Finite Group Databasebeta

← C3⋊D21×D115 #44394649

Subgroups — C3⋊D21×D115 #44394649

Order 28980.

240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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×D115C211yesmaximal, characteristic, complemented
2C5×C23×C3⋊D21C211yesmaximal, characteristic, complemented
3C3⋊D2415C211yesmaximal, characteristic, complemented
4D21×D115—34nomaximal
5C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
6D23×C3⋊D21—51nomaximal, Hall
7D2415—34no—
8C5×C23×D21—34no—
9C3×C7×D115D314yescomplemented
10C3⋊D3×D115—71nomaximal, Hall
11D7×D115—91noHall
12C3⋊D483—51no—
13C23×C3⋊D21D511yescharacteristic, complemented
14C32×C7×D23—51no—
15C3×C5×C7×C23C2×D314yescomplemented
16C3⋊D345—71no—
17C5×C3⋊D3×C23—71no—
18C32×D115D711yescharacteristic, complemented
19D21×D23—154no—
20D805—91no—
21C7×D115C3⋊D311yescharacteristic, complemented
22C5×D7×C23—91no—
23C32×C7×C23C2×D511yescharacteristic, complemented, Hall
24D3×D115—214no—
25D5×C3⋊D21—231nomaximal, Hall
26C32×C5×C23C2×D711yescharacteristic, complemented, Hall
27D483—154no—
28C23×D21—34no—
29C3×C7×D23—54no—
30C3⋊D3×D23—351noHall
31C5×C7×C23C2×C3⋊D311yescharacteristic, complemented, Hall
32D345—214no—
33C5×D3×C23—214no—
34C3×D115D2114yescomplemented
35D7×D23—451noHall
36C3⋊D105—231no—
37C5×C3⋊D21D2311yescharacteristic, complemented
38C32×C7×D5—231no—
39C3×C7×C23D3×D514yescomplemented
40C2×D115—631noHall
41D5×D21—694no—
42C3⋊D69—351no—
43C3⋊D3×C23—71no—
44C32×D23—51no—
45C3×C5×C23C2×D2114yescomplemented
46D161—451no—
47C7×D23—51no—
48D7×C23—91no—
49C32×C5×C7C2×D2311yescharacteristic, complemented, Hall
50D3×D23—1054no—
51C2×C3⋊D21—1151noHall
52C2×C5×C23—631no—
53D115—631no—
54D115C3⋊D2111yescharacteristic, direct product factor
55D105—694no—
56C5×D21—34no—
57C3×C7×D5—234no—
58C32×C23D5×D711yescharacteristic, complemented, Hall
59D5×C3⋊D3—1611noHall
60C7×C23D5×C3⋊D311yescharacteristic, complemented, Hall
61D5×D7—2071noHall
62D69—1054no—
63C3×D23—54no—
64D3×C23—214no—
65C2×C32×C7—1151no—
66C3⋊D21—1151no—
67C3⋊D21D11511yescharacteristic, direct product factor
68C5×C23C2×C3⋊D2111yescharacteristic, complemented, Hall
69C3×C5×C7D3×D2314yescomplemented
70C2×D23—3151noHall
71C3⋊D15—1611no—
72C5×C3⋊D3—71no—
73C32×D5—231no—
74C2×D21—3454no—
75D35—2071no—
76C5×D7—91no—
77C7×D5—231no—
78C3×C23D5×D2114yescomplemented
79C32×C7C2×D11511yescharacteristic, complemented, Hall
80D3×D5—4834no—
81C2×C23—631no—
82D23—51no—
83D23—3151no—
84C32×C5D7×D2311yescharacteristic, complemented, Hall
85C2×C3×C7—1154no—
86D21—34no—
87D21—3454no—
88C2×C3⋊D3—8051noHall
89C5×C7C3⋊D3×D2311yescharacteristic, complemented, Hall
90D15—4834no—
91C3×D5—234no—
92C5×D3—214no—
93C2×D7—10351noHall
94C23D5×C3⋊D2111yescharacteristic, complemented, Sylow
95C3×C7D3×D11514yescomplemented
96C2×D5—14491noHall
97C2×C32—1151no—
98C3⋊D3—71no—
99C3⋊D3—8051no—
100C3×C5D21×D2314yescomplemented
101C2×C7—1151no—
102D7—91no—
103D7—10351no—
104C2×D3—24154no—
105C2×C5—631no—
106D5—231no—
107D5—14491no—
108C32D7×D11511yescharacteristic, complemented, Sylow
109C7C3⋊D3×D11511yescharacteristic, complemented, Sylow
110C2×C3—1154no—
111D3—214no—
112D3—24154no—
113C5D23×C3⋊D2111yescharacteristic, complemented, Sylow
114C22—72451noSylow
115C3D21×D11514yescomplemented
116C2—631no—
117C2—72451no—
118C2—1151no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C23C22
LCSG ▷ C32×C5×C7×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C7×D115C2semidirect
2. C5×C23×C3⋊D21C2semidirect
3. C3⋊D2415C2semidirect
5. C32×C5×C7×C23C22semidirect
9. C3×C7×D115D3semidirect
13. C23×C3⋊D21D5semidirect
15. C3×C5×C7×C23C2×D3semidirect
18. C32×D115D7semidirect
21. C7×D115C3⋊D3semidirect
23. C32×C7×C23C2×D5semidirect
26. C32×C5×C23C2×D7semidirect
31. C5×C7×C23C2×C3⋊D3semidirect
34. C3×D115D21semidirect
37. C5×C3⋊D21D23semidirect
39. C3×C7×C23D3×D5semidirect
45. C3×C5×C23C2×D21semidirect
49. C32×C5×C7C2×D23semidirect
54. D115C3⋊D21direct (N × H)
58. C32×C23D5×D7semidirect
60. C7×C23D5×C3⋊D3semidirect
67. C3⋊D21D115direct (N × H)
68. C5×C23C2×C3⋊D21semidirect
69. C3×C5×C7D3×D23semidirect
78. C3×C23D5×D21semidirect
79. C32×C7C2×D115semidirect
84. C32×C5D7×D23semidirect
89. C5×C7C3⋊D3×D23semidirect
94. C23D5×C3⋊D21semidirect
95. C3×C7D3×D115semidirect
100. C3×C5D21×D23semidirect
108. C32D7×D115semidirect
109. C7C3⋊D3×D115semidirect
113. C5D23×C3⋊D21semidirect
115. C3D21×D115semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1152
C5×C23×C3⋊D212
C3⋊D24152
D21×D1153
D23×C3⋊D215
C3⋊D3×D1157
D5×C3⋊D2123