Finite Group Databasebeta

← C2×C3×C7×C11×D35 #44568939

Subgroups — C2×C3×C7×C11×D35 #44568939

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
1C3×C7×C11×D35C212yesmaximal, direct product factor
2C2×C3×C5×C72×C11C211yesmaximal, characteristic, complemented
3C2×C7×C11×D35C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C2×C3×C7×C11×D7—51nomaximal, Hall
6C7×C11×D35C2×C312yesdirect product factor
7C2×C5×C72×C11C2×C311yescharacteristic, complemented
8C2×C3×C11×D35C711yesmaximal, characteristic, direct product factor
9C2×C3×C7×D5×C11—71nomaximal
10C3×C7×C11×D7—52no—
11C2×C3×C72×C11D511yescharacteristic, complemented
12C2×C3×C7×D35C1111yesmaximal, characteristic, direct product factor, Hall
13C5×C72×C11C22×C311yescharacteristic, complemented, Hall
14C3×C11×D35C2×C712yesdirect product factor
15C3×C7×D5×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—51noHall
20C3×C72×C11C2×D511yescharacteristic, complemented, Hall
21C2×C11×D35C3×C711yescharacteristic, direct product factor
22C2×C7×D5×C11—71no—
23C2×C3×C5×C72C2×C1111yescharacteristic, complemented
24C3×C7×D35C2×C1112yesdirect product factor
25C3×C5×C7×C11—23no—
26C3×C5×C7×C11C2×D711yescharacteristic, complemented
27C3×C5×C7×C11C22×C711yescharacteristic, complemented
28C2×C72×C11C3×D511yescharacteristic, complemented
29C7×C11×D7—52no—
30C2×C7×D35C3×C1111yescharacteristic, direct product factor, Hall
31C22×C3×C7×C11—351no—
32C2×C3×C11×D7—51no—
33C2×C5×C7×C11—23no—
34C2×C5×C7×C11C3×D711yescharacteristic, complemented
35C2×C5×C7×C11C2×C3×C711yescharacteristic, complemented
36C11×D35C2×C3×C712yesdirect product factor
37C7×D5×C11—72no—
38C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
39C2×C3×D5×C11—71noHall
40C2×C3×C7×D7—51noHall
41C72×C11C2×C3×D511yescharacteristic, complemented, Hall
42C2×C5×C72C2×C3×C1111yescharacteristic, complemented
43C7×D35C2×C3×C1112yesdirect product factor
44C2×C3×C7×C11—23no—
45C2×C3×C7×C11—352no—
46C2×C3×C7×C11C7×D511yescharacteristic, complemented
47C2×C3×C7×C11D3511yescharacteristic, direct product factor
48C3×C11×D7—52no—
49C2×C3×D35C7×C1111yescharacteristic, direct product factor
50C2×C3×C7×D5—71no—
51C5×C7×C11—23no—
52C5×C7×C11C2×C3×D711yescharacteristic, complemented
53C5×C7×C11C22×C3×C711yescharacteristic, complemented
54C2×C3×C5×C11C7×D711yescharacteristic, complemented
55C3×D5×C11—72no—
56C22×C7×C11—351no—
57C2×C11×D7—51no—
58C2×C3×C72D5×C1111yescharacteristic, complemented
59C3×C7×D7—52no—
60C5×C72C22×C3×C1111yescharacteristic, complemented, Hall
61C3×C7×C11—23no—
62C3×C7×C11C2×C7×D511yescharacteristic, complemented
63C3×C7×C11C2×D3511yescharacteristic, direct product factor
64C2×D5×C11—71noHall
65C2×C3×C5×C7—23no—
66C2×C3×C5×C7C11×D711yescharacteristic, complemented
67C2×C3×C5×C7C2×C7×C1111yescharacteristic, complemented
68C3×D35C2×C7×C1112yesdirect product factor
