Finite Group Databasebeta

← C3×C7×D5×C11×D7 #44568821

Subgroups — C3×C7×D5×C11×D7 #44568821

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×C7×C11×D7C211yesmaximal, characteristic, complemented
2C3×C72×D5×C11C211yesmaximal, characteristic, complemented
3C3×C7×C11×D35C211yesmaximal, characteristic, complemented
4C7×D5×C11×D7C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C2×C3×C7×C11×D7—51nomaximal, Hall
7C7×C11×D35C2×C311yescharacteristic, complemented
8C72×D5×C11C2×C311yescharacteristic, complemented
9C5×C7×C11×D7C2×C311yescharacteristic, complemented
10C2×C3×C7×D5×C11—71nomaximal
11C3×D5×C11×D7C711yesmaximal, characteristic, direct product factor
12C3×C7×C11×D7—51no—
13C3×C7×C11×D7D511yescharacteristic, direct product factor
14C2×C3×C72×C11—51no—
15C3×C7×D5×D7C1111yesmaximal, characteristic, direct product factor, Hall
16C5×C72×C11C22×C311yescharacteristic, complemented, Hall
17C3×C11×D35C2×C711yescharacteristic, complemented
18C3×C7×D5×C11—23no—
19C3×C7×D5×C11—71no—
20C3×C7×D5×C11D711yescharacteristic, direct product factor
21C3×C7×D5×C11C2×C711yescharacteristic, complemented
22C3×C5×C11×D7C2×C711yescharacteristic, complemented
23C2×C3×C5×C7×C11—71no—
24C2×C7×C11×D7—51noHall
25C3×C72×C11C2×D511yescharacteristic, complemented, Hall
26C2×C7×D5×C11—71no—
27D5×C11×D7C3×C711yescharacteristic, direct product factor
28C3×C7×D35C2×C1111yescharacteristic, complemented
29C3×C72×D5C2×C1111yescharacteristic, complemented
30C3×C5×C7×D7C2×C1111yescharacteristic, complemented
31C3×C5×C7×C11—23no—
32C3×C5×C7×C11C2×D711yescharacteristic, complemented
33C3×C5×C7×C11C22×C711yescharacteristic, complemented
34C2×C72×C11—51no—
35C7×C11×D7—51no—
36C7×C11×D7C3×D511yescharacteristic, direct product factor
37C7×D5×D7C3×C1111yescharacteristic, direct product factor, Hall
38C22×C3×C7×C11—351no—
39C2×C3×C11×D7—51no—
40C2×C5×C7×C11—71no—
41C11×D35C2×C3×C711yescharacteristic, complemented
42C7×D5×C11—23no—
43C7×D5×C11—71no—
44C7×D5×C11C3×D711yescharacteristic, direct product factor
45C7×D5×C11C2×C3×C711yescharacteristic, complemented
46C5×C11×D7C2×C3×C711yescharacteristic, complemented
47C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
48C2×C3×D5×C11—71noHall
49C2×C3×C7×D7—51noHall
50C72×C11C2×C3×D511yescharacteristic, complemented, Hall
51C7×D35C2×C3×C1111yescharacteristic, complemented
52C72×D5C2×C3×C1111yescharacteristic, complemented
53C5×C7×D7C2×C3×C1111yescharacteristic, complemented
54C2×C3×C7×C11—51no—
55C2×C3×C7×C11—51no—
56C2×C3×C7×C11—71no—
57C2×C3×C7×C11—103no—
58C2×C3×C7×C11—351no—
59C3×C11×D7—51no—
60C3×C11×D7C7×D511yescharacteristic, direct product factor
61C2×C3×C7×D5—71no—
62C3×D5×D7C7×C1111yescharacteristic, direct product factor
63C5×C7×C11—23no—
64C5×C7×C11C2×C3×D711yescharacteristic, complemented
65C5×C7×C11C22×C3×C711yescharacteristic, complemented
66C2×C3×C5×C11—71no—
67C3×D5×C11—71no—
68C3×D5×C11C7×D711yescharacteristic, direct product factor
69C22×C7×C11—351no—
70C2×C11×D7—51no—
71C2×C3×C72—51no—
72C3×C7×D7—51no—
73C3×C7×D7D5×C1111yescharacteristic, direct product factor
