Finite Group Databasebeta

← #46825696

Subgroups — #46825696

Order 34432.

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#31771442C2112yesmaximal, complemented
2#31771441C2115yesmaximal, complemented
3C2×#22575499C2115yesmaximal, complemented
4H(5,𝔽2)×D269C2120yesmaximal, complemented
5#585×C269C211yesmaximal, characteristic, complemented
6#22575501C22130yescomplemented
7#22575500C22120yescomplemented
8#22575499C221120yescomplemented
9#22575499C22160yescomplemented
10#22575498C22190yescomplemented
11C2×#16864403C22130yescomplemented
12C2×#16864402C22145yescomplemented
13#41×D269C221120yescomplemented
14C22×D1076C22115yescomplemented
15C2×D4×D269C22190yescomplemented
162−1+4×C269C2216yescomplemented
17H(5,𝔽2)×C269C22110yescomplemented
18C2×#41×C269C22115yescomplemented
19C23×D269C23130yescomplemented
20#16864403C231120yescomplemented
21#16864402C231180yescomplemented
22#16864402C23160yescomplemented
23#16864401C231120yescomplemented
24C2×Dic538C23115yescomplemented
25Q8×D269C23140yescomplemented
26C2×D1076C23190yescomplemented
27C2×D1076C23145yescomplemented
28C2×C22⋊D269C23190yescomplemented
29D4×D269C231360yescomplemented
30C2×C4×D269C23190yescomplemented
31#41×C269C23160yescomplemented
32#41×C269C23120yescomplemented
33C2×Q8×C269C23115yescomplemented
34C2×D4×C269C23145yescomplemented
35C22×C4×C269C23115yescomplemented
36C22×D269—830no—
37C22×D269C24190yes—
38Dic538C24130yes—
39Dic538C2416yes—
40D1076C24190yes—
41D1076C24110yes—
42C22⋊D269C241120yes—
43C2×Dic269C24130yes—
44C4×D269C241120yes—
45C23×C269C24115yes—
46Q8×C269C24120yes—
47D4×C269C24160yes—
48C2×C4×C269C24115yes—
49C2×C4×C269C24145yes—
50C22×C269—415no—
51C22×C269C25115yes—
52C2×D269—490no—
53C2×D269C25120yes—
54C4×C269C2511yescharacteristic
55C4×C269C25115yes—
56Dic269C25112yes—
57C2×C269—215no—
58C2×C269C2611yescharacteristic
59D269—220no—
60C269H(7,𝔽2)11yescharacteristic, complemented, Sylow
61H(7,𝔽2)—2691nomaximal, Sylow
62#585—26912no—
63#585—26915no—
64#585D26911yescharacteristic, complemented
65C2×H(5,𝔽2)—26920no—
66C2×H(5,𝔽2)—26915no—
672−1+4—26920no—
682−1+4—26930no—
692−1+4C2×D26916yescomplemented
70H(5,𝔽2)—269120no—
71H(5,𝔽2)—26960no—
72H(5,𝔽2)—26990no—
73H(5,𝔽2)C2×D269110yescomplemented
74C2×#41—269120no—
75C2×#41—26930no—
76C2×#41—26945no—
77C2×#41C2×D269115yescomplemented
78C22×D4—26990no—
79C22×D4—26915no—
80C24—26930no—
81#41—269120no—
82#41—269120no—
83#41—269180no—
84#41—26960no—
85#41C22×D269160yescomplemented
86#41C22×D269120yescomplemented
87C2×Q8—26940no—
88C2×Q8—26915no—
89C2×Q8C22×D269115yescomplemented
90C2×D4—26990no—
91C2×D4—269360no—
92C2×D4—26990no—
93C2×D4—26945no—
94C2×D4C22×D269145yescomplemented
95C22×C4—26990no—
96C22×C4C22×D269115yescomplemented
97C23—26990no—
98C23—215230no—
99C23C23×D269115yes—
100Q8—26930no—
101Q8—2696no—
102Q8C23×D269120yes—
103D4—269120no—
104D4—26990no—
105D4—26910no—
106D4C23×D269160yes—
107C2×C4—26930no—
108C2×C4—269120no—
109C2×C4C23×D269145yes—
110C2×C4C23×D269115yes—
111C22—415no—
112C22—26920no—
113C22—107690no—
114C22C24×D269115yes—
115C4—26912no—
116C4C24×D269115yes—
117C4C24×D26911yescharacteristic
118C2—215no—
119C2—53820no—
120C2C25×D26911yescharacteristic
subgroupG/H
center, FrattiniC2C25×D269
commutator, socle, cosocleC2×C269C26
Fitting#585×C269C2
hypercenter#585D269
hypocenterC269H(7,𝔽2)
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #31771442C2semidirect
2. #31771441C2semidirect
3. C2×#22575499C2semidirect
4. H(5,𝔽2)×D269C2semidirect
5. #585×C269C2semidirect
6. #22575501C22semidirect
7. #22575500C22semidirect
8. #22575499C22semidirect
9. #22575499C22semidirect
10. #22575498C22semidirect
11. C2×#16864403C22semidirect
12. C2×#16864402C22semidirect
13. #41×D269C22semidirect
14. C22×D1076C22semidirect
15. C2×D4×D269C22semidirect
16. 2−1+4×C269C22semidirect
17. H(5,𝔽2)×C269C22semidirect
18. C2×#41×C269C22semidirect
19. C23×D269C23semidirect
20. #16864403C23semidirect
21. #16864402C23semidirect
22. #16864402C23semidirect
23. #16864401C23semidirect
24. C2×Dic538C23semidirect
25. Q8×D269C23semidirect
26. C2×D1076C23semidirect
27. C2×D1076C23semidirect
28. C2×C22⋊D269C23semidirect
29. D4×D269C23semidirect
30. C2×C4×D269C23semidirect
31. #41×C269C23semidirect
32. #41×C269C23semidirect
33. C2×Q8×C269C23semidirect
34. C2×D4×C269C23semidirect
35. C22×C4×C269C23semidirect
60. C269H(7,𝔽2)semidirect
64. #585D269semidirect
69. 2−1+4C2×D269semidirect
73. H(5,𝔽2)C2×D269semidirect
77. C2×#41C2×D269semidirect
85. #41C22×D269semidirect
86. #41C22×D269semidirect
89. C2×Q8C22×D269semidirect
94. C2×D4C22×D269semidirect
96. C22×C4C22×D269semidirect

Maximal subgroups

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

subgroupindex
#317714422
#317714412
C2×#225754992
H(5,𝔽2)×D2692
#585×C2692
H(7,𝔽2)269