Finite Group Databasebeta

← #37561573

Subgroups — #37561573

Order 23940.

176 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 43 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×D399C211yesmaximal, characteristic, complemented
2C3×C19×D105C211yesmaximal, characteristic, complemented
3C7×C3⋊D285C211yesmaximal, characteristic, complemented
4D35⋊D57—31nomaximal
5D133⋊D15—31nomaximal
6C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
7D21⋊D57—51nomaximal, Hall
8C19×D105D311yescharacteristic, complemented
9C7×D285—31no—
10C7×D285—31no—
11C7×D285—61no—
12C5×D399D311yescharacteristic, complemented
13C3×C19×D35—31no—
14C3×C5×D133—31no—
15D15×D57—71nomaximal, Hall
16D35⋊D19—91noHall
17C7×C3⋊D57—51no—
18C3×D399D511yescharacteristic, complemented
19C3×C19×D21—51no—
20C3×C5×C7×C19—21no—
21C3×C5×C7×C19C2×D311yescharacteristic, complemented
22C3×C5×C7×C19C2×D311yescharacteristic, complemented
23C3⋊D285D711yescharacteristic, complemented
24C3×C19×D15—71no—
25C3×C5×D57—71no—
26D21⋊D19—151no—
27D7×D57—151no—
28C19×D35—31no—
29C7×D95—91no—
30C5×D133—31no—
31D21⋊D15—191nomaximal, Hall
32C32×C7×C19C2×D511yescharacteristic, complemented, Hall
33D5×D57—211no—
34D15×D19—211no—
35C32×C5×C19C2×D711yescharacteristic, complemented, Hall
36D399D1511yescharacteristic, complemented
37C19×D21—51no—
38C7×D57—151no—
39C7×D57—151no—
40C7×D57—301no—
41C3×D133—31no—
42C3×D7×C19—151no—
43D3×D57—351noHall
44C5×C7×C19D3211yescharacteristic, complemented, Hall
45C7×C3⋊D15—191no—
46C3×D105D1911yescharacteristic, complemented
47C3×C5×D21—191no—
48D285—31no—
49D285—31no—
50D285—61no—
51C19×D15—71no—
52C5×D57—71no—
53C3×D5×C19—211no—
54C3×C5×D19—211no—
55D7×D19—451noHall
56D15⋊D7—571no—
57D7×D15—571no—
58C3×C7×C19—21no—
59C3×C7×C19D3×D511yescharacteristic, complemented
60C3×C7×C19C2×D1511yescharacteristic, complemented
61D5×D19—631noHall
62C3⋊D57—51no—
63C3×D57—71no—
64C3×D3×C19—351no—
65C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
66C3×C5×C19—21no—
67C3×C5×C19D3×D711yescharacteristic, complemented
68C3×C5×C19D3×D711yescharacteristic, complemented
69D133—31no—
70C7×D19—451no—
71D7×C19—151no—
72(C3⋊D3)⋊D7—951noHall
73C2×D57—1051no—
74D3×D19—1051no—
75D105D5711yescharacteristic, complemented
76C7×D15—571no—
77C7×D15—571no—
78C7×D15—1141no—
79C5×D21—191no—
80C3×D35—31no—
81C3×C5×D7—571no—
82D95—91no—
83C5×D19—211no—
84D5×C19—211no—
85D3×D15—1331noHall
86C32×C19D5×D711yescharacteristic, complemented, Hall
87D5×D7—1711noHall
88C7×C19D3×D1511yescharacteristic, complemented, Hall
89C7×C3⋊D3—951no—
90C3×D21—51no—
91C3×D21—191no—
92C2×C3×C19—1051no—
93D57—71no—
94D57—151no—
95D57—151no—
96D57—301no—
97C3×D19—211no—
98D3×C19—351no—
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—71no—
105C3×C5×D3—1331no—
106D3×D7—2851no—
107D3×D7—2851no—
108C2×D19—3151noHall
109D35—31no—
110C5×D7—571no—
111C7×D5—1711no—
112C32×C7D5×D1911yescharacteristic, 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—51no—
120D21—191no—
121C3×D7—151no—
122C3×D7—571no—
123D3×C7—2851no—
124D3×C7—2851no—
125D3×C7—5701no—
126C2×C19—1051no—
127D19—211no—
128D19—451no—
129D32—6651noHall
130C5×C7D3×D5711yescharacteristic, complemented, Hall
131C2×C3×C5—3991no—
132D15—71no—
133D15—571no—
134D15—571no—
135D15—1141no—
136C3×D5—211no—
137C5×D3—1331no—
138C2×D7—8551noHall
139C3×C7—21no—
140C3×C7D15×D1911yescharacteristic, complemented
141C3×C7D5×D5711yescharacteristic, complemented
142C2×D5—11971noHall
143C19D21⋊D1511yescharacteristic, complemented, Sylow
144C3⋊D3—951no—
145C3×D3—351no—
146C3×D3—1331no—
147C3×C5—21no—
148C3×C5D7×D5711yescharacteristic, complemented
149C3×C5D21⋊D1911yescharacteristic, complemented
150C2×C7—8551no—
151D7—151no—
152D7—571no—
153C2×D3—19951no—
154C2×D3—19951no—
155C2×C5—3991no—
156D5—211no—
157D5—1711no—
158C32D35⋊D1911yescharacteristic, complemented, Sylow
159C7D15×D5711yescharacteristic, complemented, Sylow
160C2×C3—1051no—
161C2×C3—3991no—
162D3—2851no—
163D3—2851no—
164D3—351no—
165D3—5701no—
166D3—1331no—
167C5D21⋊D5711yescharacteristic, complemented, Sylow
168C22—59851noSylow
169C3—21no—
170C3D133⋊D1511yescharacteristic, complemented
171C3D35⋊D5711yescharacteristic, complemented
172C2—8551no—
173C2—1051no—
174C2—3991no—
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×D399C2semidirect
2. C3×C19×D105C2semidirect
3. C7×C3⋊D285C2semidirect
6. C32×C5×C7×C19C22semidirect
8. C19×D105D3semidirect
12. C5×D399D3semidirect
18. C3×D399D5semidirect
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
36. D399D15semidirect
44. C5×C7×C19D32semidirect
46. C3×D105D19semidirect
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
75. D105D57semidirect
86. C32×C19D5×D7semidirect
88. C7×C19D3×D15semidirect
100. C3×C5×C7D3×D19semidirect
101. C3×C5×C7C2×D57semidirect
102. C5×C19(C3⋊D3)⋊D7semidirect
112. C32×C7D5×D19semidirect
116. C3×C19D7×D15semidirect
117. C3×C19D15⋊D7semidirect
118. C32×C5D7×D19semidirect
130. C5×C7D3×D57semidirect
140. C3×C7D15×D19semidirect
141. C3×C7D5×D57semidirect
143. C19D21⋊D15semidirect
148. C3×C5D7×D57semidirect
149. C3×C5D21⋊D19semidirect
158. C32D35⋊D19semidirect
159. C7D15×D57semidirect
167. C5D21⋊D57semidirect
170. C3D133⋊D15semidirect
171. C3D35⋊D57semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3992
C3×C19×D1052
C7×C3⋊D2852
D35⋊D573
D133⋊D153
D21⋊D575
D15×D577
D21⋊D1519