74C5×C72C22×C3×C1111yescharacteristic, complemented, Hall
75C3×C7×C11—23no—
76C3×C7×C11D5×D711yescharacteristic, direct product factor
77C3×C7×C11C2×C7×D511yescharacteristic, complemented
78C2×D5×C11—71noHall
79C2×C3×C5×C7—71no—
80C3×D35C2×C7×C1111yescharacteristic, complemented
81C3×C7×D5—23no—
82C3×C7×D5—71no—
83C3×C7×D5C11×D711yescharacteristic, direct product factor
84C3×C7×D5C2×C7×C1111yescharacteristic, complemented
85C3×C5×D7C2×C7×C1111yescharacteristic, complemented
86C2×C7×D7—51noHall
87C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C11—51no—
89C2×C7×C11—51no—
90C2×C7×C11—71no—
91C2×C7×C11—103no—
92C2×C7×C11—351no—
93C11×D7—51no—
94C11×D7C3×C7×D511yescharacteristic, direct product factor
95C3×C72C2×D5×C1111yescharacteristic, complemented, Hall
96C2×C7×D5—71no—
97D5×D7C3×C7×C1111yescharacteristic, direct product factor
98C22×C3×C11—351noHall
99C2×C5×C11—71no—
100D5×C11—71no—
101D5×C11C3×C7×D711yescharacteristic, direct product factor
102C3×C5×C7—23no—
103C3×C5×C7C2×C11×D711yescharacteristic, complemented
104C3×C5×C7C22×C7×C1111yescharacteristic, complemented
105C2×C72—51no—
106C7×D7—51no—
107C7×D7C3×D5×C1111yescharacteristic, direct product factor
108C22×C3×C7—351no—
109C2×C3×D7—51no—
110C7×C11—23no—
111C7×C11C3×D5×D711yescharacteristic, direct product factor
112C7×C11C2×C3×C7×D511yescharacteristic, complemented
113C2×C5×C7—71no—
114D35C2×C3×C7×C1111yescharacteristic, complemented
115C5×D7C2×C3×C7×C1111yescharacteristic, complemented
116C7×D5—23no—
117C7×D5—71no—
118C7×D5C3×C11×D711yescharacteristic, direct product factor
119C7×D5C2×C3×C7×C1111yescharacteristic, complemented
120C2×C3×C11—51no—
121C2×C3×C11—71no—
122C2×C3×C11—351no—
123C2×C3×D5—71noHall
124C5×C11C2×C3×C7×D711yescharacteristic, complemented, Hall
125C72C2×C3×D5×C1111yescharacteristic, complemented, Sylow
126C22×C11—351noHall
127C2×C3×C7—51no—
128C2×C3×C7—51no—
129C2×C3×C7—71no—
130C2×C3×C7—103no—
131C2×C3×C7—351no—
132C3×D7—51no—
133C3×D7C7×D5×C1111yescharacteristic, direct product factor
134C5×C7—23no—
135C5×C7C2×C3×C11×D711yescharacteristic, complemented
136C5×C7C22×C3×C7×C1111yescharacteristic, complemented
137C3×C11C7×D5×D711yescharacteristic, direct product factor, Hall
138C2×C3×C5—71no—
139C3×D5—71no—
140C3×D5C7×C11×D711yescharacteristic, direct product factor
141C22×C7—351no—
142C2×D7—51no—
143C2×C11—51no—
144C2×C11—71no—
145C2×C11—351no—
146C3×C7—23no—
147C3×C7D5×C11×D711yescharacteristic, direct product factor
148C3×C7C2×C7×D5×C1111yescharacteristic, complemented
149C2×D5—71noHall
150C3×C5C2×C7×C11×D711yescharacteristic, complemented, Hall
151C2×C7—51no—
152C2×C7—51no—
153C2×C7—71no—
154C2×C7—103no—
155C2×C7—351no—
156D7—51no—
157D7C3×C7×D5×C1111yescharacteristic, direct product factor
158C22×C3—351noHall
159C11C3×C7×D5×D711yescharacteristic, direct product factor, Sylow
160C2×C5—71no—
161D5—71no—
162D5C3×C7×C11×D711yescharacteristic, direct product factor
163C7—23no—
164C7C3×D5×C11×D711yescharacteristic, direct product factor
165C7C2×C3×C7×D5×C1111yescharacteristic, complemented
166C2×C3—51no—
167C2×C3—71no—
168C2×C3—351no—
