Finite Group Databasebeta

← D3×#19150292 #45692479

Subgroups — D3×#19150292 #45692479

Order 33516.

216 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 38 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
1D3×C19×#3862C211yesmaximal, characteristic, complemented
2C3⋊#19150292C211yesmaximal, characteristic, complemented
3C3×#19150292C211yesmaximal, characteristic, complemented
4D3×C7⋊D133C311yesmaximal, characteristic, complemented
5C2×#19150292—31nomaximal
6C3×C19×#3862C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D133)C2×C311yescharacteristic, complemented
8D3×C72×C19C2×C311yescharacteristic, complemented
9C3×C7⋊D133C2×C311yescharacteristic, complemented
10C2×C19×#3862—31no—
11#19150292—21no—
12#19150292—31no—
13#19150292D311yescharacteristic, direct product factor
14D3×ΓL(1,𝔽8)⋊D19—72nomaximal
15C2×C7⋊D133—31noHall
16C19×#3862—21no—
17C19×#3862C2×D311yescharacteristic, complemented
18C3×C72×C19C22×C311yescharacteristic, complemented
19D3×C19×ΓL(1,𝔽8)—72no—
20C3⋊(ΓL(1,𝔽8)⋊D19)—72no—
21C3×ΓL(1,𝔽8)⋊D19—72no—
22C2×C72×C19—31no—
23C7⋊D133—31no—
24C7⋊D133C3×D311yescharacteristic, complemented
25D3×#64425—191nomaximal, Hall
26D3×D133—72no—
27D3×D133—212no—
28C2×ΓL(1,𝔽8)⋊D19—212no—
29C3×C19×ΓL(1,𝔽8)—72no—
30C72×C19C2×C3×D311yescharacteristic, complemented, Hall
31C3⋊#64425—191no—
32D3×#3862D1911yescharacteristic, complemented
33C3×#64425—191no—
34D399—72no—
35D399—212no—
36D3×C7×C19—32no—
37D3×C7×C19AGL(1,𝔽7)12yescomplemented
38C3×D133—72no—
39C3×D133—212no—
40C2×C19×ΓL(1,𝔽8)—212no—
41ΓL(1,𝔽8)⋊D19—72no—
42ΓL(1,𝔽8)⋊D19—142no—
43ΓL(1,𝔽8)⋊D19—212no—
44C3×D3×D19—491noHall
45D3×C7⋊D7—191no—
46C2×#64425—571no—
47C2×D133—212no—
48C2×D133—632no—
49C3×#3862C2×D1911yescharacteristic, complemented, Hall
50C3×C7×C19—32no—
51C3×C7×C19C2×AGL(1,𝔽7)12yescomplemented
52C19×ΓL(1,𝔽8)—72no—
53C19×ΓL(1,𝔽8)—142no—
54C3×D57—491no—
55C3×D3×C19—491no—
56C32×D19—491no—
57C3⋊(C7⋊D7)—191no—
58D3×C72C3×D1911yescharacteristic, complemented
59C3×C7⋊D7—191no—
60C2×#3862—31no—
61#64425—191no—
62#64425—381no—
63#64425—571no—
64C2×C7×C19—32no—
65C2×C7×C19—92no—
66D133—72no—
67D133—212no—
68D133—212no—
69D133—632no—
70D3×AGL(1,𝔽7)—1332no—
71C2×C3×D19—1471no—
72D3×D19—491no—
73C2×C7⋊D7—571noHall
74C32×C19—491noHall
75C3×C72C2×C3×D1911yescharacteristic, complemented
76#3862—21no—
77#3862D3×D1911yescharacteristic, complemented
78C7×C19—32no—
79C7×C19D3×AGL(1,𝔽7)12yescomplemented
80C3⋊AGL(1,𝔽7)—1332no—
81D3×ΓL(1,𝔽8)—72no—
82C3×AGL(1,𝔽7)—1332no—
83C2×C3×C19—1471no—
84D57—491no—
85C3×D19—491no—
86C3×D19—491no—
87C3×D19—981no—
