Finite Group Databasebeta

← C7×D17×C3⋊D21 #44472984

Subgroups — C7×D17×C3⋊D21 #44472984

Order 29988.

312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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×C72×D17C211yesmaximal, characteristic, complemented
2C7×C17×C3⋊D21C211yesmaximal, characteristic, complemented
3C7×C3⋊D357C211yesmaximal, characteristic, complemented
4C7×D17×D21—34nomaximal
5C32×C72×C17C2211yescharacteristic, complemented, Hall
6C7×D357—34no—
7C7×C17×D21—34no—
8C3×C72×D17D314yescomplemented
9D17×C3⋊D21C711yesmaximal, characteristic, direct product factor
10C7×C3⋊D3×D17—71nomaximal
11C7×D7×D17—91noHall
12C3×C72×C17C2×D314yescomplemented
13C3⋊D357C2×C711yescharacteristic, complemented
14C17×C3⋊D21C2×C711yescharacteristic, complemented
15C7×C3⋊D51—71no—
16C7×C17×C3⋊D3—71no—
17C32×C7×D17—23no—
18C32×C7×D17D711yescharacteristic, complemented
19C32×C7×D17C2×C711yescharacteristic, complemented
20C2×C7×C3⋊D21—171nomaximal, Hall
21C7×D119—91no—
22C7×D7×C17—91no—
23C72×D17C3⋊D311yescharacteristic, complemented
24D17×D21—34no—
25D3×C7×D17—214no—
26C32×C7×C17—23no—
27C32×C7×C17C2×D711yescharacteristic, complemented
28C32×C7×C17C22×C711yescharacteristic, complemented
29C2×C32×C72—171no—
30C7×C3⋊D21—171no—
31C7×C3⋊D21D1711yescharacteristic, direct product factor
32C72×C17C2×C3⋊D311yescharacteristic, complemented, Hall
33D357—34no—
34C17×D21—34no—
35C7×D51—214no—
36D3×C7×C17—214no—
37C3×C7×D17—212no—
38C3×C7×D17D3×C714yescomplemented
39C3×C7×D17D2114yescomplemented
40C3⋊D3×D17—71noHall
41C2×C7×D21—514no—
42C2×C7×D17—631no—
43D7×D17—91no—
44C32×C72C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—212no—
46C3×C7×C17C2×D3×C714yescomplemented
47C3×C7×C17C2×D2114yescomplemented
48C3⋊D51—71no—
49C17×C3⋊D3—71no—
50C32×D17C7×D711yescharacteristic, complemented
51C2×C3×C72—174no—
52C7×D21—34no—
53C7×D21—514no—
54C2×C3⋊D21—171no—
55C2×C7×C3⋊D3—1191no—
56C2×C7×C17—631no—
57D119—91no—
58C7×D17—23no—
59C7×D17—631no—
60C7×D17C7×C3⋊D311yescharacteristic, complemented
61C7×D17C3⋊D2111yescharacteristic, direct product factor
62D7×C17—91no—
63D3×D17—214no—
64C2×C7×D7—1531noHall
65C32×C17C2×C7×D711yescharacteristic, complemented, Hall
66C3×C72D3×D1714yescomplemented
67C2×C32×C7—171no—
68C2×C32×C7—171no—
69C2×C32×C7—343no—
70C3⋊D21—171no—
71C3⋊D21C7×D1711yescharacteristic, direct product factor
72C7×C3⋊D3—71no—
73C7×C3⋊D3—1191no—
74C7×C17—23no—
75C7×C17C2×C7×C3⋊D311yescharacteristic, complemented
76C7×C17C2×C3⋊D2111yescharacteristic, complemented
77D51—214no—
78C3×D17C7×D2114yescomplemented
79D3×C17—214no—
80C2×C72—171no—
81C7×D7—91no—
82C7×D7—1531no—
83C2×D21—514no—
84C2×D3×C7—3574no—
85C2×D17—631noHall
86C32×C7—23no—
