Finite Group Databasebeta

← C2×C3×C7×D7×C11⋊C5 #44568751

Subgroups — C2×C3×C7×D7×C11⋊C5 #44568751

Order 32340.

208 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×C3×C72×C11⋊C5C211yesmaximal, characteristic, complemented
2C3×C7×D7×C11⋊C5C212yesmaximal, direct product factor
3C2×C7×D7×C11⋊C5C311yesmaximal, characteristic, direct product factor, Hall
4C3×C72×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×C3×C7×C11×D7C511yesmaximal, characteristic, complemented, Hall
6C2×C72×C11⋊C5C2×C311yescharacteristic, complemented
7C7×D7×C11⋊C5C2×C312yesdirect product factor
8C22×C3×C7×C11⋊C5—71nomaximal
9C2×C3×D7×C11⋊C5C711yesmaximal, characteristic, direct product factor
10C3×C7×C11×D7C2×C512yescomplemented
11C2×C3×C72×C11C2×C511yescharacteristic, complemented
12C2×C3×C5×C7×D7—111nomaximal, Hall
13C72×C11⋊C5C22×C311yescharacteristic, complemented, Hall
14C3×D7×C11⋊C5C2×C712yesdirect product factor
15C2×C3×C7×C11⋊C5—23no—
16C2×C3×C7×C11⋊C5—72no—
17C2×C3×C7×C11⋊C5D711yescharacteristic, direct product factor
18C2×C3×C7×C11⋊C5C2×C711yescharacteristic, complemented
19C2×C7×C11×D7C3×C511yescharacteristic, complemented, Hall
20C3×C72×C11C22×C511yescharacteristic, complemented, Hall
21C22×C7×C11⋊C5—71no—
22C2×D7×C11⋊C5C3×C711yescharacteristic, direct product factor
23C2×C3×C5×C72—111no—
24C3×C5×C7×D7—112no—
25C3×C7×C11⋊C5—23no—
26C3×C7×C11⋊C5C2×D711yescharacteristic, direct product factor
27C3×C7×C11⋊C5C22×C711yescharacteristic, complemented
28C2×C72×C11C2×C3×C511yescharacteristic, complemented
29C7×C11×D7C2×C3×C512yescomplemented
30C2×C5×C7×D7—111noHall
31C22×C3×C7×C11—71no—
32C2×C3×C11×D7C5×C711yescharacteristic, complemented
33C2×C7×C11⋊C5—23no—
34C2×C7×C11⋊C5—72no—
35C2×C7×C11⋊C5C3×D711yescharacteristic, direct product factor
36C2×C7×C11⋊C5C2×C3×C711yescharacteristic, complemented
37D7×C11⋊C5C2×C3×C712yesdirect product factor
38C3×C5×C72—111noHall
39C22×C3×C11⋊C5—71noHall
40C2×C3×C7×D7C11⋊C511yescharacteristic, direct product factor, Hall
41C72×C11C22×C3×C511yescharacteristic, complemented, Hall
42C2×C5×C72—111no—
43C5×C7×D7—112no—
44C2×C3×C7×C11—23no—
45C2×C3×C7×C11—72no—
46C2×C3×C7×C11C5×D711yescharacteristic, complemented
47C2×C3×C7×C11C2×C5×C711yescharacteristic, complemented
48C3×C11×D7C2×C5×C712yescomplemented
49C22×C3×C5×C7—771no—
50C2×C3×C5×D7—111no—
51C7×C11⋊C5—23no—
52C7×C11⋊C5C2×C3×D711yescharacteristic, direct product factor
53C7×C11⋊C5C22×C3×C711yescharacteristic, complemented
54C2×C3×C11⋊C5—72no—
55C2×C3×C11⋊C5C7×D711yescharacteristic, direct product factor
56C22×C7×C11—71no—
57C2×C11×D7C3×C5×C711yescharacteristic, complemented
58C2×C3×C72C2×C11⋊C511yescharacteristic, complemented
59C3×C7×D7C2×C11⋊C512yesdirect product factor
60C5×C72—111noHall
61C3×C7×C11—23no—
62C3×C7×C11C2×C5×D711yescharacteristic, complemented
63C3×C7×C11C22×C5×C711yescharacteristic, complemented
64C22×C11⋊C5—71noHall
