Finite Group Databasebeta

← #26010500

Subgroups — #26010500

Order 11008.

59452 conjugacy classes of subgroups; only the 32039 normal subgroups are shown.

normal subgroups only

This group has 59452 conjugacy classes of subgroups — too many to draw. Only its 32039 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#19149407C2127yesmaximal, complemented
2#19149406C2136yesmaximal, complemented
3C2×#14583736C2127yesmaximal, complemented
4#585×D43C2136yesmaximal, complemented
5C43×2−1+6C211yesmaximal, characteristic, complemented
6#14583736C221216yescomplemented
7#14583736C221432yescomplemented
8#14583735C221540yescomplemented
9#14583734C221120yescomplemented
10C2×#13063373C221135yescomplemented
112−1+4×D43C221216yescomplemented
12C2×#13063371C221270yescomplemented
13H(5,𝔽2)×D43C221360yescomplemented
14C22×#10621902C22145yescomplemented
15C2×#41×D43C221270yescomplemented
16C43×#585C22136yescomplemented
17C2×2−1+4×C43C22127yescomplemented
18#13063373C2311080yescomplemented
19#13063372C231720yescomplemented
20#13063371C2312160yescomplemented
21#13063370C2311080yescomplemented
22C2×#10621902C231270yescomplemented
23C2×#10621902C231540yescomplemented
24C2×#10621898C231810yescomplemented
25C2×#10621900C231270yescomplemented
26#41×D43C231720yescomplemented
27#41×D43C2312160yescomplemented
28C2×Q8×D43C231270yescomplemented
29C22×D172C231135yescomplemented
30C2×D4×D43C231810yescomplemented
31C22×C4×D43C231135yescomplemented
322−1+4×C43C231216yescomplemented
33H(5,𝔽2)×C43C231120yescomplemented
34C2×#41×C43C231270yescomplemented
35C22×Q8×C43C23145yescomplemented
36C23×D43C241135yes—
37#41×C43C241720yes—
38C2×Q8×C43C241270yes—
39C2×D4×C43C241270yes—
40C22×C4×C43C241135yes—
41C2×C22⋊D43C241540yes—
42C22×Dic43C24145yes—
43#10621902C241120yes—
44#10621902C2411080yes—
45Q8×D43C241720yes—
46#10621900C241216yes—
47#10621900C2411080yes—
48D4×D43C2412160yes—
49#10621898C2412160yes—
50C2×D172C241810yes—
51C2×C4×D43C241270yes—
52C2×C4×D43C241810yes—
53C2×Dic86C241270yes—
54C23×C43C25145yes—
55C22×D43—8135no—
56C22×D43C251270yes—
57Q8×C43C251120yes—
58D4×C43C251216yes—
59C2×C4×C43C251270yes—
60C22⋊D43C251432yes—
61C2×Dic43C251135yes—
62C2×Dic43C25127yes—
63D172C251360yes—
64C4×D43C25136yes—
65C4×D43C251540yes—
66Dic86C251216yes—
67#63103—431nomaximal, Sylow
68C22×C43—445no—
69C22×C43C26127yes—
70C2×D43—4270no—
71C2×D43C26136yes—
72C4×C43C26136yes—
73Dic43C26127yes—
74Dic43C2611yescharacteristic
752−1+6—4327no—
762−1+6D4311yescharacteristic, complemented
77H(7,𝔽2)—4336no—
78C2×#585—4336no—
79C2×#585—4327no—
80C2×C43—227no—
81C2×C43C2711yescharacteristic
82D43—236no—
83#585—43216no—
84#585—43432no—
85#585—43120no—
86#585—43540no—
87#585C2×D43136yescomplemented
88C2×2−1+4—43216no—
89C2×2−1+4—43135no—
90C2×2−1+4C2×D43127yescomplemented
91C2×H(5,𝔽2)—43360no—
92C2×H(5,𝔽2)—43270no—
93C22×#41—43270no—
94C22×#41—4345no—
95C43#6310311yescharacteristic, complemented, Sylow
962−1+4—43720no—
972−1+4—431080no—
982−1+4C22×D431216yescomplemented
99H(5,𝔽2)—432160no—
100H(5,𝔽2)—431080no—
101H(5,𝔽2)C22×D431120yescomplemented
102C2×#41—43720no—
103C2×#41—432160no—
104C2×#41—43270no—
105C2×#41—43540no—
106C2×#41—43270no—
107C2×#41—43810no—
108C2×#41C22×D431270yescomplemented
109C22×Q8—43270no—
110C22×Q8C22×D43145yescomplemented
111C22×D4—43810no—
112C22×D4—43135no—
113C23×C4—43135no—
114C24—43135no—
115#41—43120no—
116#41—431080no—
117#41—43216no—
118#41—431080no—
119#41—432160no—
120#41C23×D431720yes—
121C2×Q8—43720no—
122C2×Q8—43270no—
123C2×Q8C23×D431270yes—
124C2×D4—43540no—
125C2×D4—432160no—
126C2×D4—43810no—
127C2×D4C23×D431270yes—
128C22×C4—4345no—
129C22×C4—43270no—
130C22×C4—43810no—
131C22×C4C23×D431135yes—
132C23—43270no—
133C23—344135no—
134C23C24×D43145yes—
135Q8—43216no—
136Q8C24×D431120yes—
137D4—43432no—
138D4—43360no—
139D4C24×D431216yes—
140C2×C4—4327no—
141C2×C4—43135no—
142C2×C4—4336no—
143C2×C4—43540no—
144C2×C4C24×D431270yes—
145C22—445no—
146C22—4336no—
147C22—172270no—
148C22C25×D43127yes—
149C4—431no—
150C4—4327no—
151C4C25×D43136yes—
152C2—227no—
153C2—8636no—
154C2C26×D4311yescharacteristic
subgroupG/H
center, FrattiniC2C26×D43
commutator, socle, cosocleC2×C43C27
FittingC43×2−1+6C2
hypercenter2−1+6D43
hypocenterC43#63103
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ 2−1+6

