Finite Group Databasebeta

← C2×C3×C13×D231 #49115022

Subgroups — C2×C3×C13×D231 #49115022

Order 36036.

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

normal subgroups only

This group has 176 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
1C3×C13×D231C212yesmaximal, direct product factor
2C2×C32×C7×C11×C13C211yesmaximal, characteristic, complemented
3C2×C3×C13×D77—31nomaximal
4C2×C13×D231C311yesmaximal, characteristic, direct product factor
5C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
6C13×D231C2×C312yesdirect product factor
7C3×C13×D77—32no—
8C2×C3×C7×C11×C13—21no—
9C2×C3×C7×C11×C13D311yescharacteristic, complemented
10C2×C3×C7×C11×C13C2×C311yescharacteristic, complemented
11C2×C3×C13×D33—71nomaximal, Hall
12C2×C13×D77—31noHall
13C2×C3×C13×D21—111nomaximal, Hall
14C3×C7×C11×C13—21no—
15C3×C7×C11×C13C2×D311yescharacteristic, complemented
16C3×C7×C11×C13C22×C311yescharacteristic, complemented
17C2×C3×D231C1311yesmaximal, characteristic, direct product factor, Hall
18C3×C13×D33—72no—
19C2×C32×C11×C13D711yescharacteristic, complemented
20C13×D77—32no—
21C2×C7×C11×C13C3×D311yescharacteristic, complemented
22C2×C13×D33—71no—
23C2×C3×C13×D11—211no—
24C2×C32×C7×C13D1111yescharacteristic, complemented
25C3×C13×D21—112no—
26C2×C32×C7×C11C2×C1311yescharacteristic, complemented
27C3×D231C2×C1312yesdirect product factor
28C32×C11×C13C2×D711yescharacteristic, complemented, Hall
29C2×C13×D21—111no—
30C2×C3×C13×D7—331no—
31C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
32C2×D231C3×C1311yescharacteristic, direct product factor
33C2×C3×D77—31no—
34C2×C3×C11×C13—21no—
35C2×C3×C11×C13C3×D711yescharacteristic, complemented
36C2×C3×C11×C13D2111yescharacteristic, complemented
37C13×D33—72no—
38C3×C13×D11—212no—
39C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
40C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
41C2×C13×D11—211noHall
42C2×C3×C7×C13—21no—
43C2×C3×C7×C13C3×D1111yescharacteristic, complemented
44C2×C3×C7×C13D3311yescharacteristic, complemented
45C13×D21—112no—
46C3×C13×D7—332no—
47C2×C3×D3×C13—771noHall
48C2×C3×C7×C11—21no—
49C2×C3×C7×C11D3×C1311yescharacteristic, complemented
50C2×C3×C7×C11C2×C3×C1311yescharacteristic, complemented
51D231C2×C3×C1312yesdirect product factor
52C3×D77—32no—
53C3×C11×C13—21no—
54C3×C11×C13C2×C3×D711yescharacteristic, complemented
55C3×C11×C13C2×D2111yescharacteristic, complemented
56C2×C3×D33—71noHall
57C2×C13×D7—331noHall
58C2×D77—31noHall
59C2×C11×C13C3×D2111yescharacteristic, complemented
60C13×D11—212no—
61C3×C7×C13—21no—
62C3×C7×C13C2×C3×D1111yescharacteristic, complemented
63C3×C7×C13C2×D3311yescharacteristic, complemented
64C2×C3×D21—111noHall
65C2×C32×C13D7711yescharacteristic, complemented
66C3×D3×C13—772no—
67C3×C7×C11—21no—
68C3×C7×C11C2×D3×C1311yescharacteristic, complemented
69C3×C7×C11C22×C3×C1311yescharacteristic, complemented
70C2×C32×C11C13×D711yescharacteristic, complemented
71C3×D33—72no—
72C2×C7×C13C3×D3311yescharacteristic, complemented
73C13×D7—332no—
74C22×C3×C13—2311no—
75C2×D3×C13—771no—
76C2×C7×C11C3×D3×C1311yescharacteristic, complemented
77D77—32no—
78C11×C13C2×C3×D2111yescharacteristic, complemented, Hall
79C2×D33—71no—
80C2×C3×D11—211no—
81C2×C32×C7C13×D1111yescharacteristic, complemented
82C3×D21—112no—
83C32×C13C2×D7711yescharacteristic, complemented, Hall
84C32×C11C2×C13×D711yescharacteristic, complemented, Hall
85C7×C13C2×C3×D3311yescharacteristic, complemented, Hall
86C2×D21—111no—
87C2×C3×D7—331no—
88C2×C3×C13—21no—
89C2×C3×C13—2312no—
90C2×C3×C13C3×D7711yescharacteristic, complemented
91C2×C3×C13D23111yescharacteristic, direct product factor
92D3×C13—772no—
93C7×C11C2×C3×D3×C1311yescharacteristic, complemented, Hall
94C2×C3×C11—21no—
95C2×C3×C11C3×C13×D711yescharacteristic, complemented
96C2×C3×C11C13×D2111yescharacteristic, complemented
97D33—72no—
98C3×D11—212no—
99C32×C7C2×C13×D1111yescharacteristic, complemented, Hall
100C22×C13—2311noHall
101C2×D11—211noHall
102C2×C3×C7—21no—
103C2×C3×C7C3×C13×D1111yescharacteristic, complemented
104C2×C3×C7C13×D3311yescharacteristic, complemented
105D21—112no—
106C3×D7—332no—
107C3×C13—21no—
108C3×C13C2×C3×D7711yescharacteristic, complemented
109C3×C13C2×D23111yescharacteristic, direct product factor
110C2×C3×D3—771noHall
111C3×C11—21no—
112C3×C11C2×C3×C13×D711yescharacteristic, complemented
113C3×C11C2×C13×D2111yescharacteristic, complemented
114C2×D7—331noHall
115C2×C13—2312no—
116C2×C13C3×D23111yescharacteristic, direct product factor
117C2×C11C3×C13×D2111yescharacteristic, complemented
118D11—212no—
119C3×C7—21no—
120C3×C7C2×C3×C13×D1111yescharacteristic, complemented
121C3×C7C2×C13×D3311yescharacteristic, complemented
122C2×C32C13×D7711yescharacteristic, complemented
123C3×D3—772no—
124C2×C7C3×C13×D3311yescharacteristic, complemented
125D7—332no—
126C13C2×C3×D23111yescharacteristic, direct product factor, Sylow
127C22×C3—2311no—
128C2×D3—771no—
129C11C2×C3×C13×D2111yescharacteristic, complemented, Sylow
130C32C2×C13×D7711yescharacteristic, complemented, Sylow
131C7C2×C3×C13×D3311yescharacteristic, complemented, Sylow
132C2×C3—21no—
133C2×C3—2312no—
134C2×C3C3×C13×D7711yescharacteristic, complemented
135C2×C3C13×D23111yescharacteristic, direct product factor
136D3—772no—
137C22—2311noSylow
138C3—21no—
139C3C2×C13×D23111yescharacteristic, direct product factor
140C3C2×C3×C13×D7711yescharacteristic, complemented
141C2—2312no—
142C2C3×C13×D23111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C13D231
commutator, cosocle, hypocenterC3×C7×C11C22×C3×C13
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C3×C13

