Finite Group Databasebeta

← #44416943

Subgroups — #44416943

Order 29248.

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#28410598C211yesmaximal, characteristic, complemented
2#28410578C211yesmaximal, characteristic, complemented
3#28410548C211yesmaximal, characteristic, complemented
4#28410479C211yesmaximal, characteristic, complemented
5#28410478C211yesmaximal, characteristic, complemented
6#28410468C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C457C211yesmaximal, characteristic, complemented
8#20300742—21no—
9#20300741—21no—
10#20300741C2211yescharacteristic
11C2×D1828—21no—
12C2×D1828C2211yescharacteristic
13C2×C22⋊D457—22no—
14D4×D457—22no—
15D4×D457—21no—
16#20300729—21no—
17#20300726—21no—
18#20300725C2211yescharacteristic, complemented
19C4×Dic457C2211yescharacteristic, complemented
20#41×C457C2211yescharacteristic
21C2×D4×C457C2211yescharacteristic, complemented
22SD16×C457—21no—
23D8×C457—21no—
24M16×C457C2211yescharacteristic, complemented
25C22×D457—22no—
26C22×D457D412yes—
27Dic914D411yescharacteristic, complemented
28D1828—22no—
29D1828—21no—
30D1828—21no—
31D1828D411yescharacteristic, complemented
32C22⋊D457—22no—
33C22⋊D457—21no—
34C22⋊D457—44no—
35C2×Dic457—21no—
36C4×D457—22no—
37C4×D457—21no—
38#16814532—21no—
39C23×C457—21no—
40Q8×C457D411yescharacteristic, complemented
41D4×C457—21no—
42D4×C457—21no—
43D4×C457—21no—
44D4×C457D411yescharacteristic, complemented
45C2×C4×C457—21no—
46C2×C4×C457C2311yescharacteristic
47C8×C457—21no—
48C22×C457—21no—
49C22×C457—42no—
50C22×C457—41no—
51C22×C457C2×D411yescharacteristic
52C2×D457—22no—
53C2×D457—21no—
54C2×D457—42no—
55C2×D457—82no—
56C4×C457—21no—
57C4×C457C2×D411yescharacteristic
58C4×C457C2×D411yescharacteristic
59Dic457—22no—
60Dic457—21no—
61C2×C457—21no—
62C2×C457—41no—
63C2×C457—81no—
64C2×C457#12011yescharacteristic
65D457—42no—
66D457—41no—
67C457#45311yescharacteristic, complemented, Sylow
68#453—4571nomaximal, Sylow
69H(5,𝔽2)—4571no—
70AGL(1,ℤ/8)—4571no—
71AGL(1,ℤ/8)D45711yescharacteristic, complemented
72#127—4571no—
73#104—4571no—
74#104—4571no—
75#100—4571no—
76#41—9141no—
77#41—9141no—
78#41—4571no—
79#41C2×D45711yescharacteristic
80C2×D4—9141no—
81C2×D4—9142no—
82C2×D4—9142no—
83C2×D4—9141no—
84C2×D4—4571no—
85C2×D4C2×D45711yescharacteristic, complemented
86SD16—21no—
87SD16—9141no—
88D8—21no—
89D8—9141no—
90M16—4571no—
91M16C2×D45711yescharacteristic, complemented
92C42—4571no—
93C23—21no—
94C23—9142no—
95C23—4572no—
96Q8—4571no—
97Q8C22⋊D45711yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—18284no—
102D4—9142no—
103D4—9142no—
104D4—9141no—
105D4—9141no—
106D4—9141no—
107D4—4571no—
108D4C22⋊D45711yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—9142no—
111C2×C4—9141no—
112C2×C4—9141no—
113C2×C4C22×D45711yescharacteristic
114C8—21no—
115C8—9141no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—18282no—
120C22—36562no—
121C22—9142no—
122C22—9141no—
123C22D4×D45711yescharacteristic
124C4—21no—
125C4—9142no—
126C4—9141no—
127C4D4×D45711yescharacteristic
128C4C2×C22⋊D45711yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—18282no—
133C2—18281no—
134C2#2841052011yescharacteristic
subgroupG/H
centerC2#28410520
commutator, cosocleC2×C4×C457C23
FrattiniC2×C4C22×D457
FittingAGL(1,ℤ/8)×C457C2
socleC2×C457#120
hypercenterAGL(1,ℤ/8)D457
hypocenterC457#453
LCSG ▷ C2×C4×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28410598C2semidirect
2. #28410578C2semidirect
3. #28410548C2semidirect
4. #28410479C2semidirect
5. #28410478C2semidirect
6. #28410468C2semidirect
7. AGL(1,ℤ/8)×C457C2semidirect
18. #20300725C22semidirect
19. C4×Dic457C22semidirect
21. C2×D4×C457C22semidirect
24. M16×C457C22semidirect
27. Dic914D4semidirect
31. D1828D4semidirect
40. Q8×C457D4semidirect
44. D4×C457D4semidirect
67. C457#453semidirect
71. AGL(1,ℤ/8)D457semidirect
85. C2×D4C2×D457semidirect
91. M16C2×D457semidirect
97. Q8C22⋊D457semidirect
108. D4C22⋊D457semidirect

Maximal subgroups

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

subgroupindex
#284105982
#284105782
#284105482
#284104792
#284104782
#284104682
AGL(1,ℤ/8)×C4572
#453457