Finite Group Databasebeta

← #44500561

Subgroups — #44500561

Order 30656.

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

normal subgroups only

This group has 168 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, complemented
2#29506408C211yesmaximal, characteristic, complemented
3#29506378C211yesmaximal, characteristic, complemented
4#29506309C211yesmaximal, characteristic, complemented
5#29506308C211yesmaximal, characteristic, complemented
6#29506298C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C479C211yesmaximal, characteristic, complemented
8#21440163—21no—
9#21440162—21no—
10#21440162C2211yescharacteristic
11C2×D1916—21no—
12C2×D1916C2211yescharacteristic
13C2×C22⋊D479—22no—
14D4×D479—22no—
15D4×D479—21no—
16#21440150—21no—
17#21440147—21no—
18#21440146C2211yescharacteristic, complemented
19C4×Dic479C2211yescharacteristic, complemented
20#41×C479C2211yescharacteristic
21C2×D4×C479C2211yescharacteristic, complemented
22SD16×C479—21no—
23D8×C479—21no—
24M16×C479C2211yescharacteristic, complemented
25C22×D479—22no—
26C22×D479D412yes—
27Dic958D411yescharacteristic, complemented
28D1916—22no—
29D1916—21no—
30D1916—21no—
31D1916D411yescharacteristic, complemented
32C22⋊D479—22no—
33C22⋊D479—21no—
34C22⋊D479—44no—
35C2×Dic479—21no—
36C4×D479—22no—
37C4×D479—21no—
38C479⋊C8—21no—
39C23×C479—21no—
40Q8×C479D411yescharacteristic, complemented
41D4×C479—21no—
42D4×C479—21no—
43D4×C479—21no—
44D4×C479D411yescharacteristic, complemented
45C2×C4×C479—21no—
46C2×C4×C479C2311yescharacteristic
47C8×C479—21no—
48C22×C479—21no—
49C22×C479—42no—
50C22×C479—41no—
51C22×C479C2×D411yescharacteristic
52C2×D479—22no—
53C2×D479—21no—
54C2×D479—42no—
55C2×D479—82no—
56C4×C479—21no—
57C4×C479C2×D411yescharacteristic
58C4×C479C2×D411yescharacteristic
59Dic479—22no—
60Dic479—21no—
61C2×C479—21no—
62C2×C479—41no—
63C2×C479—81no—
64C2×C479#12011yescharacteristic
65D479—42no—
66D479—41no—
67C479#45311yescharacteristic, complemented, Sylow
68#453—4791nomaximal, Sylow
69H(5,𝔽2)—4791no—
70AGL(1,ℤ/8)—4791no—
71AGL(1,ℤ/8)D47911yescharacteristic, complemented
72#127—4791no—
73#104—4791no—
74#104—4791no—
75#100—4791no—
76#41—9581no—
77#41—9581no—
78#41—4791no—
79#41C2×D47911yescharacteristic
80C2×D4—9581no—
81C2×D4—9582no—
82C2×D4—9582no—
83C2×D4—9581no—
84C2×D4—4791no—
85C2×D4C2×D47911yescharacteristic, complemented
86SD16—21no—
87SD16—9581no—
88D8—21no—
89D8—9581no—
90M16—4791no—
91M16C2×D47911yescharacteristic, complemented
92C42—4791no—
93C23—21no—
94C23—9582no—
95C23—4792no—
96Q8—4791no—
97Q8C22⋊D47911yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—19164no—
102D4—9582no—
103D4—9582no—
104D4—9581no—
105D4—9581no—
106D4—9581no—
107D4—4791no—
108D4C22⋊D47911yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—9582no—
111C2×C4—9581no—
112C2×C4—9581no—
113C2×C4C22×D47911yescharacteristic
114C8—21no—
115C8—9581no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—19162no—
120C22—9582no—
121C22—9581no—
122C22—38322no—
123C22D4×D47911yescharacteristic
124C4—21no—
125C4—9582no—
126C4—9581no—
127C4D4×D47911yescharacteristic
128C4C2×C22⋊D47911yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—19162no—
133C2—19161no—
134C2#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#453
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. #29506428C2semidirect
2. #29506408C2semidirect
3. #29506378C2semidirect
4. #29506309C2semidirect
5. #29506308C2semidirect
6. #29506298C2semidirect
7. AGL(1,ℤ/8)×C479C2semidirect
18. #21440146C22semidirect
19. C4×Dic479C22semidirect
21. C2×D4×C479C22semidirect
24. M16×C479C22semidirect
27. Dic958D4semidirect
31. D1916D4semidirect
40. Q8×C479D4semidirect
44. D4×C479D4semidirect
67. C479#453semidirect
71. AGL(1,ℤ/8)D479semidirect
85. C2×D4C2×D479semidirect
91. M16C2×D479semidirect
97. Q8C22⋊D479semidirect
108. D4C22⋊D479semidirect

Maximal subgroups

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

subgroupindex
#295064282
#295064082
#295063782
#295063092
#295063082
#295062982
AGL(1,ℤ/8)×C4792
#453479