Finite Group Databasebeta

← #31821215

Subgroups — #31821215

Order 17792.

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#22581790C2112yesmaximal, complemented
2#22581789C2115yesmaximal, complemented
3C2×#17984888C2115yesmaximal, complemented
4H(5,𝔽2)×D139C2120yesmaximal, complemented
5#585×C139C211yesmaximal, characteristic, complemented
6#17984890C22130yescomplemented
7#17984889C22120yescomplemented
8#17984888C221120yescomplemented
9#17984888C22160yescomplemented
10#17984887C22190yescomplemented
11C2×#14555786C22130yescomplemented
12C2×#14555785C22145yescomplemented
13#41×D139C221120yescomplemented
14C22×D556C22115yescomplemented
15C2×D4×D139C22190yescomplemented
162−1+4×C139C2216yescomplemented
17H(5,𝔽2)×C139C22110yescomplemented
18C2×#41×C139C22115yescomplemented
19C23×D139C23130yescomplemented
20#14555786C231120yescomplemented
21#14555785C231180yescomplemented
22#14555785C23160yescomplemented
23#14555784C231120yescomplemented
24C2×Dic278C23115yescomplemented
25Q8×D139C23140yescomplemented
26C2×D556C23190yescomplemented
27C2×D556C23145yescomplemented
28C2×C22⋊D139C23190yescomplemented
29D4×D139C231360yescomplemented
30C2×C4×D139C23190yescomplemented
31#41×C139C23160yescomplemented
32#41×C139C23120yescomplemented
33C2×Q8×C139C23115yescomplemented
34C2×D4×C139C23145yescomplemented
35C22×C4×C139C23115yescomplemented
36C22×D139—830no—
37C22×D139C24190yes—
38Dic278C24130yes—
39Dic278C2416yes—
40D556C24190yes—
41D556C24110yes—
42C22⋊D139C241120yes—
43C2×Dic139C24130yes—
44C4×D139C241120yes—
45C23×C139C24115yes—
46Q8×C139C24120yes—
47D4×C139C24160yes—
48C2×C4×C139C24115yes—
49C2×C4×C139C24145yes—
50C22×C139—415no—
51C22×C139C25115yes—
52C2×D139—490no—
53C2×D139C25120yes—
54C4×C139C2511yescharacteristic
55C4×C139C25115yes—
56Dic139C25112yes—
57C2×C139—215no—
58C2×C139C2611yescharacteristic
59D139—220no—
60C139H(7,𝔽2)11yescharacteristic, complemented, Sylow
61H(7,𝔽2)—1391nomaximal, Sylow
62#585—13912no—
63#585—13915no—
64#585D13911yescharacteristic, complemented
65C2×H(5,𝔽2)—13920no—
66C2×H(5,𝔽2)—13915no—
672−1+4—13920no—
682−1+4—13930no—
692−1+4C2×D13916yescomplemented
70H(5,𝔽2)—139120no—
71H(5,𝔽2)—13960no—
72H(5,𝔽2)—13990no—
73H(5,𝔽2)C2×D139110yescomplemented
74C2×#41—139120no—
75C2×#41—13930no—
76C2×#41—13945no—
77C2×#41C2×D139115yescomplemented
78C22×D4—13990no—
79C22×D4—13915no—
80C24—13930no—
81#41—139120no—
82#41—139120no—
83#41—139180no—
84#41—13960no—
85#41C22×D139160yescomplemented
86#41C22×D139120yescomplemented
87C2×Q8—13940no—
88C2×Q8—13915no—
89C2×Q8C22×D139115yescomplemented
90C2×D4—13990no—
91C2×D4—139360no—
92C2×D4—13990no—
93C2×D4—13945no—
94C2×D4C22×D139145yescomplemented
95C22×C4—13990no—
96C22×C4C22×D139115yescomplemented
97C23—111230no—
98C23—13990no—
99C23C23×D139115yes—
100Q8—13930no—
101Q8—1396no—
102Q8C23×D139120yes—
103D4—139120no—
104D4—13990no—
105D4—13910no—
106D4C23×D139160yes—
107C2×C4—13930no—
108C2×C4—139120no—
109C2×C4C23×D139145yes—
110C2×C4C23×D139115yes—
111C22—415no—
112C22—55690no—
113C22—13920no—
114C22C24×D139115yes—
115C4—13912no—
116C4C24×D139115yes—
117C4C24×D13911yescharacteristic
118C2—215no—
119C2—27820no—
120C2C25×D13911yescharacteristic
subgroupG/H
center, FrattiniC2C25×D139
commutator, socle, cosocleC2×C139C26
Fitting#585×C139C2
hypercenter#585D139
hypocenterC139H(7,𝔽2)
LCSG ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #22581790C2semidirect
2. #22581789C2semidirect
3. C2×#17984888C2semidirect
4. H(5,𝔽2)×D139C2semidirect
5. #585×C139C2semidirect
6. #17984890C22semidirect
7. #17984889C22semidirect
8. #17984888C22semidirect
9. #17984888C22semidirect
10. #17984887C22semidirect
11. C2×#14555786C22semidirect
12. C2×#14555785C22semidirect
13. #41×D139C22semidirect
14. C22×D556C22semidirect
15. C2×D4×D139C22semidirect
16. 2−1+4×C139C22semidirect
17. H(5,𝔽2)×C139C22semidirect
18. C2×#41×C139C22semidirect
19. C23×D139C23semidirect
20. #14555786C23semidirect
21. #14555785C23semidirect
22. #14555785C23semidirect
23. #14555784C23semidirect
24. C2×Dic278C23semidirect
25. Q8×D139C23semidirect
26. C2×D556C23semidirect
27. C2×D556C23semidirect
28. C2×C22⋊D139C23semidirect
29. D4×D139C23semidirect
30. C2×C4×D139C23semidirect
31. #41×C139C23semidirect
32. #41×C139C23semidirect
33. C2×Q8×C139C23semidirect
34. C2×D4×C139C23semidirect
35. C22×C4×C139C23semidirect
60. C139H(7,𝔽2)semidirect
64. #585D139semidirect
69. 2−1+4C2×D139semidirect
73. H(5,𝔽2)C2×D139semidirect
77. C2×#41C2×D139semidirect
85. #41C22×D139semidirect
86. #41C22×D139semidirect
89. C2×Q8C22×D139semidirect
94. C2×D4C22×D139semidirect
96. C22×C4C22×D139semidirect

Maximal subgroups

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

subgroupindex
#225817902
#225817892
C2×#179848882
H(5,𝔽2)×D1392
#585×C1392
H(7,𝔽2)139