Finite Group Databasebeta

← #44543249

Subgroups — #44543249

Order 31936.

188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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×#22547799C212yesmaximal, complemented
2#30630330C211yesmaximal, characteristic, complemented
3#30630272C212yesmaximal, complemented
4C22⋊(C499⋊C8)C211yesmaximal, characteristic, complemented
5C22×D4×C499C211yesmaximal, characteristic
6C2×Dic998C2211yescharacteristic, complemented
7#22547799—24no—
8C2×C499⋊C8C2212yescomplemented
9C4⋊Dic499C2211yescharacteristic, complemented
10Dic499⋊C4—21no—
11C22⋊Dic499—21no—
12C24×C499—21no—
13C2×D4×C499—24no—
14C2×D4×C499—21no—
15C2×D4×C499C2212yes—
16C22×C4×C499C2211yescharacteristic
17Dic998—22no—
18C2×Dic499—21no—
19C2×Dic499—21no—
20C499⋊C8—22no—
21C23×C499—24no—
22C23×C499—22no—
23C23×C499—42no—
24C23×C499—42no—
25C23×C499D411yescharacteristic
26D4×C499—24no—
27D4×C499—22no—
28D4×C499D414yes—
29C2×C4×C499—22no—
30C2×C4×C499D411yescharacteristic
31C2×C4×C499C2311yescharacteristic
32C22×C499—21no—
33C22×C499—21no—
34C22×C499—24no—
35C22×C499—48no—
36C22×C499—42no—
37C22×C499—42no—
38C22×C499SD1612yescomplemented
39C22×C499C2×D411yescharacteristic
40C4×C499—21no—
41C4×C499C2×D412yes—
42Dic499—41no—
43Dic499—41no—
44C2×C499—22no—
45C2×C499—44no—
46C2×C499#12011yescharacteristic
47C2×C499C2×SD1611yescharacteristic
48C2×C499AGL(1,ℤ/8)11yescharacteristic
49C499#45011yescharacteristic, complemented, Sylow
50#450—4991nomaximal, Sylow
51C22×D4D49911yescharacteristic
52C2×SD16—4992no—
53C22⋊Q8—4991no—
54#102—4992no—
55C22⋊C8—4991no—
56C24—21no—
57C2×Q8—4991no—
58C2×D4—24no—
59C2×D4—21no—
60C2×D4C2×D49912yes—
61C22×C4C2×D49911yescharacteristic
62SD16—9984no—
63C2×C8—4992no—
64C4⋊C4—9981no—
65C4⋊C4—4991no—
66C22⋊C4—9981no—
67C23—24no—
68C23—22no—
69C23—42no—
70C23—42no—
71C23C22⋊D49911yescharacteristic
72Q8—9982no—
73D4—24no—
74D4—22no—
75D4C22⋊D49914yes—
76C2×C4—22no—
77C2×C4—9981no—
78C2×C4—9981no—
79C2×C4C22⋊D49911yescharacteristic
80C2×C4C22×D49911yescharacteristic
81C8—9982no—
82C22—21no—
83C22—21no—
84C22—24no—
85C22—48no—
86C22—42no—
87C22—42no—
88C22#2254779912yescomplemented
89C22C2×C22⋊D49911yescharacteristic
90C4—21no—
91C4—19961no—
92C4—19961no—
93C4C2×C22⋊D49912yes—
94C2—22no—
95C2—44no—
96C2#3063032011yescharacteristic
97C2C2×#2254779911yescharacteristic
98C2#3063037711yescharacteristic
subgroupG/H
centerC22C2×C22⋊D499
commutator, cosocleC2×C4×C499C23
FrattiniC2×C4C22×D499
Fitting, prime radicalC22×D4×C499C2
socleC22×C499C2×D4
hypercenterC22×D4D499
hypocenterC499#450
LCSG ▷ C2×C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22547799C2semidirect
2. #30630330C2semidirect
3. #30630272C2semidirect
4. C22⋊(C499⋊C8)C2semidirect
6. C2×Dic998C22semidirect
8. C2×C499⋊C8C22semidirect
9. C4⋊Dic499C22semidirect
38. C22×C499SD16semidirect
49. C499#450semidirect
88. C22#22547799semidirect

Maximal subgroups

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

subgroupindex
C2×#225477992
#306303302
#306302722
C22⋊(C499⋊C8)2
C22×D4×C4992
#450499