Finite Group Databasebeta

← C22×#22583656 #49136063

Subgroups — C22×#22583656 #49136063

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×#22583656C2148yesmaximal, direct product factor
2C22×#17985393C212yesmaximal, complemented
3C22×#17985392C213yesmaximal, complemented
4C23×D1132C213yesmaximal, complemented
5C22×D4×D283C216yesmaximal, complemented
6C22×#41×C283C211yesmaximal, characteristic, complemented
7C24×D283C2216yescomplemented
8#22583656C221256yesdirect product factor
9C2×#17985393C22148yescomplemented
10C2×#17985392C22172yescomplemented
11C22×Dic566C2211yescharacteristic, complemented
12C22×D1132C2216yescomplemented
13C22×D1132C2213yescomplemented
14C22×D1132C22172yescomplemented
15C22×C22⋊D283C2216yescomplemented
16C2×D4×D283C221144yescomplemented
17C22×C4×D283C2216yescomplemented
18C2×#41×C283C22124yescomplemented
19C22×Q8×C283C2211yescharacteristic, complemented
20C22×D4×C283C2213yescomplemented
21C23×C4×C283C2213yescomplemented
22C23×D283—424no—
23C23×D283C2316yes—
24C23×D283C23172yescomplemented
25#17985393C231128yescomplemented
26#17985392C231192yescomplemented
27C2×Dic566C23112yescomplemented
28C2×D1132C23172yescomplemented
29C2×D1132C23136yescomplemented
30C2×D1132C231192yescomplemented
31C2×C22⋊D283C23172yescomplemented
32D4×D283C231384yescomplemented
33C22×Dic283C2312yes—
34C2×C4×D283C23172yescomplemented
35C24×C283C2313yes—
36#41×C283C23164yescomplemented
37C2×Q8×C283C23112yescomplemented
38C2×D4×C283C23136yescomplemented
39C22×C4×C283C2313yes—
40C22×C4×C283C2311yescharacteristic
41C22×C4×C283C23136yescomplemented
42C22×D283—224no—
43C22×D283—4144no—
44C22×D283C24136yes—
45C22×D283C24196yescomplemented
46Dic566C24116yescomplemented
47D1132C24196yescomplemented
48D1132C24148yescomplemented
49C22⋊D283C24196yescomplemented
50C2×Dic283C24112yes—
51C4×D283C24196yescomplemented
52C23×C283—212no—
53C23×C283C24118yes—
54C23×C283C2411yescharacteristic
55Q8×C283C24116yescomplemented
56D4×C283C24148yescomplemented
57C2×C4×C283C2416yes—
58C2×C4×C283C24118yes—
59C2×C4×C283C24148yescomplemented
60C22×C283—236no—
61C22×C283H(5,𝔽2)14yescomplemented
62C22×C283C25112yes—
63C22×C283C2513yes—
64C2×D283—272no—
65C2×D283—496no—
66C2×D283C25124yes—
67C4×C283C2514yes—
68C4×C283C25112yes—
69Dic283C2518yes—
70C2×C283—212no—
71C2×C283C2×H(5,𝔽2)16yescomplemented
72C2×C283C2611yescharacteristic
73D283—224no—
74C283C22×H(5,𝔽2)11yescharacteristic, complemented, Sylow
75C22×H(5,𝔽2)—2831nomaximal, Sylow
76C2×H(5,𝔽2)—28348no—
77C22×#41—2832no—
78C22×#41—2833no—
79C22×#41D28311yescharacteristic, complemented
80C23×D4—2836no—
81C23×D4—2833no—
82C25—2836no—
83H(5,𝔽2)—283256no—
84C2×#41—28348no—
85C2×#41—28372no—
86C2×#41C2×D283124yescomplemented
87C22×Q8—2831no—
88C22×Q8C2×D28311yescharacteristic, complemented
89C22×D4—2836no—
90C22×D4—283144no—
91C22×D4—2836no—
92C22×D4—2833no—
93C22×D4—28372no—
94C22×D4C2×D28313yescomplemented
95C23×C4—2836no—
96C23×C4C2×D28313yescomplemented
97C24—2836no—
98C24—28372no—
99C24—113224no—
100C24C22×D28313yes—
101#41—283128no—
102#41—283192no—
103#41C22×D283164yescomplemented
