Finite Group Databasebeta

← D19×C3⋊#64425 #45692472

Subgroups — D19×C3⋊#64425 #45692472

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
1C3⋊#19150292C211yesmaximal, characteristic, complemented
2C19×C3⋊#64425C211yesmaximal, characteristic, complemented
3C3×D19×#3862C211yesmaximal, characteristic, complemented
4D19×C3⋊(C7⋊D7)C311yesmaximal, characteristic, complemented
5D19×#64425—31nomaximal
6C3×C19×#3862C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D133)C2×C311yescharacteristic, complemented
8C19×C3⋊(C7⋊D7)C2×C311yescharacteristic, complemented
9C3×C72×D19C2×C311yescharacteristic, complemented
10D19×#3862—21no—
11D19×#3862D311yescharacteristic, complemented
12#19150292—31no—
13C19×#64425—31no—
14D19×C3⋊AGL(1,𝔽7)—72nomaximal
15D19×C7⋊D7—31noHall
16C19×#3862—21no—
17C19×#3862C2×D311yescharacteristic, complemented
18C3×C72×C19C22×C311yescharacteristic, complemented
19C3⋊(ΓL(1,𝔽8)⋊D19)—72no—
20C19×C3⋊AGL(1,𝔽7)—72no—
21C3×ΓL(1,𝔽8)×D19—72no—
22C7⋊D133—31no—
23C19×C7⋊D7—31no—
24C72×D19C3×D311yescharacteristic, complemented
25C2×C3⋊#64425—191nomaximal, Hall
26D19×D21—72no—
27D19×D21—212no—
28D19×AGL(1,𝔽7)—212no—
29C3×C19×ΓL(1,𝔽8)—72no—
30C72×C19C2×C3×D311yescharacteristic, complemented, Hall
31C2×C3×#3862—191no—
32C3⋊#64425—191no—
33C3⋊#64425D1911yescharacteristic, direct product factor
34D399—72no—
35D399—212no—
36C19×D21—72no—
37C19×D21—212no—
38C3×C7×D19—32no—
39C3×C7×D19AGL(1,𝔽7)12yescomplemented
40ΓL(1,𝔽8)⋊D19—212no—
41C19×AGL(1,𝔽7)—212no—
42ΓL(1,𝔽8)×D19—72no—
43ΓL(1,𝔽8)×D19—142no—
44C3×D3×D19—491noHall
45C2×C3⋊(C7⋊D7)—191no—
46C2×#64425—571no—
47D7×D19—212no—
48D7×D19—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—
57C2×C3×C72—191no—
58C3⋊(C7⋊D7)—191no—
59C3⋊(C7⋊D7)C3×D1911yescharacteristic, complemented
60C2×#3862—191no—
61C2×#3862—381no—
62#64425—31no—
63#64425—571no—
64D133—212no—
65D133—632no—
66C7×D19—32no—
67C7×D19C3⋊AGL(1,𝔽7)12yescomplemented
68D7×C19—212no—
69D7×C19—632no—
70C2×C3⋊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×C19C2×C3⋊AGL(1,𝔽7)12yescomplemented
80C2×C3×ΓL(1,𝔽8)—1332no—
81C3⋊AGL(1,𝔽7)—72no—
82C3⋊AGL(1,𝔽7)—1332no—
83C2×C3×C19—1471no—
84D57—491no—
85C3×D19—491no—
86C3×D19—981no—
87C3×D19—1471no—
88C3×D19#6442511yescharacteristic, complemented
89D3×C19—491no—
90C2×C72—191no—
91C7⋊D7—31no—
92C7⋊D7—571no—
93C2×D21—1332no—
94C2×D21—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
102C2×C3×C7—192no—
103C2×C3×C7—572no—
104D21—72no—
105D21—212no—
106D21—1332no—
107D21—3992no—
108C2×ΓL(1,𝔽8)—2662no—
109C2×ΓL(1,𝔽8)—1332no—
110AGL(1,𝔽7)—212no—
111AGL(1,𝔽7)—3992no—
112C2×C19—1471no—
113D19—1471no—
114D19C3⋊#6442511yescharacteristic, direct product factor
115C2×C3×D3—9311noHall
116C2×D7—3992no—
117C2×D7—11972no—
118C3×C7—32no—
119C3×C7D19×AGL(1,𝔽7)12yescomplemented
120ΓL(1,𝔽8)—72no—
121ΓL(1,𝔽8)—142no—
122C19C2×C3⋊#6442511yescharacteristic, complemented, Sylow
123C2×C32—9311no—
124C3×D3—491no—
125C3×D3—9311no—
126C2×C7—192no—
127C2×C7—572no—
128D7—212no—
129D7—632no—
130D7—3992no—
131D7—11972no—
132C22×C3—27931no—
133C2×D3—9311no—
134C32—491noSylow
135C7—32no—
136C7D19×C3⋊AGL(1,𝔽7)12yescomplemented
137C2×C3—191no—
138C2×C3—18621no—
139C2×C3—1471no—
140C2×C3—9311no—
141C2×C3—27931no—
142D3—491no—
143D3—9311no—
144C22—27931noSylow
145C3—491no—
146C3—981no—
147C3D19×#6442511yescharacteristic, complemented
148C2—191no—
149C2—1471no—
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. C3⋊#19150292C2semidirect
2. C19×C3⋊#64425C2semidirect
3. C3×D19×#3862C2semidirect
4. D19×C3⋊(C7⋊D7)C3semidirect
6. C3×C19×#3862C22semidirect
7. C3⋊(C7⋊D133)C2×C3semidirect
8. C19×C3⋊(C7⋊D7)C2×C3semidirect
9. C3×C72×D19C2×C3semidirect
11. D19×#3862D3semidirect
17. C19×#3862C2×D3semidirect
18. C3×C72×C19C22×C3semidirect
24. C72×D19C3×D3semidirect
30. C72×C19C2×C3×D3semidirect
33. C3⋊#64425D19direct (N × H)
39. C3×C7×D19AGL(1,𝔽7)semidirect
49. C3×#3862C2×D19semidirect
51. C3×C7×C19C2×AGL(1,𝔽7)semidirect
59. C3⋊(C7⋊D7)C3×D19semidirect
67. C7×D19C3⋊AGL(1,𝔽7)semidirect
75. C3×C72C2×C3×D19semidirect
77. #3862D3×D19semidirect
79. C7×C19C2×C3⋊AGL(1,𝔽7)semidirect
88. C3×D19#64425semidirect
100. C3×C19C2×#64425semidirect
101. C72C3×D3×D19semidirect
114. D19C3⋊#64425direct (N × H)
119. C3×C7D19×AGL(1,𝔽7)semidirect
122. C19C2×C3⋊#64425semidirect
136. C7D19×C3⋊AGL(1,𝔽7)semidirect
147. C3D19×#64425semidirect

Maximal subgroups

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

subgroupindex
C3⋊#191502922
C19×C3⋊#644252
C3×D19×#38622
D19×C3⋊(C7⋊D7)3
D19×#644253
D19×C3⋊AGL(1,𝔽7)7
C2×C3⋊#6442519