65C2×C3×C5×C7—111no—
66C2×C3×C5×C7—111no—
67C2×C3×C5×C7—223no—
68C2×C3×C5×C7—772no—
69C3×C5×D7—112no—
70C2×C7×D7C3×C11⋊C511yescharacteristic, direct product factor, Hall
71C3×C11⋊C5C2×C7×D711yescharacteristic, direct product factor, Hall
72C2×C7×C11—23no—
73C2×C7×C11—72no—
74C2×C7×C11C3×C5×D711yescharacteristic, complemented
75C2×C7×C11C2×C3×C5×C711yescharacteristic, complemented
76C11×D7C2×C3×C5×C712yescomplemented
77C3×C72C22×C11⋊C511yescharacteristic, complemented, Hall
78C22×C5×C7—771no—
79C2×C5×D7—111no—
80C22×C3×C11—71noHall
81C2×C11⋊C5—72no—
82C2×C11⋊C5C3×C7×D711yescharacteristic, direct product factor
83C3×C5×C7—111no—
84C3×C5×C7—111no—
85C3×C5×C7—223no—
86C2×C72C2×C3×C11⋊C511yescharacteristic, complemented
87C7×D7C2×C3×C11⋊C512yesdirect product factor
88C22×C3×C7—71no—
89C2×C3×D7C7×C11⋊C511yescharacteristic, direct product factor
90C7×C11—23no—
91C7×C11C2×C3×C5×D711yescharacteristic, complemented
92C7×C11C22×C3×C5×C711yescharacteristic, complemented
93C2×C5×C7—111no—
94C2×C5×C7—111no—
95C2×C5×C7—223no—
96C2×C5×C7—772no—
97C5×D7—112no—
98C2×C3×C11—72no—
99C2×C3×C11C5×C7×D711yescharacteristic, complemented
100C22×C3×C5—771noHall
101C11⋊C5C2×C3×C7×D711yescharacteristic, direct product factor, Hall
102C72C22×C3×C11⋊C511yescharacteristic, complemented, Sylow
103C22×C11—71noHall
104C2×C3×C7—23no—
105C2×C3×C7—72no—
106C2×C3×C7D7×C11⋊C511yescharacteristic, direct product factor
107C2×C3×C7C2×C7×C11⋊C511yescharacteristic, complemented
108C3×D7C2×C7×C11⋊C512yesdirect product factor
109C5×C7—111no—
110C5×C7—111no—
111C5×C7—223no—
112C3×C11C2×C5×C7×D711yescharacteristic, complemented, Hall
113C2×C3×C5—111no—
114C2×C3×C5—772no—
115C22×C7—71no—
116C2×D7C3×C7×C11⋊C511yescharacteristic, direct product factor
117C2×C11—72no—
118C2×C11C3×C5×C7×D711yescharacteristic, complemented
119C3×C7—23no—
120C3×C7C2×D7×C11⋊C511yescharacteristic, direct product factor
121C3×C7C22×C7×C11⋊C511yescharacteristic, complemented
122C22×C5—771noHall
123C3×C5—111noHall
124C2×C7—23no—
125C2×C7—72no—
126C2×C7C2×C3×C7×C11⋊C511yescharacteristic, complemented
127C2×C7C3×D7×C11⋊C511yescharacteristic, direct product factor
128D7C2×C3×C7×C11⋊C512yesdirect product factor
129C22×C3—71noHall
130C11C2×C3×C5×C7×D711yescharacteristic, complemented, Sylow
131C2×C5—111no—
132C2×C5—772no—
133C7—23no—
134C7C2×C3×D7×C11⋊C511yescharacteristic, direct product factor
135C7C22×C3×C7×C11⋊C511yescharacteristic, complemented
136C2×C3—72no—
137C2×C3C7×D7×C11⋊C511yescharacteristic, direct product factor
138C5—111noSylow
139C22—71noSylow
140C3C2×C7×D7×C11⋊C511yescharacteristic, direct product factor, Sylow
141C2—72no—
142C2C3×C7×D7×C11⋊C511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7D7×C11⋊C5
commutator, cosocle, hypocenterC7×C11C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C72×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C7

