Finite Group Databasebeta

← C3×C11×D7×D35 #44568825

Subgroups — C3×C11×D7×D35 #44568825

Order 32340.

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

normal subgroups only

This group has 208 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
1C3×C5×C7×C11×D7C211yesmaximal, characteristic, complemented
2C3×C7×C11×D35C211yesmaximal, characteristic, complemented
3C3×C11×C5⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
4C11×D7×D35C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C3×C11×D72—51nomaximal, Hall
7C11×C5⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C7×C11×D35C2×C311yescharacteristic, complemented
9C5×C7×C11×D7C2×C311yescharacteristic, complemented
10C2×C3×C11×D35—71nomaximal
11C3×D5×C11×D7—71nomaximal
12C3×C11×C7⋊D7—51no—
13C3×C7×C11×D7—51no—
14C3×C7×C11×D7D511yescharacteristic, complemented
15C3×D7×D35C1111yesmaximal, characteristic, direct product factor, Hall
16C5×C72×C11C22×C311yescharacteristic, complemented, Hall
17C3×C11×D35—71no—
18C3×C11×D35—71no—
19C3×C11×D35—143no—
20C3×C11×D35D711yescharacteristic, direct product factor
21C3×C7×D5×C11—71no—
22C3×C5×C11×D7D711yescharacteristic, complemented
23C2×C3×C5×C7×C11—71no—
24C11×D72—51noHall
25C3×C72×C11C2×D511yescharacteristic, complemented, Hall
26C2×C11×D35—71no—
27D5×C11×D7—71no—
28C3×C5⋊(C7⋊D7)C2×C1111yescharacteristic, complemented
29C3×C7×D35C2×C1111yescharacteristic, complemented
30C3×C5×C7×D7C2×C1111yescharacteristic, complemented
31C3×C5×C7×C11—23no—
32C3×C5×C7×C11C2×D711yescharacteristic, complemented
33C3×C5×C7×C11C2×D711yescharacteristic, complemented
34C11×C7⋊D7—51no—
35C7×C11×D7—51no—
36C7×C11×D7C3×D511yescharacteristic, complemented
37D7×D35C3×C1111yescharacteristic, direct product factor, Hall
38C2×C3×C11×D7—351no—
39C2×C3×C11×D7—351no—
40C2×C5×C7×C11—71no—
41C11×D35—71no—
42C11×D35—71no—
43C11×D35—143no—
44C11×D35C3×D711yescharacteristic, direct product factor
45C7×D5×C11—71no—
46C5×C11×D7C3×D711yescharacteristic, complemented
47C3×C5×C72C22×C1111yescharacteristic, complemented, Hall
48C2×C3×D5×C11—491noHall
49C3×D72—51noHall
50C72×C11C2×C3×D511yescharacteristic, complemented, Hall
51C5⋊(C7⋊D7)C2×C3×C1111yescharacteristic, complemented
52C7×D35C2×C3×C1111yescharacteristic, complemented
53C5×C7×D7C2×C3×C1111yescharacteristic, complemented
54C2×C3×C7×C11—71no—
55C2×C3×C7×C11—351no—
56C3×C11×D7—51no—
57C3×C11×D7—351no—
58C3×C11×D7—351no—
59C3×C11×D7—703no—
60C3×C11×D7D3511yescharacteristic, direct product factor
61C2×C3×D35—71no—
62C3×D5×D7—71no—
63C5×C7×C11—23no—
64C5×C7×C11C2×C3×D711yescharacteristic, complemented
65C5×C7×C11C2×C3×D711yescharacteristic, complemented
