Finite Group Databasebeta

← #585×D89 #26035058

Subgroups — #585×D89 #26035058

Order 11392.

5956 conjugacy classes of subgroups; only the 3203 normal subgroups are shown.

normal subgroups only

This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3203 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
1#19152435C216yesmaximal, complemented
2#19152434C2115yesmaximal, complemented
3#19152433C2110yesmaximal, complemented
42−1+4×D89C216yesmaximal, complemented
5H(5,𝔽2)×D89C2110yesmaximal, complemented
6C2×#41×D89C2115yesmaximal, complemented
7#585×C89C211yesmaximal, characteristic, complemented
8#15668060C22130yescomplemented
9#15668059C22160yescomplemented
10#15668058C22160yescomplemented
11#15668057C22190yescomplemented
12C2×#13083575C22115yescomplemented
13C2×#13083574C22145yescomplemented
14C2×#13083573C22145yescomplemented
15#41×D89C22120yescomplemented
16#41×D89C22160yescomplemented
17#41×D89C22160yescomplemented
18#41×D89C22160yescomplemented
19C2×Q8×D89C22115yescomplemented
20C2×D4×D89C22145yescomplemented
21C22×C4×D89C22115yescomplemented
222−1+4×C89C2216yescomplemented
23H(5,𝔽2)×C89C22110yescomplemented
24C2×#41×C89C22115yescomplemented
25C23×D89C23115yes—
26#13083575C23120yescomplemented
27#13083575C23160yescomplemented
28#13083574C23160yescomplemented
29#13083574C231180yescomplemented
30#13083573C23160yescomplemented
31#13083573C231180yescomplemented
32C2×Dic178C23145yescomplemented
33Q8×D89C23120yes—
34Q8×D89C23160yescomplemented
35C2×D356C23145yescomplemented
36C2×C22⋊D89C23190yescomplemented
37D4×D89C23160yes—
38D4×D89C231180yescomplemented
39C22×Dic89C23115yescomplemented
40C2×C4×D89C23115yes—
41C2×C4×D89C23145yes—
42C2×C4×D89C23145yescomplemented
43C2×C4×D89C23145yescomplemented
44#41×C89C23120yescomplemented
45#41×C89C23160yescomplemented
46C2×Q8×C89C23115yescomplemented
47C2×D4×C89C23145yescomplemented
48C22×C4×C89C23115yescomplemented
49C23×C89C24115yes—
50C22×D89—430no—
51C22×D89C24115yes—
52C22×D89C24145yes—
53Q8×C89C24120yes—
54D4×C89C24160yes—
55C2×C4×C89C24115yes—
56C2×C4×C89C24145yes—
57C22⋊D89C241120yes—
58C2×Dic89C24115yes—
59C2×Dic89C24145yes—
60D356C24160yes—
61C4×D89C2411yescharacteristic
62C4×D89C24115yes—
63C4×D89C24115yes—
64C4×D89C24115yes—
65C4×D89C24190yes—
66Dic178C24160yes—
67C22×C89—415no—
68C22×C89C25115yes—
69C2×D89—230no—
70C2×D89—445no—
71C2×D89C25115yes—
72C2×D89C2511yescharacteristic
73C4×C89C25115yes—
74C4×C89C2511yescharacteristic
75Dic89C25115yes—
76Dic89C2511yescharacteristic
77C2×C89—215no—
78C2×C89C2611yescharacteristic
79D89—215no—
80D89#58512yesdirect product factor
81C2×#585—891nomaximal, Sylow
82C89C2×#58511yescharacteristic, complemented, Sylow
83#585—896no—
84#585—8910no—
85#585—8915no—
86#585D8911yescharacteristic, direct product factor
87C2×2−1+4—896no—
88C2×H(5,𝔽2)—8910no—
89C22×#41—8915no—
902−1+4—8960no—
912−1+4—8930no—
922−1+4C2×D8916yescomplemented
93H(5,𝔽2)—8960no—
94H(5,𝔽2)—8990no—
95H(5,𝔽2)C2×D89110yescomplemented
96C2×#41—8920no—
97C2×#41—8960no—
98C2×#41—8960no—
99C2×#41—8960no—
