Finite Group Databasebeta

← C3×D3×C11×C13×D7 #49114916

Subgroups — C3×D3×C11×C13×D7 #49114916

Order 36036.

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C32×C11×C13×D7C211yesmaximal, characteristic, complemented
2C3×D3×C7×C11×C13C211yesmaximal, characteristic, complemented
3C3×C11×C13×D21C211yesmaximal, characteristic, complemented
4C2×C3×C11×C13×D7—31nomaximal
5D3×C11×C13×D7C311yesmaximal, characteristic, direct product factor
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C11×C13×D21C2×C311yescharacteristic, complemented
8D3×C7×C11×C13C2×C311yescharacteristic, complemented
9C3×C11×C13×D7—21no—
10C3×C11×C13×D7—31no—
11C3×C11×C13×D7D311yescharacteristic, direct product factor
12C3×C11×C13×D7C2×C311yescharacteristic, complemented
13C2×C3×C7×C11×C13—31no—
14C2×C3×D3×C11×C13—71nomaximal, Hall
15C2×C11×C13×D7—31noHall
16C3×D3×C13×D7C1111yesmaximal, characteristic, direct product factor, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D3×C11×D7C1311yesmaximal, characteristic, direct product factor, Hall
21C3×D3×C11×C13—71no—
22C3×D3×C11×C13D711yescharacteristic, direct product factor
23C2×C32×C11×C13—71no—
24C11×C13×D7—31no—
25C11×C13×D7C3×D311yescharacteristic, direct product factor
26C2×C7×C11×C13—31no—
27C22×C3×C11×C13—211no—
28C2×D3×C11×C13—71no—
29C3×C13×D21C2×C1111yescharacteristic, complemented
30C3×D3×C7×C13C2×C1111yescharacteristic, complemented
31C32×C13×D7C2×C1111yescharacteristic, complemented
32C3×C11×D21C2×C1311yescharacteristic, complemented
33C3×D3×C7×C11C2×C1311yescharacteristic, complemented
34C32×C11×D7C2×C1311yescharacteristic, complemented
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36C2×C3×C13×D7—31no—
37D3×C13×D7C3×C1111yescharacteristic, direct product factor
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C3×C11×D7—31no—
40D3×C11×D7C3×C1311yescharacteristic, direct product factor
41C2×C3×C11×C13—31no—
42C2×C3×C11×C13—71no—
43C2×C3×C11×C13—71no—
44C2×C3×C11×C13—141no—
45C2×C3×C11×C13—211no—
46D3×C11×C13—71no—
47D3×C11×C13C3×D711yescharacteristic, direct product factor
48C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
49C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
50C22×C11×C13—211noHall
51C2×C3×C7×C13—31no—
52C13×D21C2×C3×C1111yescharacteristic, complemented
53D3×C7×C13C2×C3×C1111yescharacteristic, complemented
54C3×C13×D7—21no—
55C3×C13×D7—31no—
56C3×C13×D7D3×C1111yescharacteristic, direct product factor
57C3×C13×D7C2×C3×C1111yescharacteristic, complemented
58C2×C3×D3×C13—71noHall
59C2×C3×C7×C11—31no—
60C11×D21C2×C3×C1311yescharacteristic, complemented
61D3×C7×C11C2×C3×C1311yescharacteristic, complemented
62C3×C11×D7—21no—
63C3×C11×D7—31no—
64C3×C11×D7D3×C1311yescharacteristic, direct product factor
65C3×C11×D7C2×C3×C1311yescharacteristic, complemented
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, direct product factor
68C3×C11×C13C2×C3×D711yescharacteristic, complemented
69C2×C3×D3×C11—71noHall
70C2×C13×D7—31noHall
71C2×C11×D7—31noHall
72C2×C11×C13—31no—
73C2×C11×C13—71no—
74C2×C11×C13—211no—
75C3×C7×C13—21no—
76C3×C7×C13C2×D3×C1111yescharacteristic, complemented
77C3×C7×C13C22×C3×C1111yescharacteristic, complemented
78C3×D3×D7C11×C1311yescharacteristic, direct product factor, Hall
79C2×C32×C13—71no—
80C3×D3×C13—71no—
