Finite Group Databasebeta

← #44500571

Subgroups — #44500571

Order 30656.

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

normal subgroups only

This group has 152 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#29506428C211yesmaximal, characteristic
2#29506413C211yesmaximal, characteristic, complemented
3#29506371C211yesmaximal, characteristic, complemented
4#29506309C211yesmaximal, characteristic, complemented
5#29506308C211yesmaximal, characteristic, complemented
6#29506298C211yesmaximal, characteristic, complemented
7#137×C479C211yesmaximal, characteristic, complemented
8#21440163—21no—
9#21440162—21no—
10#21440162C2211yescharacteristic
11C2×D1916—21no—
12C2×D1916C2211yescharacteristic
13D4×D479—22no—
14D4×D479—21no—
15#21440152—21no—
16#21440149—21no—
17#21440146C2211yescharacteristic, complemented
18(C2×D479)⋊C4—22no—
19C4×Dic479C2211yescharacteristic, complemented
20#41×C479C2211yescharacteristic
21C2×Q8×C479C2211yescharacteristic, complemented
22Q16×C479—21no—
23SD16×C479—21no—
24M16×C479C2211yescharacteristic, complemented
25C22×D479—22no—
26C22×D479D412yes—
27Dic958D411yescharacteristic
28D1916—22no—
29D1916—21no—
30D1916—21no—
31D1916D411yescharacteristic
32C22⋊D479—22no—
33C22⋊D479—21no—
34C2×Dic479—21no—
35C4×D479—22no—
36C4×D479—21no—
37C479⋊C8—21no—
38Q8×C479—21no—
39Q8×C479—21no—
40Q8×C479D411yescharacteristic
41D4×C479—21no—
42D4×C479D411yescharacteristic
43C2×C4×C479—21no—
44C2×C4×C479—21no—
45C2×C4×C479C2311yescharacteristic
46C8×C479—21no—
47C22×C479—21no—
48C22×C479C2×D411yescharacteristic
49C2×D479—22no—
50C2×D479—21no—
51C2×D479—42no—
52C2×D479—82no—
53C4×C479—21no—
54C4×C479—41no—
55C4×C479C2×D411yescharacteristic
56C4×C479C2×D411yescharacteristic
57Dic479—21no—
58Dic479—41no—
59C2×C479—21no—
60C2×C479—41no—
61C2×C479#12011yescharacteristic
62D479—42no—
63D479—41no—
64C479#45511yescharacteristic, complemented, Sylow
65#455—4791nomaximal, Sylow
66H(5,𝔽2)—4791no—
67#137—4791no—
68#137D47911yescharacteristic, complemented
69#124—4791no—
70#104—4791no—
71#104—4791no—
72#100—4791no—
73#41—9581no—
74#41—9581no—
75#41—4791no—
76#41C2×D47911yescharacteristic
77C2×Q8C2×D47911yescharacteristic, complemented
78C2×D4—9581no—
79C2×D4—9582no—
80C2×D4—9581no—
81C2×D4—4791no—
82Q16—21no—
83Q16—9581no—
84SD16—21no—
85SD16—9581no—
86M16—4791no—
87M16C2×D47911yescharacteristic, complemented
88C22⋊C4—9582no—
89C42—4791no—
90C23—9582no—
91C23—4792no—
92Q8—21no—
93Q8—21no—
94Q8—4791no—
95Q8C22⋊D47911yescharacteristic
96D4—21no—
97D4—9582no—
98D4—9582no—
99D4—9581no—
100D4—9581no—
101D4—9581no—
102D4—4791no—
103D4C22⋊D47911yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—9582no—
107C2×C4—9581no—
108C2×C4—9581no—
109C2×C4C22×D47911yescharacteristic
110C8—21no—
111C8—9581no—
112C22—21no—
113C22—19162no—
114C22—9582no—
115C22—9581no—
116C22—38322no—
117C22D4×D47911yescharacteristic
118C4—21no—
119C4—41no—
120C4—19161no—
121C4—9581no—
122C4D4×D47911yescharacteristic
123C4C2×C22⋊D47911yescharacteristic
124C2—21no—
125C2—41no—
126C2—19162no—
127C2—19161no—
128C2#2950635011yescharacteristic
subgroupG/H
centerC2#29506350
commutator, cosocleC2×C4×C479C23
FrattiniC2×C4C22×D479
Fitting#137×C479C2
socleC2×C479#120
prime radical#29506428C2
hypercenter#137D479
hypocenterC479#455
LCSG ▷ C2×C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #29506413C2semidirect
3. #29506371C2semidirect
4. #29506309C2semidirect
5. #29506308C2semidirect
6. #29506298C2semidirect
7. #137×C479C2semidirect
17. #21440146C22semidirect
19. C4×Dic479C22semidirect
21. C2×Q8×C479C22semidirect
24. M16×C479C22semidirect
64. C479#455semidirect
68. #137D479semidirect
77. C2×Q8C2×D479semidirect
87. M16C2×D479semidirect

Maximal subgroups

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

subgroupindex
#295064282
#295064132
#295063712
#295063092
#295063082
#295062982
#137×C4792
#455479