Finite Group Databasebeta

← C3×D3×C7×D115 #44394577

Subgroups — C3×D3×C7×D115 #44394577

Order 28980.

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×D115C211yesmaximal, characteristic, complemented
2C3×C5×D3×C7×C23C211yesmaximal, characteristic, complemented
3C3×C7×D345C211yesmaximal, characteristic, complemented
4C2×C3×C7×D115—31nomaximal
5D3×C7×D115C311yesmaximal, characteristic, direct product factor
6C32×C5×C7×C23C2211yescharacteristic, complemented, Hall
7C3×D3×C7×D23—51nomaximal, Hall
8C7×D345C2×C311yescharacteristic, complemented
9C5×D3×C7×C23C2×C311yescharacteristic, complemented
10C3×C7×D115—21no—
11C3×C7×D115—31no—
12C3×C7×D115D311yescharacteristic, direct product factor
13C3×C7×D115C2×C311yescharacteristic, complemented
14C2×C3×C5×C7×C23—31no—
15C3×D3×D115C711yesmaximal, characteristic, direct product factor, Hall
16C2×C7×D115—31noHall
17C3×C7×D69—51no—
18C3×D3×C7×C23D511yescharacteristic, complemented
19C32×C7×D23—51no—
20C3×C5×C7×C23—21no—
21C3×C5×C7×C23C2×D311yescharacteristic, complemented
22C3×C5×C7×C23C22×C311yescharacteristic, complemented
23C3×D345C2×C711yescharacteristic, complemented
24C3×C5×D3×C23C2×C711yescharacteristic, complemented
25C32×D115C2×C711yescharacteristic, complemented
26C2×C3×C7×D23—151no—
27D3×C7×D23—51no—
28C2×C5×C7×C23—31no—
29C7×D115—31no—
30C7×D115C3×D311yescharacteristic, direct product factor
31C32×C7×C23C2×D511yescharacteristic, complemented, Hall
32C2×C3×D115—31no—
33D3×D115C3×C711yescharacteristic, direct product factor
34C3×D3×C7×D5—231nomaximal, Hall
35C32×C5×C23C22×C711yescharacteristic, complemented, Hall
36C2×C3×C7×C23—31no—
37C7×D69—51no—
38D3×C7×C23C3×D511yescharacteristic, complemented
39C3×C7×D23—51no—
40C3×C7×D23—51no—
41C3×C7×D23—101no—
42C3×C7×D23—151no—
43C3×D3×D23—51noHall
44C5×C7×C23C2×C3×D311yescharacteristic, complemented, Hall
45C2×C3×C5×C23—31no—
46D345C2×C3×C711yescharacteristic, complemented
47C5×D3×C23C2×C3×C711yescharacteristic, complemented
48C3×D115—21no—
49C3×D115—31no—
50C3×D115D3×C711yescharacteristic, direct product factor
51C3×D115C2×C3×C711yescharacteristic, complemented
52C2×C7×D23—151noHall
53C3×C7×D15—231no—
54C3×C5×D3×C7D2311yescharacteristic, complemented
55C32×C7×D5—231no—
56C3×C7×C23—21no—
57C3×C7×C23D3×D511yescharacteristic, complemented
58C3×C7×C23C2×C3×D511yescharacteristic, complemented
59C2×D115—31noHall
60C2×C3×C7×D5—691no—
61D3×C7×D5—231no—
62C3×D69—51no—
63C3×D3×C23C7×D511yescharacteristic, complemented
64C32×D23—51no—
65C3×C5×C23—21no—
66C3×C5×C23C2×D3×C711yescharacteristic, complemented
67C3×C5×C23C22×C3×C711yescharacteristic, complemented
68C2×C7×C23—31no—
