Finite Group Databasebeta

← #13083426

Subgroups — #13083426

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
1C2×C11×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#10623455C2116yesmaximal, complemented
3D11×H(5,𝔽2)C2116yesmaximal, complemented
4#10623453C2112yesmaximal, complemented
5C2×#67037C2118yesmaximal, complemented
6C11×H(5,𝔽2)C22116yescomplemented
7C2×C11×#41C2216yescomplemented
8C22×D4×C11C2219yescomplemented
9C22×C22⋊D11C22124yescomplemented
10#67043C22148yescomplemented
11#67042C22148yescomplemented
12#41×D11C22196yescomplemented
13#67040C2218yescomplemented
14#67037C22172yescomplemented
15#67037C221144yescomplemented
16C2×#4341C22172yescomplemented
17C2×D4×D11C22172yescomplemented
18C2×#4339C22136yescomplemented
19C24×C11C2316yescomplemented
20C23×D11C23124yescomplemented
21C11×#41C23148yescomplemented
22C2×Q8×C11C2312yescomplemented
23C2×D4×C11C23172yescomplemented
24C2×D4×C11C23118yescomplemented
25C22×C4×C11C2319yescomplemented
26C2×C22⋊D11C23172yescomplemented
27C2×C22⋊D11C231144yescomplemented
28C22×Dic11C23124yescomplemented
29#4343C23132yescomplemented
30Q8×D11C23132yescomplemented
31#4341C231288yescomplemented
32D4×D11C231288yescomplemented
33#4339C23148yescomplemented
34#4339C231144yescomplemented
35C2×D44C23136yescomplemented
36C2×C4×D11C23172yescomplemented
37C2×Dic22C23136yescomplemented
38H(7,𝔽2)—111nomaximal, Sylow
39C23×C11—86no—
40C23×C11C24124yes—
41C23×C11C2419yes—
42C22×D11—824no—
43C22×D11C24172yes—
44Q8×C11C2418yes—
45D4×C11C24172yes—
46C2×C4×C11C24136yes—
47C2×C4×C11C2416yes—
48C22⋊D11C24116yes—
49C22⋊D11C241144yes—
50C2×Dic11C24172yes—
51D44C24148yes—
52C4×D11C24196yes—
53Dic22C24148yes—
54#585—1116no—
55#585—1112no—
56C2×H(5,𝔽2)—1116no—
57C2×H(5,𝔽2)—1118no—
58C2×H(5,𝔽2)D1111yescharacteristic, complemented
59C22×C11—424no—
60C22×C11—49no—
61C22×C11C2511yescharacteristic
62C22×C11C25118yes—
63C2×D11—472no—
64C2×D11C25116yes—
65C4×C11C25112yes—
66Dic11C25116yes—
672−1+4—1148no—
682−1+4—118no—
69H(5,𝔽2)—1148no—
70H(5,𝔽2)—11144no—
71H(5,𝔽2)—1172no—
72H(5,𝔽2)C2×D11116yescomplemented
73C2×#41—1196no—
74C2×#41—1172no—
75C2×#41—1136no—
76C2×#41C2×D1116yescomplemented
77C22×D4—1124no—
78C22×D4—1172no—
79C22×D4C2×D1119yescomplemented
80C2×C11—218no—
81C2×C11—21no—
82C2×C11C2611yescharacteristic
83D11—216no—
84C24—1124no—
85C24C22×D1116yescomplemented
86#41—1132no—
87#41—11288no—
88#41—11144no—
89#41—1148no—
90#41C22×D11148yescomplemented
91C2×Q8—1132no—
92C2×Q8—1136no—
93C2×Q8C22×D1112yescomplemented
94C2×D4—11144no—
95C2×D4—1172no—
96C2×D4—11288no—
97C2×D4—1136no—
98C2×D4C22×D11172yescomplemented
99C2×D4C22×D11118yescomplemented
100C22×C4—1124no—
101C22×C4—1172no—
102C22×C4C22×D1119yescomplemented
103C11H(7,𝔽2)11yescharacteristic, complemented, Sylow
104C23—86no—
105C23—1172no—
106C23—8824no—
107C23C23×D11124yes—
108C23C23×D1119yes—
109Q8—1148no—
110Q8C23×D1118yes—
111D4—11144no—
112D4—1116no—
113D4—1148no—
114D4C23×D11172yes—
115C2×C4—1172no—
116C2×C4—1196no—
117C2×C4C23×D11136yes—
118C2×C4C23×D1116yes—
119C22—49no—
120C22—424no—
121C22—1116no—
122C22—4472no—
123C22C24×D11118yes—
124C22C24×D1111yescharacteristic
125C4—1116no—
126C4C24×D11112yes—
127C2—21no—
128C2—218no—
129C2—2216no—
130C2C25×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C25×D11
commutator, socle, cosocleC2×C11C26
FittingC2×C11×H(5,𝔽2)C2
hypercenterC2×H(5,𝔽2)D11
hypocenterC11H(7,𝔽2)
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×C11×H(5,𝔽2)C2semidirect
2. #10623455C2semidirect
3. D11×H(5,𝔽2)C2semidirect
4. #10623453C2semidirect
5. C2×#67037C2semidirect
6. C11×H(5,𝔽2)C22semidirect
7. C2×C11×#41C22semidirect
8. C22×D4×C11C22semidirect
9. C22×C22⋊D11C22semidirect
10. #67043C22semidirect
11. #67042C22semidirect
12. #41×D11C22semidirect
13. #67040C22semidirect
14. #67037C22semidirect
15. #67037C22semidirect
16. C2×#4341C22semidirect
17. C2×D4×D11C22semidirect
18. C2×#4339C22semidirect
19. C24×C11C23semidirect
20. C23×D11C23semidirect
21. C11×#41C23semidirect
22. C2×Q8×C11C23semidirect
23. C2×D4×C11C23semidirect
24. C2×D4×C11C23semidirect
25. C22×C4×C11C23semidirect
26. C2×C22⋊D11C23semidirect
27. C2×C22⋊D11C23semidirect
28. C22×Dic11C23semidirect
29. #4343C23semidirect
30. Q8×D11C23semidirect
31. #4341C23semidirect
32. D4×D11C23semidirect
33. #4339C23semidirect
34. #4339C23semidirect
35. C2×D44C23semidirect
36. C2×C4×D11C23semidirect
37. C2×Dic22C23semidirect
58. C2×H(5,𝔽2)D11semidirect
72. H(5,𝔽2)C2×D11semidirect
76. C2×#41C2×D11semidirect
79. C22×D4C2×D11semidirect
85. C24C22×D11semidirect
90. #41C22×D11semidirect
93. C2×Q8C22×D11semidirect
98. C2×D4C22×D11semidirect
99. C2×D4C22×D11semidirect
102. C22×C4C22×D11semidirect
103. C11H(7,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C2×C11×H(5,𝔽2)2
#106234552
D11×H(5,𝔽2)2
#106234532
C2×#670372
H(7,𝔽2)11