169C5C2×C3×C7×C11×D711yescharacteristic, complemented, Sylow
170C22—351noSylow
171C3C7×D5×C11×D711yescharacteristic, direct product factor, Sylow
172C2—51no—
173C2—71no—
174C2—351no—
subgroupG/H
center, hypercenterC3×C7×C11D5×D7
commutator, cosocle, hypocenterC5×C7C22×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C5×C7
UCSC1 ◁ C3×C7×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×C11×D7C2semidirect
2. C3×C72×D5×C11C2semidirect
3. C3×C7×C11×D35C2semidirect
4. C7×D5×C11×D7C3direct (N × H)
5. C3×C5×C72×C11C22semidirect
7. C7×C11×D35C2×C3semidirect
8. C72×D5×C11C2×C3semidirect
9. C5×C7×C11×D7C2×C3semidirect
11. C3×D5×C11×D7C7direct (N × H)
13. C3×C7×C11×D7D5direct (N × H)
15. C3×C7×D5×D7C11direct (N × H)
16. C5×C72×C11C22×C3semidirect
17. C3×C11×D35C2×C7semidirect
20. C3×C7×D5×C11D7direct (N × H)
21. C3×C7×D5×C11C2×C7semidirect
22. C3×C5×C11×D7C2×C7semidirect
25. C3×C72×C11C2×D5semidirect
27. D5×C11×D7C3×C7direct (N × H)
28. C3×C7×D35C2×C11semidirect
29. C3×C72×D5C2×C11semidirect
30. C3×C5×C7×D7C2×C11semidirect
32. C3×C5×C7×C11C2×D7semidirect
33. C3×C5×C7×C11C22×C7semidirect
36. C7×C11×D7C3×D5direct (N × H)
37. C7×D5×D7C3×C11direct (N × H)
41. C11×D35C2×C3×C7semidirect
44. C7×D5×C11C3×D7direct (N × H)
45. C7×D5×C11C2×C3×C7semidirect
46. C5×C11×D7C2×C3×C7semidirect
47. C3×C5×C72C22×C11semidirect
50. C72×C11C2×C3×D5semidirect
51. C7×D35C2×C3×C11semidirect
52. C72×D5C2×C3×C11semidirect
53. C5×C7×D7C2×C3×C11semidirect
60. C3×C11×D7C7×D5direct (N × H)
62. C3×D5×D7C7×C11direct (N × H)
64. C5×C7×C11C2×C3×D7semidirect
65. C5×C7×C11C22×C3×C7semidirect
68. C3×D5×C11C7×D7direct (N × H)
73. C3×C7×D7D5×C11direct (N × H)
74. C5×C72C22×C3×C11semidirect
76. C3×C7×C11D5×D7direct (N × H)
77. C3×C7×C11C2×C7×D5semidirect
80. C3×D35C2×C7×C11semidirect
83. C3×C7×D5C11×D7direct (N × H)
84. C3×C7×D5C2×C7×C11semidirect
85. C3×C5×D7C2×C7×C11semidirect
87. C3×C5×C11C2×C7×D7semidirect
94. C11×D7C3×C7×D5direct (N × H)
95. C3×C72C2×D5×C11semidirect
97. D5×D7C3×C7×C11direct (N × H)
101. D5×C11C3×C7×D7direct (N × H)
103. C3×C5×C7C2×C11×D7semidirect
104. C3×C5×C7C22×C7×C11semidirect
107. C7×D7C3×D5×C11direct (N × H)
111. C7×C11C3×D5×D7direct (N × H)
112. C7×C11C2×C3×C7×D5semidirect
114. D35C2×C3×C7×C11semidirect
115. C5×D7C2×C3×C7×C11semidirect
118. C7×D5C3×C11×D7direct (N × H)
119. C7×D5C2×C3×C7×C11semidirect
124. C5×C11C2×C3×C7×D7semidirect
125. C72C2×C3×D5×C11semidirect
133. C3×D7C7×D5×C11direct (N × H)
135. C5×C7C2×C3×C11×D7semidirect
136. C5×C7C22×C3×C7×C11semidirect
137. C3×C11C7×D5×D7direct (N × H)
140. C3×D5C7×C11×D7direct (N × H)
147. C3×C7D5×C11×D7direct (N × H)
148. C3×C7C2×C7×D5×C11semidirect
150. C3×C5C2×C7×C11×D7semidirect
157. D7C3×C7×D5×C11direct (N × H)
159. C11C3×C7×D5×D7direct (N × H)
162. D5C3×C7×C11×D7direct (N × H)
164. C7C3×D5×C11×D7direct (N × H)
165. C7C2×C3×C7×D5×C11semidirect
169. C5C2×C3×C7×C11×D7semidirect
171. C3C7×D5×C11×D7direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×C11×D72
C3×C72×D5×C112
C3×C7×C11×D352
C7×D5×C11×D73
C2×C3×C7×C11×D75
C2×C3×C7×D5×C117
C3×D5×C11×D77
C3×C7×D5×D711