Finite Group Databasebeta

← C2×C3×C5×C7×C11×D7 #44568933

Subgroups — C2×C3×C5×C7×C11×D7 #44568933

Order 32340.

208 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 112 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×C5×C7×C11×D7C212yesmaximal, direct product factor
2C2×C3×C5×C72×C11C211yesmaximal, characteristic, complemented
3C2×C5×C7×C11×D7C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C2×C3×C7×C11×D7C511yesmaximal, characteristic, direct product factor, Hall
6C5×C7×C11×D7C2×C312yesdirect product factor
7C2×C5×C72×C11C2×C311yescharacteristic, complemented
8C2×C3×C5×C11×D7C711yesmaximal, characteristic, direct product factor
9C22×C3×C5×C7×C11—71nomaximal
10C3×C7×C11×D7C2×C512yesdirect product factor
11C2×C3×C72×C11C2×C511yescharacteristic, complemented
12C2×C3×C5×C7×D7C1111yesmaximal, characteristic, direct product factor, Hall
13C5×C72×C11C22×C311yescharacteristic, complemented, Hall
14C3×C5×C11×D7C2×C712yesdirect product factor
15C2×C3×C5×C7×C11—23no—
16C2×C3×C5×C7×C11—72no—
17C2×C3×C5×C7×C11D711yescharacteristic, direct product factor
18C2×C3×C5×C7×C11C2×C711yescharacteristic, complemented
19C2×C7×C11×D7C3×C511yescharacteristic, direct product factor, Hall
20C3×C72×C11C22×C511yescharacteristic, complemented, Hall
21C22×C5×C7×C11—71no—
22C2×C5×C11×D7C3×C711yescharacteristic, direct product factor
23C2×C3×C5×C72C2×C1111yescharacteristic, complemented
24C3×C5×C7×D7C2×C1112yesdirect product factor
25C3×C5×C7×C11—23no—
26C3×C5×C7×C11C2×D711yescharacteristic, direct product factor
27C3×C5×C7×C11C22×C711yescharacteristic, complemented
28C2×C72×C11C2×C3×C511yescharacteristic, complemented
29C7×C11×D7C2×C3×C512yesdirect product factor
30C2×C5×C7×D7C3×C1111yescharacteristic, direct product factor, Hall
31C22×C3×C7×C11—71no—
32C2×C3×C11×D7C5×C711yescharacteristic, direct product factor
33C2×C5×C7×C11—23no—
34C2×C5×C7×C11—72no—
35C2×C5×C7×C11C3×D711yescharacteristic, direct product factor
36C2×C5×C7×C11C2×C3×C711yescharacteristic, complemented
37C5×C11×D7C2×C3×C712yesdirect product factor
38C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
39C22×C3×C5×C11—71noHall
40C2×C3×C7×D7C5×C1111yescharacteristic, direct product factor, Hall
41C72×C11C22×C3×C511yescharacteristic, complemented, Hall
42C2×C5×C72C2×C3×C1111yescharacteristic, complemented
43C5×C7×D7C2×C3×C1112yesdirect product factor
44C2×C3×C7×C11—23no—
45C2×C3×C7×C11—72no—
46C2×C3×C7×C11C5×D711yescharacteristic, direct product factor
47C2×C3×C7×C11C2×C5×C711yescharacteristic, complemented
48C3×C11×D7C2×C5×C712yesdirect product factor
49C22×C3×C5×C7—71no—
50C2×C3×C5×D7C7×C1111yescharacteristic, direct product factor
51C5×C7×C11—23no—
52C5×C7×C11C2×C3×D711yescharacteristic, direct product factor
53C5×C7×C11C22×C3×C711yescharacteristic, complemented
54C2×C3×C5×C11—72no—
55C2×C3×C5×C11C7×D711yescharacteristic, direct product factor
56C22×C7×C11—71no—
57C2×C11×D7C3×C5×C711yescharacteristic, direct product factor
58C2×C3×C72C2×C5×C1111yescharacteristic, complemented
59C3×C7×D7C2×C5×C1112yesdirect product factor
60C5×C72C22×C3×C1111yescharacteristic, complemented, Hall
61C3×C7×C11—23no—
62C3×C7×C11C2×C5×D711yescharacteristic, direct product factor
63C3×C7×C11C22×C5×C711yescharacteristic, complemented
64C22×C5×C11—71noHall
65C2×C3×C5×C7—23no—
66C2×C3×C5×C7—72no—
67C2×C3×C5×C7C11×D711yescharacteristic, direct product factor
68C2×C3×C5×C7C2×C7×C1111yescharacteristic, complemented
