Finite Group Databasebeta

← D3×C11×C13×D21 #49114942

Subgroups — D3×C11×C13×D21 #49114942

Order 36036.

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
1C3×D3×C7×C11×C13C211yesmaximal, characteristic, complemented
2C3×C11×C13×D21C211yesmaximal, characteristic, complemented
3C11×C13×C3⋊D21C211yesmaximal, characteristic, complemented
4C2×C11×C13×D21—31nomaximal
5D3×C11×C13×D7—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C11×C13×D21—31no—
8C11×C13×D21—31no—
9C11×C13×D21—61no—
10C11×C13×D21D311yescharacteristic, direct product factor
11D3×C7×C11×C13D311yescharacteristic, complemented
12C3×C11×C13×D7—31no—
13C2×C3×C7×C11×C13—31no—
14D32×C11×C13—71nomaximal, Hall
15C2×C11×C13×D7—91noHall
16D3×C13×D21C1111yesmaximal, characteristic, direct product factor, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20D3×C11×D21C1311yesmaximal, characteristic, direct product factor, Hall
21C11×C13×C3⋊D3—71no—
22C3×D3×C11×C13—71no—
23C3×D3×C11×C13D711yescharacteristic, complemented
24C11×C13×D7—31no—
25C11×C13×D7—91no—
26C2×C7×C11×C13—31no—
27C2×D3×C11×C13—211no—
28C2×D3×C11×C13—211no—
29C13×C3⋊D21C2×C1111yescharacteristic, complemented
30C3×C13×D21C2×C1111yescharacteristic, complemented
31C3×D3×C7×C13C2×C1111yescharacteristic, complemented
32C11×C3⋊D21C2×C1311yescharacteristic, complemented
33C3×C11×D21C2×C1311yescharacteristic, complemented
34C3×D3×C7×C11C2×C1311yescharacteristic, complemented
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36C2×C13×D21—31no—
37D3×C13×D7—31no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39C2×C11×D21—31no—
40D3×C11×D7—31no—
41C2×C3×C11×C13—31no—
42C2×C3×C11×C13—211no—
43D3×C11×C13—71no—
44D3×C11×C13—211no—
45D3×C11×C13—211no—
46D3×C11×C13—421no—
47D3×C11×C13D2111yescharacteristic, direct product factor
48C32×C7×C13C22×C1111yescharacteristic, complemented, Hall
49C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
50C22×C11×C13—631noHall
51C2×C3×C7×C13—31no—
52C13×D21—31no—
53C13×D21—31no—
54C13×D21—61no—
55C13×D21D3×C1111yescharacteristic, direct product factor
56D3×C7×C13D3×C1111yescharacteristic, complemented
57C3×C13×D7—31no—
58D32×C13—71noHall
59C2×C3×C7×C11—31no—
60C11×D21—31no—
61C11×D21—31no—
62C11×D21—61no—
63C11×D21D3×C1311yescharacteristic, direct product factor
64D3×C7×C11D3×C1311yescharacteristic, complemented
65C3×C11×D7—31no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69D32×C11—71noHall
70C2×C13×D7—91noHall
71C2×C11×D7—91noHall
72C2×C11×C13—31no—
73C2×C11×C13—211no—
74C2×C11×C13—631no—
75C3×C7×C13—21no—
76C3×C7×C13C2×D3×C1111yescharacteristic, complemented
77C3×C7×C13C2×D3×C1111yescharacteristic, complemented
78D3×D21C11×C1311yescharacteristic, direct product factor, Hall
79C13×C3⋊D3—71no—
80C3×D3×C13—71no—
81C3×D3×C13C11×D711yescharacteristic, complemented
82C3×C7×C11—21no—
83C3×C7×C11C2×D3×C1311yescharacteristic, complemented
84C3×C7×C11C2×D3×C1311yescharacteristic, complemented
85C11×C3⋊D3—71no—
86C3×D3×C11—71no—
87C3×D3×C11C13×D711yescharacteristic, complemented
88C2×C7×C13—31no—
89C13×D7—31no—
90C13×D7—91no—
91C2×D3×C13—211no—
92C2×D3×C13—211no—
93C2×C7×C11—31no—
94C11×D7—31no—
95C11×D7—91no—
96C11×C13D3×D2111yescharacteristic, direct product factor, Hall
97C2×D3×C11—211no—
98C2×D3×C11—211no—
99C3⋊D21C2×C11×C1311yescharacteristic, complemented
100C3×D21C2×C11×C1311yescharacteristic, complemented
101C3×D3×C7C2×C11×C1311yescharacteristic, complemented
102C32×C13C2×C11×D711yescharacteristic, complemented, Hall
103C32×C11C2×C13×D711yescharacteristic, complemented, Hall
104C7×C13D32×C1111yescharacteristic, complemented, Hall
105C2×D21—31no—
106D3×D7—31no—
107C2×C3×C13—31no—
108C2×C3×C13—211no—
109D3×C13—71no—
110D3×C13—211no—
111D3×C13—211no—
112D3×C13—421no—
113D3×C13C11×D2111yescharacteristic, direct product factor
114C7×C11D32×C1311yescharacteristic, complemented, Hall
115C2×C3×C11—31no—
116C2×C3×C11—211no—
117D3×C11—71no—
118D3×C11—211no—
119D3×C11—211no—
120D3×C11—421no—
121D3×C11C13×D2111yescharacteristic, direct product factor
122C32×C7C22×C11×C1311yescharacteristic, complemented, Hall
123C22×C13—631noHall
124C22×C11—631noHall
125C2×C3×C7—31no—
126D21—31no—
127D21—31no—
128D21—61no—
129D21D3×C11×C1311yescharacteristic, direct product factor
130C3×D7—31no—
131D3×C7D3×C11×C1311yescharacteristic, complemented
132C3×C13—21no—
133C3×C13D3×C11×D711yescharacteristic, complemented
134C3×C13C2×C11×D2111yescharacteristic, complemented
135D32—71noHall
136C3×C11—21no—
137C3×C11D3×C13×D711yescharacteristic, complemented
138C3×C11C2×C13×D2111yescharacteristic, complemented
139C2×D7—91noHall
140C2×C13—31no—
141C2×C13—211no—
142C2×C13—631no—
143C2×C11—31no—
144C2×C11—211no—
145C2×C11—631no—
146C3×C7—21no—
147C3×C7C2×D3×C11×C1311yescharacteristic, complemented
148C3×C7C2×D3×C11×C1311yescharacteristic, complemented
149C3⋊D3—71no—
150C3×D3—71no—
151C3×D3C11×C13×D711yescharacteristic, complemented
152C2×C7—31no—
153D7—31no—
154D7—91no—
155C13D3×C11×D2111yescharacteristic, direct product factor, Sylow
156C2×D3—211no—
157C2×D3—211no—
158C11D3×C13×D2111yescharacteristic, direct product factor, Sylow
159C32C2×C11×C13×D711yescharacteristic, complemented, Sylow
160C7D32×C11×C1311yescharacteristic, complemented, Sylow
161C2×C3—31no—
162C2×C3—211no—
163D3—71no—
164D3—211no—
165D3—211no—
166D3—421no—
167D3C11×C13×D2111yescharacteristic, direct product factor
168C22—631noSylow
169C3—21no—
170C3D3×C11×C13×D711yescharacteristic, complemented
171C3C2×C11×C13×D2111yescharacteristic, complemented
172C2—31no—
173C2—211no—
174C2—631no—
subgroupG/H
center, hypercenterC11×C13D3×D21
commutator, cosocle, hypocenterC32×C7C22×C11×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7
UCSC1 ◁ C11×C13

