Finite Group Databasebeta

← #44500586

Subgroups — #44500586

Order 30656.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#29506427C211yesmaximal, characteristic
2#29506366C212yesmaximal, complemented
3#29506363C211yesmaximal, characteristic, complemented
4#29506296C212yesmaximal, complemented
5#99×C479C211yesmaximal, characteristic, complemented
6#21440162—21no—
7#21440161—22no—
8C2×C22⋊D479—21no—
9C2×C22⋊D479C2212yes—
10D4×D479—22no—
11C22×Dic479C2211yescharacteristic, complemented
12C4⋊Dic479—22no—
13Dic479⋊C4—21no—
14C22⋊Dic479—21no—
15C22⋊Dic479C2211yescharacteristic, complemented
16(C2×D479)⋊C4—22no—
17C2×D4×C479C2211yescharacteristic
18C22⋊C4×C479C2212yescomplemented
19C22×D479—21no—
20C22×D479D412yes—
21Dic958—21no—
22D1916—21no—
23C22⋊D479—22no—
24C22⋊D479—22no—
25C22⋊D479—22no—
26C2×Dic479—21no—
27C2×Dic479—22no—
28C2×Dic479—21no—
29C2×Dic479—21no—
30C2×Dic479D412yes—
31C4×D479—22no—
32C23×C479D411yescharacteristic
33C23×C479C2311yescharacteristic
34D4×C479—22no—
35C2×C4×C479—22no—
36C2×C4×C479D411yescharacteristic
37C22×C479—21no—
38C22×C479—41no—
39C22×C479—41no—
40C22×C479C2×D412yes—
41C22×C479C2×D411yescharacteristic
42C2×D479—22no—
43C2×D479—42no—
44C2×D479—81no—
45C4×C479—21no—
46C4×C479—42no—
47Dic479—22no—
48Dic479—41no—
49Dic479—41no—
50C2×C479—21no—
51C2×C479—22no—
52C2×C479—41no—
53C2×C479#12011yescharacteristic
54D479—42no—
55C479#45811yescharacteristic, complemented, Sylow
56#458—4791nomaximal, Sylow
57H(5,𝔽2)—4791no—
58#123—4791no—
59#123—4792no—
60#99—4792no—
61#99D47911yescharacteristic, complemented
62#41—9582no—
63#41—9581no—
64C2×D4—9582no—
65C2×D4—9581no—
66C2×D4—4792no—
67C2×D4C2×D47911yescharacteristic
68C22×C4—4791no—
69C4⋊C4—9582no—
70C4⋊C4—9581no—
71C22⋊C4—9582no—
72C22⋊C4—9581no—
73C22⋊C4—4791no—
74C22⋊C4C2×D47912yescomplemented
75C23—9581no—
76C23—4792no—
77C23D191611yescharacteristic
78C23C22×D47911yescharacteristic
79Q8—9581no—
80D4—22no—
81D4—9581no—
82D4—9582no—
83D4—9582no—
84D4—9582no—
85C2×C4—22no—
86C2×C4—9582no—
87C2×C4—9582no—
88C2×C4—9581no—
89C2×C4—9581no—
90C2×C4—9581no—
91C2×C4—4792no—
92C2×C4D191611yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—19162no—
97C22—9582no—
98C22—38321no—
99C22D4×D47912yes—
100C22C2×D191611yescharacteristic
101C4—21no—
102C4—42no—
103C4—19161no—
104C4—19161no—
105C4—9582no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—19162no—
110C2#2950635211yescharacteristic
subgroupG/H
centerC2#29506352
commutator, cosocleC23×C479C23
FrattiniC23C22×D479
Fitting#99×C479C2
socleC2×C479#120
prime radical#29506427C2
hypercenter#99D479
hypocenterC479#458
LCSG ▷ C23×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #29506366C2semidirect
3. #29506363C2semidirect
4. #29506296C2semidirect
5. #99×C479C2semidirect
11. C22×Dic479C22semidirect
15. C22⋊Dic479C22semidirect
18. C22⋊C4×C479C22semidirect
55. C479#458semidirect
61. #99D479semidirect
74. C22⋊C4C2×D479semidirect

Maximal subgroups

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

subgroupindex
#295064272
#295063662
#295063632
#295062962
#99×C4792
#458479