Finite Group Databasebeta

← #44442242

Subgroups — #44442242

Order 29504.

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#28414164C211yesmaximal, characteristic, complemented
2#28414144C211yesmaximal, characteristic, complemented
3#28414114C211yesmaximal, characteristic, complemented
4#28414045C211yesmaximal, characteristic, complemented
5#28414044C211yesmaximal, characteristic, complemented
6#28414034C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C461C211yesmaximal, characteristic, complemented
8#20301502—21no—
9#20301501—21no—
10#20301501C2211yescharacteristic
11C2×D1844—21no—
12C2×D1844C2211yescharacteristic
13C2×C22⋊D461—22no—
14D4×D461—22no—
15D4×D461—21no—
16#20301489—21no—
17#20301486—21no—
18#20301485C2211yescharacteristic, complemented
19C4×Dic461C2211yescharacteristic, complemented
20#41×C461C2211yescharacteristic
21C2×D4×C461C2211yescharacteristic, complemented
22SD16×C461—21no—
23D8×C461—21no—
24M16×C461C2211yescharacteristic, complemented
25C22×D461—22no—
26C22×D461D412yes—
27Dic922D411yescharacteristic, complemented
28D1844—22no—
29D1844—21no—
30D1844—21no—
31D1844D411yescharacteristic, complemented
32C22⋊D461—22no—
33C22⋊D461—21no—
34C22⋊D461—44no—
35C2×Dic461—21no—
36C4×D461—22no—
37C4×D461—21no—
38#16814779—21no—
39C23×C461—21no—
40Q8×C461D411yescharacteristic, complemented
41D4×C461—21no—
42D4×C461—21no—
43D4×C461—21no—
44D4×C461D411yescharacteristic, complemented
45C2×C4×C461—21no—
46C2×C4×C461C2311yescharacteristic
47C8×C461—21no—
48C22×C461—21no—
49C22×C461—42no—
50C22×C461—41no—
51C22×C461C2×D411yescharacteristic
52C2×D461—22no—
53C2×D461—21no—
54C2×D461—42no—
55C2×D461—82no—
56C4×C461—21no—
57C4×C461C2×D411yescharacteristic
58C4×C461C2×D411yescharacteristic
59Dic461—22no—
60Dic461—21no—
61C2×C461—21no—
62C2×C461—41no—
63C2×C461—81no—
64C2×C461#12011yescharacteristic
65D461—42no—
66D461—41no—
67C461#45311yescharacteristic, complemented, Sylow
68#453—4611nomaximal, Sylow
69H(5,𝔽2)—4611no—
70AGL(1,ℤ/8)—4611no—
71AGL(1,ℤ/8)D46111yescharacteristic, complemented
72#127—4611no—
73#104—4611no—
74#104—4611no—
75#100—4611no—
76#41—9221no—
77#41—9221no—
78#41—4611no—
79#41C2×D46111yescharacteristic
80C2×D4—9221no—
81C2×D4—9222no—
82C2×D4—9222no—
83C2×D4—9221no—
84C2×D4—4611no—
85C2×D4C2×D46111yescharacteristic, complemented
86SD16—21no—
87SD16—9221no—
88D8—21no—
89D8—9221no—
90M16—4611no—
91M16C2×D46111yescharacteristic, complemented
92C42—4611no—
93C23—21no—
94C23—9222no—
95C23—4612no—
96Q8—4611no—
97Q8C22⋊D46111yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—18444no—
102D4—9222no—
103D4—9222no—
104D4—9221no—
105D4—9221no—
106D4—9221no—
107D4—4611no—
108D4C22⋊D46111yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—9222no—
111C2×C4—9221no—
112C2×C4—9221no—
113C2×C4C22×D46111yescharacteristic
114C8—21no—
115C8—9221no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—18442no—
120C22—36882no—
121C22—9222no—
122C22—9221no—
123C22D4×D46111yescharacteristic
124C4—21no—
125C4—9222no—
126C4—9221no—
127C4D4×D46111yescharacteristic
128C4C2×C22⋊D46111yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—18442no—
133C2—18441no—
134C2#2841408611yescharacteristic
subgroupG/H
centerC2#28414086
commutator, cosocleC2×C4×C461C23
FrattiniC2×C4C22×D461
FittingAGL(1,ℤ/8)×C461C2
socleC2×C461#120
hypercenterAGL(1,ℤ/8)D461
hypocenterC461#453
LCSG ▷ C2×C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28414164C2semidirect
2. #28414144C2semidirect
3. #28414114C2semidirect
4. #28414045C2semidirect
5. #28414044C2semidirect
6. #28414034C2semidirect
7. AGL(1,ℤ/8)×C461C2semidirect
18. #20301485C22semidirect
19. C4×Dic461C22semidirect
21. C2×D4×C461C22semidirect
24. M16×C461C22semidirect
27. Dic922D4semidirect
31. D1844D4semidirect
40. Q8×C461D4semidirect
44. D4×C461D4semidirect
67. C461#453semidirect
71. AGL(1,ℤ/8)D461semidirect
85. C2×D4C2×D461semidirect
91. M16C2×D461semidirect
97. Q8C22⋊D461semidirect
108. D4C22⋊D461semidirect

Maximal subgroups

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

subgroupindex
#284141642
#284141442
#284141142
#284140452
#284140442
#284140342
AGL(1,ℤ/8)×C4612
#453461