Complements

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

NH ≅ G/Ntype
1. C2×C3×C72×C11⋊C5C2semidirect
2. C3×C7×D7×C11⋊C5C2direct (N × H)
3. C2×C7×D7×C11⋊C5C3direct (N × H)
4. C3×C72×C11⋊C5C22semidirect
5. C2×C3×C7×C11×D7C5semidirect
6. C2×C72×C11⋊C5C2×C3semidirect
7. C7×D7×C11⋊C5C2×C3direct (N × H)
9. C2×C3×D7×C11⋊C5C7direct (N × H)
10. C3×C7×C11×D7C2×C5semidirect
11. C2×C3×C72×C11C2×C5semidirect
13. C72×C11⋊C5C22×C3semidirect
14. C3×D7×C11⋊C5C2×C7direct (N × H)
17. C2×C3×C7×C11⋊C5D7direct (N × H)
18. C2×C3×C7×C11⋊C5C2×C7semidirect
19. C2×C7×C11×D7C3×C5semidirect
20. C3×C72×C11C22×C5semidirect
22. C2×D7×C11⋊C5C3×C7direct (N × H)
26. C3×C7×C11⋊C5C2×D7direct (N × H)
27. C3×C7×C11⋊C5C22×C7semidirect
28. C2×C72×C11C2×C3×C5semidirect
29. C7×C11×D7C2×C3×C5semidirect
32. C2×C3×C11×D7C5×C7semidirect
35. C2×C7×C11⋊C5C3×D7direct (N × H)
36. C2×C7×C11⋊C5C2×C3×C7semidirect
37. D7×C11⋊C5C2×C3×C7direct (N × H)
40. C2×C3×C7×D7C11⋊C5direct (N × H)
41. C72×C11C22×C3×C5semidirect
46. C2×C3×C7×C11C5×D7semidirect
47. C2×C3×C7×C11C2×C5×C7semidirect
48. C3×C11×D7C2×C5×C7semidirect
52. C7×C11⋊C5C2×C3×D7direct (N × H)
53. C7×C11⋊C5C22×C3×C7semidirect
55. C2×C3×C11⋊C5C7×D7direct (N × H)
57. C2×C11×D7C3×C5×C7semidirect
58. C2×C3×C72C2×C11⋊C5semidirect
59. C3×C7×D7C2×C11⋊C5direct (N × H)
62. C3×C7×C11C2×C5×D7semidirect
63. C3×C7×C11C22×C5×C7semidirect
70. C2×C7×D7C3×C11⋊C5direct (N × H)
71. C3×C11⋊C5C2×C7×D7direct (N × H)
74. C2×C7×C11C3×C5×D7semidirect
75. C2×C7×C11C2×C3×C5×C7semidirect
76. C11×D7C2×C3×C5×C7semidirect
77. C3×C72C22×C11⋊C5semidirect
82. C2×C11⋊C5C3×C7×D7direct (N × H)
86. C2×C72C2×C3×C11⋊C5semidirect
87. C7×D7C2×C3×C11⋊C5direct (N × H)
89. C2×C3×D7C7×C11⋊C5direct (N × H)
91. C7×C11C2×C3×C5×D7semidirect
92. C7×C11C22×C3×C5×C7semidirect
99. C2×C3×C11C5×C7×D7semidirect
101. C11⋊C5C2×C3×C7×D7direct (N × H)
102. C72C22×C3×C11⋊C5semidirect
106. C2×C3×C7D7×C11⋊C5direct (N × H)
107. C2×C3×C7C2×C7×C11⋊C5semidirect
108. C3×D7C2×C7×C11⋊C5direct (N × H)
112. C3×C11C2×C5×C7×D7semidirect
116. C2×D7C3×C7×C11⋊C5direct (N × H)
118. C2×C11C3×C5×C7×D7semidirect
120. C3×C7C2×D7×C11⋊C5direct (N × H)
121. C3×C7C22×C7×C11⋊C5semidirect
126. C2×C7C2×C3×C7×C11⋊C5semidirect
127. C2×C7C3×D7×C11⋊C5direct (N × H)
128. D7C2×C3×C7×C11⋊C5direct (N × H)
130. C11C2×C3×C5×C7×D7semidirect
134. C7C2×C3×D7×C11⋊C5direct (N × H)
135. C7C22×C3×C7×C11⋊C5semidirect
137. C2×C3C7×D7×C11⋊C5direct (N × H)
140. C3C2×C7×D7×C11⋊C5direct (N × H)
142. C2C3×C7×D7×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C72×C11⋊C52
C3×C7×D7×C11⋊C52
C2×C7×D7×C11⋊C53
C2×C3×C7×C11×D75
C22×C3×C7×C11⋊C57
C2×C3×D7×C11⋊C57
C2×C3×C5×C7×D711