Finite Group Databasebeta

← #14271965

Subgroups — #14271965

Order 1856.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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#11745364C212yesmaximal, complemented
2C29×#135C211yesmaximal, characteristic, complemented
3#11745311C212yesmaximal, complemented
4#11745281C212yesmaximal, complemented
5#11745276C214yesmaximal, complemented
6D8×D29C212yesmaximal, complemented
7C2×D232C211yesmaximal, characteristic, complemented
8#11745263C211yesmaximal, characteristic, complemented
9#41×C29C2212yescomplemented
10#90809C2214yescomplemented
11D4×D29—24no—
12D4×D29C2214yescomplemented
13#90805—22no—
14#90805C2211yescharacteristic
15C2×D116—22no—
16C2×D116C2212yescomplemented
17Q16×C29C2211yescharacteristic, complemented
18SD16×C29C2212yescomplemented
19D8×C29C2211yescharacteristic, complemented
20C2×C8×C29C2211yescharacteristic, complemented
21#90784C2214yescomplemented
22#90782C2214yescomplemented
23#90777C2211yescharacteristic, complemented
24D232C2212yescomplemented
25D232C2212yescomplemented
26#90772C2212yescomplemented
27C8×D29C2212yescomplemented
28C22×D29—22no—
29C22×D29—24no—
30Q8×C29C2312yes—
31D4×C29—22no—
32D4×C29C2312yes—
33C2×C4×C29—22no—
34C2×C4×C29C2311yescharacteristic
35C22⋊D29—24no—
36C22⋊D29D412yes—
37D116—24no—
38D116—22no—
39D116D411yescharacteristic
40D116C2314yes—
41C4×D29—24no—
42C4×D29C2312yes—
43Dic58D411yescharacteristic
44C8×C29C2311yescharacteristic
45C8×C29C2311yescharacteristic
46#6597C2312yes—
47C22×C29—22no—
48C22×C29C2×D411yescharacteristic
49C2×D29—24no—
50C2×D29—84no—
51C2×D29—82no—
52C2×D29C2×D412yes—
53C4×C29—22no—
54C4×C29C2×D411yescharacteristic
55C4×C29C2411yescharacteristic
56Dic29C2×D412yes—
57#576—291nomaximal, Sylow
58C2×C29—21no—
59C2×C29—42no—
60C2×C29C22×D411yescharacteristic
61D29—22no—
62D29—44no—
63H(5,𝔽2)—292no—
64AGL(1,ℤ/8)—292no—
65AGL(1,ℤ/8)—294no—
66#135—292no—
67#135D2911yescharacteristic, complemented
68C2×D8—292no—
69C2×D8—291no—
70#131—291no—
71C29#57611yescharacteristic, complemented, Sylow
72#41—291no—
73#41—294no—
74#41—582no—
75#41C2×D2912yescomplemented
76C2×D4—294no—
77C2×D4—292no—
78C2×D4—582no—
79C2×D4—584no—
80Q16C2×D2911yescharacteristic, complemented
81SD16—294no—
82SD16C2×D2912yescomplemented
83D8—294no—
84D8—292no—
85D8—292no—
86D8C2×D2911yescharacteristic, complemented
87M16—291no—
88M16—292no—
89C2×C8—292no—
90C2×C8C2×D2911yescharacteristic, complemented
91C23—584no—
92C23—582no—
93Q8—291no—
94Q8C22×D2912yes—
95D4—22no—
96D4—292no—
97D4—291no—
98D4—294no—
99D4—584no—
100D4—584no—
101D4—582no—
102D4C22×D2912yes—
103C2×C4—22no—
104C2×C4—292no—
105C2×C4—584no—
106C2×C4C22×D2911yescharacteristic
107C8—292no—
108C8C22×D2911yescharacteristic
109C8C22×D2911yescharacteristic
110C22—22no—
111C22—292no—
112C22—584no—
113C22—2322no—
114C22—2324no—
115C22D4×D2911yescharacteristic
116C4—22no—
117C4—292no—
118C4D4×D2911yescharacteristic
119C4C23×D2911yescharacteristic
120C2—21no—
121C2—42no—
122C2—582no—
123C2—1164no—
124C2C2×D4×D2911yescharacteristic
subgroupG/H
centerC2C2×D4×D29
commutator, cosocleC4×C29C24
FrattiniC4C23×D29
FittingC29×#135C2
socleC2×C29C22×D4
hypercenter#135D29
hypocenterC29#576
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #11745364C2semidirect
2. C29×#135C2semidirect
3. #11745311C2semidirect
4. #11745281C2semidirect
5. #11745276C2semidirect
6. D8×D29C2semidirect
7. C2×D232C2semidirect
8. #11745263C2semidirect
9. #41×C29C22semidirect
10. #90809C22semidirect
12. D4×D29C22semidirect
16. C2×D116C22semidirect
17. Q16×C29C22semidirect
18. SD16×C29C22semidirect
19. D8×C29C22semidirect
20. C2×C8×C29C22semidirect
21. #90784C22semidirect
22. #90782C22semidirect
23. #90777C22semidirect
24. D232C22semidirect
25. D232C22semidirect
26. #90772C22semidirect
27. C8×D29C22semidirect
67. #135D29semidirect
71. C29#576semidirect
75. #41C2×D29semidirect
80. Q16C2×D29semidirect
82. SD16C2×D29semidirect
86. D8C2×D29semidirect
90. C2×C8C2×D29semidirect

Maximal subgroups

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

subgroupindex
#117453642
C29×#1352
#117453112
#117452812
#117452762
D8×D292
C2×D2322
#117452632
#57629