Finite Group Databasebeta

← D21⋊(C3⋊(C11⋊D11)) #44479228

Subgroups — D21⋊(C3⋊(C11⋊D11)) #44479228

Order 30492.

616 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 145 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×C112×D21C211yesmaximal, characteristic, complemented
2C3×C3⋊(C7⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
3C7×C3⋊(C3⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
4D21⋊(C11⋊D11)—31nomaximal
5D7×C3⋊(C11⋊D11)—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊(C11⋊D11))D311yescharacteristic, complemented
8C112×D21D311yescharacteristic, complemented
9C7×C3⋊(C11⋊D11)—31no—
10C7×C3⋊(C11⋊D11)—31no—
11C7×C3⋊(C11⋊D11)—61no—
12C3×C7⋊(C11⋊D11)—31no—
13C3×C112×D7—31no—
14D3×C3⋊(C11⋊D11)—71nomaximal, Hall
15D7×C11⋊D11—91noHall
16D21⋊D33—1112nomaximal
17C3×C7×C112—21no—
18C3×C7×C112C2×D311yescharacteristic, complemented
19C3×C7×C112C2×D311yescharacteristic, complemented
20C3⋊(C3⋊(C11⋊D11))D711yescharacteristic, complemented
21C3×C3⋊(C11⋊D11)—71no—
22C3×D3×C112—71no—
23C7⋊(C11⋊D11)—31no—
24C112×D7—31no—
25C7×C11⋊D11—91no—
26C2×C3⋊(C11⋊D11)—211no—
27D3×C11⋊D11—211no—
28C7×C3⋊D33—1112no—
29C3×D231—1112no—
30C3×C11×D21D11112yescomplemented
31C32×C112C2×D711yescharacteristic, complemented, Hall
32D21⋊D11—3312no—
33D7×D33—3312no—
34C7×C112D3211yescharacteristic, complemented, Hall
35C2×C3×C112—211no—
36C3⋊(C11⋊D11)—31no—
37C3⋊(C11⋊D11)—31no—
38C3⋊(C11⋊D11)—61no—
39C3⋊(C11⋊D11)—71no—
40D3×C112—71no—
41C3×C11⋊D11—211no—
42C32×C7×C11C2×D11112yescomplemented
43C2×C11⋊D11—631noHall
44D231—1112no—
45C11×D21D33112yescomplemented
46C7×D33—3312no—
47C7×D33—3312no—
48C7×D33—6612no—
49C3×D77—3312no—
50C3×C11×D7—312no—
51D3×D33—7712no—
52C3×C112—21no—
53C3×C112D3×D711yescharacteristic, complemented
54C3×C112D3×D711yescharacteristic, complemented
55D7×D11—9912no—
56(C3⋊D3)⋊D7—1211noHall
57C2×C112—211no—
58C11⋊D11—91no—
59C11⋊D11—211no—
60C3×C7×C11—212no—
61C3×C7×C11D3×D11112yescomplemented
62C3×C7×C11C2×D33112yescomplemented
63C3⋊D33—1112no—
64C3×D33—7712no—
65C3×D3×C11—712no—
66D77—3312no—
67C7×D11—9912no—
68C11×D7—312no—
69C2×D33—23112no—
70D3×D11—23112no—
71C7×C3⋊D3—1211no—
72C3×D21—1211no—
73C3×D21C11⋊D1111yescharacteristic, complemented
74C112(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
75C32×C11D7×D11112yescomplemented
76D3×D7—3631no—
77D3×D7—3631no—
78C7×C11D3×D33112yescomplemented
79C2×C3×C11—2112no—
80D33—3312no—
81D33—3312no—
82D33—6612no—
83D33—7712no—
84C3×D11—23112no—
85D3×C11—712no—
86C32×C7C2×C11⋊D1111yescharacteristic, complemented, Hall
87C2×D11—69312no—
88D21—1211no—
89D21C3⋊(C11⋊D11)11yescharacteristic, complemented
90C3×D7—31no—
91C3×D7—3631no—
92D3×C7—3631no—
93D3×C7—3631no—
94D3×C7—7261no—
95D32—8471noHall
96C3×C11—212no—
97C3×C11D7×D33112yescomplemented
98C3×C11D21⋊D11112yescomplemented
99C2×D7—10891noHall
100C2×C11—2112no—
101D11—9912no—
102D11—23112no—
103C3×C7—21no—
104C3×C7D3×C11⋊D1111yescharacteristic, complemented
105C3×C7C2×C3⋊(C11⋊D11)11yescharacteristic, complemented
106C3⋊D3—1211no—
107C3×D3—71no—
108C3×D3—8471no—
109C2×C7—10891no—
110D7—31no—
111D7—3631no—
112C2×D3—25411no—
113C2×D3—25411no—
114C11D21⋊D33112yescomplemented
115C32D7×C11⋊D1111yescharacteristic, complemented, Sylow
116C7D3×C3⋊(C11⋊D11)11yescharacteristic, complemented, Sylow
117C2×C3—211no—
118C2×C3—25411no—
119D3—71no—
120D3—8471no—
121D3—3631no—
122D3—3631no—
123D3—7261no—
124C22—76231noSylow
125C3—21no—
126C3D7×C3⋊(C11⋊D11)11yescharacteristic, complemented
127C3D21⋊(C11⋊D11)11yescharacteristic, complemented
128C2—211no—
129C2—10891no—
130C2—25411no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C112C22
LCSG ▷ C32×C7×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C112×D21C2semidirect
2. C3×C3⋊(C7⋊(C11⋊D11))C2semidirect
3. C7×C3⋊(C3⋊(C11⋊D11))C2semidirect
6. C32×C7×C112C22semidirect
7. C3⋊(C7⋊(C11⋊D11))D3semidirect
8. C112×D21D3semidirect
18. C3×C7×C112C2×D3semidirect
19. C3×C7×C112C2×D3semidirect
20. C3⋊(C3⋊(C11⋊D11))D7semidirect
30. C3×C11×D21D11semidirect
31. C32×C112C2×D7semidirect
34. C7×C112D32semidirect
42. C32×C7×C11C2×D11semidirect
45. C11×D21D33semidirect
53. C3×C112D3×D7semidirect
54. C3×C112D3×D7semidirect
61. C3×C7×C11D3×D11semidirect
62. C3×C7×C11C2×D33semidirect
73. C3×D21C11⋊D11semidirect
74. C112(C3⋊D3)⋊D7semidirect
75. C32×C11D7×D11semidirect
78. C7×C11D3×D33semidirect
86. C32×C7C2×C11⋊D11semidirect
89. D21C3⋊(C11⋊D11)semidirect
97. C3×C11D7×D33semidirect
98. C3×C11D21⋊D11semidirect
104. C3×C7D3×C11⋊D11semidirect
105. C3×C7C2×C3⋊(C11⋊D11)semidirect
114. C11D21⋊D33semidirect
115. C32D7×C11⋊D11semidirect
116. C7D3×C3⋊(C11⋊D11)semidirect
126. C3D7×C3⋊(C11⋊D11)semidirect
127. C3D21⋊(C11⋊D11)semidirect

Maximal subgroups

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

subgroupindex
C3×C112×D212
C3×C3⋊(C7⋊(C11⋊D11))2
C7×C3⋊(C3⋊(C11⋊D11))2
D21⋊(C11⋊D11)3
D7×C3⋊(C11⋊D11)3
D3×C3⋊(C11⋊D11)7
D21⋊D3311