Finite Group Databasebeta

← C2×C7×D1071 #44472625

Subgroups — C2×C7×D1071 #44472625

Order 29988.

156 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C7×D1071C212yesmaximal, direct product factor
2C2×C72×C9×C17C211yesmaximal, characteristic, complemented
3C2×C7×D357—31nomaximal
4C72×C9×C17C2211yescharacteristic, complemented, Hall
5C7×D357—32no—
6C2×C3×C72×C17D311yescharacteristic
7C2×D1071C711yesmaximal, characteristic, direct product factor
8C2×C7×D153—71nomaximal
9C2×C7×D119—91noHall
10C3×C72×C17C2×D311yescharacteristic
11D1071C2×C712yesdirect product factor
12C7×D153—72no—
13C2×C7×C9×C17—23no—
14C2×C7×C9×C17D711yescharacteristic, complemented
15C2×C7×C9×C17C2×C711yescharacteristic, complemented
16C2×C7×D63—171nomaximal, Hall
17C2×C72×C17D911yescharacteristic, complemented
18C7×D119—92no—
19C2×D357—31no—
20C2×C7×D51—211no—
21C7×C9×C17—23no—
22C7×C9×C17C2×D711yescharacteristic, complemented
23C7×C9×C17C22×C711yescharacteristic, complemented
24C2×C72×C9D1711yescharacteristic, complemented
25C7×D63—172no—
26C72×C17C2×D911yescharacteristic, complemented, Hall
27C2×C3×C7×C17—23no—
28C2×C3×C7×C17D3×C711yescharacteristic
29C2×C3×C7×C17D2111yescharacteristic
30D357—32no—
31C7×D51—212no—
32C2×D153—71noHall
33C2×C7×D21—511no—
34C2×D119—91no—
35C2×C7×D17—631no—
36C72×C9C2×D1711yescharacteristic, complemented, Hall
37C3×C7×C17—23no—
38C3×C7×C17C2×D3×C711yescharacteristic
39C3×C7×C17C2×D2111yescharacteristic
40C2×C9×C17C7×D711yescharacteristic, complemented
41D153—72no—
42C2×C3×C72D5111yescharacteristic
43C7×D21—512no—
44C2×D63—171no—
45C2×C7×D9—1191no—
46C2×C7×C17—23no—
47C2×C7×C17C7×D911yescharacteristic, complemented
48C2×C7×C17D6311yescharacteristic, complemented
49D119—92no—
50C7×D17—632no—
51C2×D51—211no—
52C2×C7×D7—1531noHall
53C9×C17C2×C7×D711yescharacteristic, complemented, Hall
54C3×C72C2×D5111yescharacteristic
55C2×C7×C9—23no—
56C2×C7×C9C7×D1711yescharacteristic, complemented
57C2×C7×C9D11911yescharacteristic, complemented
58D63—172no—
59C7×D9—1192no—
60C7×C17—23no—
61C7×C17C2×C7×D911yescharacteristic, complemented
62C7×C17C2×D6311yescharacteristic, complemented
63C2×C3×C17C7×D2111yescharacteristic
64D51—212no—
65C2×C72D15311yescharacteristic, complemented
66C7×D7—1532no—
67C2×D21—511no—
68C2×D3×C7—3571no—
69C2×D17—631noHall
70C7×C9—23no—
71C7×C9C2×C7×D1711yescharacteristic, complemented
72C7×C9C2×D11911yescharacteristic, complemented
73C3×C17C2×C7×D2111yescharacteristic
74C72C2×D15311yescharacteristic, complemented, Sylow
75C2×C3×C7—23no—
76C2×C3×C7C7×D5111yescharacteristic
77C2×C3×C7D35711yescharacteristic
78D21—512no—
79D3×C7—3572no—
80C2×D9—1191noHall
81C2×C17C7×D6311yescharacteristic, complemented
82D17—632no—
83C22×C7—10711no—
84C2×D7—1531no—
85C3×C7—23no—
86C3×C7C2×C7×D5111yescharacteristic
87C3×C7C2×D35711yescharacteristic
88C2×C9C7×D11911yescharacteristic, complemented
89D9—1192no—
90C17C2×C7×D6311yescharacteristic, complemented, Sylow
91C2×C7—23no—
92C2×C7—10712no—
93C2×C7C7×D15311yescharacteristic, complemented
94C2×C7D107111yescharacteristic, direct product factor
95D7—1532no—
96C2×D3—3571no—
97C9C2×C7×D11911yescharacteristic, complemented, Sylow
98C7—23no—
99C7C2×C7×D15311yescharacteristic, complemented
100C7C2×D107111yescharacteristic, direct product factor
101C2×C3C7×D35711yescharacteristic
102D3—3572no—
103C22—10711noSylow
104C3C2×C7×D35711yescharacteristic
105C2—10712no—
106C2C7×D107111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C7D1071
commutator, cosocle, hypocenterC7×C9×C17C22×C7
FrattiniC3C2×C7×D357
FittingC2×C72×C9×C17C2
socleC2×C3×C72×C17D3
LCSG ▷ C7×C9×C17
UCSC1 ◁ C2×C7

Complements

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

NH ≅ G/Ntype
1. C7×D1071C2direct (N × H)
2. C2×C72×C9×C17C2semidirect
4. C72×C9×C17C22semidirect
7. C2×D1071C7direct (N × H)
11. D1071C2×C7direct (N × H)
14. C2×C7×C9×C17D7semidirect
15. C2×C7×C9×C17C2×C7semidirect
17. C2×C72×C17D9semidirect
22. C7×C9×C17C2×D7semidirect
23. C7×C9×C17C22×C7semidirect
24. C2×C72×C9D17semidirect
26. C72×C17C2×D9semidirect
36. C72×C9C2×D17semidirect
40. C2×C9×C17C7×D7semidirect
47. C2×C7×C17C7×D9semidirect
48. C2×C7×C17D63semidirect
53. C9×C17C2×C7×D7semidirect
56. C2×C7×C9C7×D17semidirect
57. C2×C7×C9D119semidirect
61. C7×C17C2×C7×D9semidirect
62. C7×C17C2×D63semidirect
65. C2×C72D153semidirect
71. C7×C9C2×C7×D17semidirect
72. C7×C9C2×D119semidirect
74. C72C2×D153semidirect
81. C2×C17C7×D63semidirect
88. C2×C9C7×D119semidirect
90. C17C2×C7×D63semidirect
93. C2×C7C7×D153semidirect
94. C2×C7D1071direct (N × H)
97. C9C2×C7×D119semidirect
99. C7C2×C7×D153semidirect
100. C7C2×D1071direct (N × H)
106. C2C7×D1071direct (N × H)

Maximal subgroups

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

subgroupindex
C7×D10712
C2×C72×C9×C172
C2×C7×D3573
C2×D10717
C2×C7×D1537
C2×C7×D6317