81C3×D3×C13C11×D711yescharacteristic, direct product factor
82C3×C7×C11—21no—
83C3×C7×C11C2×D3×C1311yescharacteristic, complemented
84C3×C7×C11C22×C3×C1311yescharacteristic, complemented
85C2×C32×C11—71no—
86C3×D3×C11—71no—
87C3×D3×C11C13×D711yescharacteristic, direct product factor
88C2×C7×C13—31no—
89C13×D7—31no—
90C13×D7C3×D3×C1111yescharacteristic, direct product factor
91C22×C3×C13—211no—
92C2×D3×C13—71no—
93C2×C7×C11—31no—
94C11×D7—31no—
95C11×D7C3×D3×C1311yescharacteristic, direct product factor
96C11×C13C3×D3×D711yescharacteristic, direct product factor, Hall
97C22×C3×C11—211no—
98C2×D3×C11—71no—
99C3×D21C2×C11×C1311yescharacteristic, complemented
100C3×D3×C7C2×C11×C1311yescharacteristic, complemented
101C32×D7C2×C11×C1311yescharacteristic, complemented
102C32×C13C2×C11×D711yescharacteristic, complemented, Hall
103C32×C11C2×C13×D711yescharacteristic, complemented, Hall
104C7×C13C2×C3×D3×C1111yescharacteristic, complemented, Hall
105C2×C3×D7—31no—
106D3×D7C3×C11×C1311yescharacteristic, direct product factor
107C2×C3×C13—31no—
108C2×C3×C13—71no—
109C2×C3×C13—71no—
110C2×C3×C13—141no—
111C2×C3×C13—211no—
112D3×C13—71no—
113D3×C13C3×C11×D711yescharacteristic, direct product factor
114C7×C11C2×C3×D3×C1311yescharacteristic, complemented, Hall
115C2×C3×C11—31no—
116C2×C3×C11—71no—
117C2×C3×C11—71no—
118C2×C3×C11—141no—
119C2×C3×C11—211no—
120D3×C11—71no—
121D3×C11C3×C13×D711yescharacteristic, direct product factor
122C32×C7C22×C11×C1311yescharacteristic, complemented, Hall
123C22×C13—211noHall
124C22×C11—211noHall
125C2×C3×C7—31no—
126D21C2×C3×C11×C1311yescharacteristic, complemented
127C3×D7—21no—
128C3×D7—31no—
129C3×D7D3×C11×C1311yescharacteristic, direct product factor
130C3×D7C2×C3×C11×C1311yescharacteristic, complemented
131D3×C7C2×C3×C11×C1311yescharacteristic, complemented
132C3×C13—21no—
133C3×C13D3×C11×D711yescharacteristic, direct product factor
134C3×C13C2×C3×C11×D711yescharacteristic, complemented
135C2×C3×D3—71noHall
136C3×C11—21no—
137C3×C11D3×C13×D711yescharacteristic, direct product factor
138C3×C11C2×C3×C13×D711yescharacteristic, complemented
139C2×D7—31noHall
140C2×C13—31no—
141C2×C13—71no—
142C2×C13—211no—
143C2×C11—31no—
144C2×C11—71no—
145C2×C11—211no—
146C3×C7—21no—
147C3×C7C2×D3×C11×C1311yescharacteristic, complemented
148C3×C7C22×C3×C11×C1311yescharacteristic, complemented
149C2×C32—71no—
150C3×D3—71no—
151C3×D3C11×C13×D711yescharacteristic, direct product factor
152C2×C7—31no—
153D7—31no—
154D7C3×D3×C11×C1311yescharacteristic, direct product factor
155C13C3×D3×C11×D711yescharacteristic, direct product factor, Sylow
156C22×C3—211no—
157C2×D3—71no—
158C11C3×D3×C13×D711yescharacteristic, direct product factor, Sylow
159C32C2×C11×C13×D711yescharacteristic, complemented, Sylow
160C7C2×C3×D3×C11×C1311yescharacteristic, complemented, Sylow
161C2×C3—31no—
162C2×C3—71no—
163C2×C3—71no—
164C2×C3—141no—
165C2×C3—211no—
166D3—71no—
167D3C3×C11×C13×D711yescharacteristic, direct product factor
168C22—211noSylow
169C3—21no—
170C3D3×C11×C13×D711yescharacteristic, direct product factor
171C3C2×C3×C11×C13×D711yescharacteristic, complemented
172C2—31no—
173C2—71no—
174C2—211no—
subgroupG/H
center, hypercenterC3×C11×C13D3×D7
commutator, cosocle, hypocenterC3×C7C22×C3×C11×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C3×C7
UCSC1 ◁ C3×C11×C13

