Finite Group Databasebeta

← C4×H(5,𝔽2)×C283 #49118912

Subgroups — C4×H(5,𝔽2)×C283 #49118912

Order 36224.

1660 conjugacy classes of subgroups.

The subgroup lattice has 124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×H(5,𝔽2)×C283C211yesmaximal, characteristic
2#520×C283C216yesmaximal, complemented
3#518×C283C219yesmaximal, complemented
4C4×#41×C283C216yesmaximal, complemented
5C2×C4×D4×C283C219yesmaximal, complemented
6H(5,𝔽2)×C283C4116yesdirect product factor
7C2×#41×C283C2216yes—
8C22×D4×C283C2219yes—
9C23×C4×C283C2216yescomplemented
10C4×Q8×C283C2212yescomplemented
11C4×Q8×C283C2216yescomplemented
12C4×D4×C283C22118yescomplemented
13C4×D4×C283C22136yescomplemented
14C4×D4×C283C22118yescomplemented
15#117×C283C22118yescomplemented
16C2×C4⋊C4×C283C2219yescomplemented
17C2×C22⋊C4×C283C22118yescomplemented
18C2×C42×C283C2219yescomplemented
19C24×C283C2316yes—
20#41×C283C2×C4148yescomplemented
21C2×Q8×C283C2312yes—
22C2×D4×C283C2×C4172yescomplemented
23C2×D4×C283C23118yes—
24C22×C4×C283—412no—
25C22×C4×C283C2319yes—
26C22×C4×C283C2319yes—
27C22×C4×C283C23118yes—
28C22×C4×C283C2319yes—
29C4⋊C4×C283C23118yes—
30C4⋊C4×C283C2316yes—
31C22⋊C4×C283C23136yes—
32C42×C283C23118yes—
33C42×C283C2316yes—
34C23×C283—46no—
35C23×C283—46no—
36C23×C283C22×C4124yescomplemented
37C23×C283C2419yes—
38Q8×C283C22×C418yescomplemented
39D4×C283C22×C4172yescomplemented
40C2×C4×C283—218no—
41C2×C4×C283—418no—
42C2×C4×C283—49no—
43C2×C4×C283C22×C4136yescomplemented
44C2×C4×C283C2416yes—
45C2×C4×C283C2419yes—
46C2×C4×C283C2416yes—
47C2×C4×C283C2411yescharacteristic
48C22×C283—29no—
49C22×C283—29no—
50C22×C283—424no—
51C22×C283C23×C4118yes—
52C22×C283C2511yescharacteristic
53C4×C283—29no—
54C4×C283—26no—
55C4×C283C23×C4112yes—
56C4×C283H(5,𝔽2)12yesdirect product factor
57C2×C283—218no—
58C2×C283C24×C411yescharacteristic
59C2×C283C2×H(5,𝔽2)11yescharacteristic
60C2×C283#58511yescharacteristic
61C283C4×H(5,𝔽2)11yescharacteristic, direct product factor, Sylow
62C4×H(5,𝔽2)C28311yesmaximal, characteristic, direct product factor, Sylow
63C2×H(5,𝔽2)C2×C28311yescharacteristic
64#520C2×C28316yescomplemented
65#518C2×C28319yescomplemented
66C4×#41C2×C28316yescomplemented
67C2×C4×D4C2×C28319yescomplemented
68H(5,𝔽2)C4×C283116yesdirect product factor
69C2×#41C22×C28316yes—
70C22×D4C22×C28319yes—
71C23×C4C22×C28316yescomplemented
72C4×Q8C22×C28312yescomplemented
73C4×Q8C22×C28316yescomplemented
74C4×D4C22×C283118yescomplemented
75C4×D4C22×C283136yescomplemented
76C4×D4C22×C283118yescomplemented
77#117C22×C283118yescomplemented
78C2×C4⋊C4C22×C28319yescomplemented
79C2×C22⋊C4C22×C283118yescomplemented
80C2×C42C22×C28319yescomplemented
81C24C23×C28316yes—
82#41C2×C4×C283148yescomplemented
83C2×Q8C23×C28312yes—
84C2×D4C2×C4×C283172yescomplemented
85C2×D4C23×C283118yes—
86C22×C4—412no—
87C22×C4C23×C28319yes—
88C22×C4C23×C28319yes—
89C22×C4C23×C283118yes—
90C22×C4C23×C28319yes—
91C4⋊C4C23×C283118yes—
92C4⋊C4C23×C28316yes—
93C22⋊C4C23×C283136yes—
94C42C23×C28316yes—
95C42C23×C283118yes—
96C23—46no—
97C23—46no—
98C23C22×C4×C283124yescomplemented
99C23C24×C28319yes—
100Q8C22×C4×C28318yescomplemented
101D4C22×C4×C283172yescomplemented
102C2×C4—218no—
103C2×C4—418no—
104C2×C4—49no—
105C2×C4C22×C4×C283136yescomplemented
106C2×C4C24×C28316yes—
107C2×C4C24×C28319yes—
108C2×C4C24×C28316yes—
109C2×C4C24×C28311yescharacteristic
110C22—29no—
111C22—29no—
112C22—424no—
113C22C23×C4×C283118yes—
114C22C25×C28311yescharacteristic
115C4—29no—
116C4—26no—
117C4C23×C4×C283112yes—
118C4H(5,𝔽2)×C28312yesdirect product factor
119C2—218no—
120C2C24×C4×C28311yescharacteristic
121C2C2×H(5,𝔽2)×C28311yescharacteristic
122C2#585×C28311yescharacteristic
subgroupG/H
centerC2×C4×C283C24
commutatorC2C24×C4×C283
Frattini, cosocleC22C25×C283
socleC22×C283C25
prime radicalC2×H(5,𝔽2)×C283C2
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C283 ◁ G

