Finite Group Databasebeta

← C11×D21×D39 #49114945

Subgroups — C11×D21×D39 #49114945

Order 36036.

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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×C7×C11×D39C211yesmaximal, characteristic, complemented
2C3×C11×C13×D21C211yesmaximal, characteristic, complemented
3C11×C3⋊D273C211yesmaximal, characteristic, complemented
4C11×D7×D39—31nomaximal
5C11×D13×D21—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C11×D273—31no—
8C11×D273—31no—
9C11×D273—61no—
10C11×C13×D21D311yescharacteristic, complemented
11C7×C11×D39D311yescharacteristic, complemented
12C3×C11×C13×D7—31no—
13C3×C7×C11×D13—31no—
14D3×C11×D39—71nomaximal, Hall
15C11×D7×D13—91noHall
16D21×D39C1111yesmaximal, characteristic, direct product factor, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20D3×C11×D21—131nomaximal, Hall
21C11×C3⋊D39—71no—
22C3×C11×D39D711yescharacteristic, complemented
23C3×D3×C11×C13—71no—
24C11×D91—91no—
25C11×C13×D7—31no—
26C7×C11×D13—31no—
27C2×C11×D39—211no—
28D3×C11×D13—211no—
29C3⋊D273C2×C1111yescharacteristic, complemented
30C3×C13×D21C2×C1111yescharacteristic, complemented
31C3×C7×D39C2×C1111yescharacteristic, complemented
32C11×C3⋊D21—131no—
33C3×C11×D21D1311yescharacteristic, complemented
34C3×D3×C7×C11—131no—
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36D7×D39—31no—
37D13×D21—31no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39C2×C11×D21—391no—
40D3×C11×D7—391no—
41C2×C3×C11×C13—211no—
42C11×D39—211no—
43C11×D39—211no—
44C11×D39—421no—
45C11×D39D2111yescharacteristic, direct product factor
46D3×C11×C13—71no—
47C3×C11×D13—31no—
48C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
49C32×C7×C11C2×D1311yescharacteristic, complemented, Hall
50C2×C11×D13—631noHall
51D273—31no—
52D273—31no—
53D273—61no—
54C13×D21D3×C1111yescharacteristic, complemented
55C7×D39D3×C1111yescharacteristic, complemented
56C3×C13×D7—31no—
57C3×C7×D13—31no—
58D3×D39—71noHall
59C2×C3×C7×C11—391no—
60C11×D21—391no—
61C11×D21—391no—
62C11×D21—781no—
63C11×D21D3911yescharacteristic, direct product factor
64D3×C7×C11—131no—
65C3×C11×D7—31no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69D32×C11—911noHall
70D7×D13—91noHall
71C2×C11×D7—1171noHall
72C2×C11×C13—211no—
73C11×D13—31no—
74C11×D13—631no—
75C3×C7×C13—21no—
76C3×C7×C13C2×D3×C1111yescharacteristic, complemented
77C3×C7×C13C2×D3×C1111yescharacteristic, complemented
78D3×D21—131noHall
79C3⋊D39—71no—
80C3×D39C11×D711yescharacteristic, complemented
81C3×D3×C13—71no—
82C3×C7×C11—21no—
83C3×C7×C11D3×D1311yescharacteristic, complemented
84C3×C7×C11C2×D3911yescharacteristic, complemented
85C11×C3⋊D3—911no—
86C3×D3×C11—71no—
87C3×D3×C11—131no—
88D91—91no—
89C7×D13—31no—
90C13×D7—31no—
91C2×D39—211no—
92D3×D13—211no—
93C2×C7×C11—391no—
94C11×D7—31no—
95C11×D7—1171no—
96C11×C13D3×D2111yescharacteristic, complemented, Hall
97C2×D3×C11—2731no—
98C2×D3×C11—2731no—
99C3⋊D21—131no—
100C3×D21C11×D1311yescharacteristic, complemented
101C3×D3×C7—131no—
102C32×C13C2×C11×D711yescharacteristic, complemented, Hall
103C32×C11D7×D1311yescharacteristic, complemented, Hall
104C7×C13D32×C1111yescharacteristic, complemented, Hall
105C2×D21—391no—
106D3×D7—391no—
107C2×C3×C13—211no—
108D39—211no—
109D39—211no—
110D39—421no—
111D39C11×D2111yescharacteristic, direct product factor
