Finite Group Databasebeta

← D3×C112×D21 #44479213

Subgroups — D3×C112×D21 #44479213

Order 30492.

616 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 224 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×D3×C7×C112C211yesmaximal, characteristic, complemented
2C3×C112×D21C211yesmaximal, characteristic, complemented
3C112×C3⋊D21C211yesmaximal, characteristic, complemented
4C2×C112×D21—31nomaximal
5D3×C112×D7—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C112×D21—31no—
8C112×D21—31no—
9C112×D21—61no—
10C112×D21D311yescharacteristic, direct product factor
11D3×C7×C112D311yescharacteristic, complemented
12C3×C112×D7—31no—
13C2×C3×C7×C112—31no—
14D32×C112—71nomaximal, Hall
15C2×C112×D7—91noHall
16D3×C11×D21C11112yesmaximal, direct product factor
17C3×C7×C112—21no—
18C3×C7×C112C2×D311yescharacteristic, complemented
19C3×C7×C112C2×D311yescharacteristic, complemented
20C112×C3⋊D3—71no—
21C3×D3×C112—71no—
22C3×D3×C112D711yescharacteristic, complemented
23C2×C7×C112—31no—
24C112×D7—31no—
25C112×D7—91no—
26C2×D3×C112—211no—
27C2×D3×C112—211no—
28C11×C3⋊D21C2×C11112yescomplemented
29C3×C11×D21C2×C11112yescomplemented
30C3×D3×C7×C11C2×C11112yescomplemented
31C32×C112C2×D711yescharacteristic, complemented, Hall
32C2×C11×D21—312no—
33D3×C11×D7—312no—
34C7×C112D3211yescharacteristic, complemented, Hall
35C2×C3×C112—31no—
36C2×C3×C112—211no—
37D3×C112—71no—
38D3×C112—211no—
39D3×C112—211no—
40D3×C112—421no—
41D3×C112D2111yescharacteristic, direct product factor
42C32×C7×C11C22×C11112yescomplemented
43C22×C112—631noHall
44C2×C3×C7×C11—312no—
45C11×D21—312no—
46C11×D21—312no—
47C11×D21—612no—
48C11×D21D3×C11112yesdirect product factor
49D3×C7×C11D3×C11112yescomplemented
50C3×C11×D7—312no—
51D32×C11—712no—
52C3×C112—21no—
53C3×C112D3×D711yescharacteristic, complemented
54C3×C112C2×D2111yescharacteristic, complemented
55C2×C11×D7—912no—
56D3×D21C11211yescharacteristic, direct product factor, Hall
57C2×C112—31no—
58C2×C112—211no—
59C2×C112—631no—
60C3×C7×C11—212no—
61C3×C7×C11C2×D3×C11112yescomplemented
62C3×C7×C11C2×D3×C11112yescomplemented
63C11×C3⋊D3—712no—
64C3×D3×C11—712no—
65C3×D3×C11C11×D7112yescomplemented
66C2×C7×C11—312no—
67C11×D7—312no—
68C11×D7—912no—
69C2×D3×C11—2112no—
70C2×D3×C11—2112no—
71C3⋊D21C2×C11211yescharacteristic, complemented
72C3×D21C2×C11211yescharacteristic, complemented
73C3×D3×C7C2×C11211yescharacteristic, complemented
74C112D3×D2111yescharacteristic, direct product factor, Sylow
75C32×C11C2×C11×D7112yescomplemented
76C2×D21—31no—
77D3×D7—31no—
78C7×C11D32×C11112yescomplemented
79C2×C3×C11—312no—
80C2×C3×C11—2112no—
81D3×C11—712no—
82D3×C11—2112no—
83D3×C11—2112no—
84D3×C11—4212no—
85D3×C11C11×D21112yesdirect product factor
86C32×C7C22×C11211yescharacteristic, complemented, Hall
87C22×C11—6312no—
88C2×C3×C7—31no—
89D21—31no—
90D21—31no—
91D21—61no—
92D21D3×C11211yescharacteristic, direct product factor
93C3×D7—31no—
94D3×C7D3×C11211yescharacteristic, complemented
95D32—71noHall
96C3×C11—212no—
97C3×C11D3×C11×D7112yescomplemented
98C3×C11C2×C11×D21112yescomplemented
99C2×D7—91noHall
100C2×C11—312no—
101C2×C11—2112no—
102C2×C11—6312no—
103C3×C7—21no—
104C3×C7C2×D3×C11211yescharacteristic, complemented
105C3×C7C2×D3×C11211yescharacteristic, complemented
106C3⋊D3—71no—
107C3×D3—71no—
108C3×D3C112×D711yescharacteristic, complemented
109C2×C7—31no—
110D7—31no—
111D7—91no—
112C2×D3—211no—
113C2×D3—211no—
114C11D3×C11×D21112yesdirect product factor
115C32C2×C112×D711yescharacteristic, complemented, Sylow
116C7D32×C11211yescharacteristic, complemented, Sylow
117C2×C3—31no—
118C2×C3—211no—
119D3—71no—
120D3—211no—
121D3—211no—
122D3—421no—
123D3C112×D2111yescharacteristic, direct product factor
124C22—631noSylow
125C3—21no—
126C3D3×C112×D711yescharacteristic, complemented
127C3C2×C112×D2111yescharacteristic, complemented
128C2—31no—
129C2—211no—
130C2—631no—
subgroupG/H
center, hypercenterC112D3×D21
commutator, cosocle, hypocenterC32×C7C22×C112
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C32×C7
UCSC1 ◁ C112

