Finite Group Databasebeta

← C2×C3×C5×C7×D77 #44568934

Subgroups — C2×C3×C5×C7×D77 #44568934

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×C5×C7×D77C212yesmaximal, direct product factor
2C2×C3×C5×C72×C11C211yesmaximal, characteristic, complemented
3C2×C5×C7×D77C311yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C2×C3×C7×D77C511yesmaximal, characteristic, direct product factor, Hall
6C5×C7×D77C2×C312yesdirect product factor
7C2×C5×C72×C11C2×C311yescharacteristic, complemented
8C2×C3×C5×D77C711yesmaximal, characteristic, direct product factor
9C2×C3×C5×C7×D11—71nomaximal
10C3×C7×D77C2×C512yesdirect product factor
11C2×C3×C72×C11C2×C511yescharacteristic, complemented
12C2×C3×C5×C7×D7—111nomaximal, Hall
13C5×C72×C11C22×C311yescharacteristic, complemented, Hall
14C3×C5×D77C2×C712yesdirect product factor
15C3×C5×C7×D11—72no—
16C2×C3×C5×C7×C11—23no—
17C2×C3×C5×C7×C11D711yescharacteristic, complemented
18C2×C3×C5×C7×C11C2×C711yescharacteristic, complemented
19C2×C7×D77C3×C511yescharacteristic, direct product factor, Hall
20C3×C72×C11C22×C511yescharacteristic, complemented, Hall
21C2×C5×D77C3×C711yescharacteristic, direct product factor
22C2×C5×C7×D11—71no—
23C2×C3×C5×C72D1111yescharacteristic, complemented
24C3×C5×C7×D7—112no—
25C3×C5×C7×C11—23no—
26C3×C5×C7×C11C2×D711yescharacteristic, complemented
27C3×C5×C7×C11C22×C711yescharacteristic, complemented
28C2×C72×C11C2×C3×C511yescharacteristic, complemented
29C7×D77C2×C3×C512yesdirect product factor
30C2×C5×C7×D7—111noHall
31C2×C3×D77C5×C711yescharacteristic, direct product factor
32C2×C3×C7×D11—71no—
33C2×C5×C7×C11—23no—
34C2×C5×C7×C11C3×D711yescharacteristic, complemented
35C2×C5×C7×C11C2×C3×C711yescharacteristic, complemented
36C5×D77C2×C3×C712yesdirect product factor
37C5×C7×D11—72no—
38C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
39C2×C3×C5×D11—71noHall
40C2×C3×C7×D7—111noHall
41C72×C11C22×C3×C511yescharacteristic, complemented, Hall
42C2×C5×C72C3×D1111yescharacteristic, complemented
43C5×C7×D7—112no—
44C2×C3×C7×C11—23no—
45C2×C3×C7×C11C5×D711yescharacteristic, complemented
46C2×C3×C7×C11C2×C5×C711yescharacteristic, complemented
47C3×D77C2×C5×C712yesdirect product factor
48C3×C7×D11—72no—
49C22×C3×C5×C7—771no—
50C2×C3×C5×D7—111no—
51C5×C7×C11—23no—
52C5×C7×C11C2×C3×D711yescharacteristic, complemented
53C5×C7×C11C22×C3×C711yescharacteristic, complemented
54C2×C3×C5×C11C7×D711yescharacteristic, complemented
55C3×C5×D11—72no—
56C2×D77C3×C5×C711yescharacteristic, direct product factor
57C2×C7×D11—71no—
58C2×C3×C72C5×D1111yescharacteristic, complemented
59C3×C7×D7—112no—
60C5×C72C2×C3×D1111yescharacteristic, complemented, Hall
61C3×C7×C11—23no—
62C3×C7×C11C2×C5×D711yescharacteristic, complemented
63C3×C7×C11C22×C5×C711yescharacteristic, complemented
64C2×C5×D11—71noHall
65C2×C3×C5×C7—23no—
66C2×C3×C5×C7—772no—
