Finite Group Databasebeta

← #26010498

Subgroups — #26010498

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#19149408C2128yesmaximal, complemented
2#19149405C2135yesmaximal, complemented
3C2×#14583734C2135yesmaximal, complemented
4#585×D43C2128yesmaximal, complemented
5C43×H(7,𝔽2)C211yesmaximal, characteristic, complemented
6#14583736C22156yescomplemented
7#14583735C221420yescomplemented
8#14583734C221280yescomplemented
9#14583734C221560yescomplemented
10C2×#13063372C221210yescomplemented
112−1+4×D43C221168yescomplemented
12C2×#13063370C221315yescomplemented
13H(5,𝔽2)×D43C221280yescomplemented
14C22×#10621900C221105yescomplemented
15C2×#41×D43C221210yescomplemented
16C43×#585C22128yescomplemented
17C2×H(5,𝔽2)×C43C22135yescomplemented
18#13063373C231280yescomplemented
19#13063372C2311680yescomplemented
20#13063371C231560yescomplemented
21#13063370C2312520yescomplemented
22C2×#10621902C23170yescomplemented
23C2×#10621898C231630yescomplemented
24C2×#10621900C231630yescomplemented
25C2×#10621900C2311260yescomplemented
26#41×D43C231560yescomplemented
27#41×D43C2311680yescomplemented
28C22×Dic86C231105yescomplemented
29C2×Q8×D43C231210yescomplemented
30C22×C22⋊D43C231210yescomplemented
31C2×D4×D43C231630yescomplemented
32C23×Dic43C23130yescomplemented
33C22×C4×D43C231105yescomplemented
342−1+4×C43C23156yescomplemented
35H(5,𝔽2)×C43C231280yescomplemented
36C2×#41×C43C231210yescomplemented
37C22×D4×C43C231105yescomplemented
38C24×C43C24130yes—
39C23×D43C241105yes—
40#41×C43C241560yes—
41C2×Q8×C43C24170yes—
42C2×D4×C43C241630yes—
43C22×C4×C43C241105yes—
44C2×C22⋊D43C2411260yes—
45C22×Dic43C241105yes—
46C22×Dic43C241210yes—
47#10621902C24156yes—
48#10621902C241280yes—
49Q8×D43C241560yes—
50#10621900C241280yes—
51#10621900C2412520yes—
52D4×D43C2411680yes—
53#10621898C2411680yes—
54C2×D172C241210yes—
55C2×C4×D43C241210yes—
56C2×C4×D43C241630yes—
57C2×Dic86C241630yes—
58C23×C43—830no—
59C23×C43C251105yes—
60C22×D43—8105no—
61C22×D43C251210yes—
62Q8×C43C25156yes—
63D4×C43C251280yes—
64C2×C4×C43C251210yes—
65C22⋊D43C251560yes—
66C2×Dic43C251315yes—
67C2×Dic43C25135yes—
68D172C251168yes—
69C4×D43C25128yes—
70C4×D43C251420yes—
71Dic86C251280yes—
72#63103—431nomaximal, Sylow
73C22×C43—4105no—
74C22×C43C26135yes—
75C2×D43—4210no—
76C2×D43C26128yes—
77C4×C43C26128yes—
78Dic43C26135yes—
79Dic43C2611yescharacteristic
802−1+6—4328no—
81H(7,𝔽2)—4335no—
82H(7,𝔽2)D4311yescharacteristic, complemented
83C2×#585—4328no—
84C2×#585—4335no—
85C2×C43—235no—
86C2×C43C2711yescharacteristic
87D43—228no—
88#585—4356no—
89#585—43280no—
90#585—43560no—
91#585—43420no—
92#585C2×D43128yescomplemented
93C2×2−1+4—43168no—
94C2×2−1+4—43210no—
95C2×H(5,𝔽2)—43280no—
96C2×H(5,𝔽2)—43315no—
97C2×H(5,𝔽2)C2×D43135yescomplemented
98C22×#41—43210no—
99C22×#41—43105no—
100C43#6310311yescharacteristic, complemented, Sylow
1012−1+4—431680no—
1022−1+4—43280no—