87C32×C7D7×D1711yescharacteristic, complemented
88C32×C7C2×C7×D1711yescharacteristic, complemented
89C3×C17C2×C7×D2114yescomplemented
90C72C3⋊D3×D1711yescharacteristic, complemented, Sylow
91C2×C3×C7—174no—
92C2×C3×C7—174no—
93C2×C3×C7—3412no—
94D21—34no—
95D21—514no—
96D3×C7—214no—
97D3×C7—3574no—
98C2×C3⋊D3—1191noHall
99C2×C17—631no—
100D17—631no—
101D17C7×C3⋊D2111yescharacteristic, direct product factor
102C22×C7—10711no—
103C2×D7—1531no—
104C3×C7—212no—
105C3×C7D3×C7×D1714yescomplemented
106C3×C7D17×D2114yescomplemented
107C2×C32—171no—
108C3⋊D3—71no—
109C3⋊D3—1191no—
110C17C2×C7×C3⋊D2111yescharacteristic, complemented, Sylow
111C2×C7—171no—
112C2×C7—171no—
113C2×C7—343no—
114C2×C7—10711no—
115C2×C7—631no—
116D7—91no—
117D7—1531no—
118C2×D3—3574no—
119C32C7×D7×D1711yescharacteristic, complemented, Sylow
120C7—23no—
121C7C7×C3⋊D3×D1711yescharacteristic, complemented
122C7D17×C3⋊D2111yescharacteristic, direct product factor
123C2×C3—174no—
124D3—214no—
125D3—3574no—
126C22—10711noSylow
127C3C7×D17×D2114yescomplemented
128C2—171no—
129C2—10711no—
130C2—631no—
subgroupG/H
center, hypercenterC7D17×C3⋊D21
commutator, cosocle, hypocenterC32×C7×C17C22×C7
FrattiniC1G
Fitting, socleC32×C72×C17C22
LCSG ▷ C32×C7×C17
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C72×D17C2semidirect
2. C7×C17×C3⋊D21C2semidirect
3. C7×C3⋊D357C2semidirect
5. C32×C72×C17C22semidirect
8. C3×C72×D17D3semidirect
9. D17×C3⋊D21C7direct (N × H)
12. C3×C72×C17C2×D3semidirect
13. C3⋊D357C2×C7semidirect
14. C17×C3⋊D21C2×C7semidirect
18. C32×C7×D17D7semidirect
19. C32×C7×D17C2×C7semidirect
23. C72×D17C3⋊D3semidirect
27. C32×C7×C17C2×D7semidirect
28. C32×C7×C17C22×C7semidirect
31. C7×C3⋊D21D17direct (N × H)
32. C72×C17C2×C3⋊D3semidirect
38. C3×C7×D17D3×C7semidirect
39. C3×C7×D17D21semidirect
44. C32×C72C2×D17semidirect
46. C3×C7×C17C2×D3×C7semidirect
47. C3×C7×C17C2×D21semidirect
50. C32×D17C7×D7semidirect
60. C7×D17C7×C3⋊D3semidirect
61. C7×D17C3⋊D21direct (N × H)
65. C32×C17C2×C7×D7semidirect
66. C3×C72D3×D17semidirect
71. C3⋊D21C7×D17direct (N × H)
75. C7×C17C2×C7×C3⋊D3semidirect
76. C7×C17C2×C3⋊D21semidirect
78. C3×D17C7×D21semidirect
87. C32×C7D7×D17semidirect
88. C32×C7C2×C7×D17semidirect
89. C3×C17C2×C7×D21semidirect
90. C72C3⋊D3×D17semidirect
101. D17C7×C3⋊D21direct (N × H)
105. C3×C7D3×C7×D17semidirect
106. C3×C7D17×D21semidirect
110. C17C2×C7×C3⋊D21semidirect
119. C32C7×D7×D17semidirect
121. C7C7×C3⋊D3×D17semidirect
122. C7D17×C3⋊D21direct (N × H)
127. C3C7×D17×D21semidirect

Maximal subgroups

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

subgroupindex
C32×C72×D172
C7×C17×C3⋊D212
C7×C3⋊D3572
C7×D17×D213
D17×C3⋊D217
C7×C3⋊D3×D177
C2×C7×C3⋊D2117