D3×C37D75direct (N × H)
70. D75D3×C37direct (N × H)
72. D3×C25D3×C37semidirect
75. C3×C37D3×D25semidirect
76. C3×C37C2×D75semidirect
82. C3×C25C2×D3×C37semidirect
83. C3×C25C2×D3×C37semidirect
93. C37D3×D75direct (N × H)
102. C25D32×C37semidirect
106. C3×D3C37×D25semidirect
115. C32C2×C37×D25semidirect
122. D3C37×D75direct (N × H)
126. C3D3×C37×D25semidirect
127. C3C2×C37×D75semidirect

Maximal subgroups

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

subgroupindex
C37×C3⋊D752
C3×C37×D752
C3×D3×C25×C372
C2×C37×D753
D3×C37×D253
D3×D15×C375
D3×D7537