69C3×C5×D7C2×C7×C1112yesdirect product factor
70C2×C7×D7C3×C5×C1111yescharacteristic, direct product factor, Hall
71C3×C5×C11C2×C7×D711yescharacteristic, direct product factor, Hall
72C2×C7×C11—23no—
73C2×C7×C11—72no—
74C2×C7×C11C3×C5×D711yescharacteristic, direct product factor
75C2×C7×C11C2×C3×C5×C711yescharacteristic, complemented
76C11×D7C2×C3×C5×C712yesdirect product factor
77C3×C72C22×C5×C1111yescharacteristic, complemented, Hall
78C22×C5×C7—71no—
79C2×C5×D7C3×C7×C1111yescharacteristic, direct product factor
80C22×C3×C11—71noHall
81C2×C5×C11—72no—
82C2×C5×C11C3×C7×D711yescharacteristic, direct product factor
83C3×C5×C7—23no—
84C3×C5×C7C2×C11×D711yescharacteristic, direct product factor
85C3×C5×C7C22×C7×C1111yescharacteristic, complemented
86C2×C72C2×C3×C5×C1111yescharacteristic, complemented
87C7×D7C2×C3×C5×C1112yesdirect product factor
88C22×C3×C7—71no—
89C2×C3×D7C5×C7×C1111yescharacteristic, direct product factor
90C7×C11—23no—
91C7×C11C2×C3×C5×D711yescharacteristic, direct product factor
92C7×C11C22×C3×C5×C711yescharacteristic, complemented
93C2×C5×C7—23no—
94C2×C5×C7—72no—
95C2×C5×C7C3×C11×D711yescharacteristic, direct product factor
96C2×C5×C7C2×C3×C7×C1111yescharacteristic, complemented
97C5×D7C2×C3×C7×C1112yesdirect product factor
98C2×C3×C11—72no—
99C2×C3×C11C5×C7×D711yescharacteristic, direct product factor
100C22×C3×C5—71noHall
101C5×C11C2×C3×C7×D711yescharacteristic, direct product factor, Hall
102C72C22×C3×C5×C1111yescharacteristic, complemented, Sylow
103C22×C11—71noHall
104C2×C3×C7—23no—
105C2×C3×C7—72no—
106C2×C3×C7C5×C11×D711yescharacteristic, direct product factor
107C2×C3×C7C2×C5×C7×C1111yescharacteristic, complemented
108C3×D7C2×C5×C7×C1112yesdirect product factor
109C5×C7—23no—
110C5×C7C2×C3×C11×D711yescharacteristic, direct product factor
111C5×C7C22×C3×C7×C1111yescharacteristic, complemented
112C3×C11C2×C5×C7×D711yescharacteristic, direct product factor, Hall
113C2×C3×C5—72no—
114C2×C3×C5C7×C11×D711yescharacteristic, direct product factor
115C22×C7—71no—
116C2×D7C3×C5×C7×C1111yescharacteristic, direct product factor
117C2×C11—72no—
118C2×C11C3×C5×C7×D711yescharacteristic, direct product factor
119C3×C7—23no—
120C3×C7C2×C5×C11×D711yescharacteristic, direct product factor
121C3×C7C22×C5×C7×C1111yescharacteristic, complemented
122C22×C5—71noHall
123C3×C5C2×C7×C11×D711yescharacteristic, direct product factor, Hall
124C2×C7—23no—
125C2×C7—72no—
126C2×C7C2×C3×C5×C7×C1111yescharacteristic, complemented
127C2×C7C3×C5×C11×D711yescharacteristic, direct product factor
128D7C2×C3×C5×C7×C1112yesdirect product factor
129C22×C3—71noHall
130C11C2×C3×C5×C7×D711yescharacteristic, direct product factor, Sylow
131C2×C5—72no—
132C2×C5C3×C7×C11×D711yescharacteristic, direct product factor
133C7—23no—
134C7C22×C3×C5×C7×C1111yescharacteristic, complemented
135C7C2×C3×C5×C11×D711yescharacteristic, direct product factor
136C2×C3—72no—
137C2×C3C5×C7×C11×D711yescharacteristic, direct product factor
138C5C2×C3×C7×C11×D711yescharacteristic, direct product factor, Sylow
139C22—71noSylow
140C3C2×C5×C7×C11×D711yescharacteristic, direct product factor, Sylow
141C2—72no—
142C2C3×C5×C7×C11×D711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5×C7×C11D7
commutator, cosocle, hypocenterC7C22×C3×C5×C7×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C7×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×C11×D7C2direct (N × H)
2. C2×C3×C5×C72×C11C2semidirect