Complements

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

NH ≅ G/Ntype
2. #520×C283C2semidirect
3. #518×C283C2semidirect
4. C4×#41×C283C2semidirect
5. C2×C4×D4×C283C2semidirect
6. H(5,𝔽2)×C283C4direct (N × H)
9. C23×C4×C283C22semidirect
10. C4×Q8×C283C22semidirect
11. C4×Q8×C283C22semidirect
12. C4×D4×C283C22semidirect
13. C4×D4×C283C22semidirect
14. C4×D4×C283C22semidirect
15. #117×C283C22semidirect
16. C2×C4⋊C4×C283C22semidirect
17. C2×C22⋊C4×C283C22semidirect
18. C2×C42×C283C22semidirect
20. #41×C283C2×C4semidirect
22. C2×D4×C283C2×C4semidirect
36. C23×C283C22×C4semidirect
38. Q8×C283C22×C4semidirect
39. D4×C283C22×C4semidirect
43. C2×C4×C283C22×C4semidirect
56. C4×C283H(5,𝔽2)direct (N × H)
61. C283C4×H(5,𝔽2)direct (N × H)
62. C4×H(5,𝔽2)C283direct (N × H)
64. #520C2×C283semidirect
65. #518C2×C283semidirect
66. C4×#41C2×C283semidirect
67. C2×C4×D4C2×C283semidirect
68. H(5,𝔽2)C4×C283direct (N × H)
71. C23×C4C22×C283semidirect
72. C4×Q8C22×C283semidirect
73. C4×Q8C22×C283semidirect
74. C4×D4C22×C283semidirect
75. C4×D4C22×C283semidirect
76. C4×D4C22×C283semidirect
77. #117C22×C283semidirect
78. C2×C4⋊C4C22×C283semidirect
79. C2×C22⋊C4C22×C283semidirect
80. C2×C42C22×C283semidirect
82. #41C2×C4×C283semidirect
84. C2×D4C2×C4×C283semidirect
98. C23C22×C4×C283semidirect
100. Q8C22×C4×C283semidirect
101. D4C22×C4×C283semidirect
105. C2×C4C22×C4×C283semidirect
118. C4H(5,𝔽2)×C283direct (N × H)

Maximal subgroups

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

subgroupindex
C2×H(5,𝔽2)×C2832
#520×C2832
#518×C2832
C4×#41×C2832
C2×C4×D4×C2832
C4×H(5,𝔽2)283