69C3×C7×D5—72no—
70C2×C7×D7—51noHall
71C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
72C2×C7×C11—23no—
73C2×C7×C11—352no—
74C2×C7×C11C3×C7×D511yescharacteristic, complemented
75C2×C7×C11C3×D3511yescharacteristic, direct product factor
76C11×D7—52no—
77C3×C72C2×D5×C1111yescharacteristic, complemented, Hall
78C2×D35C3×C7×C1111yescharacteristic, direct product factor
79C2×C7×D5—71no—
80C22×C3×C11—351noHall
81C2×C5×C11C3×C7×D711yescharacteristic, complemented
82D5×C11—72no—
83C3×C5×C7—23no—
84C3×C5×C7C2×C11×D711yescharacteristic, complemented
85C3×C5×C7C22×C7×C1111yescharacteristic, complemented
86C2×C72C3×D5×C1111yescharacteristic, complemented
87C7×D7—52no—
88C22×C3×C7—351no—
89C2×C3×D7—51no—
90C7×C11—23no—
91C7×C11C2×C3×C7×D511yescharacteristic, complemented
92C7×C11C2×C3×D3511yescharacteristic, direct product factor
93C2×C5×C7—23no—
94C2×C5×C7C3×C11×D711yescharacteristic, complemented
95C2×C5×C7C2×C3×C7×C1111yescharacteristic, complemented
96D35C2×C3×C7×C1112yesdirect product factor
97C7×D5—72no—
98C2×C3×C11—352no—
99C2×C3×C11C7×D3511yescharacteristic, direct product factor
100C2×C3×D5—71noHall
101C5×C11C2×C3×C7×D711yescharacteristic, complemented, Hall
102C72C2×C3×D5×C1111yescharacteristic, complemented, Sylow
103C22×C11—351noHall
104C2×C3×C7—23no—
105C2×C3×C7—352no—
106C2×C3×C7C7×D5×C1111yescharacteristic, complemented
107C2×C3×C7C11×D3511yescharacteristic, direct product factor
108C3×D7—52no—
109C5×C7—23no—
110C5×C7C2×C3×C11×D711yescharacteristic, complemented
111C5×C7C22×C3×C7×C1111yescharacteristic, complemented
112C3×C11C2×C7×D3511yescharacteristic, direct product factor, Hall
113C2×C3×C5C7×C11×D711yescharacteristic, complemented
114C3×D5—72no—
115C22×C7—351no—
116C2×D7—51no—
117C2×C11—352no—
118C2×C11C3×C7×D3511yescharacteristic, direct product factor
119C3×C7—23no—
120C3×C7C2×C7×D5×C1111yescharacteristic, complemented
121C3×C7C2×C11×D3511yescharacteristic, direct product factor
122C2×D5—71noHall
123C3×C5C2×C7×C11×D711yescharacteristic, complemented, Hall
124C2×C7—23no—
125C2×C7—352no—
126C2×C7C3×C7×D5×C1111yescharacteristic, complemented
127C2×C7C3×C11×D3511yescharacteristic, direct product factor
128D7—52no—
129C22×C3—351noHall
130C11C2×C3×C7×D3511yescharacteristic, direct product factor, Sylow
131C2×C5C3×C7×C11×D711yescharacteristic, complemented
132D5—72no—
133C7—23no—
134C7C2×C3×C7×D5×C1111yescharacteristic, complemented
135C7C2×C3×C11×D3511yescharacteristic, direct product factor
136C2×C3—352no—
137C2×C3C7×C11×D3511yescharacteristic, direct product factor
138C5C2×C3×C7×C11×D711yescharacteristic, complemented, Sylow
139C22—351noSylow
140C3C2×C7×C11×D3511yescharacteristic, direct product factor, Sylow
141C2—352no—
142C2C3×C7×C11×D3511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7×C11D35
