Finite Group Databasebeta

← C3×D3×C7×D145 #49141580

Subgroups — C3×D3×C7×D145 #49141580

Order 36540.

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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×C7×D145C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C29C211yesmaximal, characteristic, complemented
3C3×C7×D435C211yesmaximal, characteristic, complemented
4C2×C3×C7×D145—31nomaximal
5D3×C7×D145C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7C3×D3×C7×D29—51nomaximal, Hall
8C7×D435C2×C311yescharacteristic, complemented
9C5×D3×C7×C29C2×C311yescharacteristic, complemented
10C3×C7×D145—21no—
11C3×C7×D145—31no—
12C3×C7×D145D311yescharacteristic, direct product factor
13C3×C7×D145C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C29—31no—
15C3×D3×D145C711yesmaximal, characteristic, direct product factor, Hall
16C2×C7×D145—31noHall
17C3×C7×D87—51no—
18C3×D3×C7×C29D511yescharacteristic, complemented
19C32×C7×D29—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C22×C311yescharacteristic, complemented
23C3×D435C2×C711yescharacteristic, complemented
24C3×C5×D3×C29C2×C711yescharacteristic, complemented
25C32×D145C2×C711yescharacteristic, complemented
26C2×C3×C7×D29—151no—
27D3×C7×D29—51no—
28C7×D145—31no—
29C7×D145C3×D311yescharacteristic, direct product factor
30C2×C5×C7×C29—31no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32C2×C3×D145—31no—
33D3×D145C3×C711yescharacteristic, direct product factor
34C32×C5×C29C22×C711yescharacteristic, complemented, Hall
35C3×D3×C7×D5—291nomaximal, Hall
36C2×C3×C7×C29—31no—
37C7×D87—51no—
38D3×C7×C29C3×D511yescharacteristic, complemented
39C3×C7×D29—51no—
40C3×C7×D29—51no—
41C3×C7×D29—101no—
42C3×C7×D29—151no—
43C3×D3×D29—51noHall
44C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C29—31no—
46D435C2×C3×C711yescharacteristic, complemented
47C5×D3×C29C2×C3×C711yescharacteristic, complemented
48C3×D145—21no—
49C3×D145—31no—
50C3×D145D3×C711yescharacteristic, direct product factor
51C3×D145C2×C3×C711yescharacteristic, complemented
52C2×C7×D29—151noHall
53C3×C7×D15—291no—
54C3×C5×D3×C7D2911yescharacteristic, complemented
55C32×C7×D5—291no—
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29C2×C3×D511yescharacteristic, complemented
59C2×D145—31noHall
60C3×D87—51no—
61C3×D3×C29C7×D511yescharacteristic, complemented
62C32×D29—51no—
63C3×C5×C29—21no—
64C3×C5×C29C2×D3×C711yescharacteristic, complemented
65C3×C5×C29C22×C3×C711yescharacteristic, complemented
66C2×C3×C7×D5—871no—
67D3×C7×D5—291no—
68C2×C7×C29—31no—
69C7×D29—51no—
70C7×D29—151no—
71C2×C3×D29—151no—
72D3×D29—51no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74C2×C5×C29—31no—
75D145—31no—
76D145C3×D3×C711yescharacteristic, direct product factor
77C32×C29C2×C7×D511yescharacteristic, complemented, Hall
78C2×C3×D3×C7—1451noHall
79C2×C3×C5×C7—31no—
80C7×D15—291no—
81C5×D3×C7C3×D2911yescharacteristic, complemented
82C3×C7×D5—291no—
83C3×C7×D5—291no—
84C3×C7×D5—581no—
85C3×C7×D5—871no—
86C7×C29C3×D3×D511yescharacteristic, complemented, Hall
87C3×D3×D5—291noHall
88C2×C3×C29—31no—
89D87—51no—
90C3×D29—51no—
91C3×D29—51no—
92C3×D29—101no—
93C3×D29—151no—
94D3×C29C3×C7×D511yescharacteristic, complemented
95C5×C29C2×C3×D3×C711yescharacteristic, complemented, Hall
96C2×C7×D5—871noHall
97C2×C32×C7—1451no—
98C3×D3×C7—1451no—
99C3×D3×C7D14511yescharacteristic, direct product factor
100C2×D29—151noHall
101C3×C5×C7—21no—
102C3×C5×C7D3×D2911yescharacteristic, complemented
103C3×C5×C7C2×C3×D2911yescharacteristic, complemented
104C3×D15—291no—
105C3×C5×D3C7×D2911yescharacteristic, complemented
106C32×D5—291no—
107C3×C29—21no—
108C3×C29D3×C7×D511yescharacteristic, complemented
109C3×C29C2×C3×C7×D511yescharacteristic, complemented
110C22×C3×C7—4351no—
111C2×D3×C7—1451no—
112C2×C5×C7—31no—
113C7×D5—291no—
114C7×D5—871no—
115C32×C7C2×D14511yescharacteristic, complemented, Hall
