Finite Group Databasebeta

← C2×C5×C7×C11×D21 #44568945

Subgroups — C2×C5×C7×C11×D21 #44568945

Order 32340.

208 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C5×C7×C11×D21C212yesmaximal, direct product factor
2C2×C3×C5×C72×C11C211yesmaximal, characteristic, complemented
3C2×C5×C7×C11×D7—31nomaximal, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C2×C7×C11×D21C511yesmaximal, characteristic, direct product factor, Hall
6C5×C7×C11×D7—32no—
7C2×C5×C72×C11D311yescharacteristic, complemented
8C2×C5×C11×D21C711yesmaximal, characteristic, direct product factor
9C2×C5×D3×C7×C11—71nomaximal
10C7×C11×D21C2×C512yesdirect product factor
11C2×C3×C72×C11C2×C511yescharacteristic, complemented
12C2×C5×C7×D21C1111yesmaximal, characteristic, direct product factor, Hall
13C5×C72×C11C2×D311yescharacteristic, complemented, Hall
14C5×C11×D21C2×C712yesdirect product factor
15C5×D3×C7×C11—72no—
16C2×C3×C5×C7×C11—23no—
17C2×C3×C5×C7×C11D711yescharacteristic, complemented
18C2×C3×C5×C7×C11C2×C711yescharacteristic, complemented
19C2×C7×C11×D7—31noHall
20C3×C72×C11C22×C511yescharacteristic, complemented, Hall
21C22×C5×C7×C11—211no—
22C2×C5×C11×D7—31no—
23C2×C3×C5×C72C2×C1111yescharacteristic, complemented
24C5×C7×D21C2×C1112yesdirect product factor
25C3×C5×C7×C11—23no—
26C3×C5×C7×C11C2×D711yescharacteristic, complemented
27C3×C5×C7×C11C22×C711yescharacteristic, complemented
28C2×C72×C11C5×D311yescharacteristic, complemented
29C7×C11×D7—32no—
30C2×C5×C7×D7—31noHall
31C2×C11×D21C5×C711yescharacteristic, direct product factor
32C2×D3×C7×C11—71no—
33C2×C5×C7×C11—23no—
34C2×C5×C7×C11—212no—
35C2×C5×C7×C11D3×C711yescharacteristic, complemented
36C2×C5×C7×C11D2111yescharacteristic, direct product factor
37C5×C11×D7—32no—
38C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
39C2×C5×D3×C11—71noHall
40C2×C7×D21C5×C1111yescharacteristic, direct product factor, Hall
41C72×C11C2×C5×D311yescharacteristic, complemented, Hall
42C2×C5×C72D3×C1111yescharacteristic, complemented
43C5×C7×D7—32no—
44C2×C3×C7×C11—23no—
45C2×C3×C7×C11C5×D711yescharacteristic, complemented
46C2×C3×C7×C11C2×C5×C711yescharacteristic, complemented
47C11×D21C2×C5×C712yesdirect product factor
48D3×C7×C11—72no—
49C2×C5×D21C7×C1111yescharacteristic, direct product factor
50C2×C5×D3×C7—71no—
51C5×C7×C11—23no—
52C5×C7×C11C2×D3×C711yescharacteristic, complemented
53C5×C7×C11C2×D2111yescharacteristic, direct product factor
54C2×C3×C5×C11C7×D711yescharacteristic, complemented
55C5×D3×C11—72no—
56C22×C7×C11—211no—
57C2×C11×D7—31no—
58C2×C3×C72C2×C5×C1111yescharacteristic, complemented
59C7×D21C2×C5×C1112yesdirect product factor
60C5×C72C2×D3×C1111yescharacteristic, complemented, Hall
61C3×C7×C11—23no—
62C3×C7×C11C2×C5×D711yescharacteristic, complemented
63C3×C7×C11C22×C5×C711yescharacteristic, complemented
64C22×C5×C11—211noHall
65C2×C3×C5×C7—23no—
66C2×C3×C5×C7C11×D711yescharacteristic, complemented
67C2×C3×C5×C7C2×C7×C1111yescharacteristic, complemented