112C3×D13—31no—
113D3×C13—71no—
114C7×C11D3×D3911yescharacteristic, complemented, Hall
115C2×C3×C11—211no—
116C2×C3×C11—391no—
117D3×C11—71no—
118D3×C11—131no—
119D3×C11—2731no—
120D3×C11—2731no—
121D3×C11—5461no—
122C32×C7C2×C11×D1311yescharacteristic, complemented, Hall
123C2×D13—631noHall
124C22×C11—8191noHall
125C2×C3×C7—391no—
126D21—391no—
127D21—391no—
128D21—781no—
129D21C11×D3911yescharacteristic, direct product factor
130C3×D7—31no—
131D3×C7—131no—
132C3×C13—21no—
133C3×C13D3×C11×D711yescharacteristic, complemented
134C3×C13C2×C11×D2111yescharacteristic, complemented
135D32—911noHall
136C3×C11—21no—
137C3×C11D13×D2111yescharacteristic, complemented
138C3×C11D7×D3911yescharacteristic, complemented
139C2×D7—1171noHall
140C2×C13—211no—
141D13—31no—
142D13—631no—
143C2×C11—211no—
144C2×C11—391no—
145C2×C11—8191no—
146C3×C7—21no—
147C3×C7D3×C11×D1311yescharacteristic, complemented
148C3×C7C2×C11×D3911yescharacteristic, complemented
149C3⋊D3—911no—
150C3×D3—71no—
151C3×D3—131no—
152C2×C7—391no—
153D7—31no—
154D7—1171no—
155C13D3×C11×D2111yescharacteristic, complemented, Sylow
156C2×D3—2731no—
157C2×D3—2731no—
158C11D21×D3911yescharacteristic, direct product factor, Sylow
159C32C11×D7×D1311yescharacteristic, complemented, Sylow
160C7D3×C11×D3911yescharacteristic, complemented, Sylow
161C2×C3—211no—
162C2×C3—391no—
163D3—71no—
164D3—131no—
165D3—2731no—
166D3—2731no—
167D3—5461no—
168C22—8191noSylow
169C3—21no—
170C3C11×D13×D2111yescharacteristic, complemented
171C3C11×D7×D3911yescharacteristic, complemented
172C2—211no—
173C2—391no—
174C2—8191no—
subgroupG/H
center, hypercenterC11D21×D39
commutator, cosocle, hypocenterC32×C7×C13C22×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×D39C2semidirect
2. C3×C11×C13×D21C2semidirect
3. C11×C3⋊D273C2semidirect
6. C32×C7×C11×C13C22semidirect
10. C11×C13×D21D3semidirect
11. C7×C11×D39D3semidirect
16. D21×D39C11direct (N × H)
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
22. C3×C11×D39D7semidirect
29. C3⋊D273C2×C11semidirect
30. C3×C13×D21C2×C11semidirect
31. C3×C7×D39C2×C11semidirect
33. C3×C11×D21D13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
45. C11×D39D21direct (N × H)
48. C32×C7×C13C22×C11semidirect
49. C32×C7×C11C2×D13semidirect
54. C13×D21D3×C11semidirect
55. C7×D39D3×C11semidirect
63. C11×D21D39direct (N × H)
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×D21semidirect
76. C3×C7×C13C2×D3×C11semidirect
77. C3×C7×C13C2×D3×C11semidirect
80. C3×D39C11×D7semidirect
83. C3×C7×C11D3×D13semidirect
84. C3×C7×C11C2×D39semidirect
96. C11×C13D3×D21semidirect
100. C3×D21C11×D13semidirect
102. C32×C13C2×C11×D7semidirect
103. C32×C11D7×D13semidirect
104. C7×C13D32×C11semidirect
111. D39C11×D21direct (N × H)
114. C7×C11D3×D39semidirect
122. C32×C7C2×C11×D13semidirect
129. D21C11×D39direct (N × H)
133. C3×C13D3×C11×D7semidirect
134. C3×C13C2×C11×D21semidirect
137. C3×C11D13×D21semidirect
138. C3×C11D7×D39semidirect
147. C3×C7D3×C11×D13semidirect
148. C3×C7C2×C11×D39semidirect
155. C13D3×C11×D21semidirect
158. C11D21×D39direct (N × H)
159. C32C11×D7×D13semidirect
160. C7D3×C11×D39semidirect
170. C3C11×D13×D21semidirect
171. C3C11×D7×D39semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C11×D392
C3×C11×C13×D212
C11×C3⋊D2732
C11×D7×D393
C11×D13×D213
D3×C11×D397
D21×D3911
D3×C11×D2113