Finite Group Databasebeta

← #43243770

Subgroups — #43243770

Order 28096.

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#28380789C211yesmaximal, characteristic, complemented
2#28380769C211yesmaximal, characteristic, complemented
3#28380739C211yesmaximal, characteristic, complemented
4#28380670C211yesmaximal, characteristic, complemented
5#28380669C211yesmaximal, characteristic, complemented
6#28380659C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C439C211yesmaximal, characteristic, complemented
8#20296330—21no—
9#20296329—21no—
10#20296329C2211yescharacteristic
11C2×D1756—21no—
12C2×D1756C2211yescharacteristic
13C2×C22⋊D439—22no—
14D4×D439—22no—
15D4×D439—21no—
16#20296317—21no—
17#20296314—21no—
18#20296313C2211yescharacteristic, complemented
19C4×Dic439C2211yescharacteristic, complemented
20#41×C439C2211yescharacteristic
21C2×D4×C439C2211yescharacteristic, complemented
22SD16×C439—21no—
23D8×C439—21no—
24M16×C439C2211yescharacteristic, complemented
25C22×D439—22no—
26C22×D439D412yes—
27Dic878D411yescharacteristic, complemented
28D1756—22no—
29D1756—21no—
30D1756—21no—
31D1756D411yescharacteristic, complemented
32C22⋊D439—22no—
33C22⋊D439—21no—
34C22⋊D439—44no—
35C2×Dic439—21no—
36C4×D439—22no—
37C4×D439—21no—
38C439⋊C8—21no—
39C23×C439—21no—
40Q8×C439D411yescharacteristic, complemented
41D4×C439—21no—
42D4×C439—21no—
43D4×C439—21no—
44D4×C439D411yescharacteristic, complemented
45C2×C4×C439—21no—
46C2×C4×C439C2311yescharacteristic
47C8×C439—21no—
48C22×C439—21no—
49C22×C439—42no—
50C22×C439—41no—
51C22×C439C2×D411yescharacteristic
52C2×D439—22no—
53C2×D439—21no—
54C2×D439—42no—
55C2×D439—82no—
56C4×C439—21no—
57C4×C439C2×D411yescharacteristic
58C4×C439C2×D411yescharacteristic
59Dic439—22no—
60Dic439—21no—
61C2×C439—21no—
62C2×C439—41no—
63C2×C439—81no—
64C2×C439#12011yescharacteristic
65D439—42no—
66D439—41no—
67C439#45311yescharacteristic, complemented, Sylow
68#453—4391nomaximal, Sylow
69H(5,𝔽2)—4391no—
70AGL(1,ℤ/8)—4391no—
71AGL(1,ℤ/8)D43911yescharacteristic, complemented
72#127—4391no—
73#104—4391no—
74#104—4391no—
75#100—4391no—
76#41—8781no—
77#41—8781no—
78#41—4391no—
79#41C2×D43911yescharacteristic
80C2×D4—8781no—
81C2×D4—8782no—
82C2×D4—8781no—
83C2×D4—8782no—
84C2×D4—4391no—
85C2×D4C2×D43911yescharacteristic, complemented
86SD16—21no—
87SD16—8781no—
88D8—21no—
89D8—8781no—
90M16—4391no—
91M16C2×D43911yescharacteristic, complemented
92C42—4391no—
93C23—21no—
94C23—8782no—
95C23—4392no—
96Q8—4391no—
97Q8C22⋊D43911yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—8782no—
102D4—8782no—
103D4—8781no—
104D4—8781no—
105D4—8781no—
106D4—4391no—
107D4—17564no—
108D4C22⋊D43911yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—8782no—
111C2×C4—8781no—
112C2×C4—8781no—
113C2×C4C22×D43911yescharacteristic
114C8—21no—
115C8—8781no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—8782no—
120C22—8781no—
121C22—35122no—
122C22—17562no—
123C22D4×D43911yescharacteristic
124C4—21no—
125C4—8782no—
126C4—8781no—
127C4D4×D43911yescharacteristic
128C4C2×C22⋊D43911yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—17561no—
133C2—17562no—
134C2#2838071111yescharacteristic
subgroupG/H
centerC2#28380711
commutator, cosocleC2×C4×C439C23
FrattiniC2×C4C22×D439
FittingAGL(1,ℤ/8)×C439C2
socleC2×C439#120
hypercenterAGL(1,ℤ/8)D439
hypocenterC439#453
LCSG ▷ C2×C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28380789C2semidirect
2. #28380769C2semidirect
3. #28380739C2semidirect
4. #28380670C2semidirect
5. #28380669C2semidirect
6. #28380659C2semidirect
7. AGL(1,ℤ/8)×C439C2semidirect
18. #20296313C22semidirect
19. C4×Dic439C22semidirect
21. C2×D4×C439C22semidirect
24. M16×C439C22semidirect
27. Dic878D4semidirect
31. D1756D4semidirect
40. Q8×C439D4semidirect
44. D4×C439D4semidirect
67. C439#453semidirect
71. AGL(1,ℤ/8)D439semidirect
85. C2×D4C2×D439semidirect
91. M16C2×D439semidirect
97. Q8C22⋊D439semidirect
108. D4C22⋊D439semidirect

Maximal subgroups

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

subgroupindex
#283807892
#283807692
#283807392
#283806702
#283806692
#283806592
AGL(1,ℤ/8)×C4392
#453439