Finite Group Databasebeta

← C3×C13×D11×D21 #49114912

Subgroups — C3×C13×D11×D21 #49114912

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
1C32×C7×C13×D11C211yesmaximal, characteristic, complemented
2C3×C11×C13×D21C211yesmaximal, characteristic, complemented
3C3×C13×D231C211yesmaximal, characteristic, complemented
4C13×D11×D21C311yesmaximal, characteristic, direct product factor
5C3×C13×D7×D11—31nomaximal
6C32×C7×C11×C13C2211yescharacteristic, complemented, Hall
7C13×D231C2×C311yescharacteristic, complemented
8C11×C13×D21C2×C311yescharacteristic, complemented
9C3×C13×D77—31no—
10C3×C11×C13×D7—31no—
11C3×C7×C13×D11—21no—
12C3×C7×C13×D11D311yescharacteristic, complemented
13C3×C7×C13×D11C2×C311yescharacteristic, complemented
14C3×D3×C13×D11—71nomaximal, Hall
15C13×D7×D11—31noHall
16C2×C3×C13×D21—111nomaximal, Hall
17C3×C7×C11×C13—21no—
18C3×C7×C11×C13C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D11×D21C1311yesmaximal, characteristic, direct product factor, Hall
21C3×C13×D33—71no—
22C3×D3×C11×C13—71no—
23C32×C13×D11D711yescharacteristic, complemented
24C13×D77—31no—
25C11×C13×D7—31no—
26C7×C13×D11C3×D311yescharacteristic, complemented
27C2×C3×C13×D11—211no—
28D3×C13×D11—71no—
29C2×C32×C7×C13—111no—
30C3×C13×D21—111no—
31C3×C13×D21D1111yescharacteristic, direct product factor
32C3×D231C2×C1311yescharacteristic, complemented
33C3×C11×D21C2×C1311yescharacteristic, complemented
34C32×C7×D11C2×C1311yescharacteristic, complemented
35C32×C11×C13C2×D711yescharacteristic, complemented, Hall
36C2×C13×D21—111no—
37C2×C3×C13×D7—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D11×D21C3×C1311yescharacteristic, direct product factor
40C3×D7×D11—31no—
41C2×C3×C11×C13—211no—
42C13×D33—71no—
43D3×C11×C13—71no—
44C3×C13×D11—21no—
45C3×C13×D11—211no—
46C3×C13×D11C3×D711yescharacteristic, complemented
47C3×C13×D11D2111yescharacteristic, direct product factor
48C32×C7×C13C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11C22×C1311yescharacteristic, complemented, Hall
50C2×C13×D11—211noHall
51C2×C3×C7×C13—111no—
52C2×C3×C7×C13—111no—
53C2×C3×C7×C13—221no—
54C13×D21—111no—
55C13×D21C3×D1111yescharacteristic, direct product factor
56C3×C13×D7—31no—
57C3×C13×D7—331no—
58C2×C3×D3×C13—771noHall
59D231C2×C3×C1311yescharacteristic, complemented
60C11×D21C2×C3×C1311yescharacteristic, complemented
61C3×D77—31no—
62C3×C11×D7—31no—
63C3×C7×D11—21no—
64C3×C7×D11D3×C1311yescharacteristic, complemented
65C3×C7×D11C2×C3×C1311yescharacteristic, complemented
66C3×C11×C13—21no—
67C3×C11×C13C2×C3×D711yescharacteristic, complemented
68C3×C11×C13C2×D2111yescharacteristic, complemented
69C3×D3×D11—71noHall
70C2×C13×D7—331noHall
71D7×D11—31noHall
72C2×C11×C13—211no—
73C13×D11—211no—
74C13×D11C3×D2111yescharacteristic, direct product factor
75C3×C7×C13—21no—
76C3×C7×C13D3×D1111yescharacteristic, complemented
77C3×C7×C13C2×C3×D1111yescharacteristic, complemented
78C2×C3×D21—111noHall
79C2×C32×C13—111no—
80C3×D3×C13—71no—
81C3×D3×C13—771no—
82C3×C7×C11—21no—
83C3×C7×C11C2×D3×C1311yescharacteristic, complemented
84C3×C7×C11C22×C3×C1311yescharacteristic, complemented
85C3×D33—71no—
86C3×D3×C11—71no—
87C32×D11C13×D711yescharacteristic, complemented
88C2×C7×C13—111no—
89C13×D7—31no—
90C13×D7—331no—
91C22×C3×C13—2311no—
92C2×D3×C13—771no—
93D77—31no—
94C7×D11C3×D3×C1311yescharacteristic, complemented
95C11×D7—31no—
96C11×C13C2×C3×D2111yescharacteristic, complemented, Hall
97C2×C3×D11—211no—
98D3×D11—71no—
99C2×C32×C7—111no—
100C3×D21—111no—
101C3×D21C13×D1111yescharacteristic, direct product factor
102C32×C13D7×D1111yescharacteristic, complemented, Hall
103C32×C11C2×C13×D711yescharacteristic, complemented, Hall
104C7×C13C3×D3×D1111yescharacteristic, complemented, Hall
105C2×D21—111no—
106C2×C3×D7—331no—
107C2×C3×C13—111no—
108C2×C3×C13—111no—
109C2×C3×C13—211no—
110C2×C3×C13—221no—
111C2×C3×C13—2311no—
112D3×C13—71no—
113D3×C13—771no—
114C7×C11C2×C3×D3×C1311yescharacteristic, complemented, Hall
115C2×C3×C11—211no—
116D33—71no—
117C3×D11—21no—
118C3×D11—211no—
119C3×D11C3×C13×D711yescharacteristic, complemented
120C3×D11C13×D2111yescharacteristic, direct product factor
121D3×C11—71no—
122C32×C7C2×C13×D1111yescharacteristic, complemented, Hall
123C22×C13—2311noHall
124C2×D11—211noHall
125C2×C3×C7—111no—
126C2×C3×C7—111no—
127C2×C3×C7—221no—
128D21—111no—
129D21C3×C13×D1111yescharacteristic, direct product factor
130C3×D7—31no—
131C3×D7—331no—
132C3×C13—21no—
133C3×C13C3×D7×D1111yescharacteristic, complemented
134C3×C13D11×D2111yescharacteristic, direct product factor
135C2×C3×D3—771noHall
136C3×C11—21no—
137C3×C11C2×C3×C13×D711yescharacteristic, complemented
138C3×C11C2×C13×D2111yescharacteristic, complemented
139C2×D7—331noHall
140C2×C13—111no—
141C2×C13—211no—
142C2×C13—2311no—
143C2×C11—211no—
144D11—211no—
145D11C3×C13×D2111yescharacteristic, direct product factor
146C3×C7—21no—
147C3×C7D3×C13×D1111yescharacteristic, complemented
148C3×C7C2×C3×C13×D1111yescharacteristic, complemented
149C2×C32—111no—
150C3×D3—71no—
151C3×D3—771no—
152C2×C7—111no—
153D7—31no—
154D7—331no—
155C13C3×D11×D2111yescharacteristic, direct product factor, Sylow
156C22×C3—2311no—
157C2×D3—771no—
158C11C2×C3×C13×D2111yescharacteristic, complemented, Sylow
159C32C13×D7×D1111yescharacteristic, complemented, Sylow
160C7C3×D3×C13×D1111yescharacteristic, complemented, Sylow
161C2×C3—111no—
162C2×C3—111no—
163C2×C3—211no—
164C2×C3—221no—
165C2×C3—2311no—
166D3—71no—
167D3—771no—
168C22—2311noSylow
169C3—21no—
170C3C3×C13×D7×D1111yescharacteristic, complemented
171C3C13×D11×D2111yescharacteristic, direct product factor
172C2—111no—
173C2—211no—
174C2—2311no—
subgroupG/H
center, hypercenterC3×C13D11×D21
commutator, cosocle, hypocenterC3×C7×C11C22×C3×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C3×C7×C11
UCSC1 ◁ C3×C13

