Finite Group Databasebeta

← #44500566

Subgroups — #44500566

Order 30656.

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

normal subgroups only

This group has 146 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#29506429C211yesmaximal, characteristic, complemented
2#29506408C211yesmaximal, characteristic, complemented
3#29506369C211yesmaximal, characteristic, complemented
4#29506309C211yesmaximal, characteristic, complemented
5#29506308C211yesmaximal, characteristic, complemented
6#29506300C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C479C211yesmaximal, characteristic, complemented
8#21440162—21no—
9#21440162C2211yescharacteristic
10#21440161—22no—
11#21440161—21no—
12C2×Dic958—21no—
13C2×Dic958C2211yescharacteristic
14Q8×D479—21no—
15#21440150—21no—
16#21440147—21no—
17#21440146C2211yescharacteristic
18C22⋊Dic479—22no—
19C4×Dic479C2211yescharacteristic
20#41×C479C2211yescharacteristic
21C2×D4×C479C2211yescharacteristic
22SD16×C479—21no—
23D8×C479—21no—
24M16×C479C2211yescharacteristic
25Dic958—22no—
26Dic958—21no—
27Dic958—21no—
28Dic958D411yescharacteristic
29D1916D411yescharacteristic
30C22⋊D479—22no—
31C22⋊D479—21no—
32C2×Dic479—22no—
33C2×Dic479—21no—
34C2×Dic479D412yes—
35C4×D479—22no—
36C4×D479—21no—
37C479⋊C8—21no—
38C23×C479—21no—
39Q8×C479D411yescharacteristic
40D4×C479—21no—
41D4×C479—21no—
42D4×C479—21no—
43D4×C479D411yescharacteristic
44C2×C4×C479—21no—
45C2×C4×C479C2311yescharacteristic
46C8×C479—21no—
47C22×C479—21no—
48C22×C479—42no—
49C22×C479—41no—
50C22×C479C2×D411yescharacteristic
51C2×D479—21no—
52C4×C479—21no—
53C4×C479C2×D411yescharacteristic
54C4×C479C2×D411yescharacteristic
55Dic479—21no—
56Dic479—22no—
57Dic479—41no—
58C2×C479—21no—
59C2×C479—41no—
60C2×C479—81no—
61C2×C479#12011yescharacteristic
62D479—41no—
63C479#45411yescharacteristic, complemented, Sylow
64#454—4791nomaximal, Sylow
652−1+4—4791no—
66AGL(1,ℤ/8)—4791no—
67AGL(1,ℤ/8)D47911yescharacteristic, complemented
68#124—4791no—
69#104—4791no—
70#104—4791no—
71#101—4791no—
72#41—9581no—
73#41—9581no—
74#41—9582no—
75#41—4791no—
76#41C2×D47911yescharacteristic
77C2×Q8—9581no—
78C2×Q8—9581no—
79C2×Q8—4791no—
80C2×D4C2×D47911yescharacteristic
81SD16—21no—
82SD16—9581no—
83D8—21no—
84D8—9581no—
85M16—4791no—
86M16C2×D47911yescharacteristic
87C22⋊C4—9582no—
88C42—4791no—
89C23—21no—
90Q8—9582no—
91Q8—9581no—
92Q8—9581no—
93Q8—4791no—
94Q8C22⋊D47911yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—9582no—
99D4—9581no—
100D4—4791no—
101D4C22⋊D47911yescharacteristic
102C2×C4—21no—
103C2×C4—9582no—
104C2×C4—9581no—
105C2×C4—9582no—
106C2×C4—9581no—
107C2×C4—4792no—
108C2×C4C22×D47911yescharacteristic
109C8—21no—
110C8—9581no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—9581no—
115C22D4×D47911yescharacteristic
116C4—21no—
117C4—19161no—
118C4—9581no—
119C4—9582no—
120C4D4×D47911yescharacteristic
121C4C2×C22⋊D47911yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—19161no—
126C2#2950635011yescharacteristic
subgroupG/H
centerC2#29506350
commutator, cosocleC2×C4×C479C23
FrattiniC2×C4C22×D479
FittingAGL(1,ℤ/8)×C479C2
socleC2×C479#120
hypercenterAGL(1,ℤ/8)D479
hypocenterC479#454
LCSG ▷ C2×C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #29506429C2semidirect
2. #29506408C2semidirect
3. #29506369C2semidirect
4. #29506309C2semidirect
5. #29506308C2semidirect
6. #29506300C2semidirect
7. AGL(1,ℤ/8)×C479C2semidirect
63. C479#454semidirect
67. AGL(1,ℤ/8)D479semidirect

Maximal subgroups

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

subgroupindex
#295064292
#295064082
#295063692
#295063092
#295063082
#295063002
AGL(1,ℤ/8)×C4792
#454479