Finite Group Databasebeta

← C24×C3×C42×C11 #72187331

Subgroups — C24×C3×C42×C11 #72187331

Order 8448.

48060 conjugacy classes of subgroups.

The subgroup lattice has 120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C3×C4×C11C213yesmaximal
2C23×C3×C42×C11C2160yesmaximal, direct product factor
3C26×C3×C11C2211yescharacteristic
4C24×C3×C4×C11C4196yesdirect product factor
5C24×C3×C4×C11C22190yes—
6C22×C3×C42×C11C221560yesdirect product factor
7C24×C42×C11C311yesmaximal, characteristic, direct product factor, Hall
8C25×C4×C11C2×C313yes—
9C23×C42×C11C2×C3160yesdirect product factor
10C25×C3×C11C2×C4148yes—
11C25×C3×C11C23115yes—
12C23×C3×C4×C11C2×C411440yesdirect product factor
13C23×C3×C4×C11C231420yes—
14C2×C3×C42×C11C231960yesdirect product factor
15C24×C3×C42C1111yesmaximal, characteristic, direct product factor, Hall
16C26×C11C22×C311yescharacteristic
17C24×C4×C11C3×C4196yesdirect product factor
18C24×C4×C11C22×C3190yes—
19C22×C42×C11C22×C31560yesdirect product factor
20C24×C3×C11C421256yesdirect product factor
21C24×C3×C11C22×C41360yes—
22C24×C3×C11C24135yes—
23C22×C3×C4×C11C22×C413360yesdirect product factor
24C22×C3×C4×C11C241360yes—
25C3×C42×C11C241256yesdirect product factor
26C25×C3×C4C2×C1113yes—
27C23×C3×C42C2×C11160yesdirect product factor
28C25×C11C2×C3×C4148yes—
29C25×C11C23×C3115yes—
30C23×C4×C11C2×C3×C411440yesdirect product factor
31C23×C4×C11C23×C31420yes—
32C2×C42×C11C23×C31960yesdirect product factor
33C23×C3×C11C2×C421960yesdirect product factor
34C23×C3×C11C23×C41420yes—
35C23×C3×C11C25115yes—
36C2×C3×C4×C11C23×C411440yesdirect product factor
37C2×C3×C4×C11C25148yes—
38C24×C42C3×C1111yescharacteristic, direct product factor, Sylow
39C26×C3C22×C1111yescharacteristic
40C24×C3×C4C4×C11196yesdirect product factor
41C24×C3×C4C22×C11190yes—
42C22×C3×C42C22×C111560yesdirect product factor
43C24×C11C3×C421256yesdirect product factor
44C24×C11C22×C3×C41360yes—
45C24×C11C24×C3135yes—
46C22×C4×C11C22×C3×C413360yesdirect product factor
47C22×C4×C11C24×C31360yes—
48C42×C11C24×C31256yesdirect product factor
49C22×C3×C11C22×C421560yesdirect product factor
50C22×C3×C11C24×C4190yes—
51C22×C3×C11C2611yescharacteristic
52C3×C4×C11C24×C4196yesdirect product factor
53C25×C4C2×C3×C1113yes—
54C23×C42C2×C3×C11160yesdirect product factor
55C25×C3C2×C4×C11148yes—
56C25×C3C23×C11115yes—
57C23×C3×C4C2×C4×C1111440yesdirect product factor
58C23×C3×C4C23×C111420yes—
59C2×C3×C42C23×C111960yesdirect product factor
60C23×C11C2×C3×C421960yesdirect product factor
61C23×C11C23×C3×C41420yes—
62C23×C11C25×C3115yes—
63C2×C4×C11C23×C3×C411440yesdirect product factor
64C2×C4×C11C25×C3148yes—
65C2×C3×C11C23×C42160yesdirect product factor
66C2×C3×C11C25×C413yes—
67C26C22×C3×C1111yescharacteristic
68C24×C4C3×C4×C11196yesdirect product factor
69C24×C4C22×C3×C11190yes—
70C22×C42C22×C3×C111560yesdirect product factor
71C24×C3C42×C111256yesdirect product factor
72C24×C3C22×C4×C111360yes—
73C24×C3C24×C11135yes—
74C22×C3×C4C22×C4×C1113360yesdirect product factor
75C22×C3×C4C24×C111360yes—
76C3×C42C24×C111256yesdirect product factor
77C22×C11C22×C3×C421560yesdirect product factor
78C22×C11C24×C3×C4190yes—
79C22×C11C26×C311yescharacteristic
80C4×C11C24×C3×C4196yesdirect product factor
81C3×C11C24×C4211yescharacteristic, direct product factor, Hall
82C25C2×C3×C4×C11148yes—
83C25C23×C3×C11115yes—
84C23×C4C2×C3×C4×C1111440yesdirect product factor
85C23×C4C23×C3×C111420yes—
86C2×C42C23×C3×C111960yesdirect product factor
