Finite Group Databasebeta

← D3×D19×#3862 #45692470

Subgroups — D3×D19×#3862 #45692470

Order 33516.

216 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D57×#3862C211yesmaximal, characteristic, complemented
2D3×C19×#3862C211yesmaximal, characteristic, complemented
3C3×D19×#3862C211yesmaximal, characteristic, complemented
4D3×C72×D19C311yesmaximal, characteristic, complemented
5C2×D19×#3862—31nomaximal
6C3×C19×#3862C2211yescharacteristic, complemented, Hall
7C72×D57C2×C311yescharacteristic, complemented
8D3×C72×C19C2×C311yescharacteristic, complemented
9C3×C72×D19C2×C311yescharacteristic, complemented
10C2×C19×#3862—31no—
11D19×#3862—21no—
12D19×#3862—31no—
13D19×#3862D311yescharacteristic, direct product factor
14D3×ΓL(1,𝔽8)×D19—72nomaximal
15C2×C72×D19—31noHall
16C19×#3862—21no—
17C19×#3862C2×D311yescharacteristic, complemented
18C3×C72×C19C22×C311yescharacteristic, complemented
19ΓL(1,𝔽8)×D57—72no—
20D3×C19×ΓL(1,𝔽8)—72no—
21C3×ΓL(1,𝔽8)×D19—72no—
22C2×C72×C19—31no—
23C72×D19—31no—
24C72×D19C3×D311yescharacteristic, complemented
25C2×D3×#3862—191nomaximal, Hall
26D3×C7×D19—32no—
27D3×C7×D19ΓL(1,𝔽8)12yescomplemented
28C2×ΓL(1,𝔽8)×D19—212no—
29C3×C19×ΓL(1,𝔽8)—72no—
30C72×C19C2×C3×D311yescharacteristic, complemented, Hall
31C2×C3×#3862—191no—
32D3×#3862—191no—
33D3×#3862D1911yescharacteristic, direct product factor
34C7×D57—32no—
35C7×D57C2×ΓL(1,𝔽8)12yescomplemented
36D3×C7×C19—32no—
37D3×C7×C19C2×ΓL(1,𝔽8)12yescomplemented
38C3×C7×D19—32no—
39C3×C7×D19C2×ΓL(1,𝔽8)12yescomplemented
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
45C2×D3×C72—191no—
46C22×#3862—571no—
47C2×C7×D19—32no—
48C2×C7×D19—92no—
49C3×#3862C2×D1911yescharacteristic, complemented, Hall
50C3×C7×C19—32no—
51C3×C7×C19C22×ΓL(1,𝔽8)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—
58D3×C72—191no—
59D3×C72C3×D1911yescharacteristic, complemented
60C2×#3862—31no—
61C2×#3862—191no—
62C2×#3862—381no—
63C2×#3862—571no—
64C2×C7×C19—32no—
65C2×C7×C19—92no—
66C7×D19—32no—
67C7×D19—32no—
68C7×D19—92no—
69C7×D19D3×ΓL(1,𝔽8)12yescomplemented
70C2×D3×ΓL(1,𝔽8)—1332no—
71C2×C3×D19—1471no—
72D3×D19#386211yescharacteristic, direct product factor
73C22×C72—571noHall
74C32×C19—491noHall
75C3×C72C2×C3×D1911yescharacteristic, complemented
76#3862—21no—
77#3862D3×D1911yescharacteristic, direct product factor
78C7×C19—32no—
79C7×C19C2×D3×ΓL(1,𝔽8)12yescomplemented
80C2×C3×ΓL(1,𝔽8)—1332no—
81D3×ΓL(1,𝔽8)—72no—
82D3×ΓL(1,𝔽8)—1332no—
83C2×C3×C19—1471no—
84D57C2×#386211yescharacteristic, complemented
85C3×D19—491no—
86C3×D19—981no—
87C3×D19—1471no—
88C3×D19C2×#386211yescharacteristic, complemented
89D3×C19C2×#386211yescharacteristic, complemented
90C2×C72—31no—
91C2×C72—191no—