68C5×D21C2×C7×C1112yesdirect product factor
69C5×D3×C7—72no—
70C2×C7×D7—31noHall
71C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
72C2×C7×C11—23no—
73C2×C7×C11—212no—
74C2×C7×C11C5×D3×C711yescharacteristic, complemented
75C2×C7×C11C5×D2111yescharacteristic, direct product factor
76C11×D7—32no—
77C3×C72C22×C5×C1111yescharacteristic, complemented, Hall
78C22×C5×C7—211no—
79C2×C5×D7—31no—
80C2×D3×C11—71noHall
81C2×C5×C11—212no—
82C2×C5×C11C7×D2111yescharacteristic, direct product factor
83C3×C5×C7—23no—
84C3×C5×C7C2×C11×D711yescharacteristic, complemented
85C3×C5×C7C22×C7×C1111yescharacteristic, complemented
86C2×C72C5×D3×C1111yescharacteristic, complemented
87C7×D7—32no—
88C2×D21C5×C7×C1111yescharacteristic, direct product factor
89C2×D3×C7—71no—
90C7×C11—23no—
91C7×C11C2×C5×D3×C711yescharacteristic, complemented
92C7×C11C2×C5×D2111yescharacteristic, direct product factor
93C2×C5×C7—23no—
94C2×C5×C7—212no—
95C2×C5×C7D3×C7×C1111yescharacteristic, complemented
96C2×C5×C7C11×D2111yescharacteristic, direct product factor
97C5×D7—32no—
98C2×C3×C11C5×C7×D711yescharacteristic, complemented
99D3×C11—72no—
100C2×C5×D3—71noHall
101C5×C11C2×C7×D2111yescharacteristic, direct product factor, Hall
102C72C2×C5×D3×C1111yescharacteristic, complemented, Sylow
103C22×C11—211noHall
104C2×C3×C7—23no—
105C2×C3×C7C5×C11×D711yescharacteristic, complemented
106C2×C3×C7C2×C5×C7×C1111yescharacteristic, complemented
107D21C2×C5×C7×C1112yesdirect product factor
108D3×C7—72no—
109C5×C7—23no—
110C5×C7C2×D3×C7×C1111yescharacteristic, complemented
111C5×C7C2×C11×D2111yescharacteristic, direct product factor
112C3×C11C2×C5×C7×D711yescharacteristic, complemented, Hall
113C2×C3×C5C7×C11×D711yescharacteristic, complemented
114C5×D3—72no—
115C22×C7—211no—
116C2×D7—31no—
117C2×C11—212no—
118C2×C11C5×C7×D2111yescharacteristic, direct product factor
119C3×C7—23no—
120C3×C7C2×C5×C11×D711yescharacteristic, complemented
121C3×C7C22×C5×C7×C1111yescharacteristic, complemented
122C22×C5—211noHall
123C3×C5C2×C7×C11×D711yescharacteristic, complemented, Hall
124C2×C7—23no—
125C2×C7—212no—
126C2×C7C5×D3×C7×C1111yescharacteristic, complemented
127C2×C7C5×C11×D2111yescharacteristic, direct product factor
128D7—32no—
129C2×D3—71noHall
130C11C2×C5×C7×D2111yescharacteristic, direct product factor, Sylow
131C2×C5—212no—
132C2×C5C7×C11×D2111yescharacteristic, direct product factor
133C7—23no—
134C7C2×C5×D3×C7×C1111yescharacteristic, complemented
135C7C2×C5×C11×D2111yescharacteristic, direct product factor
136C2×C3C5×C7×C11×D711yescharacteristic, complemented
137D3—72no—
138C5C2×C7×C11×D2111yescharacteristic, direct product factor, Sylow
139C22—211noSylow
140C3C2×C5×C7×C11×D711yescharacteristic, complemented, Sylow
141C2—212no—
142C2C5×C7×C11×D2111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C7×C11D21
commutator, cosocle, hypocenterC3×C7C22×C5×C7×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C5×C7×C11

