Finite Group Databasebeta

← C3×C5×C7×D7×D11 #44568804

Subgroups — C3×C5×C7×D7×D11 #44568804

Order 32340.

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

normal subgroups only

This group has 208 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
1C3×C5×C72×D11C211yesmaximal, characteristic, complemented
2C3×C5×C7×C11×D7C211yesmaximal, characteristic, complemented
3C3×C5×C7×D77C211yesmaximal, characteristic, complemented
4C5×C7×D7×D11C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C3×C7×D7×D11C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7×D77C2×C311yescharacteristic, complemented
8C5×C7×C11×D7C2×C311yescharacteristic, complemented
9C5×C72×D11C2×C311yescharacteristic, complemented
10C2×C3×C5×C7×D11—71nomaximal
11C3×C5×D7×D11C711yesmaximal, characteristic, direct product factor
12C3×C7×D77C2×C511yescharacteristic, complemented
13C3×C7×C11×D7C2×C511yescharacteristic, complemented
14C3×C72×D11C2×C511yescharacteristic, complemented
15C2×C3×C5×C7×D7—111nomaximal, Hall
16C5×C72×C11C22×C311yescharacteristic, complemented, Hall
17C3×C5×D77C2×C711yescharacteristic, complemented
18C3×C5×C11×D7C2×C711yescharacteristic, complemented
19C3×C5×C7×D11—23no—
20C3×C5×C7×D11—71no—
21C3×C5×C7×D11D711yescharacteristic, direct product factor
22C3×C5×C7×D11C2×C711yescharacteristic, complemented
23C2×C3×C5×C7×C11—71no—
24C7×D7×D11C3×C511yescharacteristic, direct product factor, Hall
25C3×C72×C11C22×C511yescharacteristic, complemented, Hall
26C2×C5×C7×D11—71no—
27C5×D7×D11C3×C711yescharacteristic, direct product factor
28C2×C3×C5×C72—111no—
29C3×C5×C7×D7—111no—
30C3×C5×C7×D7D1111yescharacteristic, direct product factor
31C3×C5×C7×C11—23no—
32C3×C5×C7×C11C2×D711yescharacteristic, complemented
33C3×C5×C7×C11C22×C711yescharacteristic, complemented
34C7×D77C2×C3×C511yescharacteristic, complemented
35C7×C11×D7C2×C3×C511yescharacteristic, complemented
36C72×D11C2×C3×C511yescharacteristic, complemented
37C2×C5×C7×D7—111noHall
38C2×C3×C7×D11—71no—
39C3×D7×D11C5×C711yescharacteristic, direct product factor
40C2×C5×C7×C11—71no—
41C5×D77C2×C3×C711yescharacteristic, complemented
42C5×C11×D7C2×C3×C711yescharacteristic, complemented
43C5×C7×D11—23no—
44C5×C7×D11—71no—
45C5×C7×D11C3×D711yescharacteristic, direct product factor
46C5×C7×D11C2×C3×C711yescharacteristic, complemented
47C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
48C2×C3×C5×D11—71noHall
49C2×C3×C7×D7—111noHall
50C72×C11C22×C3×C511yescharacteristic, complemented, Hall
51C2×C5×C72—111no—
52C5×C7×D7—111no—
53C5×C7×D7C3×D1111yescharacteristic, direct product factor
54C2×C3×C7×C11—71no—
55C3×D77C2×C5×C711yescharacteristic, complemented
56C3×C11×D7C2×C5×C711yescharacteristic, complemented
57C3×C7×D11—23no—
58C3×C7×D11—71no—
59C3×C7×D11C5×D711yescharacteristic, direct product factor
60C3×C7×D11C2×C5×C711yescharacteristic, complemented
61C22×C3×C5×C7—771no—
62C2×C3×C5×D7—111no—
63C5×C7×C11—23no—
64C5×C7×C11C2×C3×D711yescharacteristic, complemented
65C5×C7×C11C22×C3×C711yescharacteristic, complemented
66C2×C3×C5×C11—71no—
67C3×C5×D11—71no—