100C2×#41—8915no—
101C2×#41—8945no—
102C2×#41—8945no—
103C2×#41C2×D89115yescomplemented
104C22×Q8—8915no—
105C22×D4—8945no—
106C23×C4—8915no—
107C24—8915no—
108#41—8920no—
109#41—8960no—
110#41—8960no—
111#41—89180no—
112#41—8960no—
113#41—89180no—
114#41C22×D89120yescomplemented
115#41C22×D89160yescomplemented
116C2×Q8—8920no—
117C2×Q8—8960no—
118C2×Q8—8945no—
119C2×Q8C22×D89115yescomplemented
120C2×D4—8990no—
121C2×D4—8960no—
122C2×D4—89180no—
123C2×D4—8945no—
124C2×D4C22×D89145yescomplemented
125C22×C4—8915no—
126C22×C4—8915no—
127C22×C4—8945no—
128C22×C4—8945no—
129C22×C4—8945no—
130C22×C4C22×D89115yescomplemented
131C23—8945no—
132C23—8915no—
133C23—35630no—
134C23C23×D89115yes—
135Q8—8960no—
136Q8C23×D89120yes—
137D4—89120no—
138D4—8960no—
139D4C23×D89160yes—
140C2×C4—8915no—
141C2×C4—8945no—
142C2×C4—8915no—
143C2×C4—8915no—
144C2×C4—8990no—
145C2×C4—891no—
146C2×C4—8915no—
147C2×C4C23×D89145yes—
148C2×C4C23×D89115yes—
149C22—415no—
150C22—891no—
151C22—8915no—
152C22—35645no—
153C22—17830no—
154C22C24×D89115yes—
155C4—891no—
156C4—8915no—
157C4C24×D89115yes—
158C4C24×D8911yescharacteristic
159C2—215no—
160C2—892no—
161C2—17815no—
162C2C25×D8911yescharacteristic
subgroupG/H
centerC4C24×D89
commutator, socle, cosocleC2×C89C26
FrattiniC2C25×D89
Fitting#585×C89C2
hypercenter#585D89
hypocenterC89C2×#585
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #19152435C2semidirect
2. #19152434C2semidirect
3. #19152433C2semidirect
4. 2−1+4×D89C2semidirect
5. H(5,𝔽2)×D89C2semidirect
6. C2×#41×D89C2semidirect
7. #585×C89C2semidirect
8. #15668060C22semidirect
9. #15668059C22semidirect
10. #15668058C22semidirect
11. #15668057C22semidirect
12. C2×#13083575C22semidirect
13. C2×#13083574C22semidirect
14. C2×#13083573C22semidirect
15. #41×D89C22semidirect
16. #41×D89C22semidirect
17. #41×D89C22semidirect
18. #41×D89C22semidirect
19. C2×Q8×D89C22semidirect
20. C2×D4×D89C22semidirect
21. C22×C4×D89C22semidirect
22. 2−1+4×C89C22semidirect
23. H(5,𝔽2)×C89C22semidirect
24. C2×#41×C89C22semidirect
26. #13083575C23semidirect
27. #13083575C23semidirect
28. #13083574C23semidirect
29. #13083574C23semidirect
30. #13083573C23semidirect
31. #13083573C23semidirect
32. C2×Dic178C23semidirect
34. Q8×D89C23semidirect
35. C2×D356C23semidirect
36. C2×C22⋊D89C23semidirect
38. D4×D89C23semidirect
39. C22×Dic89C23semidirect
42. C2×C4×D89C23semidirect
43. C2×C4×D89C23semidirect
44. #41×C89C23semidirect
45. #41×C89C23semidirect
46. C2×Q8×C89C23semidirect
47. C2×D4×C89C23semidirect
48. C22×C4×C89C23semidirect
80. D89#585direct (N × H)
82. C89C2×#585semidirect
86. #585D89direct (N × H)
92. 2−1+4C2×D89semidirect
95. H(5,𝔽2)C2×D89semidirect
103. C2×#41C2×D89semidirect
114. #41C22×D89semidirect
115. #41C22×D89semidirect
119. C2×Q8C22×D89semidirect
124. C2×D4C22×D89semidirect
130. C22×C4C22×D89semidirect

Maximal subgroups

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

subgroupindex
#191524352
#191524342
#191524332
2−1+4×D892
H(5,𝔽2)×D892
C2×#41×D892
#585×C892
C2×#58589