67C2×C3×C5×C7C7×D1111yescharacteristic, complemented
68C2×C3×C5×C7D7711yescharacteristic, direct product factor
69C3×C5×D7—112no—
70C2×C7×D7—111noHall
71C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
72C2×C7×C11—23no—
73C2×C7×C11C3×C5×D711yescharacteristic, complemented
74C2×C7×C11C2×C3×C5×C711yescharacteristic, complemented
75D77C2×C3×C5×C712yesdirect product factor
76C7×D11—72no—
77C3×C72C2×C5×D1111yescharacteristic, complemented, Hall
78C22×C5×C7—771no—
79C2×C5×D7—111no—
80C2×C3×D11—71noHall
81C2×C5×C11C3×C7×D711yescharacteristic, complemented
82C5×D11—72no—
83C3×C5×C7—23no—
84C3×C5×C7C2×C7×D1111yescharacteristic, complemented
85C3×C5×C7C2×D7711yescharacteristic, direct product factor
86C2×C72C3×C5×D1111yescharacteristic, complemented
87C7×D7—112no—
88C22×C3×C7—771no—
89C2×C3×D7—111no—
90C7×C11—23no—
91C7×C11C2×C3×C5×D711yescharacteristic, complemented
92C7×C11C22×C3×C5×C711yescharacteristic, complemented
93C2×C5×C7—23no—
94C2×C5×C7—772no—
95C2×C5×C7C3×C7×D1111yescharacteristic, complemented
96C2×C5×C7C3×D7711yescharacteristic, direct product factor
97C5×D7—112no—
98C2×C3×C11C5×C7×D711yescharacteristic, complemented
99C3×D11—72no—
100C22×C3×C5—771noHall
101C5×C11C2×C3×C7×D711yescharacteristic, complemented, Hall
102C72C2×C3×C5×D1111yescharacteristic, complemented, Sylow
103C2×D11—71noHall
104C2×C3×C7—23no—
105C2×C3×C7—772no—
106C2×C3×C7C5×C7×D1111yescharacteristic, complemented
107C2×C3×C7C5×D7711yescharacteristic, direct product factor
108C3×D7—112no—
109C5×C7—23no—
110C5×C7C2×C3×C7×D1111yescharacteristic, complemented
111C5×C7C2×C3×D7711yescharacteristic, direct product factor
112C3×C11C2×C5×C7×D711yescharacteristic, complemented, Hall
113C2×C3×C5—772no—
114C2×C3×C5C7×D7711yescharacteristic, direct product factor
115C22×C7—771no—
116C2×D7—111no—
117C2×C11C3×C5×C7×D711yescharacteristic, complemented
118D11—72no—
119C3×C7—23no—
120C3×C7C2×C5×C7×D1111yescharacteristic, complemented
121C3×C7C2×C5×D7711yescharacteristic, direct product factor
122C22×C5—771noHall
123C3×C5C2×C7×D7711yescharacteristic, direct product factor, Hall
124C2×C7—23no—
125C2×C7—772no—
126C2×C7C3×C5×C7×D1111yescharacteristic, complemented
127C2×C7C3×C5×D7711yescharacteristic, direct product factor
128D7—112no—
129C22×C3—771noHall
130C11C2×C3×C5×C7×D711yescharacteristic, complemented, Sylow
131C2×C5—772no—
132C2×C5C3×C7×D7711yescharacteristic, direct product factor
133C7—23no—
134C7C2×C3×C5×C7×D1111yescharacteristic, complemented
135C7C2×C3×C5×D7711yescharacteristic, direct product factor
136C2×C3—772no—
137C2×C3C5×C7×D7711yescharacteristic, direct product factor
138C5C2×C3×C7×D7711yescharacteristic, direct product factor, Sylow
139C22—771noSylow
140C3C2×C5×C7×D7711yescharacteristic, direct product factor, Sylow
141C2—772no—
142C2C3×C5×C7×D7711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5×C7D77