69C7×D23—51no—
70C7×D23—151no—
71C32×C5×C7C2×D2311yescharacteristic, complemented, Hall
72C2×C3×D23—151no—
73D3×D23—51no—
74C2×C3×D3×C7—1151noHall
75C2×C5×C23—31no—
76D115—31no—
77D115C3×D3×C711yescharacteristic, direct product factor
78C2×C3×C5×C7—31no—
79C7×D15—231no—
80C5×D3×C7C3×D2311yescharacteristic, complemented
81C3×C7×D5—231no—
82C3×C7×D5—231no—
83C3×C7×D5—461no—
84C3×C7×D5—691no—
85C32×C23C2×C7×D511yescharacteristic, complemented, Hall
86C3×D3×D5—231noHall
87C7×C23C3×D3×D511yescharacteristic, complemented, Hall
88C2×C7×D5—691noHall
89C2×C3×C23—31no—
90D69—51no—
91C3×D23—51no—
92C3×D23—51no—
93C3×D23—101no—
94C3×D23—151no—
95D3×C23C3×C7×D511yescharacteristic, complemented
96C2×C32×C7—1151no—
97C3×D3×C7—1151no—
98C3×D3×C7D11511yescharacteristic, direct product factor
99C5×C23C2×C3×D3×C711yescharacteristic, complemented, Hall
100C3×C5×C7—21no—
101C3×C5×C7D3×D2311yescharacteristic, complemented
102C3×C5×C7C2×C3×D2311yescharacteristic, complemented
103C2×D23—151noHall
104C3×D15—231no—
105C3×C5×D3C7×D2311yescharacteristic, complemented
106C32×D5—231no—
107C22×C3×C7—3451no—
108C2×D3×C7—1151no—
109C2×C5×C7—31no—
110C7×D5—231no—
111C7×D5—691no—
112C3×C23—21no—
113C3×C23D3×C7×D511yescharacteristic, complemented
114C3×C23C2×C3×C7×D511yescharacteristic, complemented
115C32×C7C2×D11511yescharacteristic, complemented, Hall
116C2×C3×D5—691no—
117D3×D5—231no—
118C2×C23—31no—
119D23—51no—
120D23—151no—
121C32×C5C2×C7×D2311yescharacteristic, complemented, Hall
122C2×C3×C7—31no—
123C2×C3×C7—3451no—
124C2×C3×C7—1151no—
125C2×C3×C7—1151no—
126C2×C3×C7—2301no—
127D3×C7—1151no—
128D3×C7C3×D11511yescharacteristic, direct product factor
129C2×C3×D3—1151noHall
130C5×C7C3×D3×D2311yescharacteristic, complemented, Hall
131C2×C3×C5—31no—
132D15—231no—
133C3×D5—231no—
134C3×D5—231no—
135C3×D5—461no—
136C3×D5—691no—
137C5×D3C3×C7×D2311yescharacteristic, complemented
138C22×C7—3451noHall
139C23C3×D3×C7×D511yescharacteristic, complemented, Sylow
140C3×C7—21no—
141C3×C7D3×D11511yescharacteristic, direct product factor
142C3×C7C2×C3×D11511yescharacteristic, complemented
143C2×D5—691noHall
144C2×C32—1151no—
145C3×D3—1151no—
146C3×D3C7×D11511yescharacteristic, direct product factor
147C3×C5—21no—
148C3×C5D3×C7×D2311yescharacteristic, complemented
149C3×C5C2×C3×C7×D2311yescharacteristic, complemented
150C2×C7—31no—
151C2×C7—3451no—
152C2×C7—1151no—
153C22×C3—3451no—
154C2×D3—1151no—
155C2×C5—31no—
156D5—231no—
157D5—691no—
158C32C2×C7×D11511yescharacteristic, complemented, Sylow
159C7C3×D3×D11511yescharacteristic, direct product factor, Sylow
160C2×C3—31no—
161C2×C3—3451no—
