Finite Group Databasebeta

← #44529239

Subgroups — #44529239

Order 31168.

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

normal subgroups only

This group has 160 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
2#29510198C212yesmaximal, complemented
3#29510130C211yesmaximal, characteristic, complemented
4#29510129C212yesmaximal, complemented
5#123×C487C211yesmaximal, characteristic, complemented
6#21441261—21no—
7#21441260—22no—
8C2×C22⋊D487—21no—
9C2×C22⋊D487C2212yes—
10D4×D487—22no—
11Dic487⋊C4—22no—
12C22⋊Dic487C2212yescomplemented
13(C2×D487)⋊C4—22no—
14C2×D4×C487C2211yescharacteristic
15C22×C4×C487C2211yescharacteristic, complemented
16C4⋊C4×C487—21no—
17C22⋊C4×C487—21no—
18C22⋊C4×C487C2211yescharacteristic, complemented
19C22×D487—21no—
20C22×D487D412yes—
21Dic974—21no—
22D1948—21no—
23C22⋊D487—22no—
24C22⋊D487—22no—
25C22⋊D487—22no—
26C2×Dic487—21no—
27C2×Dic487—22no—
28C2×Dic487D412yes—
29C4×D487—22no—
30C23×C487D411yescharacteristic
31C23×C487C2311yescharacteristic
32D4×C487—22no—
33C2×C4×C487—21no—
34C2×C4×C487—21no—
35C2×C4×C487—22no—
36C2×C4×C487D411yescharacteristic
37C22×C487—21no—
38C22×C487—41no—
39C22×C487—41no—
40C22×C487C2×D412yes—
41C22×C487C2×D411yescharacteristic
42C2×D487—22no—
43C2×D487—42no—
44C2×D487—81no—
45C4×C487—21no—
46C4×C487—41no—
47C4×C487—41no—
48Dic487—22no—
49Dic487—42no—
50C2×C487—22no—
51C2×C487—21no—
52C2×C487—41no—
53C2×C487#12011yescharacteristic
54D487—42no—
55C487#45811yescharacteristic, complemented, Sylow
56#458—4871nomaximal, Sylow
57H(5,𝔽2)—4871no—
58#123—4872no—
59#123D48711yescharacteristic, complemented
60#99—4871no—
61#99—4872no—
62#41—9742no—
63#41—9741no—
64C2×D4—9742no—
65C2×D4—9741no—
66C2×D4—4872no—
67C2×D4C2×D48711yescharacteristic
68C22×C4C2×D48711yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—9742no—
71C22⋊C4—21no—
72C22⋊C4—9742no—
73C22⋊C4—4872no—
74C22⋊C4C2×D48711yescharacteristic, complemented
75C23—9741no—
76C23—4872no—
77C23C22⋊D48711yescharacteristic
78C23C22×D48711yescharacteristic
79Q8—9741no—
80D4—22no—
81D4—9741no—
82D4—9742no—
83D4—9742no—
84D4—9742no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—9742no—
89C2×C4—9742no—
90C2×C4—9741no—
91C2×C4—4872no—
92C2×C4C22⋊D48711yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—38961no—
97C22—19482no—
98C22—9742no—
99C22D4×D48712yes—
100C22C2×C22⋊D48711yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—19482no—
105C4—9742no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—19482no—
110C2#2951018311yescharacteristic
subgroupG/H
centerC2#29510183
commutator, cosocleC23×C487C23
FrattiniC23C22×D487
Fitting#123×C487C2
socleC2×C487#120
prime radical#29510260C2
hypercenter#123D487
hypocenterC487#458
LCSG ▷ C23×C487 ▷ C2×C487 ▷ C487
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #29510198C2semidirect
3. #29510130C2semidirect
4. #29510129C2semidirect
5. #123×C487C2semidirect
12. C22⋊Dic487C22semidirect
15. C22×C4×C487C22semidirect
18. C22⋊C4×C487C22semidirect
55. C487#458semidirect
59. #123D487semidirect
68. C22×C4C2×D487semidirect
74. C22⋊C4C2×D487semidirect

Maximal subgroups

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

subgroupindex
#295102602
#295101982
#295101302
#295101292
#123×C4872
#458487