Finite Group Databasebeta

← C22×#22583655 #49136062

Subgroups — C22×#22583655 #49136062

Order 36224.

6560 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.

normal subgroups only

This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3221 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
1C2×#22583655C2148yesmaximal, direct product factor
2C22×#17985392C212yesmaximal, complemented
3C22×#17985391C214yesmaximal, complemented
4C23×C22⋊D283C214yesmaximal, complemented
5C22×D4×D283C214yesmaximal, complemented
6C23×D4×C283C211yesmaximal, characteristic, complemented
7C24×D283C2214yescomplemented
8#22583655C221256yesdirect product factor
9C2×#17985392C22148yescomplemented
10C2×#17985391C22196yescomplemented
11C22×Dic566C2212yescomplemented
12C22×D1132C2212yescomplemented
13C22×C22⋊D283C2218yescomplemented
14C22×C22⋊D283C2214yescomplemented
15C22×C22⋊D283C22196yescomplemented
16C2×D4×D283C22196yescomplemented
17C23×Dic283C2214yescomplemented
18C22×C4×D283C2214yescomplemented
19C25×C283C2212yescomplemented
20C22×D4×C283C2214yescomplemented
21C22×D4×C283C22124yescomplemented
22C23×C4×C283C2211yescharacteristic, complemented
23C23×D283—416no—
24C23×D283C2314yes—
25C23×D283C23148yescomplemented
26#17985392C231128yescomplemented
27#17985391C231256yescomplemented
28C2×Dic566C23124yescomplemented
29C2×D1132C23124yescomplemented
30C2×C22⋊D283C23196yescomplemented
31C2×C22⋊D283C23148yescomplemented
32C2×C22⋊D283C231256yescomplemented
33D4×D283C231256yescomplemented
34C22×Dic283C2314yes—
35C22×Dic283C23148yescomplemented
36C2×C4×D283C23148yescomplemented
37C24×C283—48no—
38C24×C283C2314yes—
39C24×C283C2311yescharacteristic
40C24×C283C23124yescomplemented
41C2×D4×C283C23148yescomplemented
42C2×D4×C283C23164yescomplemented
43C22×C4×C283C2312yes—
44C22×C4×C283C23112yescomplemented
45C22×D283—216no—
46C22×D283—496no—
47C22×D283C24124yes—
48C22×D283C24164yescomplemented
49Dic566C24132yescomplemented
50D1132C24132yescomplemented
51C22⋊D283C241128yescomplemented
52C22⋊D283C24164yescomplemented
53C2×Dic283C24124yes—
54C2×Dic283C24164yescomplemented
55C4×D283C24164yescomplemented
56C23×C283—24no—
57C23×C283—216no—
58C23×C283—448no—
59C23×C283C2416yes—
60C23×C283C24124yes—
61C23×C283C2411yescharacteristic
62C23×C283C24132yescomplemented
63D4×C283C24164yescomplemented
64C2×C4×C283C24112yes—
65C2×C4×C283C24116yescomplemented
66C22×C283—212no—
67C22×C283—248no—
68C22×C283—432no—
69C22×C283H(5,𝔽2)14yescomplemented
70C22×C283C2514yes—
71C22×C283C25116yes—
72C22×C283C2513yes—
73C2×D283—248no—
74C2×D283—464no—
75C2×D283C25116yes—
76C4×C283C2518yes—
77Dic283C25116yes—
78C2×C283—216no—
79C2×C283—24no—
80C2×C283C2×H(5,𝔽2)16yescomplemented
81C2×C283C2611yescharacteristic
82D283—216no—
83C283C22×H(5,𝔽2)11yescharacteristic, complemented, Sylow
84C22×H(5,𝔽2)—2831nomaximal, Sylow
85C2×H(5,𝔽2)—28348no—
86C22×#41—2834no—
87C22×#41—2832no—
88C23×D4—2834no—
89C23×D4—2834no—
90C23×D4D28311yescharacteristic, complemented
91C25—2834no—
92C25C2×D28312yescomplemented
93H(5,𝔽2)—283256no—
94C2×#41—28396no—
95C2×#41—28348no—
96C22×Q8—2832no—
97C22×D4—2838no—
98C22×D4—2834no—
99C22×D4—28396no—
100C22×D4—28396no—
101C22×D4—2832no—
102C22×D4C2×D28314yescomplemented
103C22×D4C2×D283124yescomplemented
104C23×C4—2834no—
105C23×C4—2834no—
106C23×C4C2×D28311yescharacteristic, complemented
107C24—48no—
108C24—2834no—
109C24—28348no—