116C2×C3×D5—871no—
117D3×D5—291no—
118C2×C29—31no—
119D29—51no—
120D29—151no—
121C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
122C2×C3×C7—31no—
123C2×C3×C7—2901no—
124C2×C3×C7—1451no—
125C2×C3×C7—1451no—
126C2×C3×C7—4351no—
127D3×C7—1451no—
128D3×C7C3×D14511yescharacteristic, direct product factor
129C2×C3×D3—1451noHall
130C5×C7C3×D3×D2911yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132D15—291no—
133C3×D5—291no—
134C3×D5—291no—
135C3×D5—581no—
136C3×D5—871no—
137C5×D3C3×C7×D2911yescharacteristic, complemented
138C29C3×D3×C7×D511yescharacteristic, complemented, Sylow
139C22×C7—4351noHall
140C3×C7—21no—
141C3×C7D3×D14511yescharacteristic, direct product factor
142C3×C7C2×C3×D14511yescharacteristic, complemented
143C2×D5—871noHall
144C2×C32—1451no—
145C3×D3—1451no—
146C3×D3C7×D14511yescharacteristic, direct product factor
147C3×C5—21no—
148C3×C5D3×C7×D2911yescharacteristic, complemented
149C3×C5C2×C3×C7×D2911yescharacteristic, complemented
150C2×C7—31no—
151C2×C7—1451no—
152C2×C7—4351no—
153C22×C3—4351no—
154C2×D3—1451no—
155C2×C5—31no—
156D5—291no—
157D5—871no—
158C32C2×C7×D14511yescharacteristic, complemented, Sylow
159C7C3×D3×D14511yescharacteristic, direct product factor, Sylow
160C2×C3—31no—
161C2×C3—2901no—
162C2×C3—1451no—
163C2×C3—1451no—
164C2×C3—4351no—
165D3—1451no—
166D3C3×C7×D14511yescharacteristic, direct product factor
167C5C3×D3×C7×D2911yescharacteristic, complemented, Sylow
168C22—4351noSylow
169C3—21no—
170C3D3×C7×D14511yescharacteristic, direct product factor
171C3C2×C3×C7×D14511yescharacteristic, complemented
172C2—31no—
173C2—1451no—
174C2—4351no—
subgroupG/H
center, hypercenterC3×C7D3×D145
commutator, cosocle, hypocenterC3×C5×C29C22×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C3×C5×C29
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D145C2semidirect
2. C3×C5×D3×C7×C29C2semidirect
3. C3×C7×D435C2semidirect
5. D3×C7×D145C3direct (N × H)
6. C32×C5×C7×C29C22semidirect
8. C7×D435C2×C3semidirect
9. C5×D3×C7×C29C2×C3semidirect
12. C3×C7×D145D3direct (N × H)
13. C3×C7×D145C2×C3semidirect
15. C3×D3×D145C7direct (N × H)
18. C3×D3×C7×C29D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C22×C3semidirect
23. C3×D435C2×C7semidirect
24. C3×C5×D3×C29C2×C7semidirect
25. C32×D145C2×C7semidirect
29. C7×D145C3×D3direct (N × H)
31. C32×C7×C29C2×D5semidirect
33. D3×D145C3×C7direct (N × H)
34. C32×C5×C29C22×C7semidirect
38. D3×C7×C29C3×D5semidirect
44. C5×C7×C29C2×C3×D3semidirect
46. D435C2×C3×C7semidirect
47. C5×D3×C29C2×C3×C7semidirect
50. C3×D145D3×C7direct (N × H)
51. C3×D145C2×C3×C7semidirect
54. C3×C5×D3×C7D29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29C2×C3×D5semidirect
61. C3×D3×C29C7×D5semidirect
64. C3×C5×C29C2×D3×C7semidirect
65. C3×C5×C29C22×C3×C7semidirect
73. C32×C5×C7C2×D29semidirect
76. D145C3×D3×C7direct (N × H)
77. C32×C29C2×C7×D5semidirect
81. C5×D3×C7C3×D29semidirect
86. C7×C29C3×D3×D5semidirect
94. D3×C29C3×C7×D5semidirect
95. C5×C29C2×C3×D3×C7semidirect
99. C3×D3×C7D145direct (N × H)
102. C3×C5×C7D3×D29semidirect
103. C3×C5×C7C2×C3×D29semidirect
105. C3×C5×D3C7×D29semidirect
108. C3×C29D3×C7×D5semidirect
109. C3×C29C2×C3×C7×D5semidirect
115. C32×C7C2×D145semidirect
121. C32×C5C2×C7×D29semidirect
128. D3×C7C3×D145direct (N × H)
130. C5×C7C3×D3×D29semidirect
137. C5×D3C3×C7×D29semidirect
138. C29C3×D3×C7×D5semidirect
141. C3×C7D3×D145direct (N × H)
142. C3×C7C2×C3×D145semidirect
146. C3×D3C7×D145direct (N × H)
148. C3×C5D3×C7×D29semidirect
149. C3×C5C2×C3×C7×D29semidirect
158. C32C2×C7×D145semidirect
159. C7C3×D3×D145direct (N × H)
166. D3C3×C7×D145direct (N × H)
167. C5C3×D3×C7×D29semidirect
170. C3D3×C7×D145direct (N × H)
171. C3C2×C3×C7×D145semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1452
C3×C5×D3×C7×C292
C3×C7×D4352
C2×C3×C7×D1453
D3×C7×D1453
C3×D3×C7×D295
C3×D3×D1457
C3×D3×C7×D529