68C3×C5×D11C7×D711yescharacteristic, direct product factor
69C2×C7×D11—71no—
70D7×D11C3×C5×C711yescharacteristic, direct product factor
71C2×C3×C72—111no—
72C3×C7×D7—111no—
73C3×C7×D7C5×D1111yescharacteristic, direct product factor
74C5×C72C2×C3×D1111yescharacteristic, complemented, Hall
75C3×C7×C11—23no—
76C3×C7×C11C2×C5×D711yescharacteristic, complemented
77C3×C7×C11C22×C5×C711yescharacteristic, complemented
78C2×C5×D11—71noHall
79C2×C3×C5×C7—71no—
80C2×C3×C5×C7—111no—
81C2×C3×C5×C7—111no—
82C2×C3×C5×C7—223no—
83C2×C3×C5×C7—771no—
84C3×C5×D7—111no—
85C3×C5×D7C7×D1111yescharacteristic, direct product factor
86C2×C7×D7—111noHall
87C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C11—71no—
89D77C2×C3×C5×C711yescharacteristic, complemented
90C7×D11—23no—
91C7×D11—71no—
92C7×D11C3×C5×D711yescharacteristic, direct product factor
93C7×D11C2×C3×C5×C711yescharacteristic, complemented
94C11×D7C2×C3×C5×C711yescharacteristic, complemented
95C3×C72C2×C5×D1111yescharacteristic, complemented, Hall
96C22×C5×C7—771no—
97C2×C5×D7—111no—
98C2×C3×D11—71noHall
99C2×C5×C11—71no—
100C5×D11—71no—
101C5×D11C3×C7×D711yescharacteristic, direct product factor
102C3×C5×C7—23no—
103C3×C5×C7D7×D1111yescharacteristic, direct product factor
104C3×C5×C7C2×C7×D1111yescharacteristic, complemented
105C2×C72—111no—
106C7×D7—111no—
107C7×D7C3×C5×D1111yescharacteristic, direct product factor
108C22×C3×C7—771no—
109C2×C3×D7—111no—
110C7×C11—23no—
111C7×C11C2×C3×C5×D711yescharacteristic, complemented
112C7×C11C22×C3×C5×C711yescharacteristic, complemented
113C2×C5×C7—71no—
114C2×C5×C7—111no—
115C2×C5×C7—111no—
116C2×C5×C7—223no—
117C2×C5×C7—771no—
118C5×D7—111no—
119C5×D7C3×C7×D1111yescharacteristic, direct product factor
120C2×C3×C11—71no—
121C3×D11—71no—
122C3×D11C5×C7×D711yescharacteristic, direct product factor
123C22×C3×C5—771noHall
124C5×C11C2×C3×C7×D711yescharacteristic, complemented, Hall
125C72C2×C3×C5×D1111yescharacteristic, complemented, Sylow
126C2×D11—71noHall
127C2×C3×C7—71no—
128C2×C3×C7—111no—
129C2×C3×C7—111no—
130C2×C3×C7—223no—
131C2×C3×C7—771no—
132C3×D7—111no—
133C3×D7C5×C7×D1111yescharacteristic, direct product factor
134C5×C7—23no—
135C5×C7C3×D7×D1111yescharacteristic, direct product factor
136C5×C7C2×C3×C7×D1111yescharacteristic, complemented
137C3×C11C2×C5×C7×D711yescharacteristic, complemented, Hall
138C2×C3×C5—71no—
139C2×C3×C5—111no—
140C2×C3×C5—771no—
141C22×C7—771no—
142C2×D7—111no—
143C2×C11—71no—
144D11—71no—
145D11C3×C5×C7×D711yescharacteristic, direct product factor
146C3×C7—23no—
147C3×C7C5×D7×D1111yescharacteristic, direct product factor
148C3×C7C2×C5×C7×D1111yescharacteristic, complemented
149C22×C5—771noHall
150C3×C5C7×D7×D1111yescharacteristic, direct product factor, Hall
151C2×C7—71no—
152C2×C7—111no—
153C2×C7—111no—
154C2×C7—223no—
155C2×C7—771no—
156D7—111no—
157D7C3×C5×C7×D1111yescharacteristic, direct product factor
158C22×C3—771noHall
159C11C2×C3×C5×C7×D711yescharacteristic, complemented, Sylow
160C2×C5—71no—
161C2×C5—111no—
162C2×C5—771no—
163C7—23no—
164C7C3×C5×D7×D1111yescharacteristic, direct product factor