87C23×C3C2×C42×C111960yesdirect product factor
88C23×C3C23×C4×C111420yes—
89C23×C3C25×C11115yes—
90C2×C3×C4C23×C4×C1111440yesdirect product factor
91C2×C3×C4C25×C11148yes—
92C2×C11C23×C3×C42160yesdirect product factor
93C2×C11C25×C3×C413yes—
94C24C3×C42×C111256yesdirect product factor
95C24C22×C3×C4×C111360yes—
96C24C24×C3×C11135yes—
97C22×C4C22×C3×C4×C1113360yesdirect product factor
98C22×C4C24×C3×C111360yes—
99C42C24×C3×C111256yesdirect product factor
100C22×C3C22×C42×C111560yesdirect product factor
101C22×C3C24×C4×C11190yes—
102C22×C3C26×C1111yescharacteristic
103C3×C4C24×C4×C11196yesdirect product factor
104C11C24×C3×C4211yescharacteristic, direct product factor, Sylow
105C23C2×C3×C42×C111960yesdirect product factor
106C23C23×C3×C4×C111420yes—
107C23C25×C3×C11115yes—
108C2×C4C23×C3×C4×C1111440yesdirect product factor
109C2×C4C25×C3×C11148yes—
110C2×C3C23×C42×C11160yesdirect product factor
111C2×C3C25×C4×C1113yes—
112C22C22×C3×C42×C111560yesdirect product factor
113C22C24×C3×C4×C11190yes—
114C22C26×C3×C1111yescharacteristic
115C4C24×C3×C4×C11196yesdirect product factor
116C3C24×C42×C1111yescharacteristic, direct product factor, Sylow
117C2C23×C3×C42×C11160yesdirect product factor
118C2C25×C3×C4×C1113yes—
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C26×C3×C11
socle, prime radicalC26×C3×C11C22
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C3×C42×C11C2direct (N × H)
4. C24×C3×C4×C11C4direct (N × H)
6. C22×C3×C42×C11C22direct (N × H)
7. C24×C42×C11C3direct (N × H)
9. C23×C42×C11C2×C3direct (N × H)
12. C23×C3×C4×C11C2×C4direct (N × H)
14. C2×C3×C42×C11C23direct (N × H)
15. C24×C3×C42C11direct (N × H)
17. C24×C4×C11C3×C4direct (N × H)
19. C22×C42×C11C22×C3direct (N × H)
20. C24×C3×C11C42direct (N × H)
23. C22×C3×C4×C11C22×C4direct (N × H)
25. C3×C42×C11C24direct (N × H)
27. C23×C3×C42C2×C11direct (N × H)
30. C23×C4×C11C2×C3×C4direct (N × H)
32. C2×C42×C11C23×C3direct (N × H)
33. C23×C3×C11C2×C42direct (N × H)
36. C2×C3×C4×C11C23×C4direct (N × H)
38. C24×C42C3×C11direct (N × H)
40. C24×C3×C4C4×C11direct (N × H)
42. C22×C3×C42C22×C11direct (N × H)
43. C24×C11C3×C42direct (N × H)
46. C22×C4×C11C22×C3×C4direct (N × H)
48. C42×C11C24×C3direct (N × H)
49. C22×C3×C11C22×C42direct (N × H)
52. C3×C4×C11C24×C4direct (N × H)
54. C23×C42C2×C3×C11direct (N × H)
57. C23×C3×C4C2×C4×C11direct (N × H)
59. C2×C3×C42C23×C11direct (N × H)
60. C23×C11C2×C3×C42direct (N × H)
63. C2×C4×C11C23×C3×C4direct (N × H)
65. C2×C3×C11C23×C42direct (N × H)
68. C24×C4C3×C4×C11direct (N × H)
70. C22×C42C22×C3×C11direct (N × H)
71. C24×C3C42×C11direct (N × H)
74. C22×C3×C4C22×C4×C11direct (N × H)
76. C3×C42C24×C11direct (N × H)
77. C22×C11C22×C3×C42direct (N × H)
80. C4×C11C24×C3×C4direct (N × H)
81. C3×C11C24×C42direct (N × H)
84. C23×C4C2×C3×C4×C11direct (N × H)
86. C2×C42C23×C3×C11direct (N × H)
87. C23×C3C2×C42×C11direct (N × H)
90. C2×C3×C4C23×C4×C11direct (N × H)
92. C2×C11C23×C3×C42direct (N × H)
94. C24C3×C42×C11direct (N × H)
97. C22×C4C22×C3×C4×C11direct (N × H)
99. C42C24×C3×C11direct (N × H)
100. C22×C3C22×C42×C11direct (N × H)
103. C3×C4C24×C4×C11direct (N × H)
104. C11C24×C3×C42direct (N × H)
105. C23C2×C3×C42×C11direct (N × H)
108. C2×C4C23×C3×C4×C11direct (N × H)
110. C2×C3C23×C42×C11direct (N × H)
112. C22C22×C3×C42×C11direct (N × H)
115. C4C24×C3×C4×C11direct (N × H)
116. C3C24×C42×C11direct (N × H)
117. C2C23×C3×C42×C11direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C3×C4×C112
C23×C3×C42×C112
C24×C42×C113
C24×C3×C4211