92C2×C72—571no—
93C2×D3×C7—192no—
94C2×D3×C7—572no—
95C22×ΓL(1,𝔽8)—3992no—
96C2×D19—31noHall
97C3×ΓL(1,𝔽8)—72no—
98C3×C19—491no—
99C3×C19—981no—
100C3×C19C22×#386211yescharacteristic, complemented
101C72C3×D3×D1911yescharacteristic, complemented, Sylow
102C2×C3×C7—192no—
103C2×C3×C7—572no—
104D3×C7—32no—
105D3×C7—192no—
106D3×C7—572no—
107D3×C7ΓL(1,𝔽8)×D1912yescomplemented
108C2×ΓL(1,𝔽8)—2662no—
109C2×ΓL(1,𝔽8)—212no—
110C2×ΓL(1,𝔽8)—1332no—
111C2×ΓL(1,𝔽8)—3992no—
112C2×C19—31no—
113D19—31no—
114D19D3×#386211yescharacteristic, direct product factor
115C2×C3×D3—9311noHall
116C22×C7—572no—
117C22×C7—1712no—
118C3×C7—32no—
119C3×C7C2×ΓL(1,𝔽8)×D1912yescomplemented
120ΓL(1,𝔽8)—72no—
121ΓL(1,𝔽8)—142no—
122C19C2×D3×#386211yescharacteristic, complemented, Sylow
123C2×C32—9311no—
124C3×D3—491no—
125C3×D3—9311no—
126C2×C7—32no—
127C2×C7—92no—
128C2×C7—192no—
129C2×C7—572no—
130C2×C7—572no—
131C2×C7—1712no—
132C22×C3—27931no—
133C2×D3—191no—
134C32—491noSylow
135C7—32no—
136C7D3×ΓL(1,𝔽8)×D1912yescomplemented
137C2×C3—191no—
138C2×C3—18621no—
139C2×C3—1471no—
140C2×C3—9311no—
141C2×C3—27931no—
142D3—191no—
143D3D19×#386211yescharacteristic, direct product factor
144C22—571noSylow
145C3—491no—
146C3—981no—
147C3C2×D19×#386211yescharacteristic, complemented
148C2—31no—
149C2—191no—
150C2—571no—
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. D57×#3862C2semidirect
2. D3×C19×#3862C2semidirect
3. C3×D19×#3862C2semidirect
4. D3×C72×D19C3semidirect
6. C3×C19×#3862C22semidirect
7. C72×D57C2×C3semidirect
8. D3×C72×C19C2×C3semidirect
9. C3×C72×D19C2×C3semidirect
13. D19×#3862D3direct (N × H)
17. C19×#3862C2×D3semidirect
18. C3×C72×C19C22×C3semidirect
24. C72×D19C3×D3semidirect
27. D3×C7×D19ΓL(1,𝔽8)semidirect
30. C72×C19C2×C3×D3semidirect
33. D3×#3862D19direct (N × H)
35. C7×D57C2×ΓL(1,𝔽8)semidirect
37. D3×C7×C19C2×ΓL(1,𝔽8)semidirect
39. C3×C7×D19C2×ΓL(1,𝔽8)semidirect
49. C3×#3862C2×D19semidirect
51. C3×C7×C19C22×ΓL(1,𝔽8)semidirect
59. D3×C72C3×D19semidirect
69. C7×D19D3×ΓL(1,𝔽8)semidirect
72. D3×D19#3862direct (N × H)
75. C3×C72C2×C3×D19semidirect
77. #3862D3×D19direct (N × H)
79. C7×C19C2×D3×ΓL(1,𝔽8)semidirect
84. D57C2×#3862semidirect
88. C3×D19C2×#3862semidirect
89. D3×C19C2×#3862semidirect
100. C3×C19C22×#3862semidirect
101. C72C3×D3×D19semidirect
107. D3×C7ΓL(1,𝔽8)×D19semidirect
114. D19D3×#3862direct (N × H)
119. C3×C7C2×ΓL(1,𝔽8)×D19semidirect
122. C19C2×D3×#3862semidirect
136. C7D3×ΓL(1,𝔽8)×D19semidirect
143. D3D19×#3862direct (N × H)
147. C3C2×D19×#3862semidirect

Maximal subgroups

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

subgroupindex
D57×#38622
D3×C19×#38622
C3×D19×#38622
D3×C72×D193
C2×D19×#38623
D3×ΓL(1,𝔽8)×D197
C2×D3×#386219