1032−1+4C22×D43156yescomplemented
104H(5,𝔽2)—43560no—
105H(5,𝔽2)—432520no—
106H(5,𝔽2)C22×D431280yescomplemented
107C2×#41—43560no—
108C2×#41—431680no—
109C2×#41—4370no—
110C2×#41—43630no—
111C2×#41—431260no—
112C2×#41—43630no—
113C2×#41C22×D431210yescomplemented
114C22×Q8—43210no—
115C22×Q8—43105no—
116C22×D4—43210no—
117C22×D4—43630no—
118C22×D4C22×D431105yescomplemented
119C23×C4—4330no—
120C23×C4—43105no—
121C24—43105no—
122C24C23×D43130yes—
123#41—4356no—
124#41—43280no—
125#41—43280no—
126#41—432520no—
127#41—431680no—
128#41C23×D431560yes—
129C2×Q8—43560no—
130C2×Q8—43630no—
131C2×Q8C23×D43170yes—
132C2×D4—431260no—
133C2×D4—431680no—
134C2×D4—43210no—
135C2×D4C23×D431630yes—
136C22×C4—43105no—
137C22×C4—43210no—
138C22×C4—43210no—
139C22×C4—43630no—
140C22×C4C23×D431105yes—
141C23—830no—
142C23—43210no—
143C23—344105no—
144C23C24×D431105yes—
145Q8—43280no—
146Q8C24×D43156yes—
147D4—43560no—
148D4—43168no—
149D4C24×D431280yes—
150C2×C4—4335no—
151C2×C4—43315no—
152C2×C4—4328no—
153C2×C4—43420no—
154C2×C4C24×D431210yes—
155C22—4105no—
156C22—4328no—
157C22—172210no—
158C22C25×D43135yes—
159C4—431no—
160C4—4335no—
161C4C25×D43128yes—
162C2—235no—
163C2—8628no—
164C2C26×D4311yescharacteristic
subgroupG/H
center, FrattiniC2C26×D43
commutator, socle, cosocleC2×C43C27
FittingC43×H(7,𝔽2)C2
hypercenterH(7,𝔽2)D43
hypocenterC43#63103
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ H(7,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #19149408C2semidirect
2. #19149405C2semidirect
3. C2×#14583734C2semidirect
4. #585×D43C2semidirect
5. C43×H(7,𝔽2)C2semidirect
6. #14583736C22semidirect
7. #14583735C22semidirect
8. #14583734C22semidirect
9. #14583734C22semidirect
10. C2×#13063372C22semidirect
11. 2−1+4×D43C22semidirect
12. C2×#13063370C22semidirect
13. H(5,𝔽2)×D43C22semidirect
14. C22×#10621900C22semidirect
15. C2×#41×D43C22semidirect
16. C43×#585C22semidirect
17. C2×H(5,𝔽2)×C43C22semidirect
18. #13063373C23semidirect
19. #13063372C23semidirect
20. #13063371C23semidirect
21. #13063370C23semidirect
22. C2×#10621902C23semidirect
23. C2×#10621898C23semidirect
24. C2×#10621900C23semidirect
25. C2×#10621900C23semidirect
26. #41×D43C23semidirect
27. #41×D43C23semidirect
28. C22×Dic86C23semidirect
29. C2×Q8×D43C23semidirect
30. C22×C22⋊D43C23semidirect
31. C2×D4×D43C23semidirect
32. C23×Dic43C23semidirect
33. C22×C4×D43C23semidirect
34. 2−1+4×C43C23semidirect
35. H(5,𝔽2)×C43C23semidirect
36. C2×#41×C43C23semidirect
37. C22×D4×C43C23semidirect
82. H(7,𝔽2)D43semidirect
92. #585C2×D43semidirect
97. C2×H(5,𝔽2)C2×D43semidirect
100. C43#63103semidirect
103. 2−1+4C22×D43semidirect
106. H(5,𝔽2)C22×D43semidirect
113. C2×#41C22×D43semidirect
118. C22×D4C22×D43semidirect

Maximal subgroups

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

subgroupindex
#191494082
#191494052
C2×#145837342
#585×D432
C43×H(7,𝔽2)2
#6310343