Finite Group Databasebeta

← C13×D21×D33 #49114954

Subgroups — C13×D21×D33 #49114954

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×C13×D33C211yesmaximal, characteristic, complemented
2C3×C11×C13×D21C211yesmaximal, characteristic, complemented
3C13×C3⋊D231C211yesmaximal, characteristic, complemented
4C13×D7×D33—31nomaximal
5C13×D11×D21—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C13×D231—31no—
8C13×D231—31no—
9C13×D231—61no—
10C11×C13×D21D311yescharacteristic, complemented
11C7×C13×D33D311yescharacteristic, complemented
12C3×C11×C13×D7—31no—
13C3×C7×C13×D11—31no—
14D3×C13×D33—71nomaximal, Hall
15C13×D7×D11—91noHall
16D3×C13×D21—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C2×D311yescharacteristic, complemented
20D21×D33C1311yesmaximal, characteristic, direct product factor, Hall
21C13×C3⋊D33—71no—
22C3×C13×D33D711yescharacteristic, complemented
23C3×D3×C11×C13—71no—
24C13×D77—91no—
25C11×C13×D7—31no—
26C7×C13×D11—31no—
27C2×C13×D33—211no—
28D3×C13×D11—211no—
29C13×C3⋊D21—111no—
30C3×C13×D21D1111yescharacteristic, complemented
31C3×D3×C7×C13—111no—
32C3⋊D231C2×C1311yescharacteristic, complemented
33C3×C11×D21C2×C1311yescharacteristic, complemented
34C3×C7×D33C2×C1311yescharacteristic, complemented
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36C2×C13×D21—331no—
37D3×C13×D7—331no—
38C7×C11×C13D3211yescharacteristic, complemented, Hall
39D7×D33—31no—
40D11×D21—31no—
41C2×C3×C11×C13—211no—
42C13×D33—211no—
43C13×D33—211no—
44C13×D33—421no—
45C13×D33D2111yescharacteristic, direct product factor
46D3×C11×C13—71no—
47C3×C13×D11—31no—
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
50C2×C13×D11—631noHall
51C2×C3×C7×C13—331no—
52C13×D21—331no—
53C13×D21—331no—
54C13×D21—661no—
55C13×D21D3311yescharacteristic, direct product factor
56D3×C7×C13—111no—
57C3×C13×D7—31no—
58D32×C13—771noHall
59D231—31no—
60D231—31no—
61D231—61no—
62C11×D21D3×C1311yescharacteristic, complemented
63C7×D33D3×C1311yescharacteristic, complemented
64C3×C11×D7—31no—
65C3×C7×D11—31no—
66C3×C11×C13—21no—
67C3×C11×C13D3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69D3×D33—71noHall
70C2×C13×D7—991noHall
71D7×D11—91noHall
72C2×C11×C13—211no—
73C13×D11—31no—
74C13×D11—631no—
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13C2×D3311yescharacteristic, complemented
78D3×D21—111noHall
79C13×C3⋊D3—771no—
80C3×D3×C13—71no—
81C3×D3×C13—111no—
82C3×C7×C11—21no—
83C3×C7×C11C2×D3×C1311yescharacteristic, complemented
84C3×C7×C11C2×D3×C1311yescharacteristic, complemented
85C3⋊D33—71no—
86C3×D33C13×D711yescharacteristic, complemented
87C3×D3×C11—71no—
88C2×C7×C13—331no—
89C13×D7—31no—
90C13×D7—991no—
91C2×D3×C13—2311no—
92C2×D3×C13—2311no—
93D77—91no—
94C7×D11—31no—
95C11×D7—31no—
96C11×C13D3×D2111yescharacteristic, complemented, Hall
97C2×D33—211no—
98D3×D11—211no—
99C3⋊D21—111no—
100C3×D21C13×D1111yescharacteristic, complemented
101C3×D3×C7—111no—
102C32×C13D7×D1111yescharacteristic, complemented, Hall
103C32×C11C2×C13×D711yescharacteristic, complemented, Hall
104C7×C13D3×D3311yescharacteristic, complemented, Hall
105C2×D21—331no—
106D3×D7—331no—
107C2×C3×C13—211no—
108C2×C3×C13—331no—
109D3×C13—71no—
110D3×C13—111no—
111D3×C13—4621no—
112D3×C13—2311no—
113D3×C13—2311no—
114C7×C11D32×C1311yescharacteristic, complemented, Hall
115C2×C3×C11—211no—