Complements

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

NH ≅ G/Ntype
1. C5×C7×C11×D21C2direct (N × H)
2. C2×C3×C5×C72×C11C2semidirect
4. C3×C5×C72×C11C22semidirect
5. C2×C7×C11×D21C5direct (N × H)
7. C2×C5×C72×C11D3semidirect
8. C2×C5×C11×D21C7direct (N × H)
10. C7×C11×D21C2×C5direct (N × H)
11. C2×C3×C72×C11C2×C5semidirect
12. C2×C5×C7×D21C11direct (N × H)
13. C5×C72×C11C2×D3semidirect
14. C5×C11×D21C2×C7direct (N × H)
17. C2×C3×C5×C7×C11D7semidirect
18. C2×C3×C5×C7×C11C2×C7semidirect
20. C3×C72×C11C22×C5semidirect
23. C2×C3×C5×C72C2×C11semidirect
24. C5×C7×D21C2×C11direct (N × H)
26. C3×C5×C7×C11C2×D7semidirect
27. C3×C5×C7×C11C22×C7semidirect
28. C2×C72×C11C5×D3semidirect
31. C2×C11×D21C5×C7direct (N × H)
35. C2×C5×C7×C11D3×C7semidirect
36. C2×C5×C7×C11D21direct (N × H)
38. C3×C5×C72C22×C11semidirect
40. C2×C7×D21C5×C11direct (N × H)
41. C72×C11C2×C5×D3semidirect
42. C2×C5×C72D3×C11semidirect
45. C2×C3×C7×C11C5×D7semidirect
46. C2×C3×C7×C11C2×C5×C7semidirect
47. C11×D21C2×C5×C7direct (N × H)
49. C2×C5×D21C7×C11direct (N × H)
52. C5×C7×C11C2×D3×C7semidirect
53. C5×C7×C11C2×D21direct (N × H)
54. C2×C3×C5×C11C7×D7semidirect
58. C2×C3×C72C2×C5×C11semidirect
59. C7×D21C2×C5×C11direct (N × H)
60. C5×C72C2×D3×C11semidirect
62. C3×C7×C11C2×C5×D7semidirect
63. C3×C7×C11C22×C5×C7semidirect
66. C2×C3×C5×C7C11×D7semidirect
67. C2×C3×C5×C7C2×C7×C11semidirect
68. C5×D21C2×C7×C11direct (N × H)
71. C3×C5×C11C2×C7×D7semidirect
74. C2×C7×C11C5×D3×C7semidirect
75. C2×C7×C11C5×D21direct (N × H)
77. C3×C72C22×C5×C11semidirect
82. C2×C5×C11C7×D21direct (N × H)
84. C3×C5×C7C2×C11×D7semidirect
85. C3×C5×C7C22×C7×C11semidirect
86. C2×C72C5×D3×C11semidirect
88. C2×D21C5×C7×C11direct (N × H)
91. C7×C11C2×C5×D3×C7semidirect
92. C7×C11C2×C5×D21direct (N × H)
95. C2×C5×C7D3×C7×C11semidirect
96. C2×C5×C7C11×D21direct (N × H)
98. C2×C3×C11C5×C7×D7semidirect
101. C5×C11C2×C7×D21direct (N × H)
102. C72C2×C5×D3×C11semidirect
105. C2×C3×C7C5×C11×D7semidirect
106. C2×C3×C7C2×C5×C7×C11semidirect
107. D21C2×C5×C7×C11direct (N × H)
110. C5×C7C2×D3×C7×C11semidirect
111. C5×C7C2×C11×D21direct (N × H)
112. C3×C11C2×C5×C7×D7semidirect
113. C2×C3×C5C7×C11×D7semidirect
118. C2×C11C5×C7×D21direct (N × H)
120. C3×C7C2×C5×C11×D7semidirect
121. C3×C7C22×C5×C7×C11semidirect
123. C3×C5C2×C7×C11×D7semidirect
126. C2×C7C5×D3×C7×C11semidirect
127. C2×C7C5×C11×D21direct (N × H)
130. C11C2×C5×C7×D21direct (N × H)
132. C2×C5C7×C11×D21direct (N × H)
134. C7C2×C5×D3×C7×C11semidirect
135. C7C2×C5×C11×D21direct (N × H)
136. C2×C3C5×C7×C11×D7semidirect
138. C5C2×C7×C11×D21direct (N × H)
140. C3C2×C5×C7×C11×D7semidirect
142. C2C5×C7×C11×D21direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C7×C11×D212
C2×C3×C5×C72×C112
C2×C5×C7×C11×D73
C2×C7×C11×D215
C2×C5×C11×D217
C2×C5×D3×C7×C117
C2×C5×C7×D2111