Complements

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

NH ≅ G/Ntype
1. C3×D3×C7×C11×C13C2semidirect
2. C3×C11×C13×D21C2semidirect
3. C11×C13×C3⋊D21C2semidirect
6. C32×C7×C11×C13C22semidirect
10. C11×C13×D21D3direct (N × H)
11. D3×C7×C11×C13D3semidirect
16. D3×C13×D21C11direct (N × H)
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
20. D3×C11×D21C13direct (N × H)
23. C3×D3×C11×C13D7semidirect
29. C13×C3⋊D21C2×C11semidirect
30. C3×C13×D21C2×C11semidirect
31. C3×D3×C7×C13C2×C11semidirect
32. C11×C3⋊D21C2×C13semidirect
33. C3×C11×D21C2×C13semidirect
34. C3×D3×C7×C11C2×C13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
47. D3×C11×C13D21direct (N × H)
48. C32×C7×C13C22×C11semidirect
49. C32×C7×C11C22×C13semidirect
55. C13×D21D3×C11direct (N × H)
56. D3×C7×C13D3×C11semidirect
63. C11×D21D3×C13direct (N × H)
64. D3×C7×C11D3×C13semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×D21semidirect
76. C3×C7×C13C2×D3×C11semidirect
77. C3×C7×C13C2×D3×C11semidirect
78. D3×D21C11×C13direct (N × H)
81. C3×D3×C13C11×D7semidirect
83. C3×C7×C11C2×D3×C13semidirect
84. C3×C7×C11C2×D3×C13semidirect
87. C3×D3×C11C13×D7semidirect
96. C11×C13D3×D21direct (N × H)
99. C3⋊D21C2×C11×C13semidirect
100. C3×D21C2×C11×C13semidirect
101. C3×D3×C7C2×C11×C13semidirect
102. C32×C13C2×C11×D7semidirect
103. C32×C11C2×C13×D7semidirect
104. C7×C13D32×C11semidirect
113. D3×C13C11×D21direct (N × H)
114. C7×C11D32×C13semidirect
121. D3×C11C13×D21direct (N × H)
122. C32×C7C22×C11×C13semidirect
129. D21D3×C11×C13direct (N × H)
131. D3×C7D3×C11×C13semidirect
133. C3×C13D3×C11×D7semidirect
134. C3×C13C2×C11×D21semidirect
137. C3×C11D3×C13×D7semidirect
138. C3×C11C2×C13×D21semidirect
147. C3×C7C2×D3×C11×C13semidirect
148. C3×C7C2×D3×C11×C13semidirect
151. C3×D3C11×C13×D7semidirect
155. C13D3×C11×D21direct (N × H)
158. C11D3×C13×D21direct (N × H)
159. C32C2×C11×C13×D7semidirect
160. C7D32×C11×C13semidirect
167. D3C11×C13×D21direct (N × H)
170. C3D3×C11×C13×D7semidirect
171. C3C2×C11×C13×D21semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C7×C11×C132
C3×C11×C13×D212
C11×C13×C3⋊D212
C2×C11×C13×D213
D3×C11×C13×D73
D32×C11×C137
D3×C13×D2111
D3×C11×D2113