Finite Group Databasebeta

← #44472976

Subgroups — #44472976

Order 29988.

440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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×C3⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
2C3×C3⋊(C7⋊D119)C211yesmaximal, characteristic, complemented
3C72×C3⋊D51C211yesmaximal, characteristic, complemented
4D51⋊(C7⋊D7)—31nomaximal
5C7⋊D7×D51—31nomaximal
6C32×C72×C17C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊D119)D311yescharacteristic, complemented
8C17×C3⋊(C7⋊D7)D311yescharacteristic, complemented
9C72×D51—31no—
10C72×D51—31no—
11C72×D51—61no—
12C3×C7⋊D119—31no—
13C3×C17×C7⋊D7—31no—
14D21⋊D51—78nomaximal
15D17×C7⋊D7—91noHall
16C3×C72×C17—21no—
17C3×C72×C17C2×D311yescharacteristic, complemented
18C3×C72×C17C2×D311yescharacteristic, complemented
19C7×C3⋊D51D718yescomplemented
20C3×D357—78no—
21C3×C17×D21—78no—
22(C3⋊D3)⋊(C7⋊D7)—171nomaximal, Hall
23C7⋊D119—31no—
24C17×C7⋊D7—31no—
25C72×D17—91no—
26D21⋊D17—218no—
27D7×D51—218no—
28C32×C7×C17C2×D718yescomplemented
29C72×C3⋊D3—171no—
30C3×C3⋊(C7⋊D7)—171no—
31C3×C3⋊(C7⋊D7)D1711yescharacteristic, complemented
32C72×C17D3211yescharacteristic, complemented, Hall
33D357—78no—
34C17×D21—78no—
35C7×D51—38no—
36C7×D51—38no—
37C7×D51—68no—
38C3×D119—218no—
39C3×D7×C17—218no—
40D3×D51—491noHall
41D3×C7⋊D7—511no—
42D3×C7⋊D7—511no—
43D7×D17—638no—
44C32×C72C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—28no—
46C3×C7×C17D3×D718yescomplemented
47C3×C7×C17D3×D718yescomplemented
48C3⋊D51C7⋊D711yescharacteristic, complemented
49C3×D51—491no—
50C3×D3×C17—491no—
51C3⋊(C7⋊D7)—171no—
52C3⋊(C7⋊D7)D5111yescharacteristic, complemented
53D3×C72—511no—
54D3×C72—511no—
55D3×C72—1021no—
56C3×C7⋊D7—31no—
57C3×C7⋊D7—511no—
58(C3⋊D3)⋊D7—1198no—
59D119—218no—
60C7×D17—98no—
61D7×C17—218no—
62C2×D51—1471no—
63D3×D17—1471no—
64C2×C7⋊D7—1531noHall
65C32×C17C2×C7⋊D711yescharacteristic, complemented, Hall
66C3×C72—21no—
67C3×C72D3×D1711yescharacteristic, complemented
68C3×C72C2×D5111yescharacteristic, complemented
69C7×C3⋊D3—178no—
70C3×D21—78no—
71C3×D21—1198no—
72C7×C17(C3⋊D3)⋊D718yescomplemented
73C2×C3×C17—1471no—
74D51—31no—
75D51—31no—
76D51—61no—
77D51—491no—
78C3×D17—1471no—
79D3×C17—491no—
80C2×C72—1531no—
81C7⋊D7—31no—
82C7⋊D7—511no—
83D3×D7—3578no—
84D3×D7—3578no—
85C2×D17—4411noHall
86C32×C7D7×D1718yescomplemented
87C3×C17—21no—
88C3×C17D3×C7⋊D711yescharacteristic, complemented
89C3×C17D3×C7⋊D711yescharacteristic, complemented
90C72D3×D5111yescharacteristic, complemented, Sylow
91D21—78no—
92D21—1198no—
93C3×D7—218no—
94C3×D7—3578no—
95D3×C7—518no—
96D3×C7—518no—
97D3×C7—1028no—
98D32—8331noHall
99C2×C17—1471no—
100D17—91no—
101D17—1471no—
102C2×D7—10718no—
103C3×C7—28no—
104C3×C7D7×D5118yescomplemented
105C3×C7D21⋊D1718yescomplemented
106C3⋊D3—171no—
107C3×D3—491no—
108C3×D3—8331no—
109C17(C3⋊D3)⋊(C7⋊D7)11yescharacteristic, complemented, Sylow
110C2×C7—1538no—
111D7—218no—
112D7—3578no—
113C2×D3—24991no—
114C2×D3—24991no—
115C32D17×C7⋊D711yescharacteristic, complemented, Sylow
116C7D21⋊D5118yescomplemented
117C2×C3—1471no—
118C2×C3—24991no—
119D3—491no—
120D3—511no—
121D3—511no—
122D3—8331no—
123D3—1021no—
124C22—74971noSylow
125C3—21no—
126C3C7⋊D7×D5111yescharacteristic, complemented
127C3D51⋊(C7⋊D7)11yescharacteristic, complemented
128C2—1471no—
129C2—1531no—
130C2—24991no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72×C17C22
LCSG ▷ C32×C72×C17
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C17×C3⋊(C7⋊D7)C2semidirect
2. C3×C3⋊(C7⋊D119)C2semidirect
3. C72×C3⋊D51C2semidirect
6. C32×C72×C17C22semidirect
7. C3⋊(C7⋊D119)D3semidirect
8. C17×C3⋊(C7⋊D7)D3semidirect
17. C3×C72×C17C2×D3semidirect
18. C3×C72×C17C2×D3semidirect
19. C7×C3⋊D51D7semidirect
28. C32×C7×C17C2×D7semidirect
31. C3×C3⋊(C7⋊D7)D17semidirect
32. C72×C17D32semidirect
44. C32×C72C2×D17semidirect
46. C3×C7×C17D3×D7semidirect
47. C3×C7×C17D3×D7semidirect
48. C3⋊D51C7⋊D7semidirect
52. C3⋊(C7⋊D7)D51semidirect
65. C32×C17C2×C7⋊D7semidirect
67. C3×C72D3×D17semidirect
68. C3×C72C2×D51semidirect
72. C7×C17(C3⋊D3)⋊D7semidirect
86. C32×C7D7×D17semidirect
88. C3×C17D3×C7⋊D7semidirect
89. C3×C17D3×C7⋊D7semidirect
90. C72D3×D51semidirect
104. C3×C7D7×D51semidirect
105. C3×C7D21⋊D17semidirect
109. C17(C3⋊D3)⋊(C7⋊D7)semidirect
115. C32D17×C7⋊D7semidirect
116. C7D21⋊D51semidirect
126. C3C7⋊D7×D51semidirect
127. C3D51⋊(C7⋊D7)semidirect

Maximal subgroups

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

subgroupindex
C3×C17×C3⋊(C7⋊D7)2
C3×C3⋊(C7⋊D119)2
C72×C3⋊D512
D51⋊(C7⋊D7)3
C7⋊D7×D513
D21⋊D517
(C3⋊D3)⋊(C7⋊D7)17