Finite Group Databasebeta

← D57×#64425 #45692478

Subgroups — D57×#64425 #45692478

Order 33516.

216 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 37 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
2C3⋊#19150292C211yesmaximal, characteristic, complemented
3C3×C19×#64425C211yesmaximal, characteristic, complemented
4C7⋊D7×D57C311yesmaximal, characteristic, complemented
5D19×#64425—31nomaximal
6C3×C19×#3862C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D133)C2×C311yescharacteristic, complemented
8C72×D57C2×C311yescharacteristic, complemented
9C3×C19×C7⋊D7C2×C311yescharacteristic, complemented
10D19×#3862—31no—
11#19150292—31no—
12C19×#64425—21no—
13C19×#64425D311yescharacteristic, complemented
14AGL(1,𝔽7)×D57—72nomaximal
15D19×C7⋊D7—31noHall
16C19×#3862—21no—
17C19×#3862C2×D311yescharacteristic, complemented
18C3×C72×C19C22×C311yescharacteristic, complemented
19ΓL(1,𝔽8)×D57—72no—
20C3⋊(ΓL(1,𝔽8)⋊D19)—72no—
21C3×C19×AGL(1,𝔽7)—72no—
22C7⋊D133—31no—
23C19×C7⋊D7C3×D311yescharacteristic, complemented
24C72×D19—31no—
25D3×#64425—191nomaximal, Hall
26D7×D57—72no—
27D7×D57—212no—
28D19×AGL(1,𝔽7)—212no—
29C3×C19×ΓL(1,𝔽8)—72no—
30C72×C19C2×C3×D311yescharacteristic, complemented, Hall
31C3⋊#64425—191no—
32D3×#3862—191no—
33C3×#64425D1911yescharacteristic, complemented
34D399—72no—
35D399—212no—
36C7×D57—32no—
37C7×D57AGL(1,𝔽7)12yescomplemented
38C3×D7×C19—72no—
39C3×D7×C19—212no—
40ΓL(1,𝔽8)⋊D19—212no—
41C19×AGL(1,𝔽7)—72no—
42C19×AGL(1,𝔽7)—142no—
43ΓL(1,𝔽8)×D19—212no—
44C2×C3×D57—491noHall
45D3×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—
54C2×C32×C19—491no—
55C3×D57—491no—
56C3×D57—491no—
57C3⋊(C7⋊D7)—191no—
58D3×C72—191no—
59C3×C7⋊D7C3×D1911yescharacteristic, complemented
60C2×#3862—571no—
61#64425—21no—
62#64425—571no—
63#64425D5711yescharacteristic, direct product factor
64D133—212no—
65D133—632no—
66C7×D19—32no—
67C7×D19—92no—
68D7×C19—72no—
69D7×C19—212no—
70D3×AGL(1,𝔽7)—1332no—
71C2×D57—491no—
72C2×C3×D19—1471no—
73C2×C7⋊D7—571noHall
74C32×C19—491noHall
75C3×C72C2×C3×D1911yescharacteristic, complemented
76#3862—21no—
77#3862C2×D5711yescharacteristic, complemented
78C7×C19—32no—
79C7×C19D3×AGL(1,𝔽7)12yescomplemented
80C3⋊AGL(1,𝔽7)—1332no—
81D3×ΓL(1,𝔽8)—1332no—
82C3×AGL(1,𝔽7)—72no—
83C2×C3×C19—491no—
84C2×C3×C19—491no—
85C2×C3×C19—981no—
86D57—491no—
87D57#6442511yescharacteristic, direct product factor
88C3×D19—1471no—
89C3×D19—1471no—
90C2×C72—571no—
91C7⋊D7—571no—
92C7⋊D7C3×D5711yescharacteristic, complemented
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
101C72C2×C3×D5711yescharacteristic, complemented, Sylow
102D21—1332no—
103D21—3992no—
104C3×D7—72no—
105C3×D7—212no—
106D3×C7—192no—
107D3×C7—572no—
108C2×ΓL(1,𝔽8)—3992no—
109AGL(1,𝔽7)—72no—
110AGL(1,𝔽7)—142no—
111AGL(1,𝔽7)—3992no—
112C2×C19—491no—
113D19—31no—
114D19—1471no—
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—
122C19D3×#6442511yescharacteristic, complemented, Sylow
123C2×C32—491no—
124C3×D3—9311no—
125C3×D3—9311no—
126C2×C7—572no—
127C2×C7—1712no—
128D7—72no—
129D7—212no—
130D7—3992no—
131D7—11972no—
132C22×C3—27931no—
133C2×D3—9311no—
134C32—491noSylow
135C7—32no—
136C7AGL(1,𝔽7)×D5712yescomplemented
137C2×C3—491no—
138C2×C3—491no—
139C2×C3—981no—
140C2×C3—27931no—
141C2×C3—27931no—
142D3—191no—
143D3—9311no—
144C22—27931noSylow
145C3—491no—
146C3—981no—
147C3D19×#6442511yescharacteristic, complemented
148C2—491no—
149C2—571no—
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. D57×#3862C2semidirect
2. C3⋊#19150292C2semidirect
3. C3×C19×#64425C2semidirect
4. C7⋊D7×D57C3semidirect
6. C3×C19×#3862C22semidirect
7. C3⋊(C7⋊D133)C2×C3semidirect
8. C72×D57C2×C3semidirect
9. C3×C19×C7⋊D7C2×C3semidirect
13. C19×#64425D3semidirect
17. C19×#3862C2×D3semidirect
18. C3×C72×C19C22×C3semidirect
23. C19×C7⋊D7C3×D3semidirect
30. C72×C19C2×C3×D3semidirect
33. C3×#64425D19semidirect
37. C7×D57AGL(1,𝔽7)semidirect
49. C3×#3862C2×D19semidirect
51. C3×C7×C19C2×AGL(1,𝔽7)semidirect
59. C3×C7⋊D7C3×D19semidirect
63. #64425D57direct (N × H)
75. C3×C72C2×C3×D19semidirect
77. #3862C2×D57semidirect
79. C7×C19D3×AGL(1,𝔽7)semidirect
87. D57#64425direct (N × H)
92. C7⋊D7C3×D57semidirect
100. C3×C19C2×#64425semidirect
101. C72C2×C3×D57semidirect
119. C3×C7D19×AGL(1,𝔽7)semidirect
122. C19D3×#64425semidirect
136. C7AGL(1,𝔽7)×D57semidirect
147. C3D19×#64425semidirect

Maximal subgroups

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

subgroupindex
D57×#38622
C3⋊#191502922
C3×C19×#644252
C7⋊D7×D573
D19×#644253
AGL(1,𝔽7)×D577
D3×#6442519