116D33—211no—
117D33—211no—
118D33—421no—
119D33C13×D2111yescharacteristic, direct product factor
120C3×D11—31no—
121D3×C11—71no—
122C32×C7C2×C13×D1111yescharacteristic, complemented, Hall
123C22×C13—6931noHall
124C2×D11—631noHall
125C2×C3×C7—331no—
126D21—331no—
127D21—331no—
128D21—661no—
129D21C13×D3311yescharacteristic, direct product factor
130C3×D7—31no—
131D3×C7—111no—
132C3×C13—21no—
133C3×C13D11×D2111yescharacteristic, complemented
134C3×C13D7×D3311yescharacteristic, complemented
135D32—771noHall
136C3×C11—21no—
137C3×C11D3×C13×D711yescharacteristic, complemented
138C3×C11C2×C13×D2111yescharacteristic, complemented
139C2×D7—991noHall
140C2×C13—211no—
141C2×C13—331no—
142C2×C13—6931no—
143C2×C11—211no—
144D11—31no—
145D11—631no—
146C3×C7—21no—
147C3×C7D3×C13×D1111yescharacteristic, complemented
148C3×C7C2×C13×D3311yescharacteristic, complemented
149C3⋊D3—771no—
150C3×D3—71no—
151C3×D3—111no—
152C2×C7—331no—
153D7—31no—
154D7—991no—
155C13D21×D3311yescharacteristic, direct product factor, Sylow
156C2×D3—2311no—
157C2×D3—2311no—
158C11D3×C13×D2111yescharacteristic, complemented, Sylow
159C32C13×D7×D1111yescharacteristic, complemented, Sylow
160C7D3×C13×D3311yescharacteristic, complemented, Sylow
161C2×C3—211no—
162C2×C3—331no—
163D3—71no—
164D3—111no—
165D3—4621no—
166D3—2311no—
167D3—2311no—
168C22—6931noSylow
169C3—21no—
170C3C13×D11×D2111yescharacteristic, complemented
171C3C13×D7×D3311yescharacteristic, complemented
172C2—211no—
173C2—331no—
174C2—6931no—
subgroupG/H
center, hypercenterC13D21×D33
commutator, cosocle, hypocenterC32×C7×C11C22×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C11
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C3×C7×C13×D33C2semidirect
2. C3×C11×C13×D21C2semidirect
3. C13×C3⋊D231C2semidirect
6. C32×C7×C11×C13C22semidirect
10. C11×C13×D21D3semidirect
11. C7×C13×D33D3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C2×D3semidirect
20. D21×D33C13direct (N × H)
22. C3×C13×D33D7semidirect
30. C3×C13×D21D11semidirect
32. C3⋊D231C2×C13semidirect
33. C3×C11×D21C2×C13semidirect
34. C3×C7×D33C2×C13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13D32semidirect
45. C13×D33D21direct (N × H)
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C22×C13semidirect
55. C13×D21D33direct (N × H)
62. C11×D21D3×C13semidirect
63. C7×D33D3×C13semidirect
67. C3×C11×C13D3×D7semidirect
68. C3×C11×C13C2×D21semidirect
76. C3×C7×C13D3×D11semidirect
77. C3×C7×C13C2×D33semidirect
83. C3×C7×C11C2×D3×C13semidirect
84. C3×C7×C11C2×D3×C13semidirect
86. C3×D33C13×D7semidirect
96. C11×C13D3×D21semidirect
100. C3×D21C13×D11semidirect
102. C32×C13D7×D11semidirect
103. C32×C11C2×C13×D7semidirect
104. C7×C13D3×D33semidirect
114. C7×C11D32×C13semidirect
119. D33C13×D21direct (N × H)
122. C32×C7C2×C13×D11semidirect
129. D21C13×D33direct (N × H)
133. C3×C13D11×D21semidirect
134. C3×C13D7×D33semidirect
137. C3×C11D3×C13×D7semidirect
138. C3×C11C2×C13×D21semidirect
147. C3×C7D3×C13×D11semidirect
148. C3×C7C2×C13×D33semidirect
155. C13D21×D33direct (N × H)
158. C11D3×C13×D21semidirect
159. C32C13×D7×D11semidirect
160. C7D3×C13×D33semidirect
170. C3C13×D11×D21semidirect
171. C3C13×D7×D33semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C13×D332
C3×C11×C13×D212
C13×C3⋊D2312
C13×D7×D333
C13×D11×D213
D3×C13×D337
D3×C13×D2111
D21×D3313