110C24—113216no—
111C24C22×D28314yes—
112C24C22×D28311yescharacteristic
113C24C22×D283124yescomplemented
114#41—283256no—
115#41—283128no—
116C2×Q8—28324no—
117C2×D4—28396no—
118C2×D4—28348no—
119C2×D4—283256no—
120C2×D4—283256no—
121C2×D4—28324no—
122C2×D4C22×D283148yescomplemented
123C2×D4C22×D283164yescomplemented
124C22×C4—28348no—
125C22×C4—2834no—
126C22×C4—28348no—
127C22×C4C22×D28312yes—
128C22×C4C22×D283112yescomplemented
129C23—24no—
130C23—216no—
131C23—448no—
132C23—28324no—
133C23—28364no—
134C23—56616no—
135C23—113296no—
136C23C23×D283124yes—
137C23C23×D28316yes—
138C23C23×D28311yescharacteristic
139C23C23×D283132yescomplemented
140Q8—28332no—
141D4—283128no—
142D4—28364no—
143D4—28332no—
144D4C23×D283164yescomplemented
145C2×C4—28324no—
146C2×C4—28364no—
147C2×C4—28364no—
148C2×C4C23×D283112yes—
149C2×C4C23×D283116yescomplemented
150C22—212no—
151C22—248no—
152C22—432no—
153C22—28316no—
154C22—56648no—
155C22—113264no—
156C22#2258365514yesdirect product factor
157C22C24×D283116yes—
158C22C24×D28314yes—
159C22C24×D28313yes—
160C4—28316no—
161C4C24×D28318yes—
162C2—24no—
163C2—216no—
164C2—56616no—
165C2C2×#2258365516yesdirect product factor
166C2C25×D28311yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC2×C283C26
FrattiniC2C25×D283
FittingC23×D4×C283C2
socleC23×C283C24
hypercenterC23×D4D283
hypocenterC283C22×H(5,𝔽2)
LCSG ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22583655C2direct (N × H)
2. C22×#17985392C2semidirect
3. C22×#17985391C2semidirect
4. C23×C22⋊D283C2semidirect
5. C22×D4×D283C2semidirect
6. C23×D4×C283C2semidirect
7. C24×D283C22semidirect
8. #22583655C22direct (N × H)
9. C2×#17985392C22semidirect
10. C2×#17985391C22semidirect
11. C22×Dic566C22semidirect
12. C22×D1132C22semidirect
13. C22×C22⋊D283C22semidirect
14. C22×C22⋊D283C22semidirect
15. C22×C22⋊D283C22semidirect
16. C2×D4×D283C22semidirect
17. C23×Dic283C22semidirect
18. C22×C4×D283C22semidirect
19. C25×C283C22semidirect
20. C22×D4×C283C22semidirect
21. C22×D4×C283C22semidirect
22. C23×C4×C283C22semidirect
25. C23×D283C23semidirect
26. #17985392C23semidirect
27. #17985391C23semidirect
28. C2×Dic566C23semidirect
29. C2×D1132C23semidirect
30. C2×C22⋊D283C23semidirect
31. C2×C22⋊D283C23semidirect
32. C2×C22⋊D283C23semidirect
33. D4×D283C23semidirect
35. C22×Dic283C23semidirect
36. C2×C4×D283C23semidirect
40. C24×C283C23semidirect
41. C2×D4×C283C23semidirect
42. C2×D4×C283C23semidirect
44. C22×C4×C283C23semidirect
48. C22×D283C24semidirect
49. Dic566C24semidirect
50. D1132C24semidirect
51. C22⋊D283C24semidirect
52. C22⋊D283C24semidirect
54. C2×Dic283C24semidirect
55. C4×D283C24semidirect
62. C23×C283C24semidirect
63. D4×C283C24semidirect
65. C2×C4×C283C24semidirect
69. C22×C283H(5,𝔽2)semidirect
80. C2×C283C2×H(5,𝔽2)semidirect
83. C283C22×H(5,𝔽2)semidirect
90. C23×D4D283semidirect
92. C25C2×D283semidirect
102. C22×D4C2×D283semidirect
103. C22×D4C2×D283semidirect
106. C23×C4C2×D283semidirect
113. C24C22×D283semidirect
122. C2×D4C22×D283semidirect
123. C2×D4C22×D283semidirect
128. C22×C4C22×D283semidirect
139. C23C23×D283semidirect
144. D4C23×D283semidirect
149. C2×C4C23×D283semidirect
156. C22#22583655direct (N × H)
165. C2C2×#22583655direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225836552
C22×#179853922
C22×#179853912
C23×C22⋊D2832
C22×D4×D2832
C23×D4×C2832
C22×H(5,𝔽2)283