66C2×C3×C5×C11—71no—
67C3×D5×C11—71no—
68C3×D5×C11—491no—
69C2×C11×D7—351no—
70C2×C11×D7—351no—
71C3×C7⋊D7—51no—
72C3×C7×D7—51no—
73C3×C7×D7D5×C1111yescharacteristic, complemented
74C5×C72C22×C3×C1111yescharacteristic, complemented, Hall
75C3×C7×C11—23no—
76C3×C7×C11D5×D711yescharacteristic, complemented
77C3×C7×C11C2×D3511yescharacteristic, complemented
78C2×D5×C11—491noHall
79C2×C3×C5×C7—71no—
80C3×D35—71no—
81C3×D35—71no—
82C3×D35—143no—
83C3×D35C11×D711yescharacteristic, direct product factor
84C3×C7×D5—71no—
85C3×C5×D7C11×D711yescharacteristic, complemented
86D72—51noHall
87C3×C5×C11D7211yescharacteristic, complemented, Hall
88C2×C7×C11—71no—
89C2×C7×C11—351no—
90C11×D7—51no—
91C11×D7—351no—
92C11×D7—351no—
93C11×D7—703no—
94C11×D7C3×D3511yescharacteristic, direct product factor
95C3×C72C2×D5×C1111yescharacteristic, complemented, Hall
96C2×D35—71no—
97D5×D7—71no—
98C22×C3×C11—2451noHall
99C2×C5×C11—71no—
100D5×C11—71no—
101D5×C11—491no—
102C3×C5×C7—23no—
103C3×C5×C7C2×C11×D711yescharacteristic, complemented
104C3×C5×C7C2×C11×D711yescharacteristic, complemented
105C7⋊D7—51no—
106C7×D7—51no—
107C7×D7C3×D5×C1111yescharacteristic, complemented
108C2×C3×D7—351no—
109C2×C3×D7—351no—
110C7×C11—23no—
111C7×C11C3×D5×D711yescharacteristic, complemented
112C7×C11C2×C3×D3511yescharacteristic, complemented
113C2×C5×C7—71no—
114D35—71no—
115D35—71no—
116D35—143no—
117D35C3×C11×D711yescharacteristic, direct product factor
118C5×D7C3×C11×D711yescharacteristic, complemented
119C7×D5—71no—
120C2×C3×C11—71no—
121C2×C3×C11—351no—
122C2×C3×C11—2451no—
123C2×C3×D5—491noHall
124C5×C11C3×D7211yescharacteristic, complemented, Hall
125C72C2×C3×D5×C1111yescharacteristic, complemented, Sylow
126C22×C11—2451noHall
127C2×C3×C7—71no—
128C2×C3×C7—351no—
129C3×D7—51no—
130C3×D7—351no—
131C3×D7—351no—
132C3×D7—703no—
133C3×D7C11×D3511yescharacteristic, direct product factor
134C5×C7—23no—
135C5×C7C2×C3×C11×D711yescharacteristic, complemented
136C5×C7C2×C3×C11×D711yescharacteristic, complemented
137C3×C11D7×D3511yescharacteristic, direct product factor, Hall
138C2×C3×C5—71no—
139C3×D5—71no—
140C3×D5—491no—
141C2×D7—351no—
142C2×D7—351no—
143C2×C11—71no—
144C2×C11—351no—
145C2×C11—2451no—
146C3×C7—23no—
147C3×C7D5×C11×D711yescharacteristic, complemented
148C3×C7C2×C11×D3511yescharacteristic, complemented
149C2×D5—491noHall
150C3×C5C11×D7211yescharacteristic, complemented, Hall
151C2×C7—71no—
152C2×C7—351no—
153D7—51no—
154D7—351no—
155D7—351no—
156D7—703no—
157D7C3×C11×D3511yescharacteristic, direct product factor
158C22×C3—2451noHall
159C11C3×D7×D3511yescharacteristic, direct product factor, Sylow