104C2×Q8—28312no—
105C2×Q8C22×D283112yescomplemented
106C2×D4—28372no—
107C2×D4—283384no—
108C2×D4—28372no—
109C2×D4—28336no—
110C2×D4—283192no—
111C2×D4C22×D283136yescomplemented
112C22×C4—2832no—
113C22×C4—28372no—
114C22×C4C22×D28313yes—
115C22×C4C22×D28311yescharacteristic
116C22×C4C22×D283136yescomplemented
117C23—212no—
118C23—28336no—
119C23—28396no—
120C23—56624no—
121C23—1132144no—
122C23C23×D283118yes—
123C23C23×D28311yescharacteristic
124Q8—28316no—
125Q8C23×D283116yescomplemented
126D4—28396no—
127D4—28396no—
128D4—28348no—
129D4C23×D283148yescomplemented
130C2×C4—28312no—
131C2×C4—28396no—
132C2×C4C23×D283118yes—
133C2×C4C23×D28316yes—
134C2×C4C23×D283148yescomplemented
135C22—236no—
136C22—28324no—
137C22—56672no—
138C22—113296no—
139C22#2258365614yesdirect product factor
140C22C24×D283112yes—
141C22C24×D28313yes—
142C4—2838no—
143C4C24×D283112yes—
144C4C24×D28314yes—
145C2—212no—
146C2—56624no—
147C2C2×#2258365616yesdirect product factor
148C2C25×D28311yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC2×C283C26
FrattiniC2C25×D283
FittingC22×#41×C283C2
socleC23×C283C24
hypercenterC22×#41D283
hypocenterC283C22×H(5,𝔽2)
LCSG ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#22583656C2direct (N × H)
2. C22×#17985393C2semidirect
3. C22×#17985392C2semidirect
4. C23×D1132C2semidirect
5. C22×D4×D283C2semidirect
6. C22×#41×C283C2semidirect
7. C24×D283C22semidirect
8. #22583656C22direct (N × H)
9. C2×#17985393C22semidirect
10. C2×#17985392C22semidirect
11. C22×Dic566C22semidirect
12. C22×D1132C22semidirect
13. C22×D1132C22semidirect
14. C22×D1132C22semidirect
15. C22×C22⋊D283C22semidirect
16. C2×D4×D283C22semidirect
17. C22×C4×D283C22semidirect
18. C2×#41×C283C22semidirect
19. C22×Q8×C283C22semidirect
20. C22×D4×C283C22semidirect
21. C23×C4×C283C22semidirect
24. C23×D283C23semidirect
25. #17985393C23semidirect
26. #17985392C23semidirect
27. C2×Dic566C23semidirect
28. C2×D1132C23semidirect
29. C2×D1132C23semidirect
30. C2×D1132C23semidirect
31. C2×C22⋊D283C23semidirect
32. D4×D283C23semidirect
34. C2×C4×D283C23semidirect
36. #41×C283C23semidirect
37. C2×Q8×C283C23semidirect
38. C2×D4×C283C23semidirect
41. C22×C4×C283C23semidirect
45. C22×D283C24semidirect
46. Dic566C24semidirect
47. D1132C24semidirect
48. D1132C24semidirect
49. C22⋊D283C24semidirect
51. C4×D283C24semidirect
55. Q8×C283C24semidirect
56. D4×C283C24semidirect
59. C2×C4×C283C24semidirect
61. C22×C283H(5,𝔽2)semidirect
71. C2×C283C2×H(5,𝔽2)semidirect
74. C283C22×H(5,𝔽2)semidirect
79. C22×#41D283semidirect
86. C2×#41C2×D283semidirect
88. C22×Q8C2×D283semidirect
94. C22×D4C2×D283semidirect
96. C23×C4C2×D283semidirect
103. #41C22×D283semidirect
105. C2×Q8C22×D283semidirect
111. C2×D4C22×D283semidirect
116. C22×C4C22×D283semidirect
125. Q8C23×D283semidirect
129. D4C23×D283semidirect
134. C2×C4C23×D283semidirect
139. C22#22583656direct (N × H)
147. C2C2×#22583656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225836562
C22×#179853932
C22×#179853922
C23×D11322
C22×D4×D2832
C22×#41×C2832
C22×H(5,𝔽2)283