Finite Group Databasebeta

← #35229347

Subgroups — #35229347

Order 20864.

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#23782502C2112yesmaximal, complemented
2#23782501C2115yesmaximal, complemented
3C2×#19104781C2115yesmaximal, complemented
4H(5,𝔽2)×D163C2120yesmaximal, complemented
5#585×C163C211yesmaximal, characteristic, complemented
6#19104783C22130yescomplemented
7#19104782C22120yescomplemented
8#19104781C221120yescomplemented
9#19104781C22160yescomplemented
10#19104780C22190yescomplemented
11C2×#14579700C22130yescomplemented
12C2×#14579699C22145yescomplemented
13#41×D163C221120yescomplemented
14C22×D652C22115yescomplemented
15C2×D4×D163C22190yescomplemented
162−1+4×C163C2216yescomplemented
17H(5,𝔽2)×C163C22110yescomplemented
18C2×#41×C163C22115yescomplemented
19C23×D163C23130yescomplemented
20#14579700C231120yescomplemented
21#14579699C231180yescomplemented
22#14579699C23160yescomplemented
23#14579698C231120yescomplemented
24C2×Dic326C23115yescomplemented
25Q8×D163C23140yescomplemented
26C2×D652C23190yescomplemented
27C2×D652C23145yescomplemented
28C2×C22⋊D163C23190yescomplemented
29D4×D163C231360yescomplemented
30C2×C4×D163C23190yescomplemented
31#41×C163C23160yescomplemented
32#41×C163C23120yescomplemented
33C2×Q8×C163C23115yescomplemented
34C2×D4×C163C23145yescomplemented
35C22×C4×C163C23115yescomplemented
36C22×D163—830no—
37C22×D163C24190yes—
38Dic326C24130yes—
39Dic326C2416yes—
40D652C24190yes—
41D652C24110yes—
42C22⋊D163C241120yes—
43C2×Dic163C24130yes—
44C4×D163C241120yes—
45C23×C163C24115yes—
46Q8×C163C24120yes—
47D4×C163C24160yes—
48C2×C4×C163C24115yes—
49C2×C4×C163C24145yes—
50C22×C163—415no—
51C22×C163C25115yes—
52C2×D163—490no—
53C2×D163C25120yes—
54C4×C163C2511yescharacteristic
55C4×C163C25115yes—
56Dic163C25112yes—
57C2×C163—215no—
58C2×C163C2611yescharacteristic
59D163—220no—
60C163H(7,𝔽2)11yescharacteristic, complemented, Sylow
61H(7,𝔽2)—1631nomaximal, Sylow
62#585—16312no—
63#585—16315no—
64#585D16311yescharacteristic, complemented
65C2×H(5,𝔽2)—16320no—
66C2×H(5,𝔽2)—16315no—
672−1+4—16320no—
682−1+4—16330no—
692−1+4C2×D16316yescomplemented
70H(5,𝔽2)—163120no—
71H(5,𝔽2)—16360no—
72H(5,𝔽2)—16390no—
73H(5,𝔽2)C2×D163110yescomplemented
74C2×#41—163120no—
75C2×#41—16330no—
76C2×#41—16345no—
77C2×#41C2×D163115yescomplemented
78C22×D4—16390no—
79C22×D4—16315no—
80C24—16330no—
81#41—163120no—
82#41—163120no—
83#41—163180no—
84#41—16360no—
85#41C22×D163160yescomplemented
86#41C22×D163120yescomplemented
87C2×Q8—16340no—
88C2×Q8—16315no—
89C2×Q8C22×D163115yescomplemented
90C2×D4—16390no—
91C2×D4—163360no—
92C2×D4—16390no—
93C2×D4—16345no—
94C2×D4C22×D163145yescomplemented
95C22×C4—16390no—
96C22×C4C22×D163115yescomplemented
97C23—130430no—
98C23—16390no—
99C23C23×D163115yes—
100Q8—16330no—
101Q8—1636no—
102Q8C23×D163120yes—
103D4—163120no—
104D4—16390no—
105D4—16310no—
106D4C23×D163160yes—
107C2×C4—16330no—
108C2×C4—163120no—
109C2×C4C23×D163145yes—
110C2×C4C23×D163115yes—
111C22—415no—
112C22—65290no—
113C22—16320no—
114C22C24×D163115yes—
115C4—16312no—
116C4C24×D163115yes—
117C4C24×D16311yescharacteristic
118C2—215no—
119C2—32620no—
120C2C25×D16311yescharacteristic
subgroupG/H
center, FrattiniC2C25×D163
commutator, socle, cosocleC2×C163C26
Fitting#585×C163C2
hypercenter#585D163
hypocenterC163H(7,𝔽2)
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #23782502C2semidirect
2. #23782501C2semidirect
3. C2×#19104781C2semidirect
4. H(5,𝔽2)×D163C2semidirect
5. #585×C163C2semidirect
6. #19104783C22semidirect
7. #19104782C22semidirect
8. #19104781C22semidirect
9. #19104781C22semidirect
10. #19104780C22semidirect
11. C2×#14579700C22semidirect
12. C2×#14579699C22semidirect
13. #41×D163C22semidirect
14. C22×D652C22semidirect
15. C2×D4×D163C22semidirect
16. 2−1+4×C163C22semidirect
17. H(5,𝔽2)×C163C22semidirect
18. C2×#41×C163C22semidirect
19. C23×D163C23semidirect
20. #14579700C23semidirect
21. #14579699C23semidirect
22. #14579699C23semidirect
23. #14579698C23semidirect
24. C2×Dic326C23semidirect
25. Q8×D163C23semidirect
26. C2×D652C23semidirect
27. C2×D652C23semidirect
28. C2×C22⋊D163C23semidirect
29. D4×D163C23semidirect
30. C2×C4×D163C23semidirect
31. #41×C163C23semidirect
32. #41×C163C23semidirect
33. C2×Q8×C163C23semidirect
34. C2×D4×C163C23semidirect
35. C22×C4×C163C23semidirect
60. C163H(7,𝔽2)semidirect
64. #585D163semidirect
69. 2−1+4C2×D163semidirect
73. H(5,𝔽2)C2×D163semidirect
77. C2×#41C2×D163semidirect
85. #41C22×D163semidirect
86. #41C22×D163semidirect
89. C2×Q8C22×D163semidirect
94. C2×D4C22×D163semidirect
96. C22×C4C22×D163semidirect

Maximal subgroups

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

subgroupindex
#237825022
#237825012
C2×#191047812
H(5,𝔽2)×D1632
#585×C1632
H(7,𝔽2)163