commutator, cosocle, hypocenterC7×C11C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C5×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D77C2direct (N × H)
2. C2×C3×C5×C72×C11C2semidirect
3. C2×C5×C7×D77C3direct (N × H)
4. C3×C5×C72×C11C22semidirect
5. C2×C3×C7×D77C5direct (N × H)
6. C5×C7×D77C2×C3direct (N × H)
7. C2×C5×C72×C11C2×C3semidirect
8. C2×C3×C5×D77C7direct (N × H)
10. C3×C7×D77C2×C5direct (N × H)
11. C2×C3×C72×C11C2×C5semidirect
13. C5×C72×C11C22×C3semidirect
14. C3×C5×D77C2×C7direct (N × H)
17. C2×C3×C5×C7×C11D7semidirect
18. C2×C3×C5×C7×C11C2×C7semidirect
19. C2×C7×D77C3×C5direct (N × H)
20. C3×C72×C11C22×C5semidirect
21. C2×C5×D77C3×C7direct (N × H)
23. C2×C3×C5×C72D11semidirect
26. C3×C5×C7×C11C2×D7semidirect
27. C3×C5×C7×C11C22×C7semidirect
28. C2×C72×C11C2×C3×C5semidirect
29. C7×D77C2×C3×C5direct (N × H)
31. C2×C3×D77C5×C7direct (N × H)
34. C2×C5×C7×C11C3×D7semidirect
35. C2×C5×C7×C11C2×C3×C7semidirect
36. C5×D77C2×C3×C7direct (N × H)
38. C3×C5×C72C2×D11semidirect
41. C72×C11C22×C3×C5semidirect
42. C2×C5×C72C3×D11semidirect
45. C2×C3×C7×C11C5×D7semidirect
46. C2×C3×C7×C11C2×C5×C7semidirect
47. C3×D77C2×C5×C7direct (N × H)
52. C5×C7×C11C2×C3×D7semidirect
53. C5×C7×C11C22×C3×C7semidirect
54. C2×C3×C5×C11C7×D7semidirect
56. C2×D77C3×C5×C7direct (N × H)
58. C2×C3×C72C5×D11semidirect
60. C5×C72C2×C3×D11semidirect
62. C3×C7×C11C2×C5×D7semidirect
63. C3×C7×C11C22×C5×C7semidirect
67. C2×C3×C5×C7C7×D11semidirect
68. C2×C3×C5×C7D77direct (N × H)
71. C3×C5×C11C2×C7×D7semidirect
73. C2×C7×C11C3×C5×D7semidirect
74. C2×C7×C11C2×C3×C5×C7semidirect
75. D77C2×C3×C5×C7direct (N × H)
77. C3×C72C2×C5×D11semidirect
81. C2×C5×C11C3×C7×D7semidirect
84. C3×C5×C7C2×C7×D11semidirect
85. C3×C5×C7C2×D77direct (N × H)
86. C2×C72C3×C5×D11semidirect
91. C7×C11C2×C3×C5×D7semidirect
92. C7×C11C22×C3×C5×C7semidirect
95. C2×C5×C7C3×C7×D11semidirect
96. C2×C5×C7C3×D77direct (N × H)
98. C2×C3×C11C5×C7×D7semidirect
101. C5×C11C2×C3×C7×D7semidirect
102. C72C2×C3×C5×D11semidirect
106. C2×C3×C7C5×C7×D11semidirect
107. C2×C3×C7C5×D77direct (N × H)
110. C5×C7C2×C3×C7×D11semidirect
111. C5×C7C2×C3×D77direct (N × H)
112. C3×C11C2×C5×C7×D7semidirect
114. C2×C3×C5C7×D77direct (N × H)
117. C2×C11C3×C5×C7×D7semidirect
120. C3×C7C2×C5×C7×D11semidirect
121. C3×C7C2×C5×D77direct (N × H)
123. C3×C5C2×C7×D77direct (N × H)
126. C2×C7C3×C5×C7×D11semidirect
127. C2×C7C3×C5×D77direct (N × H)
130. C11C2×C3×C5×C7×D7semidirect
132. C2×C5C3×C7×D77direct (N × H)
134. C7C2×C3×C5×C7×D11semidirect
135. C7C2×C3×C5×D77direct (N × H)
137. C2×C3C5×C7×D77direct (N × H)
138. C5C2×C3×C7×D77direct (N × H)
140. C3C2×C5×C7×D77direct (N × H)
142. C2C3×C5×C7×D77direct (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×D772
C2×C3×C5×C72×C112
C2×C5×C7×D773
C2×C3×C7×D775
C2×C3×C5×D777
C2×C3×C5×C7×D117
C2×C3×C5×C7×D711