Finite Group Databasebeta

← C2×C5×C7×D231 #44568946

Subgroups — C2×C5×C7×D231 #44568946

Order 32340.

208 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 76 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×D231C212yesmaximal, direct product factor
2C2×C3×C5×C72×C11C211yesmaximal, characteristic, complemented
3C2×C5×C7×D77—31nomaximal, Hall
4C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
5C2×C7×D231C511yesmaximal, characteristic, direct product factor, Hall
6C5×C7×D77—32no—
7C2×C5×C72×C11D311yescharacteristic, complemented
8C2×C5×D231C711yesmaximal, characteristic, direct product factor
9C2×C5×C7×D33—71nomaximal
10C7×D231C2×C512yesdirect product factor
11C2×C3×C72×C11C2×C511yescharacteristic, complemented
12C2×C5×C7×D21—111nomaximal, Hall
13C5×C72×C11C2×D311yescharacteristic, complemented, Hall
14C5×D231C2×C712yesdirect product factor
15C5×C7×D33—72no—
16C2×C3×C5×C7×C11—23no—
17C2×C3×C5×C7×C11D711yescharacteristic, complemented
18C2×C3×C5×C7×C11C2×C711yescharacteristic, complemented
19C2×C7×D77—31noHall
20C3×C72×C11C22×C511yescharacteristic, complemented, Hall
21C2×C5×D77—31no—
22C2×C5×C7×D11—211no—
23C2×C3×C5×C72D1111yescharacteristic, complemented
24C5×C7×D21—112no—
25C3×C5×C7×C11—23no—
26C3×C5×C7×C11C2×D711yescharacteristic, complemented
27C3×C5×C7×C11C22×C711yescharacteristic, complemented
28C2×C72×C11C5×D311yescharacteristic, complemented
29C7×D77—32no—
30C2×C5×C7×D7—331noHall
31C2×D231C5×C711yescharacteristic, direct product factor
32C2×C7×D33—71no—
33C2×C5×C7×C11—23no—
34C2×C5×C7×C11D3×C711yescharacteristic, complemented
35C2×C5×C7×C11D2111yescharacteristic, complemented
36C5×D77—32no—
37C5×C7×D11—212no—
38C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
39C2×C5×D33—71noHall
40C2×C7×D21—111noHall
41C72×C11C2×C5×D311yescharacteristic, complemented, Hall
42C2×C5×C72D3311yescharacteristic, complemented
43C5×C7×D7—332no—
44C2×C3×C7×C11—23no—
45C2×C3×C7×C11C5×D711yescharacteristic, complemented
46C2×C3×C7×C11C2×C5×C711yescharacteristic, complemented
47D231C2×C5×C712yesdirect product factor
48C7×D33—72no—
49C2×C5×D21—111no—
50C2×C5×D3×C7—771no—
51C5×C7×C11—23no—
52C5×C7×C11C2×D3×C711yescharacteristic, complemented
53C5×C7×C11C2×D2111yescharacteristic, complemented
54C2×C3×C5×C11C7×D711yescharacteristic, complemented
55C5×D33—72no—
56C2×D77—31no—
57C2×C7×D11—211no—
58C2×C3×C72C5×D1111yescharacteristic, complemented
59C7×D21—112no—
60C5×C72C2×D3311yescharacteristic, complemented, Hall
61C3×C7×C11—23no—
62C3×C7×C11C2×C5×D711yescharacteristic, complemented
63C3×C7×C11C22×C5×C711yescharacteristic, complemented
64C2×C5×D11—211noHall
65C2×C3×C5×C7—23no—
66C2×C3×C5×C7C7×D1111yescharacteristic, complemented
67C2×C3×C5×C7D7711yescharacteristic, complemented
68C5×D21—112no—
69C5×D3×C7—772no—
70C2×C7×D7—331noHall
71C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
72C2×C7×C11—23no—
73C2×C7×C11C5×D3×C711yescharacteristic, complemented
74C2×C7×C11C5×D2111yescharacteristic, complemented
75D77—32no—
76C7×D11—212no—
77C3×C72C2×C5×D1111yescharacteristic, complemented, Hall
78C22×C5×C7—2311no—
79C2×C5×D7—331no—
80C2×D33—71noHall
81C2×C5×C11C7×D2111yescharacteristic, complemented
82C5×D11—212no—
83C3×C5×C7—23no—
84C3×C5×C7C2×C7×D1111yescharacteristic, complemented
85C3×C5×C7C2×D7711yescharacteristic, complemented
86C2×C72C5×D3311yescharacteristic, complemented
87C7×D7—332no—
88C2×D21—111no—
89C2×D3×C7—771no—
90C7×C11—23no—
91C7×C11C2×C5×D3×C711yescharacteristic, complemented
92C7×C11C2×C5×D2111yescharacteristic, complemented
93C2×C5×C7—23no—
94C2×C5×C7—2312no—
95C2×C5×C7C7×D3311yescharacteristic, complemented
96C2×C5×C7D23111yescharacteristic, direct product factor
97C5×D7—332no—
98C2×C3×C11C5×C7×D711yescharacteristic, complemented
99D33—72no—
100C2×C5×D3—771noHall
101C5×C11C2×C7×D2111yescharacteristic, complemented, Hall
102C72C2×C5×D3311yescharacteristic, complemented, Sylow
103C2×D11—211noHall
104C2×C3×C7—23no—
105C2×C3×C7C5×C7×D1111yescharacteristic, complemented
106C2×C3×C7C5×D7711yescharacteristic, complemented
107D21—112no—
108D3×C7—772no—
109C5×C7—23no—
110C5×C7C2×C7×D3311yescharacteristic, complemented
111C5×C7C2×D23111yescharacteristic, direct product factor
112C3×C11C2×C5×C7×D711yescharacteristic, complemented, Hall
113C2×C3×C5C7×D7711yescharacteristic, complemented
114C5×D3—772no—
115C22×C7—2311no—
116C2×D7—331no—
117C2×C11C5×C7×D2111yescharacteristic, complemented
118D11—212no—
119C3×C7—23no—
120C3×C7C2×C5×C7×D1111yescharacteristic, complemented
121C3×C7C2×C5×D7711yescharacteristic, complemented
122C22×C5—2311noHall
123C3×C5C2×C7×D7711yescharacteristic, complemented, Hall
124C2×C7—23no—
125C2×C7—2312no—
126C2×C7C5×C7×D3311yescharacteristic, complemented
127C2×C7C5×D23111yescharacteristic, direct product factor
128D7—332no—
129C2×D3—771noHall
130C11C2×C5×C7×D2111yescharacteristic, complemented, Sylow
131C2×C5—2312no—
132C2×C5C7×D23111yescharacteristic, direct product factor
133C7—23no—
134C7C2×C5×C7×D3311yescharacteristic, complemented
135C7C2×C5×D23111yescharacteristic, direct product factor
136C2×C3C5×C7×D7711yescharacteristic, complemented
137D3—772no—
138C5C2×C7×D23111yescharacteristic, direct product factor, Sylow
139C22—2311noSylow
140C3C2×C5×C7×D7711yescharacteristic, complemented, Sylow
141C2—2312no—
142C2C5×C7×D23111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C7D231
commutator, cosocle, hypocenterC3×C7×C11C22×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C5×C7

