Finite Group Databasebeta

← #44529216

Subgroups — #44529216

Order 31168.

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#29510261C211yesmaximal, characteristic, complemented
2#29510241C211yesmaximal, characteristic, complemented
3#29510211C211yesmaximal, characteristic, complemented
4#29510142C211yesmaximal, characteristic, complemented
5#29510141C211yesmaximal, characteristic, complemented
6#29510131C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C487C211yesmaximal, characteristic, complemented
8#21441262—21no—
9#21441261—21no—
10#21441261C2211yescharacteristic
11C2×D1948—21no—
12C2×D1948C2211yescharacteristic
13C2×C22⋊D487—22no—
14D4×D487—22no—
15D4×D487—21no—
16#21441249—21no—
17#21441246—21no—
18#21441245C2211yescharacteristic, complemented
19C4×Dic487C2211yescharacteristic, complemented
20#41×C487C2211yescharacteristic
21C2×D4×C487C2211yescharacteristic, complemented
22SD16×C487—21no—
23D8×C487—21no—
24M16×C487C2211yescharacteristic, complemented
25C22×D487—22no—
26C22×D487D412yes—
27Dic974D411yescharacteristic, complemented
28D1948—22no—
29D1948—21no—
30D1948—21no—
31D1948D411yescharacteristic, complemented
32C22⋊D487—22no—
33C22⋊D487—21no—
34C22⋊D487—44no—
35C2×Dic487—21no—
36C4×D487—22no—
37C4×D487—21no—
38C487⋊C8—21no—
39C23×C487—21no—
40Q8×C487D411yescharacteristic, complemented
41D4×C487—21no—
42D4×C487—21no—
43D4×C487—21no—
44D4×C487D411yescharacteristic, complemented
45C2×C4×C487—21no—
46C2×C4×C487C2311yescharacteristic
47C8×C487—21no—
48C22×C487—21no—
49C22×C487—42no—
50C22×C487—41no—
51C22×C487C2×D411yescharacteristic
52C2×D487—22no—
53C2×D487—21no—
54C2×D487—42no—
55C2×D487—82no—
56C4×C487—21no—
57C4×C487C2×D411yescharacteristic
58C4×C487C2×D411yescharacteristic
59Dic487—22no—
60Dic487—21no—
61C2×C487—21no—
62C2×C487—41no—
63C2×C487—81no—
64C2×C487#12011yescharacteristic
65D487—42no—
66D487—41no—
67C487#45311yescharacteristic, complemented, Sylow
68#453—4871nomaximal, Sylow
69H(5,𝔽2)—4871no—
70AGL(1,ℤ/8)—4871no—
71AGL(1,ℤ/8)D48711yescharacteristic, complemented
72#127—4871no—
73#104—4871no—
74#104—4871no—
75#100—4871no—
76#41—9741no—
77#41—9741no—
78#41—4871no—
79#41C2×D48711yescharacteristic
80C2×D4—9741no—
81C2×D4—9742no—
82C2×D4—9742no—
83C2×D4—9741no—
84C2×D4—4871no—
85C2×D4C2×D48711yescharacteristic, complemented
86SD16—21no—
87SD16—9741no—
88D8—21no—
89D8—9741no—
90M16—4871no—
91M16C2×D48711yescharacteristic, complemented
92C42—4871no—
93C23—21no—
94C23—9742no—
95C23—4872no—
96Q8—4871no—
97Q8C22⋊D48711yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—19484no—
102D4—9742no—
103D4—9742no—
104D4—9741no—
105D4—9741no—
106D4—9741no—
107D4—4871no—
108D4C22⋊D48711yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—9742no—
111C2×C4—9741no—
112C2×C4—9741no—
113C2×C4C22×D48711yescharacteristic
114C8—21no—
115C8—9741no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—38962no—
120C22—19482no—
121C22—9742no—
122C22—9741no—
123C22D4×D48711yescharacteristic
124C4—21no—
125C4—9742no—
126C4—9741no—
127C4D4×D48711yescharacteristic
128C4C2×C22⋊D48711yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—19481no—
133C2—19482no—
134C2#2951018311yescharacteristic
subgroupG/H
centerC2#29510183
commutator, cosocleC2×C4×C487C23
FrattiniC2×C4C22×D487
FittingAGL(1,ℤ/8)×C487C2
socleC2×C487#120
hypercenterAGL(1,ℤ/8)D487
hypocenterC487#453
LCSG ▷ C2×C4×C487 ▷ C2×C487 ▷ C487
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #29510261C2semidirect
2. #29510241C2semidirect
3. #29510211C2semidirect
4. #29510142C2semidirect
5. #29510141C2semidirect
6. #29510131C2semidirect
7. AGL(1,ℤ/8)×C487C2semidirect
18. #21441245C22semidirect
19. C4×Dic487C22semidirect
21. C2×D4×C487C22semidirect
24. M16×C487C22semidirect
27. Dic974D4semidirect
31. D1948D4semidirect
40. Q8×C487D4semidirect
44. D4×C487D4semidirect
67. C487#453semidirect
71. AGL(1,ℤ/8)D487semidirect
85. C2×D4C2×D487semidirect
91. M16C2×D487semidirect
97. Q8C22⋊D487semidirect
108. D4C22⋊D487semidirect

Maximal subgroups

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

subgroupindex
#295102612
#295102412
#295102112
#295101422
#295101412
#295101312
AGL(1,ℤ/8)×C4872
#453487