Complements

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

NH ≅ G/Ntype
1. C3×D3×C7×C112C2semidirect
2. C3×C112×D21C2semidirect
3. C112×C3⋊D21C2semidirect
6. C32×C7×C112C22semidirect
10. C112×D21D3direct (N × H)
11. D3×C7×C112D3semidirect
16. D3×C11×D21C11direct (N × H)
18. C3×C7×C112C2×D3semidirect
19. C3×C7×C112C2×D3semidirect
22. C3×D3×C112D7semidirect
28. C11×C3⋊D21C2×C11semidirect
29. C3×C11×D21C2×C11semidirect
30. C3×D3×C7×C11C2×C11semidirect
31. C32×C112C2×D7semidirect
34. C7×C112D32semidirect
41. D3×C112D21direct (N × H)
42. C32×C7×C11C22×C11semidirect
48. C11×D21D3×C11direct (N × H)
49. D3×C7×C11D3×C11semidirect
53. C3×C112D3×D7semidirect
54. C3×C112C2×D21semidirect
56. D3×D21C112direct (N × H)
61. C3×C7×C11C2×D3×C11semidirect
62. C3×C7×C11C2×D3×C11semidirect
65. C3×D3×C11C11×D7semidirect
71. C3⋊D21C2×C112semidirect
72. C3×D21C2×C112semidirect
73. C3×D3×C7C2×C112semidirect
74. C112D3×D21direct (N × H)
75. C32×C11C2×C11×D7semidirect
78. C7×C11D32×C11semidirect
85. D3×C11C11×D21direct (N × H)
86. C32×C7C22×C112semidirect
92. D21D3×C112direct (N × H)
94. D3×C7D3×C112semidirect
97. C3×C11D3×C11×D7semidirect
98. C3×C11C2×C11×D21semidirect
104. C3×C7C2×D3×C112semidirect
105. C3×C7C2×D3×C112semidirect
108. C3×D3C112×D7semidirect
114. C11D3×C11×D21direct (N × H)
115. C32C2×C112×D7semidirect
116. C7D32×C112semidirect
123. D3C112×D21direct (N × H)
126. C3D3×C112×D7semidirect
127. C3C2×C112×D21semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C7×C1122
C3×C112×D212
C112×C3⋊D212
C2×C112×D213
D3×C112×D73
D32×C1127
D3×C11×D2111