Complements

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

NH ≅ G/Ntype
1. C3×C13×D231C2direct (N × H)
2. C2×C32×C7×C11×C13C2semidirect
4. C2×C13×D231C3direct (N × H)
5. C32×C7×C11×C13C22semidirect
6. C13×D231C2×C3direct (N × H)
9. C2×C3×C7×C11×C13D3semidirect
10. C2×C3×C7×C11×C13C2×C3semidirect
15. C3×C7×C11×C13C2×D3semidirect
16. C3×C7×C11×C13C22×C3semidirect
17. C2×C3×D231C13direct (N × H)
19. C2×C32×C11×C13D7semidirect
21. C2×C7×C11×C13C3×D3semidirect
24. C2×C32×C7×C13D11semidirect
26. C2×C32×C7×C11C2×C13semidirect
27. C3×D231C2×C13direct (N × H)
28. C32×C11×C13C2×D7semidirect
31. C7×C11×C13C2×C3×D3semidirect
32. C2×D231C3×C13direct (N × H)
35. C2×C3×C11×C13C3×D7semidirect
36. C2×C3×C11×C13D21semidirect
39. C32×C7×C13C2×D11semidirect
40. C32×C7×C11C22×C13semidirect
43. C2×C3×C7×C13C3×D11semidirect
44. C2×C3×C7×C13D33semidirect
49. C2×C3×C7×C11D3×C13semidirect
50. C2×C3×C7×C11C2×C3×C13semidirect
51. D231C2×C3×C13direct (N × H)
54. C3×C11×C13C2×C3×D7semidirect
55. C3×C11×C13C2×D21semidirect
59. C2×C11×C13C3×D21semidirect
62. C3×C7×C13C2×C3×D11semidirect
63. C3×C7×C13C2×D33semidirect
65. C2×C32×C13D77semidirect
68. C3×C7×C11C2×D3×C13semidirect
69. C3×C7×C11C22×C3×C13semidirect
70. C2×C32×C11C13×D7semidirect
72. C2×C7×C13C3×D33semidirect
76. C2×C7×C11C3×D3×C13semidirect
78. C11×C13C2×C3×D21semidirect
81. C2×C32×C7C13×D11semidirect
83. C32×C13C2×D77semidirect
84. C32×C11C2×C13×D7semidirect
85. C7×C13C2×C3×D33semidirect
90. C2×C3×C13C3×D77semidirect
91. C2×C3×C13D231direct (N × H)
93. C7×C11C2×C3×D3×C13semidirect
95. C2×C3×C11C3×C13×D7semidirect
96. C2×C3×C11C13×D21semidirect
99. C32×C7C2×C13×D11semidirect
103. C2×C3×C7C3×C13×D11semidirect
104. C2×C3×C7C13×D33semidirect
108. C3×C13C2×C3×D77semidirect
109. C3×C13C2×D231direct (N × H)
112. C3×C11C2×C3×C13×D7semidirect
113. C3×C11C2×C13×D21semidirect
116. C2×C13C3×D231direct (N × H)
117. C2×C11C3×C13×D21semidirect
120. C3×C7C2×C3×C13×D11semidirect
121. C3×C7C2×C13×D33semidirect
122. C2×C32C13×D77semidirect
124. C2×C7C3×C13×D33semidirect
126. C13C2×C3×D231direct (N × H)
129. C11C2×C3×C13×D21semidirect
130. C32C2×C13×D77semidirect
131. C7C2×C3×C13×D33semidirect
134. C2×C3C3×C13×D77semidirect
135. C2×C3C13×D231direct (N × H)
139. C3C2×C13×D231direct (N × H)
140. C3C2×C3×C13×D77semidirect
142. C2C3×C13×D231direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C13×D2312
C2×C32×C7×C11×C132
C2×C3×C13×D773
C2×C13×D2313
C2×C3×C13×D337
C2×C3×C13×D2111
C2×C3×D23113