Finite Group Databasebeta

← #44479221

Subgroups — #44479221

Order 30492.

616 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 133 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×C7×C3⋊(C11⋊D11)C211yesmaximal, characteristic, complemented
2C3×C3⋊(C7⋊(C11⋊D11))C211yesmaximal, characteristic, complemented
3C112×C3⋊D21C211yesmaximal, characteristic, complemented
4D21⋊(C11⋊D11)—31nomaximal
5D21×C11⋊D11—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊(C11⋊D11))D311yescharacteristic, complemented
8C112×D21—31no—
9C112×D21—31no—
10C112×D21—61no—
11C7×C3⋊(C11⋊D11)D311yescharacteristic, complemented
12C3×C7⋊(C11⋊D11)—31no—
13C3×C7×C11⋊D11—31no—
14(C3⋊D3)⋊(C11⋊D11)—71nomaximal, Hall
15D7×C11⋊D11—91noHall
16D33⋊D21—1112nomaximal
17C3×C7×C112—21no—
18C3×C7×C112C2×D311yescharacteristic, complemented
19C3×C7×C112C2×D311yescharacteristic, complemented
20C112×C3⋊D3—71no—
21C3×C3⋊(C11⋊D11)—71no—
22C3×C3⋊(C11⋊D11)D711yescharacteristic, complemented
23C7⋊(C11⋊D11)—31no—
24C112×D7—91no—
25C7×C11⋊D11—31no—
26D3×C11⋊D11—211no—
27D3×C11⋊D11—211no—
28C11×C3⋊D21D11112yescomplemented
29C3×D231—1112no—
30C3×C7×D33—1112no—
31C32×C112C2×D711yescharacteristic, complemented, Hall
32D21⋊D11—3312no—
33D11×D21—3312no—
34C7×C112D3211yescharacteristic, complemented, Hall
35C3⋊(C11⋊D11)—71no—
36C3⋊(C11⋊D11)D2111yescharacteristic, complemented
37D3×C112—211no—
38D3×C112—211no—
39D3×C112—421no—
40C3×C11⋊D11—31no—
41C3×C11⋊D11—211no—
42C32×C7×C11C2×D11112yescomplemented
43C2×C11⋊D11—631noHall
44D231—1112no—
45C11×D21—312no—
46C11×D21—312no—
47C11×D21—612no—
48C7×D33—1112no—
49C3×D77—3312no—
50C3×C7×D11—3312no—
51(C3⋊D3)⋊D11—7712no—
52C3×C112—21no—
53C3×C112D3×D711yescharacteristic, complemented
54C3×C112C2×D2111yescharacteristic, complemented
55D7×D11—9912no—
56D3×D21—1211noHall
57C2×C112—631no—
58C11⋊D11—31no—
59C11⋊D11—211no—
60C3×C7×C11—212no—
61C3×C7×C11D3×D11112yescomplemented
62C3×C7×C11D3×D11112yescomplemented
63C11×C3⋊D3—712no—
64C3×D33—1112no—
65C3×D33—7712no—
66D77—3312no—
67C7×D11—3312no—
68C11×D7—912no—
69D3×D11—23112no—
70D3×D11—23112no—
71C3⋊D21C11⋊D1111yescharacteristic, complemented
72C3×D21—1211no—
73C3×D3×C7—1211no—
74C112D3×D2111yescharacteristic, complemented, Sylow
75C32×C11D7×D11112yescomplemented
76C2×D21—3631no—
77D3×D7—3631no—
78C7×C11(C3⋊D3)⋊D11112yescomplemented
79D33—1112no—
80D33—7712no—
81C3×D11—3312no—
82C3×D11—23112no—
83D3×C11—2112no—
84D3×C11—2112no—
85D3×C11—4212no—
86C32×C7C2×C11⋊D1111yescharacteristic, complemented, Hall
87C2×D11—69312no—
88C2×C3×C7—3631no—
89D21—31no—
90D21—31no—
91D21—61no—
92D21—1211no—
93C3×D7—3631no—
94D3×C7—1211no—
95D32—8471noHall
96C3×C11—212no—
97C3×C11D11×D21112yescomplemented
98C3×C11D21⋊D11112yescomplemented
99C2×D7—10891noHall
100C2×C11—6312no—
101D11—3312no—
102D11—23112no—
103C3×C7—21no—
104C3×C7D3×C11⋊D1111yescharacteristic, complemented
105C3×C7D3×C11⋊D1111yescharacteristic, complemented
106C3⋊D3—71no—
107C3×D3—8471no—
108C3×D3—1211no—
109C2×C7—3631no—
110D7—91no—
111D7—3631no—
112C2×D3—25411no—
113C2×D3—25411no—
114C11D33⋊D21112yescomplemented
115C32D7×C11⋊D1111yescharacteristic, complemented, Sylow
116C7(C3⋊D3)⋊(C11⋊D11)11yescharacteristic, complemented, Sylow
117C2×C3—3631no—
118C2×C3—25411no—
119D3—211no—
120D3—211no—
121D3—421no—
122D3—8471no—
123D3—1211no—
124C22—76231noSylow
125C3—21no—
126C3D21×C11⋊D1111yescharacteristic, complemented
127C3D21⋊(C11⋊D11)11yescharacteristic, complemented
128C2—631no—
129C2—3631no—
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×C7×C3⋊(C11⋊D11)C2semidirect
2. C3×C3⋊(C7⋊(C11⋊D11))C2semidirect
3. C112×C3⋊D21C2semidirect
6. C32×C7×C112C22semidirect
7. C3⋊(C7⋊(C11⋊D11))D3semidirect
11. C7×C3⋊(C11⋊D11)D3semidirect
18. C3×C7×C112C2×D3semidirect
19. C3×C7×C112C2×D3semidirect
22. C3×C3⋊(C11⋊D11)D7semidirect
28. C11×C3⋊D21D11semidirect
31. C32×C112C2×D7semidirect
34. C7×C112D32semidirect
36. C3⋊(C11⋊D11)D21semidirect
42. C32×C7×C11C2×D11semidirect
53. C3×C112D3×D7semidirect
54. C3×C112C2×D21semidirect
61. C3×C7×C11D3×D11semidirect
62. C3×C7×C11D3×D11semidirect
71. C3⋊D21C11⋊D11semidirect
74. C112D3×D21semidirect
75. C32×C11D7×D11semidirect
78. C7×C11(C3⋊D3)⋊D11semidirect
86. C32×C7C2×C11⋊D11semidirect
97. C3×C11D11×D21semidirect
98. C3×C11D21⋊D11semidirect
104. C3×C7D3×C11⋊D11semidirect
105. C3×C7D3×C11⋊D11semidirect
114. C11D33⋊D21semidirect
115. C32D7×C11⋊D11semidirect
116. C7(C3⋊D3)⋊(C11⋊D11)semidirect
126. C3D21×C11⋊D11semidirect
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×C7×C3⋊(C11⋊D11)2
C3×C3⋊(C7⋊(C11⋊D11))2
C112×C3⋊D212
D21⋊(C11⋊D11)3
D21×C11⋊D113
(C3⋊D3)⋊(C11⋊D11)7
D33⋊D2111