3. C2×C5×C7×C11×D7C3direct (N × H)
4. C3×C5×C72×C11C22semidirect
5. C2×C3×C7×C11×D7C5direct (N × H)
6. C5×C7×C11×D7C2×C3direct (N × H)
7. C2×C5×C72×C11C2×C3semidirect
8. C2×C3×C5×C11×D7C7direct (N × H)
10. C3×C7×C11×D7C2×C5direct (N × H)
11. C2×C3×C72×C11C2×C5semidirect
12. C2×C3×C5×C7×D7C11direct (N × H)
13. C5×C72×C11C22×C3semidirect
14. C3×C5×C11×D7C2×C7direct (N × H)
17. C2×C3×C5×C7×C11D7direct (N × H)
18. C2×C3×C5×C7×C11C2×C7semidirect
19. C2×C7×C11×D7C3×C5direct (N × H)
20. C3×C72×C11C22×C5semidirect
22. C2×C5×C11×D7C3×C7direct (N × H)
23. C2×C3×C5×C72C2×C11semidirect
24. C3×C5×C7×D7C2×C11direct (N × H)
26. C3×C5×C7×C11C2×D7direct (N × H)
27. C3×C5×C7×C11C22×C7semidirect
28. C2×C72×C11C2×C3×C5semidirect
29. C7×C11×D7C2×C3×C5direct (N × H)
30. C2×C5×C7×D7C3×C11direct (N × H)
32. C2×C3×C11×D7C5×C7direct (N × H)
35. C2×C5×C7×C11C3×D7direct (N × H)
36. C2×C5×C7×C11C2×C3×C7semidirect
37. C5×C11×D7C2×C3×C7direct (N × H)
38. C3×C5×C72C22×C11semidirect
40. C2×C3×C7×D7C5×C11direct (N × H)
41. C72×C11C22×C3×C5semidirect
42. C2×C5×C72C2×C3×C11semidirect
43. C5×C7×D7C2×C3×C11direct (N × H)
46. C2×C3×C7×C11C5×D7direct (N × H)
47. C2×C3×C7×C11C2×C5×C7semidirect
48. C3×C11×D7C2×C5×C7direct (N × H)
50. C2×C3×C5×D7C7×C11direct (N × H)
52. C5×C7×C11C2×C3×D7direct (N × H)
53. C5×C7×C11C22×C3×C7semidirect
55. C2×C3×C5×C11C7×D7direct (N × H)
57. C2×C11×D7C3×C5×C7direct (N × H)
58. C2×C3×C72C2×C5×C11semidirect
59. C3×C7×D7C2×C5×C11direct (N × H)
60. C5×C72C22×C3×C11semidirect
62. C3×C7×C11C2×C5×D7direct (N × H)
63. C3×C7×C11C22×C5×C7semidirect
67. C2×C3×C5×C7C11×D7direct (N × H)
68. C2×C3×C5×C7C2×C7×C11semidirect
69. C3×C5×D7C2×C7×C11direct (N × H)
70. C2×C7×D7C3×C5×C11direct (N × H)
71. C3×C5×C11C2×C7×D7direct (N × H)
74. C2×C7×C11C3×C5×D7direct (N × H)
75. C2×C7×C11C2×C3×C5×C7semidirect
76. C11×D7C2×C3×C5×C7direct (N × H)
77. C3×C72C22×C5×C11semidirect
79. C2×C5×D7C3×C7×C11direct (N × H)
82. C2×C5×C11C3×C7×D7direct (N × H)
84. C3×C5×C7C2×C11×D7direct (N × H)
85. C3×C5×C7C22×C7×C11semidirect
86. C2×C72C2×C3×C5×C11semidirect
87. C7×D7C2×C3×C5×C11direct (N × H)
89. C2×C3×D7C5×C7×C11direct (N × H)
91. C7×C11C2×C3×C5×D7direct (N × H)
92. C7×C11C22×C3×C5×C7semidirect
95. C2×C5×C7C3×C11×D7direct (N × H)
96. C2×C5×C7C2×C3×C7×C11semidirect
97. C5×D7C2×C3×C7×C11direct (N × H)
99. C2×C3×C11C5×C7×D7direct (N × H)
101. C5×C11C2×C3×C7×D7direct (N × H)
102. C72C22×C3×C5×C11semidirect
106. C2×C3×C7C5×C11×D7direct (N × H)
107. C2×C3×C7C2×C5×C7×C11semidirect
108. C3×D7C2×C5×C7×C11direct (N × H)
110. C5×C7C2×C3×C11×D7direct (N × H)
111. C5×C7C22×C3×C7×C11semidirect
112. C3×C11C2×C5×C7×D7direct (N × H)
114. C2×C3×C5C7×C11×D7direct (N × H)
116. C2×D7C3×C5×C7×C11direct (N × H)
118. C2×C11C3×C5×C7×D7direct (N × H)
120. C3×C7C2×C5×C11×D7direct (N × H)
121. C3×C7C22×C5×C7×C11semidirect
123. C3×C5C2×C7×C11×D7direct (N × H)
126. C2×C7C2×C3×C5×C7×C11semidirect
127. C2×C7C3×C5×C11×D7direct (N × H)
128. D7C2×C3×C5×C7×C11direct (N × H)
130. C11C2×C3×C5×C7×D7direct (N × H)
132. C2×C5C3×C7×C11×D7direct (N × H)
134. C7C22×C3×C5×C7×C11semidirect
135. C7C2×C3×C5×C11×D7direct (N × H)
137. C2×C3C5×C7×C11×D7direct (N × H)
138. C5C2×C3×C7×C11×D7direct (N × H)
140. C3C2×C5×C7×C11×D7direct (N × H)
142. C2C3×C5×C7×C11×D7direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×C11×D72
C2×C3×C5×C72×C112
C2×C5×C7×C11×D73
C2×C3×C7×C11×D75
C2×C3×C5×C11×D77
C22×C3×C5×C7×C117
C2×C3×C5×C7×D711