Finite Group Databasebeta

← D21⋊D285 #37561571

Subgroups — D21⋊D285 #37561571

Order 23940.

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 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×C5×C19×D21C211yesmaximal, characteristic, complemented
2C3×D1995C211yesmaximal, characteristic, complemented
3C7×C3⋊D285C211yesmaximal, characteristic, complemented
4D21⋊D95—31nomaximal
5D7×D285—31nomaximal
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7D21⋊D57—51nomaximal, Hall
8D1995D311yescharacteristic, complemented
9C7×D285—31no—
10C7×D285—31no—
11C7×D285—61no—
12C5×C19×D21D311yescharacteristic, complemented
13C3×D665—31no—
14C3×C5×D7×C19—31no—
15D3×D285—71nomaximal, Hall
16D7×D95—91noHall
17C7×C3⋊D57—51no—
18C3×D399—51no—
19C3×C19×D21D511yescharacteristic, complemented
20C3×C5×C7×C19—21no—
21C3×C5×C7×C19C2×D311yescharacteristic, complemented
22C3×C5×C7×C19C2×D311yescharacteristic, complemented
23C3⋊D285D711yescharacteristic, complemented
24C3×D285—71no—
25C3×C5×D3×C19—71no—
26D21⋊D19—151no—
27D7×D57—151no—
28D665—31no—
29C7×D95—91no—
30C5×D7×C19—31no—
31D21⋊D15—191nomaximal, Hall
32C32×C7×C19C2×D511yescharacteristic, complemented, Hall
33C2×D285—211no—
34D3×D95—211no—
35C32×C5×C19C2×D711yescharacteristic, complemented, Hall
36D399—51no—
37C19×D21D1511yescharacteristic, complemented
38C7×D57—151no—
39C7×D57—151no—
40C7×D57—301no—
41C3×D133—151no—
42C3×D7×C19—31no—
43D3×D57—351noHall
44C5×C7×C19D3211yescharacteristic, complemented, Hall
45C7×C3⋊D15—191no—
46C3×D105—191no—
47C3×C5×D21D1911yescharacteristic, complemented
48C2×C3×C5×C19—211no—
49D285—31no—
50D285—31no—
51D285—61no—
52D285—71no—
53C5×D3×C19—71no—
54C3×D95—211no—
55D7×D19—451noHall
56D15⋊D7—571no—
57D7×D15—571no—
58C3×C7×C19—21no—
59C3×C7×C19D3×D511yescharacteristic, complemented
60C3×C7×C19C2×D1511yescharacteristic, complemented
61C2×D95—631noHall
62C3⋊D57—51no—
63C3×D57—351no—
64C3×D3×C19—71no—
65C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19D3×D711yescharacteristic, complemented
68C3×C5×C19D3×D711yescharacteristic, complemented
69D133—151no—
70C7×D19—451no—
71D7×C19—31no—
72(C3⋊D3)⋊D7—951noHall
73C2×D57—1051no—
74D3×D19—1051no—
75D105—191no—
76C7×D15—571no—
77C7×D15—571no—
78C7×D15—1141no—
79C5×D21D5711yescharacteristic, complemented
80C3×D35—571no—
81C3×C5×D7—31no—
82C2×C5×C19—211no—
83D95—91no—
84D95—211no—
85D3×D15—1331noHall
86C32×C19D5×D711yescharacteristic, complemented, Hall
87D5×D7—1711noHall
88C7×C19D3×D1511yescharacteristic, complemented, Hall
89C7×C3⋊D3—951no—
90C3×D21—951no—
91C3×D21D9511yescharacteristic, complemented
92C2×C3×C19—211no—
93D57—151no—
94D57—151no—
95D57—301no—
96D57—351no—
97C3×D19—1051no—
98D3×C19—71no—
99C3×C5×C7—21no—
100C3×C5×C7D3×D1911yescharacteristic, complemented
101C3×C5×C7C2×D5711yescharacteristic, complemented
102C5×C19(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
103C3⋊D15—191no—
104C3×D15—1331no—
105C3×C5×D3—71no—
106D3×D7—2851no—
107D3×D7—2851no—
108C2×D19—3151noHall
109D35—571no—
110C5×D7—31no—
