Finite Group Databasebeta

← #44566447

Subgroups — #44566447

Order 32192.

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#30632910C211yesmaximal, characteristic, complemented
2#30632890C211yesmaximal, characteristic, complemented
3#30632860C211yesmaximal, characteristic, complemented
4#30632791C211yesmaximal, characteristic, complemented
5#30632790C211yesmaximal, characteristic, complemented
6#30632780C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C503C211yesmaximal, characteristic, complemented
8#22548884—21no—
9#22548883—21no—
10#22548883C2211yescharacteristic
11C2×D2012—21no—
12C2×D2012C2211yescharacteristic
13C2×C22⋊D503—22no—
14D4×D503—22no—
15D4×D503—21no—
16#22548871—21no—
17#22548868—21no—
18#22548867C2211yescharacteristic, complemented
19C4×Dic503C2211yescharacteristic, complemented
20#41×C503C2211yescharacteristic
21C2×D4×C503C2211yescharacteristic, complemented
22SD16×C503—21no—
23D8×C503—21no—
24M16×C503C2211yescharacteristic, complemented
25C22×D503—22no—
26C22×D503D412yes—
27Dic1006D411yescharacteristic, complemented
28D2012—22no—
29D2012—21no—
30D2012—21no—
31D2012D411yescharacteristic, complemented
32C22⋊D503—22no—
33C22⋊D503—21no—
34C22⋊D503—44no—
35C2×Dic503—21no—
36C4×D503—22no—
37C4×D503—21no—
38C503⋊C8—21no—
39C23×C503—21no—
40Q8×C503D411yescharacteristic, complemented
41D4×C503—21no—
42D4×C503—21no—
43D4×C503—21no—
44D4×C503D411yescharacteristic, complemented
45C2×C4×C503—21no—
46C2×C4×C503C2311yescharacteristic
47C8×C503—21no—
48C22×C503—21no—
49C22×C503—42no—
50C22×C503—41no—
51C22×C503C2×D411yescharacteristic
52C2×D503—22no—
53C2×D503—21no—
54C2×D503—42no—
55C2×D503—82no—
56C4×C503—21no—
57C4×C503C2×D411yescharacteristic
58C4×C503C2×D411yescharacteristic
59Dic503—22no—
60Dic503—21no—
61C2×C503—21no—
62C2×C503—41no—
63C2×C503—81no—
64C2×C503#12011yescharacteristic
65D503—42no—
66D503—41no—
67C503#45311yescharacteristic, complemented, Sylow
68#453—5031nomaximal, Sylow
69H(5,𝔽2)—5031no—
70AGL(1,ℤ/8)—5031no—
71AGL(1,ℤ/8)D50311yescharacteristic, complemented
72#127—5031no—
73#104—5031no—
74#104—5031no—
75#100—5031no—
76#41—10061no—
77#41—10061no—
78#41—5031no—
79#41C2×D50311yescharacteristic
80C2×D4—10061no—
81C2×D4—10062no—
82C2×D4—10062no—
83C2×D4—10061no—
84C2×D4—5031no—
85C2×D4C2×D50311yescharacteristic, complemented
86SD16—21no—
87SD16—10061no—
88D8—21no—
89D8—10061no—
90M16—5031no—
91M16C2×D50311yescharacteristic, complemented
92C42—5031no—
93C23—21no—
94C23—10062no—
95C23—5032no—
96Q8—5031no—
97Q8C22⋊D50311yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—20124no—
102D4—10062no—
103D4—10062no—
104D4—10061no—
105D4—10061no—
106D4—10061no—
107D4—5031no—
108D4C22⋊D50311yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—10062no—
111C2×C4—10061no—
112C2×C4—10061no—
113C2×C4C22×D50311yescharacteristic
114C8—21no—
115C8—10061no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—40242no—
120C22—20122no—
121C22—10062no—
122C22—10061no—
123C22D4×D50311yescharacteristic
124C4—21no—
125C4—10062no—
126C4—10061no—
127C4D4×D50311yescharacteristic
128C4C2×C22⋊D50311yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—20121no—
133C2—20122no—
134C2#3063283211yescharacteristic
subgroupG/H
centerC2#30632832
commutator, cosocleC2×C4×C503C23
FrattiniC2×C4C22×D503
FittingAGL(1,ℤ/8)×C503C2
socleC2×C503#120
hypercenterAGL(1,ℤ/8)D503
hypocenterC503#453
LCSG ▷ C2×C4×C503 ▷ C2×C503 ▷ C503
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30632910C2semidirect
2. #30632890C2semidirect
3. #30632860C2semidirect
4. #30632791C2semidirect
5. #30632790C2semidirect
6. #30632780C2semidirect
7. AGL(1,ℤ/8)×C503C2semidirect
18. #22548867C22semidirect
19. C4×Dic503C22semidirect
21. C2×D4×C503C22semidirect
24. M16×C503C22semidirect
27. Dic1006D4semidirect
31. D2012D4semidirect
40. Q8×C503D4semidirect
44. D4×C503D4semidirect
67. C503#453semidirect
71. AGL(1,ℤ/8)D503semidirect
85. C2×D4C2×D503semidirect
91. M16C2×D503semidirect
97. Q8C22⋊D503semidirect
108. D4C22⋊D503semidirect

Maximal subgroups

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

subgroupindex
#306329102
#306328902
#306328602
#306327912
#306327902
#306327802
AGL(1,ℤ/8)×C5032
#453503