Finite Group Databasebeta

← D111⋊D75 #45685908

Subgroups — D111⋊D75 #45685908

Order 33300.

132 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 35 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×D2775C211yesmaximal, characteristic, complemented
3C3×C25×D111C211yesmaximal, characteristic, complemented
4D75⋊D37—31nomaximal
5D37×D75—31nomaximal
6C32×C25×C37C2211yescharacteristic, complemented, Hall
7D111⋊D15—51nomaximal
8D2775D311yescharacteristic, complemented
9C37×D75—31no—
10C37×D75—31no—
11C37×D75—61no—
12C25×D111D311yescharacteristic, complemented
13C3×D925—31no—
14C3×C25×D37—31no—
15D25×D37—91noHall
16C37×C3⋊D15—51no—
17C3×D555—51no—
18C3×C5×D111D511yescharacteristic
19C3×C25×C37—21no—
20C3×C25×C37C2×D311yescharacteristic, complemented
21C3×C25×C37C2×D311yescharacteristic, complemented
22D15⋊D37—151no—
23D15×D37—151no—
24D925—31no—
25C25×D37—31no—
26C37×D25—91no—
27C32×C5×C37C2×D511yescharacteristic
28(C3⋊D3)⋊D37—251noHall
29D555—51no—
30D15×C37—151no—
31D15×C37—151no—
32D15×C37—301no—
33C5×D111D1511yescharacteristic
34C3×D185—151no—
35C3×C5×D37—31no—
36C25×C37D3211yescharacteristic, complemented, Hall
37D3×D75—371nomaximal, Hall
38D5×D37—451no—
39C3⋊D3×C37—251no—
40C3×D111—251no—
41C3×D111D2511yescharacteristic, complemented
42C3×C5×C37—21no—
43C3×C5×C37D3×D511yescharacteristic
44C3×C5×C37C2×D1511yescharacteristic
45C3⋊D75D3711yescharacteristic, complemented
46C3×D75—371no—
47C3×D3×C25—371no—
48D3×D37—751no—
49D3×D37—751no—
50D185—151no—
51C5×D37—31no—
52D5×C37—451no—
53C32×C37C2×D2511yescharacteristic, complemented, Hall
54C2×D75—1111no—
55D3×D25—1111no—
56C32×C25C2×D3711yescharacteristic, complemented, Hall
57D111—251no—
58D111D7511yescharacteristic, complemented
59C3×D37—31no—
60C3×D37—751no—
61D3×C37—751no—
62D3×C37—751no—
63D3×C37—1501no—
64C5×C37D3×D1511yescharacteristic
65D3×D15—1851no—
66C2×C3×C25—1111no—
67D75—31no—
68D75—31no—
69D75—61no—
70D75—371no—
71C3×D25—1111no—
72D3×C25—371no—
73C2×D37—2251noHall
74C3×C37—21no—
75C3×C37D3×D2511yescharacteristic, complemented
76C3×C37C2×D7511yescharacteristic, complemented
77C2×D25—3331noHall
78C3⋊D15—51no—
79C3×D15—1851no—
80C3×C5×D3—371no—
81C3×C25—21no—
82C3×C25D3×D3711yescharacteristic, complemented
83C3×C25D3×D3711yescharacteristic, complemented
84C2×C37—2251no—
85D37—31no—
86D37—751no—
87C2×D15—5551no—
88D3×D5—5551no—
89C2×C25—1111no—
90D25—91no—
91D25—1111no—
92C32×C5D5×D3711yescharacteristic
93C37D3×D7511yescharacteristic, complemented, Sylow
94D32—9251noHall
95C2×C3×C5—1111no—
96D15—151no—
97D15—151no—
98D15—301no—
99D15—1851no—
100C3×D5—5551no—
101C5×D3—371no—
102C25(C3⋊D3)⋊D3711yescharacteristic, complemented, Sylow
103C2×D5—16651no—
104C3⋊D3—251no—
105C3×D3—371no—
106C3×D3—9251no—
107C3×C5—21no—
108C3×C5D15×D3711yescharacteristic
109C3×C5D15⋊D3711yescharacteristic
110C2×D3—27751no—
111C2×D3—27751no—
112C2×C5—1111no—
113D5—5551no—
114D5—451no—
115C32D25×D3711yescharacteristic, complemented, Sylow
116C2×C3—1111no—
117C2×C3—27751no—
118D3—371no—
119D3—751no—
120D3—751no—
121D3—1501no—
122D3—9251no—
123C5D111⋊D1511yescharacteristic
124C22—83251noSylow
125C3—21no—
126C3D37×D7511yescharacteristic, complemented
127C3D75⋊D3711yescharacteristic, complemented
128C2—1111no—
129C2—27751no—
130C2—2251no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC32×C25×C37C22
FrattiniC5D111⋊D15
socleC32×C5×C37C2×D5
LCSG ▷ C32×C25×C37
UCSC1

Complements

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

NH ≅ G/Ntype
1. C37×C3⋊D75C2semidirect
2. C3×D2775C2semidirect
3. C3×C25×D111C2semidirect
6. C32×C25×C37C22semidirect
8. D2775D3semidirect
12. C25×D111D3semidirect
20. C3×C25×C37C2×D3semidirect
21. C3×C25×C37C2×D3semidirect
36. C25×C37D32semidirect
41. C3×D111D25semidirect
45. C3⋊D75D37semidirect
53. C32×C37C2×D25semidirect
56. C32×C25C2×D37semidirect
58. D111D75semidirect
75. C3×C37D3×D25semidirect
76. C3×C37C2×D75semidirect
82. C3×C25D3×D37semidirect
83. C3×C25D3×D37semidirect
93. C37D3×D75semidirect
102. C25(C3⋊D3)⋊D37semidirect
115. C32D25×D37semidirect
126. C3D37×D75semidirect
127. C3D75⋊D37semidirect

Maximal subgroups

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

subgroupindex
C37×C3⋊D752
C3×D27752
C3×C25×D1112
D75⋊D373
D37×D753
D111⋊D155
D3×D7537