111C7×D5—1711no—
112C32×C7C2×D9511yescharacteristic, complemented, Hall
113C2×D15—3991no—
114D3×D5—3991no—
115C3×C19—21no—
116C3×C19D7×D1511yescharacteristic, complemented
117C3×C19D15⋊D711yescharacteristic, complemented
118C32×C5D7×D1911yescharacteristic, complemented, Hall
119D21—951no—
120D21D28511yescharacteristic, complemented
121C3×D7—31no—
122C3×D7—2851no—
123D3×C7—2851no—
124D3×C7—2851no—
125D3×C7—5701no—
126C2×C19—211no—
127D19—451no—
128D19—1051no—
129D32—6651noHall
130C5×C7D3×D5711yescharacteristic, complemented, Hall
131C2×C3×C5—211no—
132D15—571no—
133D15—571no—
134D15—1141no—
135D15—1331no—
136C3×D5—3991no—
137C5×D3—71no—
138C2×D7—8551noHall
139C3×C7—21no—
140C3×C7D3×D9511yescharacteristic, complemented
141C3×C7C2×D28511yescharacteristic, complemented
142C2×D5—11971noHall
143C19D21⋊D1511yescharacteristic, complemented, Sylow
144C3⋊D3—951no—
145C3×D3—71no—
146C3×D3—6651no—
147C3×C5—21no—
148C3×C5D7×D5711yescharacteristic, complemented
149C3×C5D21⋊D1911yescharacteristic, complemented
150C2×C7—8551no—
151D7—31no—
152D7—2851no—
153C2×D3—19951no—
154C2×D3—19951no—
155C2×C5—211no—
156D5—3991no—
157D5—1711no—
158C32D7×D9511yescharacteristic, complemented, Sylow
159C7D3×D28511yescharacteristic, complemented, Sylow
160C2×C3—211no—
161C2×C3—19951no—
162D3—71no—
163D3—2851no—
164D3—2851no—
165D3—5701no—
166D3—6651no—
167C5D21⋊D5711yescharacteristic, complemented, Sylow
168C22—59851noSylow
169C3—21no—
170C3D7×D28511yescharacteristic, complemented
171C3D21⋊D9511yescharacteristic, complemented
172C2—211no—
173C2—8551no—
174C2—19951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C19C22
LCSG ▷ C32×C5×C7×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C19×D21C2semidirect
2. C3×D1995C2semidirect
3. C7×C3⋊D285C2semidirect
6. C32×C5×C7×C19C22semidirect
8. D1995D3semidirect
12. C5×C19×D21D3semidirect
19. C3×C19×D21D5semidirect
21. C3×C5×C7×C19C2×D3semidirect
22. C3×C5×C7×C19C2×D3semidirect
23. C3⋊D285D7semidirect
32. C32×C7×C19C2×D5semidirect
35. C32×C5×C19C2×D7semidirect
37. C19×D21D15semidirect
44. C5×C7×C19D32semidirect
47. C3×C5×D21D19semidirect
59. C3×C7×C19D3×D5semidirect
60. C3×C7×C19C2×D15semidirect
65. C32×C5×C7C2×D19semidirect
67. C3×C5×C19D3×D7semidirect
68. C3×C5×C19D3×D7semidirect
79. C5×D21D57semidirect
86. C32×C19D5×D7semidirect
88. C7×C19D3×D15semidirect
91. C3×D21D95semidirect
100. C3×C5×C7D3×D19semidirect
101. C3×C5×C7C2×D57semidirect
102. C5×C19(C3⋊D3)⋊D7semidirect
112. C32×C7C2×D95semidirect
116. C3×C19D7×D15semidirect
117. C3×C19D15⋊D7semidirect
118. C32×C5D7×D19semidirect
120. D21D285semidirect
130. C5×C7D3×D57semidirect
140. C3×C7D3×D95semidirect
141. C3×C7C2×D285semidirect
143. C19D21⋊D15semidirect
148. C3×C5D7×D57semidirect
149. C3×C5D21⋊D19semidirect
158. C32D7×D95semidirect
159. C7D3×D285semidirect
167. C5D21⋊D57semidirect
170. C3D7×D285semidirect
171. C3D21⋊D95semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C19×D212
C3×D19952
C7×C3⋊D2852
D21⋊D953
D7×D2853
D21⋊D575
D3×D2857
D21⋊D1519