Finite Group Databasebeta

← C2×C3×C112×D21 #44479265

Subgroups — C2×C3×C112×D21 #44479265

Order 30492.

616 conjugacy classes of subgroups; only the 308 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 308 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×C112×D21C212yesmaximal, direct product factor
2C2×C32×C7×C112C211yesmaximal, characteristic, complemented
3C2×C3×C112×D7—31nomaximal
4C2×C112×D21C311yesmaximal, characteristic, direct product factor
5C32×C7×C112C2211yescharacteristic, complemented, Hall
6C112×D21C2×C312yesdirect product factor
7C3×C112×D7—32no—
8C2×C3×C7×C112—21no—
9C2×C3×C7×C112D311yescharacteristic, complemented
10C2×C3×C7×C112C2×C311yescharacteristic, complemented
11C2×C3×D3×C112—71nomaximal, Hall
12C2×C112×D7—31noHall
13C2×C3×C11×D21C11112yesmaximal, direct product factor
14C3×C7×C112—21no—
15C3×C7×C112C2×D311yescharacteristic, complemented
16C3×C7×C112C22×C311yescharacteristic, complemented
17C3×D3×C112—72no—
18C2×C32×C112D711yescharacteristic, complemented
19C2×C7×C112C3×D311yescharacteristic, complemented
20C112×D7—32no—
21C22×C3×C112—211no—
22C2×D3×C112—71no—
23C2×C32×C7×C11C2×C11112yescomplemented
24C3×C11×D21C2×C11124yesdirect product factor
25C32×C112C2×D711yescharacteristic, complemented, Hall
26C2×C11×D21C3×C11112yesdirect product factor
27C2×C3×C11×D7—312no—
28C7×C112C2×C3×D311yescharacteristic, complemented, Hall
29C2×C3×C112—21no—
30C2×C3×C112—212no—
31C2×C3×C112C3×D711yescharacteristic, complemented
32C2×C3×C112D2111yescharacteristic, direct product factor
33D3×C112—72no—
34C32×C7×C11C22×C11112yescomplemented
35C22×C112—211noHall
36C2×C3×C7×C11—212no—
37C2×C3×C7×C11D3×C11112yescomplemented
38C2×C3×C7×C11C2×C3×C11112yescomplemented
39C11×D21C2×C3×C11124yesdirect product factor
40C3×C11×D7—324no—
41C2×C3×D3×C11—712no—
42C3×C112—21no—
43C3×C112C2×C3×D711yescharacteristic, complemented
44C3×C112C2×D2111yescharacteristic, direct product factor
45C2×C11×D7—312no—
46C2×C3×D21C11211yescharacteristic, direct product factor, Hall
47C2×C112—212no—
48C2×C112C3×D2111yescharacteristic, direct product factor
49C3×C7×C11—212no—
50C3×C7×C11C2×D3×C11112yescomplemented
51C3×C7×C11C22×C3×C11112yescomplemented
52C2×C32×C11C11×D7112yescomplemented
53C3×D3×C11—724no—
54C2×C7×C11C3×D3×C11112yescomplemented
55C11×D7—324no—
56C22×C3×C11—2112no—
57C2×D3×C11—712no—
58C2×C32×C7C2×C11211yescharacteristic, complemented
59C3×D21C2×C11212yesdirect product factor
60C112C2×C3×D2111yescharacteristic, direct product factor, Sylow
61C32×C11C2×C11×D7112yescomplemented
62C2×D21C3×C11211yescharacteristic, direct product factor
63C2×C3×D7—31no—
64C7×C11C2×C3×D3×C11112yescomplemented
65C2×C3×C11—212no—
66C2×C3×C11—2124no—
67C2×C3×C11C3×C11×D7112yescomplemented
68C2×C3×C11C11×D21112yesdirect product factor
69D3×C11—724no—
70C32×C7C22×C11211yescharacteristic, complemented, Hall
71C22×C11—2112no—
72C2×C3×C7—21no—
73C2×C3×C7D3×C11211yescharacteristic, complemented
74C2×C3×C7C2×C3×C11211yescharacteristic, complemented
75D21C2×C3×C11212yesdirect product factor
76C3×D7—32no—
77C2×C3×D3—71noHall
78C3×C11—212no—
79C3×C11C2×C3×C11×D7112yescomplemented
80C3×C11C2×C11×D21112yesdirect product factor
81C2×D7—31noHall
82C2×C11—2124no—
83C2×C11C3×C11×D21112yesdirect product factor
84C3×C7—21no—
85C3×C7C2×D3×C11211yescharacteristic, complemented
86C3×C7C22×C3×C11211yescharacteristic, complemented
87C2×C32C112×D711yescharacteristic, complemented
88C3×D3—72no—
89C2×C7C3×D3×C11211yescharacteristic, complemented
90D7—32no—
91C22×C3—211no—
92C2×D3—71no—
93C11C2×C3×C11×D21112yesdirect product factor
94C32C2×C112×D711yescharacteristic, complemented, Sylow
95C7C2×C3×D3×C11211yescharacteristic, complemented, Sylow
96C2×C3—21no—
97C2×C3—212no—
98C2×C3C3×C112×D711yescharacteristic, complemented
99C2×C3C112×D2111yescharacteristic, direct product factor
100D3—72no—
101C22—211noSylow
102C3—21no—
103C3C2×C112×D2111yescharacteristic, direct product factor
104C3C2×C3×C112×D711yescharacteristic, complemented
105C2—212no—
106C2C3×C112×D2111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C112D21
commutator, cosocle, hypocenterC3×C7C22×C3×C112
FrattiniC1G
Fitting, socleC2×C32×C7×C112C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C3×C112

