Finite Group Databasebeta

← D3×D2775 #45685907

Subgroups — D3×D2775 #45685907

Order 33300.

132 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C3⋊D2775C211yesmaximal, characteristic, complemented
2C3×D2775C211yesmaximal, characteristic, complemented
3C3×D3×C25×C37C211yesmaximal, characteristic, complemented
4C2×D2775—31nomaximal
5D3×D925—31nomaximal
6C32×C25×C37C2211yescharacteristic, complemented, Hall
7D3×D555—51nomaximal
8D2775—31no—
9D2775—31no—
10D2775—61no—
11D2775D311yescharacteristic, direct product factor
12D3×C25×C37D311yescharacteristic, complemented
13C3×D925—31no—
14C2×C3×C25×C37—31no—
15C2×D925—91noHall
16C3⋊D555—51no—
17C3×D555—51no—
18C3×C5×D3×C37D511yescharacteristic
19C3×C25×C37—21no—
20C3×C25×C37C2×D311yescharacteristic, complemented
21C3×C25×C37C2×D311yescharacteristic, complemented
22C2×D555—151no—
23D3×D185—151no—
24C2×C25×C37—31no—
25D925—31no—
26D925—91no—
27C32×C5×C37C2×D511yescharacteristic
28D3×D111—251noHall
29C2×C3×C5×C37—31no—
30D555—51no—
31D555—151no—
32D555—151no—
33D555—301no—
34C5×D3×C37D1511yescharacteristic
35C3×D185—151no—
36C25×C37D3211yescharacteristic, complemented, Hall
37D3×D75—371nomaximal, Hall
38C2×D185—451no—
39C3⋊D111—251no—
40C3×D111—251no—
41C3×D3×C37D2511yescharacteristic, complemented
42C3×C5×C37—21no—
43C3×C5×C37D3×D511yescharacteristic
44C3×C5×C37C2×D1511yescharacteristic
45C3⋊D75—371no—
46C3×D75—371no—
47C3×D3×C25D3711yescharacteristic, complemented
48C2×D111—751no—
49D3×D37—751no—
50C2×C5×C37—31no—
51D185—151no—
52D185—451no—
53C32×C37C2×D2511yescharacteristic, complemented, Hall
54C2×D75—1111no—
55D3×D25—1111no—
56C32×C25C2×D3711yescharacteristic, complemented, Hall
57C2×C3×C37—31no—
58D111—251no—
59D111—751no—
60D111—751no—
61D111—1501no—
62C3×D37—751no—
63D3×C37D7511yescharacteristic, complemented
64C5×C37D3×D1511yescharacteristic
65D3×D15—1851no—
66C2×C3×C25—31no—
67D75—371no—
68D75—1111no—
69D75—1111no—
70D75—2221no—
71C3×D25—1111no—
72D3×C25D11111yescharacteristic, complemented
73C2×D37—2251noHall
74C3×C37—21no—
75C3×C37D3×D2511yescharacteristic, complemented
76C3×C37C2×D7511yescharacteristic, complemented
77C2×D25—3331noHall
78C3⋊D15—1851no—
79C3×D15—1851no—
80C3×C5×D3D18511yescharacteristic
81C3×C25—21no—
82C3×C25D3×D3711yescharacteristic, complemented
83C3×C25C2×D11111yescharacteristic, complemented
84C2×C37—31no—
85D37—751no—
86D37—2251no—
87C2×D15—5551no—
88D3×D5—5551no—
89C2×C25—31no—
90D25—3331no—
91D25—1111no—
92C32×C5C2×D18511yescharacteristic
93C37D3×D7511yescharacteristic, complemented, Sylow
94D32—9251noHall
95C2×C3×C5—31no—
96D15—5551no—
97D15—5551no—
98D15—11101no—
99D15—1851no—
100C3×D5—5551no—
101C5×D3D55511yescharacteristic
102C25D3×D11111yescharacteristic, complemented, Sylow
103C2×D5—16651no—
104C3⋊D3—9251no—
105C3×D3—9251no—
106C3×D3D92511yescharacteristic, complemented
107C3×C5—21no—
108C3×C5D3×D18511yescharacteristic
109C3×C5C2×D55511yescharacteristic
110C2×D3—27751no—
111C2×D3—27751no—
112C2×C5—31no—
113D5—5551no—
114D5—16651no—
115C32C2×D92511yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—27751no—
118D3—9251no—
119D3—55501no—
120D3—27751no—
121D3—27751no—
122D3D277511yescharacteristic, direct product factor
123C5D3×D55511yescharacteristic
124C22—83251noSylow
125C3—21no—
126C3D3×D92511yescharacteristic, complemented
127C3C2×D277511yescharacteristic, complemented
128C2—31no—
129C2—83251no—
130C2—27751no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC32×C25×C37C22
FrattiniC5D3×D555
socleC32×C5×C37C2×D5
LCSG ▷ C32×C25×C37
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊D2775C2semidirect
2. C3×D2775C2semidirect
3. C3×D3×C25×C37C2semidirect
6. C32×C25×C37C22semidirect
11. D2775D3direct (N × H)
12. D3×C25×C37D3semidirect
20. C3×C25×C37C2×D3semidirect
21. C3×C25×C37C2×D3semidirect
36. C25×C37D32semidirect
41. C3×D3×C37D25semidirect
47. C3×D3×C25D37semidirect
53. C32×C37C2×D25semidirect
56. C32×C25C2×D37semidirect
63. D3×C37D75semidirect
72. D3×C25D111semidirect
75. C3×C37D3×D25semidirect
76. C3×C37C2×D75semidirect
82. C3×C25D3×D37semidirect
83. C3×C25C2×D111semidirect
93. C37D3×D75semidirect
102. C25D3×D111semidirect
106. C3×D3D925semidirect
115. C32C2×D925semidirect
122. D3D2775direct (N × H)
126. C3D3×D925semidirect
127. C3C2×D2775semidirect

Maximal subgroups

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

subgroupindex
C3⋊D27752
C3×D27752
C3×D3×C25×C372
C2×D27753
D3×D9253
D3×D5555
D3×D7537