Finite Group Databasebeta

← D3×C11⋊C5×D57 #49178554

Subgroups — D3×C11⋊C5×D57 #49178554

Order 37620.

176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C11⋊C5×C3⋊D57C211yesmaximal, characteristic, complemented
2C3×C11⋊C5×D57C211yesmaximal, characteristic, complemented
3C3×D3×C19×C11⋊C5C211yesmaximal, characteristic, complemented
4C2×C11⋊C5×D57—31nomaximal
5D3×D19×C11⋊C5—31nomaximal
6C32×C19×C11⋊C5C2211yescharacteristic, complemented, Hall
7D3×C11×D57C511yesmaximal, characteristic, complemented, Hall
8C11⋊C5×D57—31no—
9C11⋊C5×D57—31no—
10C11⋊C5×D57—61no—
11C11⋊C5×D57D311yescharacteristic, direct product factor
12D3×C19×C11⋊C5D311yescharacteristic, complemented
13C3×D19×C11⋊C5—31no—
14C2×C3×C19×C11⋊C5—31no—
15C2×D19×C11⋊C5—91noHall
16C11×C3⋊D57C2×C511yescharacteristic, complemented
17C3×C11×D57C2×C511yescharacteristic, complemented
18C3×D3×C11×C19C2×C511yescharacteristic, complemented
19C5×D3×D57—111nomaximal, Hall
20C3×C19×C11⋊C5—21no—
21C3×C19×C11⋊C5C2×D311yescharacteristic, complemented
22C3×C19×C11⋊C5C2×D311yescharacteristic, complemented
23C2×C11×D57—31no—
24D3×C11×D19—31no—
25D19×C11⋊C5—31no—
26D19×C11⋊C5—91no—
27C2×C19×C11⋊C5—31no—
28D32×C11⋊C5—191nomaximal, Hall
29C32×C11×C19C22×C511yescharacteristic, complemented, Hall
30C5×C3⋊D57—111no—
31C3×C5×D57—111no—
32C3×C5×D3×C19—111no—
33C2×C3×C11×C19—31no—
34C11×D57—31no—
35C11×D57—31no—
36C11×D57—61no—
37C11×D57C5×D311yescharacteristic, complemented
38D3×C11×C19C5×D311yescharacteristic, complemented
39C3×C11×D19—31no—
40C2×C5×D57—331no—
41C5×D3×D19—331no—
42C19×C11⋊C5D3211yescharacteristic, complemented, Hall
43C3⋊D3×C11⋊C5—191no—
44C3×D3×C11⋊C5—191no—
45C3×D3×C11⋊C5D1911yescharacteristic, complemented
46C32×C5×C19—111noHall
47C2×C11×D19—91noHall
48D3×D57C11⋊C511yescharacteristic, direct product factor, Hall
49C2×D3×C11⋊C5—571no—
50C2×D3×C11⋊C5—571no—
51C3×C11×C19—21no—
52C3×C11×C19C2×C5×D311yescharacteristic, complemented
53C3×C11×C19C2×C5×D311yescharacteristic, complemented
54C2×C3×C5×C19—331no—
55C5×D57—111no—
56C5×D57—331no—
57C5×D57—331no—
58C5×D57—661no—
59C5×D3×C19—111no—
60C3×C5×D19—331no—
61C32×C11⋊C5C2×D1911yescharacteristic, complemented, Hall
62C2×C11×C19—31no—
63C11×D19—31no—
64C11×D19—91no—
65D32×C11—191noHall
66C2×C5×D19—991noHall
67C3⋊D57C2×C11⋊C511yescharacteristic, complemented
68C3×D57C2×C11⋊C511yescharacteristic, complemented
69C3×D3×C19C2×C11⋊C511yescharacteristic, complemented
70C2×C3×C11⋊C5—31no—
71C2×C3×C11⋊C5—571no—
72D3×C11⋊C5—191no—
73D3×C11⋊C5—571no—
74D3×C11⋊C5—571no—
75D3×C11⋊C5—1141no—
76D3×C11⋊C5D5711yescharacteristic, direct product factor
77C3×C5×C19—111no—
78C3×C5×C19—111no—
79C3×C5×C19—221no—
80C2×D57—31no—
81D3×D19—31no—
82C22×C11⋊C5—1711noHall
83C11×C19C5×D3211yescharacteristic, complemented, Hall
84C11×C3⋊D3—191no—
85C3×D3×C11—191no—
86C3×D3×C11C5×D1911yescharacteristic, complemented
87C2×C5×C19—331no—
88C5×D19—331no—
89C5×D19—991no—
90C5×D32—2091noHall
91C32×C19C22×C11⋊C511yescharacteristic, complemented, Hall
92C3×C11⋊C5—21no—
93C3×C11⋊C5D3×D1911yescharacteristic, complemented
94C3×C11⋊C5C2×D5711yescharacteristic, complemented
95C2×D3×C11—571no—
96C2×D3×C11—571no—
97C2×C3×C19—31no—
98D57—31no—
99D57—31no—
100D57—61no—
101D57D3×C11⋊C511yescharacteristic, direct product factor
102C3×D19—31no—
103D3×C19D3×C11⋊C511yescharacteristic, complemented
104C2×C11⋊C5—31no—
105C2×C11⋊C5—571no—
106C2×C11⋊C5—1711no—
