Finite Group Databasebeta

← D17×C3⋊(D49⋊C3) #44472425

Subgroups — D17×C3⋊(D49⋊C3) #44472425

Order 29988.

132 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 32 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⋊(C17⋊(D49⋊C3))C211yesmaximal, characteristic, complemented
2C17×C3⋊(D49⋊C3)C211yesmaximal, characteristic, complemented
3C3×D17×C49⋊C3C211yesmaximal, characteristic, complemented
4D17×D147C311yesmaximal, characteristic, complemented
5D17×D49⋊C3—31nomaximal
6C3×C17×C49⋊C3C2211yescharacteristic, complemented, Hall
7D2499C2×C311yescharacteristic, complemented
8C17×D147C2×C311yescharacteristic, complemented
9C3×D17×C49C2×C311yescharacteristic, complemented
10C17⋊(D49⋊C3)—31no—
11C17×D49⋊C3—31no—
12D17×C49⋊C3—21no—
13D17×C49⋊C3D311yescharacteristic, complemented
14D17×C3⋊AGL(1,𝔽7)—71nomaximal
15D17×D49—31noHall
16C17×C49⋊C3—21no—
17C17×C49⋊C3C2×D311yescharacteristic, complemented
18C3×C17×C49C22×C311yescharacteristic, complemented
19C3⋊(C17⋊AGL(1,𝔽7))—71no—
20C17×C3⋊AGL(1,𝔽7)—71no—
21C3×ΓL(1,𝔽8)×D17—141no—
22C2×C3⋊(D49⋊C3)—171nomaximal, Hall
23D833—31no—
24D17×C49C3×D311yescharacteristic, complemented
25C17×D49—31no—
26D17×D21—71no—
27D17×AGL(1,𝔽7)—211no—
28C3×C17×ΓL(1,𝔽8)—141no—
29C2×C3×C49⋊C3—171no—
30C3⋊(D49⋊C3)—171no—
31C3⋊(D49⋊C3)D1711yescharacteristic, direct product factor
32C17×C49C2×C3×D311yescharacteristic, complemented, Hall
33D357—71no—
34C17×D21—71no—
35C3×C7×D17AGL(1,𝔽7)11yescharacteristic
36C17⋊AGL(1,𝔽7)—211no—
37C17×AGL(1,𝔽7)—211no—
38ΓL(1,𝔽8)×D17—141no—
39ΓL(1,𝔽8)×D17—141no—
40C3×D3×D17—491noHall
41C2×D147—171no—
42C2×D49⋊C3—511no—
43D7×D17—211no—
44C3×C49⋊C3C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17C2×AGL(1,𝔽7)11yescharacteristic
46C17×ΓL(1,𝔽8)—141no—
47C17×ΓL(1,𝔽8)—141no—
48C3×D51—491no—
49C3×D3×C17—491no—
50C32×D17—981no—
51C2×C3×C49—171no—
52D147—171no—
53D147C3×D1711yescharacteristic, complemented
54C2×C49⋊C3—171no—
55C2×C49⋊C3—341no—
56D49⋊C3—31no—
57D49⋊C3—511no—
58C2×C3⋊AGL(1,𝔽7)—1191no—
59D119—211no—
60C7×D17C3⋊AGL(1,𝔽7)11yescharacteristic
61D7×C17—211no—
62C2×C3×D17—1471no—
63D3×D17—491no—
64C2×D49—511noHall
65C32×C17—981noHall
66C3×C49C2×C3×D1711yescharacteristic, complemented
67C49⋊C3—21no—
68C49⋊C3D3×D1711yescharacteristic, complemented
69C2×C3×ΓL(1,𝔽8)—2381no—
70C3⋊AGL(1,𝔽7)—71no—
71C3⋊AGL(1,𝔽7)—1191no—
72C7×C17C2×C3⋊AGL(1,𝔽7)11yescharacteristic
73C2×C3×C17—1471no—
74D51—491no—
75C3×D17—981no—
76C3×D17—981no—
77C3×D17—1471no—
78C3×D17D49⋊C311yescharacteristic, complemented
79D3×C17—491no—
80C2×C49—171no—
81D49—31no—
82D49—511no—
83C2×D21—1191no—
84C2×AGL(1,𝔽7)—3571no—
85C2×D17—1471noHall
86C3×ΓL(1,𝔽8)—141no—
87C3×C17—981no—
88C3×C17—981no—
89C3×C17C2×D49⋊C311yescharacteristic, complemented
90C49C3×D3×D1711yescharacteristic, complemented, Sylow
91C2×C3×C7—171no—
92D21—71no—
93D21—1191no—
94C2×ΓL(1,𝔽8)—2381no—
95C2×ΓL(1,𝔽8)—2381no—
96AGL(1,𝔽7)—211no—
97AGL(1,𝔽7)—3571no—
98C2×C3×D3—8331noHall
99C2×C17—1471no—
100D17—1471no—
101D17C3⋊(D49⋊C3)11yescharacteristic, direct product factor
102C2×D7—3571no—
103C3×C7D17×AGL(1,𝔽7)11yescharacteristic
104ΓL(1,𝔽8)—141no—
105ΓL(1,𝔽8)—141no—
106C2×C32—16661no—
107C3×D3—491no—
108C3×D3—8331no—
109C17C2×C3⋊(D49⋊C3)11yescharacteristic, complemented, Sylow
110C2×C7—171no—
111D7—211no—
112D7—3571no—
113C22×C3—24991no—
114C2×D3—8331no—
115C32—981noSylow
116C7D17×C3⋊AGL(1,𝔽7)11yescharacteristic
117C2×C3—171no—
118C2×C3—16661no—
119C2×C3—16661no—
120C2×C3—1471no—
121C2×C3—24991no—
122D3—491no—
123D3—8331no—
124C22—24991noSylow
125C3—981no—
126C3—981no—
127C3D17×D49⋊C311yescharacteristic, complemented
128C2—171no—
129C2—1471no—
130C2—24991no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C17×C49C22×C3
FrattiniC7D17×C3⋊AGL(1,𝔽7)
socleC3×C7×C17C2×AGL(1,𝔽7)
LCSG ▷ C3×C17×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C17⋊(D49⋊C3))C2semidirect
2. C17×C3⋊(D49⋊C3)C2semidirect
3. C3×D17×C49⋊C3C2semidirect
4. D17×D147C3semidirect
6. C3×C17×C49⋊C3C22semidirect
7. D2499C2×C3semidirect
8. C17×D147C2×C3semidirect
9. C3×D17×C49C2×C3semidirect
13. D17×C49⋊C3D3semidirect
17. C17×C49⋊C3C2×D3semidirect
18. C3×C17×C49C22×C3semidirect
24. D17×C49C3×D3semidirect
31. C3⋊(D49⋊C3)D17direct (N × H)
32. C17×C49C2×C3×D3semidirect
44. C3×C49⋊C3C2×D17semidirect
53. D147C3×D17semidirect
66. C3×C49C2×C3×D17semidirect
68. C49⋊C3D3×D17semidirect
78. C3×D17D49⋊C3semidirect
89. C3×C17C2×D49⋊C3semidirect
90. C49C3×D3×D17semidirect
101. D17C3⋊(D49⋊C3)direct (N × H)
109. C17C2×C3⋊(D49⋊C3)semidirect
127. C3D17×D49⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C17⋊(D49⋊C3))2
C17×C3⋊(D49⋊C3)2
C3×D17×C49⋊C32
D17×D1473
D17×D49⋊C33
D17×C3⋊AGL(1,𝔽7)7
C2×C3⋊(D49⋊C3)17