Finite Group Databasebeta

← #26035063

Subgroups — #26035063

Order 11392.

5992 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.

normal subgroups only

This group has 5992 conjugacy classes of subgroups — too many to draw. Only its 3201 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#19152435C2112yesmaximal, complemented
2#19152434C2115yesmaximal, complemented
3C2×#15668058C2115yesmaximal, complemented
4H(5,𝔽2)×D89C2120yesmaximal, complemented
5#585×C89C211yesmaximal, characteristic, complemented
6#15668060C22130yescomplemented
7#15668059C22120yescomplemented
8#15668058C221120yescomplemented
9#15668058C22160yescomplemented
10#15668057C22190yescomplemented
11C2×#13083575C22130yescomplemented
12C2×#13083574C22145yescomplemented
13#41×D89C221120yescomplemented
14C22×D356C22115yescomplemented
15C2×D4×D89C22190yescomplemented
162−1+4×C89C2216yescomplemented
17H(5,𝔽2)×C89C22110yescomplemented
18C2×#41×C89C22115yescomplemented
19C23×D89C23130yescomplemented
20#13083575C231120yescomplemented
21#13083574C231180yescomplemented
22#13083574C23160yescomplemented
23#13083573C231120yescomplemented
24C2×Dic178C23115yescomplemented
25Q8×D89C23140yescomplemented
26C2×D356C23190yescomplemented
27C2×D356C23145yescomplemented
28C2×C22⋊D89C23190yescomplemented
29D4×D89C231360yescomplemented
30C2×C4×D89C23190yescomplemented
31#41×C89C23160yescomplemented
32#41×C89C23120yescomplemented
33C2×Q8×C89C23115yescomplemented
34C2×D4×C89C23145yescomplemented
35C22×C4×C89C23115yescomplemented
36C23×C89C24115yes—
37C22×D89—830no—
38C22×D89C24190yes—
39Q8×C89C24120yes—
40D4×C89C24160yes—
41C2×C4×C89C24115yes—
42C2×C4×C89C24145yes—
43C22⋊D89C241120yes—
44C2×Dic89C24130yes—
45D356C24190yes—
46D356C24110yes—
47C4×D89C241120yes—
48Dic178C24130yes—
49Dic178C2416yes—
50C22×C89—415no—
51C22×C89C25115yes—
52C2×D89—490no—
53C2×D89C25120yes—
54C4×C89C2511yescharacteristic
55C4×C89C25115yes—
56Dic89C25112yes—
57C2×C89—215no—
58C2×C89C2611yescharacteristic
59D89—220no—
60H(7,𝔽2)—891nomaximal, Sylow
61C89H(7,𝔽2)11yescharacteristic, complemented, Sylow
62#585—8912no—
63#585—8915no—
64#585D8911yescharacteristic, complemented
65C2×H(5,𝔽2)—8920no—
66C2×H(5,𝔽2)—8915no—
672−1+4—8920no—
682−1+4—8930no—
692−1+4C2×D8916yescomplemented
70H(5,𝔽2)—89120no—
71H(5,𝔽2)—8960no—
72H(5,𝔽2)—8990no—
73H(5,𝔽2)C2×D89110yescomplemented
74C2×#41—89120no—
75C2×#41—8930no—
76C2×#41—8945no—
77C2×#41C2×D89115yescomplemented
78C22×D4—8990no—
79C22×D4—8915no—
80C24—8930no—
81#41—89120no—
82#41—89120no—
83#41—89180no—
84#41—8960no—
85#41C22×D89160yescomplemented
86#41C22×D89120yescomplemented
87C2×Q8—8940no—
88C2×Q8—8915no—
89C2×Q8C22×D89115yescomplemented
90C2×D4—8990no—
91C2×D4—89360no—
92C2×D4—8990no—
93C2×D4—8945no—
94C2×D4C22×D89145yescomplemented
95C22×C4—8990no—
96C22×C4C22×D89115yescomplemented
97C23—8990no—
98C23—71230no—
99C23C23×D89115yes—
100Q8—8930no—
101Q8—896no—
102Q8C23×D89120yes—
103D4—89120no—
104D4—8990no—
105D4—8910no—
106D4C23×D89160yes—
107C2×C4—8930no—
108C2×C4—89120no—
109C2×C4C23×D89145yes—
110C2×C4C23×D89115yes—
111C22—415no—
112C22—8920no—
113C22—35690no—
114C22C24×D89115yes—
115C4—8912no—
116C4C24×D89115yes—
117C4C24×D8911yescharacteristic
118C2—215no—
119C2—17820no—
120C2C25×D8911yescharacteristic
subgroupG/H
center, FrattiniC2C25×D89
commutator, socle, cosocleC2×C89C26
Fitting#585×C89C2
hypercenter#585D89
hypocenterC89H(7,𝔽2)
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #19152435C2semidirect
2. #19152434C2semidirect
3. C2×#15668058C2semidirect
4. H(5,𝔽2)×D89C2semidirect
5. #585×C89C2semidirect
6. #15668060C22semidirect
7. #15668059C22semidirect
8. #15668058C22semidirect
9. #15668058C22semidirect
10. #15668057C22semidirect
11. C2×#13083575C22semidirect
12. C2×#13083574C22semidirect
13. #41×D89C22semidirect
14. C22×D356C22semidirect
15. C2×D4×D89C22semidirect
16. 2−1+4×C89C22semidirect
17. H(5,𝔽2)×C89C22semidirect
18. C2×#41×C89C22semidirect
19. C23×D89C23semidirect
20. #13083575C23semidirect
21. #13083574C23semidirect
22. #13083574C23semidirect
23. #13083573C23semidirect
24. C2×Dic178C23semidirect
25. Q8×D89C23semidirect
26. C2×D356C23semidirect
27. C2×D356C23semidirect
28. C2×C22⋊D89C23semidirect
29. D4×D89C23semidirect
30. C2×C4×D89C23semidirect
31. #41×C89C23semidirect
32. #41×C89C23semidirect
33. C2×Q8×C89C23semidirect
34. C2×D4×C89C23semidirect
35. C22×C4×C89C23semidirect
61. C89H(7,𝔽2)semidirect
64. #585D89semidirect
69. 2−1+4C2×D89semidirect
73. H(5,𝔽2)C2×D89semidirect
77. C2×#41C2×D89semidirect
85. #41C22×D89semidirect
86. #41C22×D89semidirect
89. C2×Q8C22×D89semidirect
94. C2×D4C22×D89semidirect
96. 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
C2×#156680582
H(5,𝔽2)×D892
#585×C892
H(7,𝔽2)89