160C2×C5—71no—
161D5—71no—
162D5—491no—
163C7—23no—
164C7C3×D5×C11×D711yescharacteristic, complemented
165C7C2×C3×C11×D3511yescharacteristic, complemented
166C2×C3—71no—
167C2×C3—351no—
168C2×C3—2451no—
169C5C3×C11×D7211yescharacteristic, complemented, Sylow
170C22—2451noSylow
171C3C11×D7×D3511yescharacteristic, direct product factor, Sylow
172C2—71no—
173C2—351no—
174C2—2451no—
subgroupG/H
center, hypercenterC3×C11D7×D35
commutator, cosocle, hypocenterC5×C72C22×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C5×C72
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×C11×D7C2semidirect
2. C3×C7×C11×D35C2semidirect
3. C3×C11×C5⋊(C7⋊D7)C2semidirect
4. C11×D7×D35C3direct (N × H)
5. C3×C5×C72×C11C22semidirect
7. C11×C5⋊(C7⋊D7)C2×C3semidirect
8. C7×C11×D35C2×C3semidirect
9. C5×C7×C11×D7C2×C3semidirect
14. C3×C7×C11×D7D5semidirect
15. C3×D7×D35C11direct (N × H)
16. C5×C72×C11C22×C3semidirect
20. C3×C11×D35D7direct (N × H)
22. C3×C5×C11×D7D7semidirect
25. C3×C72×C11C2×D5semidirect
28. C3×C5⋊(C7⋊D7)C2×C11semidirect
29. C3×C7×D35C2×C11semidirect
30. C3×C5×C7×D7C2×C11semidirect
32. C3×C5×C7×C11C2×D7semidirect
33. C3×C5×C7×C11C2×D7semidirect
36. C7×C11×D7C3×D5semidirect
37. D7×D35C3×C11direct (N × H)
44. C11×D35C3×D7direct (N × H)
46. C5×C11×D7C3×D7semidirect
47. C3×C5×C72C22×C11semidirect
50. C72×C11C2×C3×D5semidirect
51. C5⋊(C7⋊D7)C2×C3×C11semidirect
52. C7×D35C2×C3×C11semidirect
53. C5×C7×D7C2×C3×C11semidirect
60. C3×C11×D7D35direct (N × H)
64. C5×C7×C11C2×C3×D7semidirect
65. C5×C7×C11C2×C3×D7semidirect
73. C3×C7×D7D5×C11semidirect
74. C5×C72C22×C3×C11semidirect
76. C3×C7×C11D5×D7semidirect
77. C3×C7×C11C2×D35semidirect
83. C3×D35C11×D7direct (N × H)
85. C3×C5×D7C11×D7semidirect
87. C3×C5×C11D72semidirect
94. C11×D7C3×D35direct (N × H)
95. C3×C72C2×D5×C11semidirect
103. C3×C5×C7C2×C11×D7semidirect
104. C3×C5×C7C2×C11×D7semidirect
107. C7×D7C3×D5×C11semidirect
111. C7×C11C3×D5×D7semidirect
112. C7×C11C2×C3×D35semidirect
117. D35C3×C11×D7direct (N × H)
118. C5×D7C3×C11×D7semidirect
124. C5×C11C3×D72semidirect
125. C72C2×C3×D5×C11semidirect
133. C3×D7C11×D35direct (N × H)
135. C5×C7C2×C3×C11×D7semidirect
136. C5×C7C2×C3×C11×D7semidirect
137. C3×C11D7×D35direct (N × H)
147. C3×C7D5×C11×D7semidirect
148. C3×C7C2×C11×D35semidirect
150. C3×C5C11×D72semidirect
157. D7C3×C11×D35direct (N × H)
159. C11C3×D7×D35direct (N × H)
164. C7C3×D5×C11×D7semidirect
165. C7C2×C3×C11×D35semidirect
169. C5C3×C11×D72semidirect
171. C3C11×D7×D35direct (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×C7×C11×D352
C3×C11×C5⋊(C7⋊D7)2
C11×D7×D353
C3×C11×D725
C2×C3×C11×D357
C3×D5×C11×D77
C3×D7×D3511