Finite Group Databasebeta

← #13083427

Subgroups — #13083427

Order 1408.

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
1C11×#585C211yesmaximal, characteristic, complemented
2#10623457C2112yesmaximal, complemented
3D11×H(5,𝔽2)C2120yesmaximal, complemented
4#10623453C2115yesmaximal, complemented
5C2×#67042C2115yesmaximal, complemented
6C11×2−1+4C2216yescomplemented
7C11×H(5,𝔽2)C22110yescomplemented
8C2×C11×#41C22115yescomplemented
9#67043C22120yescomplemented
10#67042C22160yescomplemented
11#67042C221120yescomplemented
12#41×D11C221120yescomplemented
13#67040C22130yescomplemented
14C2×#4343C22130yescomplemented
15#67037C22190yescomplemented
16C2×D4×D11C22190yescomplemented
17C2×#4339C22145yescomplemented
18C22×D44C22115yescomplemented
19C23×D11C23130yescomplemented
20C11×#41C23160yescomplemented
21C11×#41C23120yescomplemented
22C2×Q8×C11C23115yescomplemented
23C2×D4×C11C23145yescomplemented
24C22×C4×C11C23115yescomplemented
25C2×C22⋊D11C23190yescomplemented
26#4343C231120yescomplemented
27Q8×D11C23140yescomplemented
28#4341C231120yescomplemented
29D4×D11C231360yescomplemented
30#4339C23160yescomplemented
31#4339C231180yescomplemented
32C2×D44C23145yescomplemented
33C2×D44C23190yescomplemented
34C2×C4×D11C23190yescomplemented
35C2×Dic22C23115yescomplemented
36H(7,𝔽2)—111nomaximal, Sylow
37C23×C11C24115yes—
38C22×D11—830no—
39C22×D11C24190yes—
40Q8×C11C24120yes—
41D4×C11C24160yes—
42C2×C4×C11C24115yes—
43C2×C4×C11C24145yes—
44C22⋊D11C241120yes—
45C2×Dic11C24130yes—
46D44C24110yes—
47D44C24190yes—
48C4×D11C241120yes—
49Dic22C2416yes—
50Dic22C24130yes—
51#585—1112no—
52#585—1115no—
53#585D1111yescharacteristic, complemented
54C2×H(5,𝔽2)—1120no—
55C2×H(5,𝔽2)—1115no—
56C22×C11—415no—
57C22×C11C25115yes—
58C2×D11—490no—
59C2×D11C25120yes—
60C4×C11C2511yescharacteristic
61C4×C11C25115yes—
62Dic11C25112yes—
632−1+4—1120no—
642−1+4—1130no—
652−1+4C2×D1116yescomplemented
66H(5,𝔽2)—11120no—
67H(5,𝔽2)—1160no—
68H(5,𝔽2)—1190no—
69H(5,𝔽2)C2×D11110yescomplemented
70C2×#41—11120no—
71C2×#41—1130no—
72C2×#41—1145no—
73C2×#41C2×D11115yescomplemented
74C22×D4—1190no—
75C22×D4—1115no—
76C2×C11—215no—
77C2×C11C2611yescharacteristic
78D11—220no—
79C24—1130no—
80#41—11120no—
81#41—11120no—
82#41—11180no—
83#41—1160no—
84#41C22×D11160yescomplemented
85#41C22×D11120yescomplemented
86C2×Q8—1140no—
87C2×Q8—1115no—
88C2×Q8C22×D11115yescomplemented
89C2×D4—1190no—
90C2×D4—11360no—
91C2×D4—1190no—
92C2×D4—1145no—
93C2×D4C22×D11145yescomplemented
94C22×C4—1190no—
95C22×C4C22×D11115yescomplemented
96C11H(7,𝔽2)11yescharacteristic, complemented, Sylow
97C23—1190no—
98C23—8830no—
99C23C23×D11115yes—
100Q8—1130no—
101Q8—116no—
102Q8C23×D11120yes—
103D4—11120no—
104D4—1190no—
105D4—1110no—
106D4C23×D11160yes—
107C2×C4—1130no—
108C2×C4—11120no—
109C2×C4C23×D11145yes—
110C2×C4C23×D11115yes—
111C22—415no—
112C22—1120no—
113C22—4490no—
114C22C24×D11115yes—
115C4—1112no—
116C4C24×D11115yes—
117C4C24×D1111yescharacteristic
118C2—215no—
119C2—2220no—
120C2C25×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C25×D11
commutator, socle, cosocleC2×C11C26
FittingC11×#585C2
hypercenter#585D11
hypocenterC11H(7,𝔽2)
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C11×#585C2semidirect
2. #10623457C2semidirect
3. D11×H(5,𝔽2)C2semidirect
4. #10623453C2semidirect
5. C2×#67042C2semidirect
6. C11×2−1+4C22semidirect
7. C11×H(5,𝔽2)C22semidirect
8. C2×C11×#41C22semidirect
9. #67043C22semidirect
10. #67042C22semidirect
11. #67042C22semidirect
12. #41×D11C22semidirect
13. #67040C22semidirect
14. C2×#4343C22semidirect
15. #67037C22semidirect
16. C2×D4×D11C22semidirect
17. C2×#4339C22semidirect
18. C22×D44C22semidirect
19. C23×D11C23semidirect
20. C11×#41C23semidirect
21. C11×#41C23semidirect
22. C2×Q8×C11C23semidirect
23. C2×D4×C11C23semidirect
24. C22×C4×C11C23semidirect
25. C2×C22⋊D11C23semidirect
26. #4343C23semidirect
27. Q8×D11C23semidirect
28. #4341C23semidirect
29. D4×D11C23semidirect
30. #4339C23semidirect
31. #4339C23semidirect
32. C2×D44C23semidirect
33. C2×D44C23semidirect
34. C2×C4×D11C23semidirect
35. C2×Dic22C23semidirect
53. #585D11semidirect
65. 2−1+4C2×D11semidirect
69. H(5,𝔽2)C2×D11semidirect
73. C2×#41C2×D11semidirect
84. #41C22×D11semidirect
85. #41C22×D11semidirect
88. C2×Q8C22×D11semidirect
93. C2×D4C22×D11semidirect
95. C22×C4C22×D11semidirect
96. C11H(7,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C11×#5852
#106234572
D11×H(5,𝔽2)2
#106234532
C2×#670422
H(7,𝔽2)11