162C2×C3—1151no—
163C2×C3—1151no—
164C2×C3—2301no—
165D3—1151no—
166D3C3×C7×D11511yescharacteristic, direct product factor
167C5C3×D3×C7×D2311yescharacteristic, complemented, Sylow
168C22—3451noSylow
169C3—21no—
170C3D3×C7×D11511yescharacteristic, direct product factor
171C3C2×C3×C7×D11511yescharacteristic, complemented
172C2—31no—
173C2—3451no—
174C2—1151no—
subgroupG/H
center, hypercenterC3×C7D3×D115
commutator, cosocle, hypocenterC3×C5×C23C22×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C23C22
LCSG ▷ C3×C5×C23
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×D115C2semidirect
2. C3×C5×D3×C7×C23C2semidirect
3. C3×C7×D345C2semidirect
5. D3×C7×D115C3direct (N × H)
6. C32×C5×C7×C23C22semidirect
8. C7×D345C2×C3semidirect
9. C5×D3×C7×C23C2×C3semidirect
12. C3×C7×D115D3direct (N × H)
13. C3×C7×D115C2×C3semidirect
15. C3×D3×D115C7direct (N × H)
18. C3×D3×C7×C23D5semidirect
21. C3×C5×C7×C23C2×D3semidirect
22. C3×C5×C7×C23C22×C3semidirect
23. C3×D345C2×C7semidirect
24. C3×C5×D3×C23C2×C7semidirect
25. C32×D115C2×C7semidirect
30. C7×D115C3×D3direct (N × H)
31. C32×C7×C23C2×D5semidirect
33. D3×D115C3×C7direct (N × H)
35. C32×C5×C23C22×C7semidirect
38. D3×C7×C23C3×D5semidirect
44. C5×C7×C23C2×C3×D3semidirect
46. D345C2×C3×C7semidirect
47. C5×D3×C23C2×C3×C7semidirect
50. C3×D115D3×C7direct (N × H)
51. C3×D115C2×C3×C7semidirect
54. C3×C5×D3×C7D23semidirect
57. C3×C7×C23D3×D5semidirect
58. C3×C7×C23C2×C3×D5semidirect
63. C3×D3×C23C7×D5semidirect
66. C3×C5×C23C2×D3×C7semidirect
67. C3×C5×C23C22×C3×C7semidirect
71. C32×C5×C7C2×D23semidirect
77. D115C3×D3×C7direct (N × H)
80. C5×D3×C7C3×D23semidirect
85. C32×C23C2×C7×D5semidirect
87. C7×C23C3×D3×D5semidirect
95. D3×C23C3×C7×D5semidirect
98. C3×D3×C7D115direct (N × H)
99. C5×C23C2×C3×D3×C7semidirect
101. C3×C5×C7D3×D23semidirect
102. C3×C5×C7C2×C3×D23semidirect
105. C3×C5×D3C7×D23semidirect
113. C3×C23D3×C7×D5semidirect
114. C3×C23C2×C3×C7×D5semidirect
115. C32×C7C2×D115semidirect
121. C32×C5C2×C7×D23semidirect
128. D3×C7C3×D115direct (N × H)
130. C5×C7C3×D3×D23semidirect
137. C5×D3C3×C7×D23semidirect
139. C23C3×D3×C7×D5semidirect
141. C3×C7D3×D115direct (N × H)
142. C3×C7C2×C3×D115semidirect
146. C3×D3C7×D115direct (N × H)
148. C3×C5D3×C7×D23semidirect
149. C3×C5C2×C3×C7×D23semidirect
158. C32C2×C7×D115semidirect
159. C7C3×D3×D115direct (N × H)
166. D3C3×C7×D115direct (N × H)
167. C5C3×D3×C7×D23semidirect
170. C3D3×C7×D115direct (N × H)
171. C3C2×C3×C7×D115semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1152
C3×C5×D3×C7×C232
C3×C7×D3452
C2×C3×C7×D1153
D3×C7×D1153
C3×D3×C7×D235
C3×D3×D1157
C3×D3×C7×D523