Complements

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

NH ≅ G/Ntype
1. C32×C7×C13×D11C2semidirect
2. C3×C11×C13×D21C2semidirect
3. C3×C13×D231C2semidirect
4. C13×D11×D21C3direct (N × H)
6. C32×C7×C11×C13C22semidirect
7. C13×D231C2×C3semidirect
8. C11×C13×D21C2×C3semidirect
12. C3×C7×C13×D11D3semidirect
13. C3×C7×C13×D11C2×C3semidirect
18. C3×C7×C11×C13C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
20. C3×D11×D21C13direct (N × H)
23. C32×C13×D11D7semidirect
26. C7×C13×D11C3×D3semidirect
31. C3×C13×D21D11direct (N × H)
32. C3×D231C2×C13semidirect
33. C3×C11×D21C2×C13semidirect
34. C32×C7×D11C2×C13semidirect
35. C32×C11×C13C2×D7semidirect
38. C7×C11×C13C2×C3×D3semidirect
39. D11×D21C3×C13direct (N × H)
46. C3×C13×D11C3×D7semidirect
47. C3×C13×D11D21direct (N × H)
48. C32×C7×C13C2×D11semidirect
49. C32×C7×C11C22×C13semidirect
55. C13×D21C3×D11direct (N × H)
59. D231C2×C3×C13semidirect
60. C11×D21C2×C3×C13semidirect
64. C3×C7×D11D3×C13semidirect
65. C3×C7×D11C2×C3×C13semidirect
67. C3×C11×C13C2×C3×D7semidirect
68. C3×C11×C13C2×D21semidirect
74. C13×D11C3×D21direct (N × H)
76. C3×C7×C13D3×D11semidirect
77. C3×C7×C13C2×C3×D11semidirect
83. C3×C7×C11C2×D3×C13semidirect
84. C3×C7×C11C22×C3×C13semidirect
87. C32×D11C13×D7semidirect
94. C7×D11C3×D3×C13semidirect
96. C11×C13C2×C3×D21semidirect
101. C3×D21C13×D11direct (N × H)
102. C32×C13D7×D11semidirect
103. C32×C11C2×C13×D7semidirect
104. C7×C13C3×D3×D11semidirect
114. C7×C11C2×C3×D3×C13semidirect
119. C3×D11C3×C13×D7semidirect
120. C3×D11C13×D21direct (N × H)
122. C32×C7C2×C13×D11semidirect
129. D21C3×C13×D11direct (N × H)
133. C3×C13C3×D7×D11semidirect
134. C3×C13D11×D21direct (N × H)
137. C3×C11C2×C3×C13×D7semidirect
138. C3×C11C2×C13×D21semidirect
145. D11C3×C13×D21direct (N × H)
147. C3×C7D3×C13×D11semidirect
148. C3×C7C2×C3×C13×D11semidirect
155. C13C3×D11×D21direct (N × H)
158. C11C2×C3×C13×D21semidirect
159. C32C13×D7×D11semidirect
160. C7C3×D3×C13×D11semidirect
170. C3C3×C13×D7×D11semidirect
171. C3C13×D11×D21direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C7×C13×D112
C3×C11×C13×D212
C3×C13×D2312
C13×D11×D213
C3×C13×D7×D113
C3×D3×C13×D117
C2×C3×C13×D2111
C3×D11×D2113