Complements

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

NH ≅ G/Ntype
1. C5×C7×D231C2direct (N × H)
2. C2×C3×C5×C72×C11C2semidirect
4. C3×C5×C72×C11C22semidirect
5. C2×C7×D231C5direct (N × H)
7. C2×C5×C72×C11D3semidirect
8. C2×C5×D231C7direct (N × H)
10. C7×D231C2×C5direct (N × H)
11. C2×C3×C72×C11C2×C5semidirect
13. C5×C72×C11C2×D3semidirect
14. C5×D231C2×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×C72D11semidirect
26. C3×C5×C7×C11C2×D7semidirect
27. C3×C5×C7×C11C22×C7semidirect
28. C2×C72×C11C5×D3semidirect
31. C2×D231C5×C7direct (N × H)
34. C2×C5×C7×C11D3×C7semidirect
35. C2×C5×C7×C11D21semidirect
38. C3×C5×C72C2×D11semidirect
41. C72×C11C2×C5×D3semidirect
42. C2×C5×C72D33semidirect
45. C2×C3×C7×C11C5×D7semidirect
46. C2×C3×C7×C11C2×C5×C7semidirect
47. D231C2×C5×C7direct (N × H)
52. C5×C7×C11C2×D3×C7semidirect
53. C5×C7×C11C2×D21semidirect
54. C2×C3×C5×C11C7×D7semidirect
58. C2×C3×C72C5×D11semidirect
60. C5×C72C2×D33semidirect
62. C3×C7×C11C2×C5×D7semidirect
63. C3×C7×C11C22×C5×C7semidirect
66. C2×C3×C5×C7C7×D11semidirect
67. C2×C3×C5×C7D77semidirect
71. C3×C5×C11C2×C7×D7semidirect
73. C2×C7×C11C5×D3×C7semidirect
74. C2×C7×C11C5×D21semidirect
77. C3×C72C2×C5×D11semidirect
81. C2×C5×C11C7×D21semidirect
84. C3×C5×C7C2×C7×D11semidirect
85. C3×C5×C7C2×D77semidirect
86. C2×C72C5×D33semidirect
91. C7×C11C2×C5×D3×C7semidirect
92. C7×C11C2×C5×D21semidirect
95. C2×C5×C7C7×D33semidirect
96. C2×C5×C7D231direct (N × H)
98. C2×C3×C11C5×C7×D7semidirect
101. C5×C11C2×C7×D21semidirect
102. C72C2×C5×D33semidirect
105. C2×C3×C7C5×C7×D11semidirect
106. C2×C3×C7C5×D77semidirect
110. C5×C7C2×C7×D33semidirect
111. C5×C7C2×D231direct (N × H)
112. C3×C11C2×C5×C7×D7semidirect
113. C2×C3×C5C7×D77semidirect
117. C2×C11C5×C7×D21semidirect
120. C3×C7C2×C5×C7×D11semidirect
121. C3×C7C2×C5×D77semidirect
123. C3×C5C2×C7×D77semidirect
126. C2×C7C5×C7×D33semidirect
127. C2×C7C5×D231direct (N × H)
130. C11C2×C5×C7×D21semidirect
132. C2×C5C7×D231direct (N × H)
134. C7C2×C5×C7×D33semidirect
135. C7C2×C5×D231direct (N × H)
136. C2×C3C5×C7×D77semidirect
138. C5C2×C7×D231direct (N × H)
140. C3C2×C5×C7×D77semidirect
142. C2C5×C7×D231direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C7×D2312
C2×C3×C5×C72×C112
C2×C5×C7×D773
C2×C7×D2315
C2×C5×D2317
C2×C5×C7×D337
C2×C5×C7×D2111