Finite Group Databasebeta

← #44500576

Subgroups — #44500576

Order 30656.

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

normal subgroups only

This group has 142 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
2#29506413C211yesmaximal, characteristic, complemented
3#29506380C211yesmaximal, characteristic, complemented
4#29506309C211yesmaximal, characteristic, complemented
5#29506308C211yesmaximal, characteristic, complemented
6#29506300C211yesmaximal, characteristic, complemented
7#137×C479C211yesmaximal, characteristic, complemented
8#21440162—21no—
9#21440162C2211yescharacteristic
10#21440161—22no—
11#21440161—21no—
12C2×Dic958—21no—
13C2×Dic958C2211yescharacteristic
14Q8×D479—21no—
15#21440152—21no—
16#21440149—21no—
17#21440146C2211yescharacteristic
18Dic479⋊C4—22no—
19C4×Dic479C2211yescharacteristic
20#41×C479C2211yescharacteristic
21C2×Q8×C479C2211yescharacteristic
22Q16×C479—21no—
23SD16×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—
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—21no—
50C4×C479—21no—
51C4×C479—41no—
52C4×C479C2×D411yescharacteristic
53C4×C479C2×D411yescharacteristic
54Dic479—22no—
55Dic479—21no—
56Dic479—22no—
57C2×C479—21no—
58C2×C479—41no—
59C2×C479#12011yescharacteristic
60D479—41no—
61C479#45611yescharacteristic, complemented, Sylow
62#456—4791nomaximal, Sylow
632−1+4—4791no—
64#137—4791no—
65#137D47911yescharacteristic, complemented
66C4⋊Q8—4791no—
67#104—4791no—
68#104—4791no—
69#101—4791no—
70#41—9581no—
71#41—9581no—
72#41—9582no—
73#41—4791no—
74#41C2×D47911yescharacteristic
75C2×Q8—9581no—
76C2×Q8—9581no—
77C2×Q8—4791no—
78C2×Q8C2×D47911yescharacteristic
79Q16—21no—
80Q16—9581no—
81SD16—21no—
82SD16—9581no—
83M16—4791no—
84M16C2×D47911yescharacteristic
85C4⋊C4—9582no—
86C42—4791no—
87Q8—21no—
88Q8—21no—
89Q8—9582no—
90Q8—9581no—
91Q8—9581no—
92Q8—4791no—
93Q8C22⋊D47911yescharacteristic
94D4—21no—
95D4—9582no—
96D4—9581no—
97D4—4791no—
98D4C22⋊D47911yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—9582no—
102C2×C4—9582no—
103C2×C4—9581no—
104C2×C4—9581no—
105C2×C4—4792no—
106C2×C4C22×D47911yescharacteristic
107C8—21no—
108C8—9581no—
109C22—21no—
110C22—9581no—
111C22D4×D47911yescharacteristic
112C4—21no—
113C4—41no—
114C4—9582no—
115C4—9581no—
116C4—9582no—
117C4D4×D47911yescharacteristic
118C4C2×C22⋊D47911yescharacteristic
119C2—21no—
120C2—41no—
121C2—19161no—
122C2#2950635011yescharacteristic
subgroupG/H
centerC2#29506350
commutator, cosocleC2×C4×C479C23
FrattiniC2×C4C22×D479
Fitting#137×C479C2
socleC2×C479#120
prime radical#29506429C2
hypercenter#137D479
hypocenterC479#456
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. #29506380C2semidirect
4. #29506309C2semidirect
5. #29506308C2semidirect
6. #29506300C2semidirect
7. #137×C479C2semidirect
61. C479#456semidirect
65. #137D479semidirect

Maximal subgroups

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

subgroupindex
#295064292
#295064132
#295063802
#295063092
#295063082
#295063002
#137×C4792
#456479