Complements

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

NH ≅ G/Ntype
1. C32×C11×C13×D7C2semidirect
2. C3×D3×C7×C11×C13C2semidirect
3. C3×C11×C13×D21C2semidirect
5. D3×C11×C13×D7C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. C11×C13×D21C2×C3semidirect
8. D3×C7×C11×C13C2×C3semidirect
11. C3×C11×C13×D7D3direct (N × H)
12. C3×C11×C13×D7C2×C3semidirect
16. C3×D3×C13×D7C11direct (N × H)
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
20. C3×D3×C11×D7C13direct (N × H)
22. C3×D3×C11×C13D7direct (N × H)
25. C11×C13×D7C3×D3direct (N × H)
29. C3×C13×D21C2×C11semidirect
30. C3×D3×C7×C13C2×C11semidirect
31. C32×C13×D7C2×C11semidirect
32. C3×C11×D21C2×C13semidirect
33. C3×D3×C7×C11C2×C13semidirect
34. C32×C11×D7C2×C13semidirect
35. C32×C11×C13C2×D7semidirect
37. D3×C13×D7C3×C11direct (N × H)
38. C7×C11×C13C2×C3×D3semidirect
40. D3×C11×D7C3×C13direct (N × H)
47. D3×C11×C13C3×D7direct (N × H)
48. C32×C7×C13C22×C11semidirect
49. C32×C7×C11C22×C13semidirect
52. C13×D21C2×C3×C11semidirect
53. D3×C7×C13C2×C3×C11semidirect
56. C3×C13×D7D3×C11direct (N × H)
57. C3×C13×D7C2×C3×C11semidirect
60. C11×D21C2×C3×C13semidirect
61. D3×C7×C11C2×C3×C13semidirect
64. C3×C11×D7D3×C13direct (N × H)
65. C3×C11×D7C2×C3×C13semidirect
67. C3×C11×C13D3×D7direct (N × H)
68. C3×C11×C13C2×C3×D7semidirect
76. C3×C7×C13C2×D3×C11semidirect
77. C3×C7×C13C22×C3×C11semidirect
78. C3×D3×D7C11×C13direct (N × H)
81. C3×D3×C13C11×D7direct (N × H)
83. C3×C7×C11C2×D3×C13semidirect
84. C3×C7×C11C22×C3×C13semidirect
87. C3×D3×C11C13×D7direct (N × H)
90. C13×D7C3×D3×C11direct (N × H)
95. C11×D7C3×D3×C13direct (N × H)
96. C11×C13C3×D3×D7direct (N × H)
99. C3×D21C2×C11×C13semidirect
100. C3×D3×C7C2×C11×C13semidirect
101. C32×D7C2×C11×C13semidirect
102. C32×C13C2×C11×D7semidirect
103. C32×C11C2×C13×D7semidirect
104. C7×C13C2×C3×D3×C11semidirect
106. D3×D7C3×C11×C13direct (N × H)
113. D3×C13C3×C11×D7direct (N × H)
114. C7×C11C2×C3×D3×C13semidirect
121. D3×C11C3×C13×D7direct (N × H)
122. C32×C7C22×C11×C13semidirect
126. D21C2×C3×C11×C13semidirect
129. C3×D7D3×C11×C13direct (N × H)
130. C3×D7C2×C3×C11×C13semidirect
131. D3×C7C2×C3×C11×C13semidirect
133. C3×C13D3×C11×D7direct (N × H)
134. C3×C13C2×C3×C11×D7semidirect
137. C3×C11D3×C13×D7direct (N × H)
138. C3×C11C2×C3×C13×D7semidirect
147. C3×C7C2×D3×C11×C13semidirect
148. C3×C7C22×C3×C11×C13semidirect
151. C3×D3C11×C13×D7direct (N × H)
154. D7C3×D3×C11×C13direct (N × H)
155. C13C3×D3×C11×D7direct (N × H)
158. C11C3×D3×C13×D7direct (N × H)
159. C32C2×C11×C13×D7semidirect
160. C7C2×C3×D3×C11×C13semidirect
167. D3C3×C11×C13×D7direct (N × H)
170. C3D3×C11×C13×D7direct (N × H)
171. C3C2×C3×C11×C13×D7semidirect

Maximal subgroups

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

subgroupindex
C32×C11×C13×D72
C3×D3×C7×C11×C132
C3×C11×C13×D212
C2×C3×C11×C13×D73
D3×C11×C13×D73
C2×C3×D3×C11×C137
C3×D3×C13×D711
C3×D3×C11×D713