Finite Group Databasebeta

← #44529238

Subgroups — #44529238

Order 31168.

198 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 198 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#29510260C211yesmaximal, characteristic, complemented
2#29510185C212yesmaximal, complemented
3#29510183C211yesmaximal, characteristic, complemented
4#29510129C212yesmaximal, complemented
5#99×C487C211yesmaximal, characteristic, complemented
6C23×D487C2211yescharacteristic, complemented
7#21441261—21no—
8#21441260—22no—
9C2×D1948—22no—
10C2×C22⋊D487—21no—
11C2×C22⋊D487—21no—
12C2×C22⋊D487C2212yes—
13D4×D487—22no—
14C22⋊Dic487C2211yescharacteristic, complemented
15(C2×D487)⋊C4—22no—
16(C2×D487)⋊C4—21no—
17C2×D4×C487C2211yescharacteristic
18C22⋊C4×C487C2212yescomplemented
19C22×D487—21no—
20C22×D487—22no—
21C22×D487—21no—
22C22×D487—42no—
23C22×D487D412yescomplemented
24Dic974—21no—
25D1948—21no—
26D1948—44no—
27C22⋊D487—22no—
28C22⋊D487—22no—
29C22⋊D487—22no—
30C22⋊D487—42no—
31C2×Dic487—21no—
32C2×Dic487—21no—
33C2×Dic487D412yescomplemented
34C4×D487—22no—
35C23×C487D411yescharacteristic, complemented
36C23×C487C2311yescharacteristic
37D4×C487—22no—
38C2×C4×C487—22no—
39C2×C4×C487D411yescharacteristic, complemented
40C22×C487—21no—
41C22×C487—41no—
42C22×C487—41no—
43C22×C487C2×D412yes—
44C22×C487C2×D411yescharacteristic
45C2×D487—22no—
46C2×D487—24no—
47C2×D487—22no—
48C2×D487—41no—
49C2×D487—42no—
50C2×D487—41no—
51C2×D487—42no—
52C2×D487—81no—
53C4×C487—21no—
54C4×C487—42no—
55Dic487—22no—
56Dic487—41no—
57C2×C487—21no—
58C2×C487—22no—
59C2×C487—41no—
60C2×C487#12011yescharacteristic
61D487—42no—
62D487—42no—
63C487B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—4871nomaximal, Sylow
65H(5,𝔽2)—4871no—
66#120—4871no—
67#120—4872no—
68#99—4872no—
69#99D48711yescharacteristic, complemented
70C24—4871no—
71#41—9742no—
72#41—9741no—
73C2×D4—9742no—
74C2×D4—9742no—
75C2×D4—9741no—
76C2×D4—9741no—
77C2×D4—4872no—
78C2×D4C2×D48711yescharacteristic
79C22⋊C4—9742no—
80C22⋊C4—9741no—
81C22⋊C4—4871no—
82C22⋊C4C2×D48712yescomplemented
83C23—19482no—
84C23—9741no—
85C23—9742no—
86C23—9741no—
87C23—4872no—
88C23D194811yescharacteristic, complemented
89C23C22×D48711yescharacteristic
90Q8—9741no—
91D4—22no—
92D4—19484no—
93D4—19482no—
94D4—9741no—
95D4—9742no—
96D4—9742no—
97D4—9742no—
98C2×C4—22no—
99C2×C4—9742no—
100C2×C4—9741no—
101C2×C4—9741no—
102C2×C4—4872no—
103C2×C4D194811yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—38961no—
108C22—19482no—
109C22—19482no—
110C22—19481no—
111C22—19481no—
112C22—9744no—
113C22—9742no—
114C22—9742no—
115C22D4×D48712yes—
116C22C2×D194811yescharacteristic
117C4—21no—
118C4—42no—
119C4—19481no—
120C4—9742no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—19482no—
125C2—19482no—
126C2#2951018511yescharacteristic
subgroupG/H
centerC2#29510185
commutator, cosocleC23×C487C23
FrattiniC23C22×D487
Fitting#99×C487C2
socleC2×C487#120
hypercenter#99D487
hypocenterC487B(4,𝔽2)
LCSG ▷ C23×C487 ▷ C2×C487 ▷ C487
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #29510260C2semidirect
2. #29510185C2semidirect
3. #29510183C2semidirect
4. #29510129C2semidirect
5. #99×C487C2semidirect
6. C23×D487C22semidirect
14. C22⋊Dic487C22semidirect
18. C22⋊C4×C487C22semidirect
23. C22×D487D4semidirect
33. C2×Dic487D4semidirect
35. C23×C487D4semidirect
39. C2×C4×C487D4semidirect
63. C487B(4,𝔽2)semidirect
69. #99D487semidirect
82. C22⋊C4C2×D487semidirect
88. C23D1948semidirect
103. C2×C4D1948semidirect

Maximal subgroups

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

subgroupindex
#295102602
#295101852
#295101832
#295101292
#99×C4872
B(4,𝔽2)487