Finite Group Databasebeta

← D57×#64424 #45692389

Subgroups — D57×#64424 #45692389

Order 33516.

440 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 67 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×#3861C211yesmaximal, characteristic, complemented
2C3⋊#19150288C211yesmaximal, characteristic, complemented
3C3×C19×#64424C211yesmaximal, characteristic, complemented
4C7⋊D7×D57C311yesmaximal, characteristic, complemented
5D19×#64424—31nomaximal
6C3×C19×#3861C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D133)C2×C311yescharacteristic, complemented
8C72×D57C2×C311yescharacteristic, complemented
9C3×C19×C7⋊D7C2×C311yescharacteristic, complemented
10D19×#3861—31no—
11#19150288—31no—
12C19×#64424—21no—
13C19×#64424D311yescharacteristic, complemented
14AGL(1,𝔽7)×D57—78nomaximal
15D19×C7⋊D7—31noHall
16C19×#3861—21no—
17C19×#3861C2×D311yescharacteristic, complemented
18C3×C72×C19C22×C311yescharacteristic, complemented
19ΓL(1,𝔽8)×D57—78no—
20C3⋊(ΓL(1,𝔽8)⋊D19)—78no—
21C3×C19×AGL(1,𝔽7)—78no—
22C7⋊D133—31no—
23C19×C7⋊D7C3×D311yescharacteristic, complemented
24C72×D19—31no—
25D3×#64424—191nomaximal, Hall
26D7×D57—78no—
27D19×AGL(1,𝔽7)—218no—
28C3×C19×ΓL(1,𝔽8)—78no—
29C72×C19C2×C3×D311yescharacteristic, complemented, Hall
30C3⋊#64424—191no—
31D3×#3861—191no—
32C3×#64424D1911yescharacteristic, complemented
33D399—78no—
34C7×D57AGL(1,𝔽7)18yescomplemented
35C3×D7×C19—78no—
36ΓL(1,𝔽8)⋊D19—218no—
37C19×AGL(1,𝔽7)—78no—
38C19×AGL(1,𝔽7)—148no—
39ΓL(1,𝔽8)×D19—218no—
40C2×C3×D57—491noHall
41D3×C7⋊D7—191no—
42C2×#64424—571no—
43D7×D19—218no—
44C3×#3861C2×D1911yescharacteristic, complemented, Hall
45C3×C7×C19C2×AGL(1,𝔽7)18yescomplemented
46C19×ΓL(1,𝔽8)—78no—
47C19×ΓL(1,𝔽8)—148no—
48C2×C32×C19—491no—
49C3×D57—491no—
50C3×D57—491no—
51C3⋊(C7⋊D7)—191no—
52D3×C72—191no—
53C3×C7⋊D7C3×D1911yescharacteristic, complemented
54C2×#3861—571no—
55#64424—21no—
56#64424—571no—
57#64424D5711yescharacteristic, direct product factor
58D133—218no—
59C7×D19—38no—
60D7×C19—78no—
61D3×AGL(1,𝔽7)—1338no—
62C2×D57—491no—
63C2×C3×D19—1471no—
64C2×C7⋊D7—571noHall
65C32×C19—491noHall
66C3×C72C2×C3×D1911yescharacteristic, complemented
67#3861—21no—
68#3861C2×D5711yescharacteristic, complemented
69C7×C19D3×AGL(1,𝔽7)18yescomplemented
70C3⋊AGL(1,𝔽7)—1338no—
71D3×ΓL(1,𝔽8)—1338no—
72C3×AGL(1,𝔽7)—78no—
73C2×C3×C19—491no—
74C2×C3×C19—491no—
75C2×C3×C19—981no—
76D57—491no—
77D57#6442411yescharacteristic, direct product factor
78C3×D19—1471no—
79C3×D19—1471no—
80C2×C72—571no—
81C7⋊D7—571no—
82C7⋊D7C3×D5711yescharacteristic, complemented
83D3×D7—1338no—
84C2×AGL(1,𝔽7)—3998no—
85C2×D19—1471noHall
86C3×ΓL(1,𝔽8)—78no—
87C3×C19—491no—
88C3×C19—981no—
89C3×C19C2×#6442411yescharacteristic, complemented
90C72C2×C3×D5711yescharacteristic, complemented, Sylow
91D21—1338no—
92C3×D7—78no—
93D3×C7—198no—
94C2×ΓL(1,𝔽8)—3998no—
95AGL(1,𝔽7)—78no—
96AGL(1,𝔽7)—148no—
97AGL(1,𝔽7)—3998no—
98C2×C19—491no—
99D19—31no—
100D19—1471no—
101C2×C3×D3—9311noHall
102C2×D7—3998no—
103C3×C7D19×AGL(1,𝔽7)18yescomplemented
104ΓL(1,𝔽8)—78no—
105ΓL(1,𝔽8)—148no—
106C19D3×#6442411yescharacteristic, complemented, Sylow
107C2×C32—491no—
108C3×D3—9311no—
109C3×D3—9311no—
110C2×C7—578no—
111D7—78no—
112D7—3998no—
113C22×C3—27931no—
114C2×D3—9311no—
115C32—491noSylow
116C7AGL(1,𝔽7)×D5718yescomplemented
117C2×C3—491no—
118C2×C3—491no—
119C2×C3—981no—
120C2×C3—27931no—
121C2×C3—27931no—
122D3—191no—
123D3—9311no—
124C22—27931noSylow
125C3—491no—
126C3—981no—
127C3D19×#6442411yescharacteristic, complemented
128C2—491no—
129C2—571no—
130C2—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×#3861C2semidirect
2. C3⋊#19150288C2semidirect
3. C3×C19×#64424C2semidirect
4. C7⋊D7×D57C3semidirect
6. C3×C19×#3861C22semidirect
7. C3⋊(C7⋊D133)C2×C3semidirect
8. C72×D57C2×C3semidirect
9. C3×C19×C7⋊D7C2×C3semidirect
13. C19×#64424D3semidirect
17. C19×#3861C2×D3semidirect
18. C3×C72×C19C22×C3semidirect
23. C19×C7⋊D7C3×D3semidirect
29. C72×C19C2×C3×D3semidirect
32. C3×#64424D19semidirect
34. C7×D57AGL(1,𝔽7)semidirect
44. C3×#3861C2×D19semidirect
45. C3×C7×C19C2×AGL(1,𝔽7)semidirect
53. C3×C7⋊D7C3×D19semidirect
57. #64424D57direct (N × H)
66. C3×C72C2×C3×D19semidirect
68. #3861C2×D57semidirect
69. C7×C19D3×AGL(1,𝔽7)semidirect
77. D57#64424direct (N × H)
82. C7⋊D7C3×D57semidirect
89. C3×C19C2×#64424semidirect
90. C72C2×C3×D57semidirect
103. C3×C7D19×AGL(1,𝔽7)semidirect
106. C19D3×#64424semidirect
116. C7AGL(1,𝔽7)×D57semidirect
127. C3D19×#64424semidirect

Maximal subgroups

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

subgroupindex
D57×#38612
C3⋊#191502882
C3×C19×#644242
C7⋊D7×D573
D19×#644243
AGL(1,𝔽7)×D577
D3×#6442419