Complements

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

NH ≅ G/Ntype
1. C3×C112×D21C2direct (N × H)
2. C2×C32×C7×C112C2semidirect
4. C2×C112×D21C3direct (N × H)
5. C32×C7×C112C22semidirect
6. C112×D21C2×C3direct (N × H)
9. C2×C3×C7×C112D3semidirect
10. C2×C3×C7×C112C2×C3semidirect
13. C2×C3×C11×D21C11direct (N × H)
15. C3×C7×C112C2×D3semidirect
16. C3×C7×C112C22×C3semidirect
18. C2×C32×C112D7semidirect
19. C2×C7×C112C3×D3semidirect
23. C2×C32×C7×C11C2×C11semidirect
24. C3×C11×D21C2×C11direct (N × H)
25. C32×C112C2×D7semidirect
26. C2×C11×D21C3×C11direct (N × H)
28. C7×C112C2×C3×D3semidirect
31. C2×C3×C112C3×D7semidirect
32. C2×C3×C112D21direct (N × H)
34. C32×C7×C11C22×C11semidirect
37. C2×C3×C7×C11D3×C11semidirect
38. C2×C3×C7×C11C2×C3×C11semidirect
39. C11×D21C2×C3×C11direct (N × H)
43. C3×C112C2×C3×D7semidirect
44. C3×C112C2×D21direct (N × H)
46. C2×C3×D21C112direct (N × H)
48. C2×C112C3×D21direct (N × H)
50. C3×C7×C11C2×D3×C11semidirect
51. C3×C7×C11C22×C3×C11semidirect
52. C2×C32×C11C11×D7semidirect
54. C2×C7×C11C3×D3×C11semidirect
58. C2×C32×C7C2×C112semidirect
59. C3×D21C2×C112direct (N × H)
60. C112C2×C3×D21direct (N × H)
61. C32×C11C2×C11×D7semidirect
62. C2×D21C3×C112direct (N × H)
64. C7×C11C2×C3×D3×C11semidirect
67. C2×C3×C11C3×C11×D7semidirect
68. C2×C3×C11C11×D21direct (N × H)
70. C32×C7C22×C112semidirect
73. C2×C3×C7D3×C112semidirect
74. C2×C3×C7C2×C3×C112semidirect
75. D21C2×C3×C112direct (N × H)
79. C3×C11C2×C3×C11×D7semidirect
80. C3×C11C2×C11×D21direct (N × H)
83. C2×C11C3×C11×D21direct (N × H)
85. C3×C7C2×D3×C112semidirect
86. C3×C7C22×C3×C112semidirect
87. C2×C32C112×D7semidirect
89. C2×C7C3×D3×C112semidirect
93. C11C2×C3×C11×D21direct (N × H)
94. C32C2×C112×D7semidirect
95. C7C2×C3×D3×C112semidirect
98. C2×C3C3×C112×D7semidirect
99. C2×C3C112×D21direct (N × H)
103. C3C2×C112×D21direct (N × H)
104. C3C2×C3×C112×D7semidirect
106. C2C3×C112×D21direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C112×D212
C2×C32×C7×C1122
C2×C3×C112×D73
C2×C112×D213
C2×C3×D3×C1127
C2×C3×C11×D2111