165C7C2×C3×C5×C7×D1111yescharacteristic, complemented
166C2×C3—71no—
167C2×C3—111no—
168C2×C3—771no—
169C5C3×C7×D7×D1111yescharacteristic, direct product factor, Sylow
170C22—771noSylow
171C3C5×C7×D7×D1111yescharacteristic, direct product factor, Sylow
172C2—71no—
173C2—111no—
174C2—771no—
subgroupG/H
center, hypercenterC3×C5×C7D7×D11
commutator, cosocle, hypocenterC7×C11C22×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C72×D11C2semidirect
2. C3×C5×C7×C11×D7C2semidirect
3. C3×C5×C7×D77C2semidirect
4. C5×C7×D7×D11C3direct (N × H)
5. C3×C5×C72×C11C22semidirect
6. C3×C7×D7×D11C5direct (N × H)
7. C5×C7×D77C2×C3semidirect
8. C5×C7×C11×D7C2×C3semidirect
9. C5×C72×D11C2×C3semidirect
11. C3×C5×D7×D11C7direct (N × H)
12. C3×C7×D77C2×C5semidirect
13. C3×C7×C11×D7C2×C5semidirect
14. C3×C72×D11C2×C5semidirect
16. C5×C72×C11C22×C3semidirect
17. C3×C5×D77C2×C7semidirect
18. C3×C5×C11×D7C2×C7semidirect
21. C3×C5×C7×D11D7direct (N × H)
22. C3×C5×C7×D11C2×C7semidirect
24. C7×D7×D11C3×C5direct (N × H)
25. C3×C72×C11C22×C5semidirect
27. C5×D7×D11C3×C7direct (N × H)
30. C3×C5×C7×D7D11direct (N × H)
32. C3×C5×C7×C11C2×D7semidirect
33. C3×C5×C7×C11C22×C7semidirect
34. C7×D77C2×C3×C5semidirect
35. C7×C11×D7C2×C3×C5semidirect
36. C72×D11C2×C3×C5semidirect
39. C3×D7×D11C5×C7direct (N × H)
41. C5×D77C2×C3×C7semidirect
42. C5×C11×D7C2×C3×C7semidirect
45. C5×C7×D11C3×D7direct (N × H)
46. C5×C7×D11C2×C3×C7semidirect
47. C3×C5×C72C2×D11semidirect
50. C72×C11C22×C3×C5semidirect
53. C5×C7×D7C3×D11direct (N × H)
55. C3×D77C2×C5×C7semidirect
56. C3×C11×D7C2×C5×C7semidirect
59. C3×C7×D11C5×D7direct (N × H)
60. C3×C7×D11C2×C5×C7semidirect
64. C5×C7×C11C2×C3×D7semidirect
65. C5×C7×C11C22×C3×C7semidirect
68. C3×C5×D11C7×D7direct (N × H)
70. D7×D11C3×C5×C7direct (N × H)
73. C3×C7×D7C5×D11direct (N × H)
74. C5×C72C2×C3×D11semidirect
76. C3×C7×C11C2×C5×D7semidirect
77. C3×C7×C11C22×C5×C7semidirect
85. C3×C5×D7C7×D11direct (N × H)
87. C3×C5×C11C2×C7×D7semidirect
89. D77C2×C3×C5×C7semidirect
92. C7×D11C3×C5×D7direct (N × H)
93. C7×D11C2×C3×C5×C7semidirect
94. C11×D7C2×C3×C5×C7semidirect
95. C3×C72C2×C5×D11semidirect
101. C5×D11C3×C7×D7direct (N × H)
103. C3×C5×C7D7×D11direct (N × H)
104. C3×C5×C7C2×C7×D11semidirect
107. C7×D7C3×C5×D11direct (N × H)
111. C7×C11C2×C3×C5×D7semidirect
112. C7×C11C22×C3×C5×C7semidirect
119. C5×D7C3×C7×D11direct (N × H)
122. C3×D11C5×C7×D7direct (N × H)
124. C5×C11C2×C3×C7×D7semidirect
125. C72C2×C3×C5×D11semidirect
133. C3×D7C5×C7×D11direct (N × H)
135. C5×C7C3×D7×D11direct (N × H)
136. C5×C7C2×C3×C7×D11semidirect
137. C3×C11C2×C5×C7×D7semidirect
145. D11C3×C5×C7×D7direct (N × H)
147. C3×C7C5×D7×D11direct (N × H)
148. C3×C7C2×C5×C7×D11semidirect
150. C3×C5C7×D7×D11direct (N × H)
157. D7C3×C5×C7×D11direct (N × H)
159. C11C2×C3×C5×C7×D7semidirect
164. C7C3×C5×D7×D11direct (N × H)
165. C7C2×C3×C5×C7×D11semidirect
169. C5C3×C7×D7×D11direct (N × H)
171. C3C5×C7×D7×D11direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C72×D112
C3×C5×C7×C11×D72
C3×C5×C7×D772
C5×C7×D7×D113
C3×C7×D7×D115
C2×C3×C5×C7×D117
C3×C5×D7×D117
C2×C3×C5×C7×D711