88C3×D19—1471no—
89D3×C19#6442511yescharacteristic, complemented
90C2×C72—31no—
91C7⋊D7—191no—
92C7⋊D7—571no—
93D3×D7—1332no—
94D3×D7—3992no—
95C2×AGL(1,𝔽7)—3992no—
96C2×D19—1471noHall
97C3×ΓL(1,𝔽8)—72no—
98C3×C19—491no—
99C3×C19—981no—
100C3×C19C2×#6442511yescharacteristic, complemented
101C72C3×D3×D1911yescharacteristic, complemented, Sylow
102D21—1332no—
103D21—3992no—
104C3×D7—1332no—
105C3×D7—3992no—
106D3×C7—32no—
107D3×C7ΓL(1,𝔽8)⋊D1912yescomplemented
108C2×ΓL(1,𝔽8)—212no—
109AGL(1,𝔽7)—2662no—
110AGL(1,𝔽7)—1332no—
111AGL(1,𝔽7)—3992no—
112C2×C19—31no—
113D19—491no—
114D19—1471no—
115C2×C3×D3—9311noHall
116C2×D7—3992no—
117C2×D7—11972no—
118C3×C7—32no—
119C3×C7C2×ΓL(1,𝔽8)⋊D1912yescomplemented
120ΓL(1,𝔽8)—72no—
121ΓL(1,𝔽8)—142no—
122C19D3×#6442511yescharacteristic, complemented, Sylow
123C2×C32—9311no—
124C3×D3—491no—
125C3×D3—9311no—
126C2×C7—32no—
127C2×C7—92no—
128D7—1332no—
129D7—3992no—
130D7—3992no—
131D7—11972no—
132C22×C3—27931no—
133C2×D3—9311no—
134C32—491noSylow
135C7—32no—
136C7D3×ΓL(1,𝔽8)⋊D1912yescomplemented
137C2×C3—18621no—
138C2×C3—1471no—
139C2×C3—9311no—
140C2×C3—9311no—
141C2×C3—27931no—
142D3—9311no—
143D3#1915029211yescharacteristic, direct product factor
144C22—27931noSylow
145C3—491no—
146C3—981no—
147C3C2×#1915029211yescharacteristic, complemented
148C2—31no—
149C2—9311no—
150C2—27931no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C19C22×C3
LCSG ▷ C3×C72×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. D3×C19×#3862C2semidirect
2. C3⋊#19150292C2semidirect
3. C3×#19150292C2semidirect
4. D3×C7⋊D133C3semidirect
6. C3×C19×#3862C22semidirect
7. C3⋊(C7⋊D133)C2×C3semidirect
8. D3×C72×C19C2×C3semidirect
9. C3×C7⋊D133C2×C3semidirect
13. #19150292D3direct (N × H)
17. C19×#3862C2×D3semidirect
18. C3×C72×C19C22×C3semidirect
24. C7⋊D133C3×D3semidirect
30. C72×C19C2×C3×D3semidirect
32. D3×#3862D19semidirect
37. D3×C7×C19AGL(1,𝔽7)semidirect
49. C3×#3862C2×D19semidirect
51. C3×C7×C19C2×AGL(1,𝔽7)semidirect
58. D3×C72C3×D19semidirect
75. C3×C72C2×C3×D19semidirect
77. #3862D3×D19semidirect
79. C7×C19D3×AGL(1,𝔽7)semidirect
89. D3×C19#64425semidirect
100. C3×C19C2×#64425semidirect
101. C72C3×D3×D19semidirect
107. D3×C7ΓL(1,𝔽8)⋊D19semidirect
119. C3×C7C2×ΓL(1,𝔽8)⋊D19semidirect
122. C19D3×#64425semidirect
136. C7D3×ΓL(1,𝔽8)⋊D19semidirect
143. D3#19150292direct (N × H)
147. C3C2×#19150292semidirect

Maximal subgroups

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

subgroupindex
D3×C19×#38622
C3⋊#191502922
C3×#191502922
D3×C7⋊D1333
C2×#191502923
D3×ΓL(1,𝔽8)⋊D197
D3×#6442519