Complements

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

NH ≅ G/Ntype
1. #19149407C2semidirect
2. #19149406C2semidirect
3. C2×#14583736C2semidirect
4. #585×D43C2semidirect
5. C43×2−1+6C2semidirect
6. #14583736C22semidirect
7. #14583736C22semidirect
8. #14583735C22semidirect
9. #14583734C22semidirect
10. C2×#13063373C22semidirect
11. 2−1+4×D43C22semidirect
12. C2×#13063371C22semidirect
13. H(5,𝔽2)×D43C22semidirect
14. C22×#10621902C22semidirect
15. C2×#41×D43C22semidirect
16. C43×#585C22semidirect
17. C2×2−1+4×C43C22semidirect
18. #13063373C23semidirect
19. #13063372C23semidirect
20. #13063371C23semidirect
21. #13063370C23semidirect
22. C2×#10621902C23semidirect
23. C2×#10621902C23semidirect
24. C2×#10621898C23semidirect
25. C2×#10621900C23semidirect
26. #41×D43C23semidirect
27. #41×D43C23semidirect
28. C2×Q8×D43C23semidirect
29. C22×D172C23semidirect
30. C2×D4×D43C23semidirect
31. C22×C4×D43C23semidirect
32. 2−1+4×C43C23semidirect
33. H(5,𝔽2)×C43C23semidirect
34. C2×#41×C43C23semidirect
35. C22×Q8×C43C23semidirect
76. 2−1+6D43semidirect
87. #585C2×D43semidirect
90. C2×2−1+4C2×D43semidirect
95. C43#63103semidirect
98. 2−1+4C22×D43semidirect
101. H(5,𝔽2)C22×D43semidirect
108. C2×#41C22×D43semidirect
110. C22×Q8C22×D43semidirect

Maximal subgroups

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

subgroupindex
#191494072
#191494062
C2×#145837362
#585×D432
C43×2−1+62
#6310343