Finite Group Databasebeta

← #44500583

Subgroups — #44500583

Order 30656.

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

normal subgroups only

This group has 198 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, complemented
2#29506352C212yesmaximal, complemented
3#29506350C211yesmaximal, characteristic, complemented
4#29506296C212yesmaximal, complemented
5#99×C479C211yesmaximal, characteristic, complemented
6C23×D479C2211yescharacteristic, complemented
7#21440162—21no—
8#21440161—22no—
9C2×D1916—22no—
10C2×C22⋊D479—21no—
11C2×C22⋊D479—21no—
12C2×C22⋊D479C2212yes—
13D4×D479—22no—
14C22⋊Dic479C2211yescharacteristic, complemented
15(C2×D479)⋊C4—22no—
16(C2×D479)⋊C4—21no—
17C2×D4×C479C2211yescharacteristic
18C22⋊C4×C479C2212yescomplemented
19C22×D479—21no—
20C22×D479—22no—
21C22×D479—21no—
22C22×D479—42no—
23C22×D479D412yescomplemented
24Dic958—21no—
25D1916—21no—
26D1916—44no—
27C22⋊D479—22no—
28C22⋊D479—22no—
29C22⋊D479—22no—
30C22⋊D479—42no—
31C2×Dic479—21no—
32C2×Dic479—21no—
33C2×Dic479D412yescomplemented
34C4×D479—22no—
35C23×C479D411yescharacteristic, complemented
36C23×C479C2311yescharacteristic
37D4×C479—22no—
38C2×C4×C479—22no—
39C2×C4×C479D411yescharacteristic, complemented
40C22×C479—21no—
41C22×C479—41no—
42C22×C479—41no—
43C22×C479C2×D412yes—
44C22×C479C2×D411yescharacteristic
45C2×D479—22no—
46C2×D479—24no—
47C2×D479—22no—
48C2×D479—41no—
49C2×D479—42no—
50C2×D479—41no—
51C2×D479—42no—
52C2×D479—81no—
53C4×C479—21no—
54C4×C479—42no—
55Dic479—22no—
56Dic479—41no—
57C2×C479—21no—
58C2×C479—22no—
59C2×C479—41no—
60C2×C479#12011yescharacteristic
61D479—42no—
62D479—42no—
63C479B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—4791nomaximal, Sylow
65H(5,𝔽2)—4791no—
66#120—4791no—
67#120—4792no—
68#99—4792no—
69#99D47911yescharacteristic, complemented
70C24—4791no—
71#41—9582no—
72#41—9581no—
73C2×D4—9582no—
74C2×D4—9582no—
75C2×D4—9581no—
76C2×D4—9581no—
77C2×D4—4792no—
78C2×D4C2×D47911yescharacteristic
79C22⋊C4—9582no—
80C22⋊C4—9581no—
81C22⋊C4—4791no—
82C22⋊C4C2×D47912yescomplemented
83C23—19162no—
84C23—9581no—
85C23—9582no—
86C23—9581no—
87C23—4792no—
88C23D191611yescharacteristic, complemented
89C23C22×D47911yescharacteristic
90Q8—9581no—
91D4—22no—
92D4—19164no—
93D4—19162no—
94D4—9581no—
95D4—9582no—
96D4—9582no—
97D4—9582no—
98C2×C4—22no—
99C2×C4—9582no—
100C2×C4—9581no—
101C2×C4—9581no—
102C2×C4—4792no—
103C2×C4D191611yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—19162no—
108C22—19162no—
109C22—19161no—
110C22—19161no—
111C22—9584no—
112C22—9582no—
113C22—9582no—
114C22—38321no—
115C22D4×D47912yes—
116C22C2×D191611yescharacteristic
117C4—21no—
118C4—42no—
119C4—19161no—
120C4—9582no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—19162no—
125C2—19162no—
126C2#2950635211yescharacteristic
subgroupG/H
centerC2#29506352
commutator, cosocleC23×C479C23
FrattiniC23C22×D479
Fitting#99×C479C2
socleC2×C479#120
hypercenter#99D479
hypocenterC479B(4,𝔽2)
LCSG ▷ C23×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #29506427C2semidirect
2. #29506352C2semidirect
3. #29506350C2semidirect
4. #29506296C2semidirect
5. #99×C479C2semidirect
6. C23×D479C22semidirect
14. C22⋊Dic479C22semidirect
18. C22⋊C4×C479C22semidirect
23. C22×D479D4semidirect
33. C2×Dic479D4semidirect
35. C23×C479D4semidirect
39. C2×C4×C479D4semidirect
63. C479B(4,𝔽2)semidirect
69. #99D479semidirect
82. C22⋊C4C2×D479semidirect
88. C23D1916semidirect
103. C2×C4D1916semidirect

Maximal subgroups

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

subgroupindex
#295064272
#295063522
#295063502
#295062962
#99×C4792
B(4,𝔽2)479