107C32×C11C2×C5×D1911yescharacteristic, complemented, Hall
108C5×C19—111noHall
109C5×C3⋊D3—2091no—
110C3×C5×D3—111no—
111C3×C5×D3—2091no—
112C2×D19—91noHall
113C2×C3×C11—31no—
114C2×C3×C11—571no—
115D3×C11—191no—
116D3×C11—571no—
117D3×C11—571no—
118D3×C11—1141no—
119D3×C11C5×D5711yescharacteristic, complemented
120C2×C5×D3—6271no—
121C2×C5×D3—6271no—
122C3×C19—21no—
123C3×C19C2×D3×C11⋊C511yescharacteristic, complemented
124C3×C19C2×D3×C11⋊C511yescharacteristic, complemented
125C11⋊C5D3×D5711yescharacteristic, direct product factor, Hall
126C32×C5—111noHall
127C22×C11—1711noHall
128C2×C19—31no—
129D19—31no—
130D19—91no—
131D32—191noHall
132C3×C11—21no—
133C3×C11C5×D3×D1911yescharacteristic, complemented
134C3×C11C2×C5×D5711yescharacteristic, complemented
135C2×C3×C5—331no—
136C2×C3×C5—6271no—
137C5×D3—111no—
138C5×D3—6271no—
139C5×D3—6271no—
140C5×D3—2091no—
141C5×D3—12541no—
142C2×C11—31no—
143C2×C11—571no—
144C2×C11—1711no—
145C22×C5—18811noHall
146C19D32×C11⋊C511yescharacteristic, complemented, Sylow
147C3⋊D3—191no—
148C3×D3—191no—
149C3×D3D19×C11⋊C511yescharacteristic, complemented
150C3×C5—111no—
151C3×C5—111no—
152C3×C5—221no—
153C2×D3—571no—
154C2×D3—571no—
155C11C5×D3×D5711yescharacteristic, complemented, Sylow
156C2×C5—331no—
157C2×C5—18811no—
158C2×C5—6271no—
159C32C2×D19×C11⋊C511yescharacteristic, complemented, Sylow
160C2×C3—31no—
161C2×C3—571no—
162D3—191no—
163D3—571no—
164D3—571no—
165D3—1141no—
166D3C11⋊C5×D5711yescharacteristic, direct product factor
167C5—111noSylow
168C22—1711noSylow
169C3—21no—
170C3D3×D19×C11⋊C511yescharacteristic, complemented
171C3C2×C11⋊C5×D5711yescharacteristic, complemented
172C2—31no—
173C2—571no—
174C2—1711no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C19C22×C5
LCSG ▷ C32×C11×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×C3⋊D57C2semidirect
2. C3×C11⋊C5×D57C2semidirect
3. C3×D3×C19×C11⋊C5C2semidirect
6. C32×C19×C11⋊C5C22semidirect
7. D3×C11×D57C5semidirect
11. C11⋊C5×D57D3direct (N × H)
12. D3×C19×C11⋊C5D3semidirect
16. C11×C3⋊D57C2×C5semidirect
17. C3×C11×D57C2×C5semidirect
18. C3×D3×C11×C19C2×C5semidirect
21. C3×C19×C11⋊C5C2×D3semidirect
22. C3×C19×C11⋊C5C2×D3semidirect
29. C32×C11×C19C22×C5semidirect
37. C11×D57C5×D3semidirect
38. D3×C11×C19C5×D3semidirect
42. C19×C11⋊C5D32semidirect
45. C3×D3×C11⋊C5D19semidirect
48. D3×D57C11⋊C5direct (N × H)
52. C3×C11×C19C2×C5×D3semidirect
53. C3×C11×C19C2×C5×D3semidirect
61. C32×C11⋊C5C2×D19semidirect
67. C3⋊D57C2×C11⋊C5semidirect
68. C3×D57C2×C11⋊C5semidirect
69. C3×D3×C19C2×C11⋊C5semidirect
76. D3×C11⋊C5D57direct (N × H)
83. C11×C19C5×D32semidirect
86. C3×D3×C11C5×D19semidirect
91. C32×C19C22×C11⋊C5semidirect
93. C3×C11⋊C5D3×D19semidirect
94. C3×C11⋊C5C2×D57semidirect
101. D57D3×C11⋊C5direct (N × H)
103. D3×C19D3×C11⋊C5semidirect
107. C32×C11C2×C5×D19semidirect
119. D3×C11C5×D57semidirect
123. C3×C19C2×D3×C11⋊C5semidirect
124. C3×C19C2×D3×C11⋊C5semidirect
125. C11⋊C5D3×D57direct (N × H)
133. C3×C11C5×D3×D19semidirect
134. C3×C11C2×C5×D57semidirect
146. C19D32×C11⋊C5semidirect
149. C3×D3D19×C11⋊C5semidirect
155. C11C5×D3×D57semidirect
159. C32C2×D19×C11⋊C5semidirect
166. D3C11⋊C5×D57direct (N × H)
170. C3D3×D19×C11⋊C5semidirect
171. C3C2×C11⋊C5×D57semidirect

Maximal subgroups

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

subgroupindex
C11⋊C5×C3⋊D572
C3×C11⋊C5×D572
C3×D3×C19×C11⋊C52
C2×C11⋊C5×D573
D3×D19×C11⋊C53
D3×C11×D575
C5×D3×D5711
D32×C11⋊C519