commutator, cosocle, hypocenterC5×C7C22×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C7×C11

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×D35C2direct (N × H)
2. C2×C3×C5×C72×C11C2semidirect
3. C2×C7×C11×D35C3direct (N × H)
4. C3×C5×C72×C11C22semidirect
6. C7×C11×D35C2×C3direct (N × H)
7. C2×C5×C72×C11C2×C3semidirect
8. C2×C3×C11×D35C7direct (N × H)
11. C2×C3×C72×C11D5semidirect
12. C2×C3×C7×D35C11direct (N × H)
13. C5×C72×C11C22×C3semidirect
14. C3×C11×D35C2×C7direct (N × H)
17. C2×C3×C5×C7×C11D7semidirect
18. C2×C3×C5×C7×C11C2×C7semidirect
20. C3×C72×C11C2×D5semidirect
21. C2×C11×D35C3×C7direct (N × H)
23. C2×C3×C5×C72C2×C11semidirect
24. C3×C7×D35C2×C11direct (N × H)
26. C3×C5×C7×C11C2×D7semidirect
27. C3×C5×C7×C11C22×C7semidirect
28. C2×C72×C11C3×D5semidirect
30. C2×C7×D35C3×C11direct (N × H)
34. C2×C5×C7×C11C3×D7semidirect
35. C2×C5×C7×C11C2×C3×C7semidirect
36. C11×D35C2×C3×C7direct (N × H)
38. C3×C5×C72C22×C11semidirect
41. C72×C11C2×C3×D5semidirect
42. C2×C5×C72C2×C3×C11semidirect
43. C7×D35C2×C3×C11direct (N × H)
46. C2×C3×C7×C11C7×D5semidirect
47. C2×C3×C7×C11D35direct (N × H)
49. C2×C3×D35C7×C11direct (N × H)
52. C5×C7×C11C2×C3×D7semidirect
53. C5×C7×C11C22×C3×C7semidirect
54. C2×C3×C5×C11C7×D7semidirect
58. C2×C3×C72D5×C11semidirect
60. C5×C72C22×C3×C11semidirect
62. C3×C7×C11C2×C7×D5semidirect
63. C3×C7×C11C2×D35direct (N × H)
66. C2×C3×C5×C7C11×D7semidirect
67. C2×C3×C5×C7C2×C7×C11semidirect
68. C3×D35C2×C7×C11direct (N × H)
71. C3×C5×C11C2×C7×D7semidirect
74. C2×C7×C11C3×C7×D5semidirect
75. C2×C7×C11C3×D35direct (N × H)
77. C3×C72C2×D5×C11semidirect
78. C2×D35C3×C7×C11direct (N × H)
81. C2×C5×C11C3×C7×D7semidirect
84. C3×C5×C7C2×C11×D7semidirect
85. C3×C5×C7C22×C7×C11semidirect
86. C2×C72C3×D5×C11semidirect
91. C7×C11C2×C3×C7×D5semidirect
92. C7×C11C2×C3×D35direct (N × H)
94. C2×C5×C7C3×C11×D7semidirect
95. C2×C5×C7C2×C3×C7×C11semidirect
96. D35C2×C3×C7×C11direct (N × H)
99. C2×C3×C11C7×D35direct (N × H)
101. C5×C11C2×C3×C7×D7semidirect
102. C72C2×C3×D5×C11semidirect
106. C2×C3×C7C7×D5×C11semidirect
107. C2×C3×C7C11×D35direct (N × H)
110. C5×C7C2×C3×C11×D7semidirect
111. C5×C7C22×C3×C7×C11semidirect
112. C3×C11C2×C7×D35direct (N × H)
113. C2×C3×C5C7×C11×D7semidirect
118. C2×C11C3×C7×D35direct (N × H)
120. C3×C7C2×C7×D5×C11semidirect
121. C3×C7C2×C11×D35direct (N × H)
123. C3×C5C2×C7×C11×D7semidirect
126. C2×C7C3×C7×D5×C11semidirect
127. C2×C7C3×C11×D35direct (N × H)
130. C11C2×C3×C7×D35direct (N × H)
131. C2×C5C3×C7×C11×D7semidirect
134. C7C2×C3×C7×D5×C11semidirect
135. C7C2×C3×C11×D35direct (N × H)
137. C2×C3C7×C11×D35direct (N × H)
138. C5C2×C3×C7×C11×D7semidirect
140. C3C2×C7×C11×D35direct (N × H)
142. C2C3×C7×C11×D35direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×C11×D352
C2×C3×C5×C72×C112
C2×C7×C11×D353
C2×C3×C7×C11×D75
C2×C3×C11×D357
C2×C3×C7×D5×C117
C2×C3×C7×D3511