Finite Group Databasebeta

← C3⋊D21×D119 #44472991

Subgroups — C3⋊D21×D119 #44472991

Order 29988.

312 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C32×C7×D119C211yesmaximal, characteristic, complemented
2C7×C17×C3⋊D21C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C7⋊D119))C211yesmaximal, characteristic, complemented
4D21×D119—34nomaximal
5C32×C72×C17C2211yescharacteristic, complemented, Hall
6C3⋊(C7⋊D119)—34no—
7C7×C17×D21—34no—
8C3×C7×D119D314yescomplemented
9C3⋊D3×D119—71nomaximal
10D17×C3⋊D21—71nomaximal
11D7×D119—91noHall
12C3×C72×C17C2×D314yescomplemented
13C3⋊D357—71no—
14C3⋊D357—71no—
15C3⋊D357—143no—
16C17×C3⋊D21D711yescharacteristic, complemented
17C7×C17×C3⋊D3—71no—
18C32×D119D711yescharacteristic, complemented
19C32×C7×D17—71no—
20D7×C3⋊D21—171nomaximal, Hall
21C7⋊D119—91no—
22C7×D119C3⋊D311yescharacteristic, complemented
23C7×D7×C17—91no—
24D3×D119—214no—
25D17×D21—214no—
26C32×C7×C17—23no—
27C32×C7×C17C2×D711yescharacteristic, complemented
28C32×C7×C17C2×D711yescharacteristic, complemented
29C3⋊(C3⋊(C7⋊D7))—171no—
30C7×C3⋊D21D1711yescharacteristic, complemented
31C32×C7×D7—171no—
32C72×C17C2×C3⋊D311yescharacteristic, complemented, Hall
33D357—214no—
34D357—214no—
35D357—4212no—
36C17×D21—34no—
37D3×C7×C17—214no—
38C3×D119D2114yescomplemented
39C3×C7×D17—74no—
40C3⋊D3×D17—491noHall
41D7×D21—514no—
42C2×D119—631no—
43D7×D17—631no—
44C32×C72C2×D1711yescharacteristic, complemented, Hall
45C3×C7×C17—212no—
46C3×C7×C17D3×D714yescomplemented
47C3×C7×C17C2×D2114yescomplemented
48C3⋊D51—491no—
49C17×C3⋊D3—71no—
50C32×D17—71no—
51C3⋊(C7⋊D7)—514no—
52C7×D21—34no—
53C3×C7×D7—174no—
54C2×C3⋊D21—1191no—
55D7×C3⋊D3—1191no—
56C2×C7×C17—631no—
57D119—631no—
58D119—631no—
59D119—1263no—
60D119C3⋊D2111yescharacteristic, direct product factor
61C7×D17—71no—
62D7×C17—91no—
63D3×D17—1474no—
64D72—1531noHall
65C32×C17D7211yescharacteristic, complemented, Hall
66C3×C72D3×D1714yescomplemented
67C2×C32×C7—1191no—
68C3⋊D21—1191no—
69C3⋊D21—1191no—
70C3⋊D21—2383no—
71C3⋊D21D11911yescharacteristic, direct product factor
72C7×C3⋊D3—71no—
73C32×D7—171no—
74C7×C17—23no—
75C7×C17D7×C3⋊D311yescharacteristic, complemented
76C7×C17C2×C3⋊D2111yescharacteristic, complemented
77D51—1474no—
78C3×D17—74no—
79D3×C17—214no—
80C7⋊D7—1531no—
81C7×D7—91no—
82C7×D7—171no—
83C2×D21—3574no—
84D3×D7—3574no—
85C2×D17—4411noHall
86C32×C7—23no—
87C32×C7D7×D1711yescharacteristic, complemented
88C32×C7C2×D11911yescharacteristic, complemented
89C3×C17D7×D2114yescomplemented
90C72C3⋊D3×D1711yescharacteristic, complemented, Sylow
91C2×C3×C7—1194no—
92D21—34no—
93D21—3574no—
94D21—3574no—
95D21—71412no—
96C3×D7—174no—
97D3×C7—214no—
98C2×C3⋊D3—8331noHall
99C2×C17—631no—
100D17—71no—
101D17—4411no—
102C2×D7—10711no—
103C2×D7—10711no—
104C3×C7—212no—
105C3×C7D17×D2114yescomplemented
106C3×C7D3×D11914yescomplemented
107C2×C32—1191no—
108C3⋊D3—71no—
109C3⋊D3—8331no—
110C17D7×C3⋊D2111yescharacteristic, complemented, Sylow
111C2×C7—631no—
112C2×C7—1191no—
113D7—91no—
114D7—171no—
115D7—10711no—
116D7—10711no—
117D7—21423no—
118C2×D3—24994no—
119C32D7×D11911yescharacteristic, complemented, Sylow
120C7—23no—
121C7D17×C3⋊D2111yescharacteristic, complemented
122C7C3⋊D3×D11911yescharacteristic, complemented
123C2×C3—1194no—
124D3—214no—
125D3—24994no—
126C22—74971noSylow
127C3D21×D11914yescomplemented
128C2—631no—
129C2—74971no—
130C2—1191no—
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. C32×C7×D119C2semidirect
2. C7×C17×C3⋊D21C2semidirect
3. C3⋊(C3⋊(C7⋊D119))C2semidirect
5. C32×C72×C17C22semidirect
8. C3×C7×D119D3semidirect
12. C3×C72×C17C2×D3semidirect
16. C17×C3⋊D21D7semidirect
18. C32×D119D7semidirect
22. C7×D119C3⋊D3semidirect
27. C32×C7×C17C2×D7semidirect
28. C32×C7×C17C2×D7semidirect
30. C7×C3⋊D21D17semidirect
32. C72×C17C2×C3⋊D3semidirect
38. C3×D119D21semidirect
44. C32×C72C2×D17semidirect
46. C3×C7×C17D3×D7semidirect
47. C3×C7×C17C2×D21semidirect
60. D119C3⋊D21direct (N × H)
65. C32×C17D72semidirect
66. C3×C72D3×D17semidirect
71. C3⋊D21D119direct (N × H)
75. C7×C17D7×C3⋊D3semidirect
76. C7×C17C2×C3⋊D21semidirect
87. C32×C7D7×D17semidirect
88. C32×C7C2×D119semidirect
89. C3×C17D7×D21semidirect
90. C72C3⋊D3×D17semidirect
105. C3×C7D17×D21semidirect
106. C3×C7D3×D119semidirect
110. C17D7×C3⋊D21semidirect
119. C32D7×D119semidirect
121. C7D17×C3⋊D21semidirect
122. C7C3⋊D3×D119semidirect
127. C3D21×D119semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D1192
C7×C17×C3⋊D212
C3⋊(C3⋊(C7⋊D119))2
D21×D1193
C3⋊D3×D1197
D17×C3⋊D217
D7×C3⋊D2117