Finite Group Databasebeta

← #34094343

Subgroups — #34094343

Order 20032.

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#23756542C211yesmaximal, characteristic
2#23756481C212yesmaximal, complemented
3#23756478C211yesmaximal, characteristic, complemented
4#23756411C212yesmaximal, complemented
5#99×C313C211yesmaximal, characteristic, complemented
6#19097561—21no—
7#19097560—22no—
8C2×C22⋊D313—21no—
9C2×C22⋊D313C2212yes—
10D4×D313—22no—
11C22×Dic313C2211yescharacteristic, complemented
12C4⋊Dic313—22no—
13#19097540—21no—
14C22⋊Dic313—21no—
15C22⋊Dic313C2211yescharacteristic, complemented
16#19097538—22no—
17C2×D4×C313C2211yescharacteristic
18C22⋊C4×C313C2212yescomplemented
19C22×D313—21no—
20C22×D313D412yes—
21Dic626—21no—
22D1252—21no—
23C22⋊D313—22no—
24C22⋊D313—22no—
25C22⋊D313—22no—
26C2×Dic313—21no—
27C2×Dic313—22no—
28C2×Dic313—21no—
29C2×Dic313—21no—
30C2×Dic313D412yes—
31C4×D313—22no—
32C23×C313D411yescharacteristic
33C23×C313C2311yescharacteristic
34D4×C313—22no—
35C2×C4×C313—22no—
36C2×C4×C313D411yescharacteristic
37C22×C313—21no—
38C22×C313—41no—
39C22×C313—41no—
40C22×C313C2×D412yes—
41C22×C313C2×D411yescharacteristic
42C2×D313—22no—
43C2×D313—42no—
44C2×D313—81no—
45C4×C313—21no—
46C4×C313—42no—
47Dic313—22no—
48Dic313—41no—
49Dic313—41no—
50C2×C313—21no—
51C2×C313—22no—
52C2×C313—41no—
53C2×C313#12011yescharacteristic
54D313—42no—
55C313#45811yescharacteristic, complemented, Sylow
56#458—3131nomaximal, Sylow
57H(5,𝔽2)—3131no—
58#123—3131no—
59#123—3132no—
60#99—3132no—
61#99D31311yescharacteristic, complemented
62#41—6262no—
63#41—6261no—
64C2×D4—3132no—
65C2×D4—6262no—
66C2×D4—6261no—
67C2×D4C2×D31311yescharacteristic
68C22×C4—3131no—
69C4⋊C4—6262no—
70C4⋊C4—6261no—
71C22⋊C4—3131no—
72C22⋊C4—6262no—
73C22⋊C4—6261no—
74C22⋊C4C2×D31312yescomplemented
75C23—3132no—
76C23—6261no—
77C23D125211yescharacteristic
78C23C22×D31311yescharacteristic
79Q8—6261no—
80D4—22no—
81D4—6261no—
82D4—6262no—
83D4—6262no—
84D4—6262no—
85C2×C4—22no—
86C2×C4—3132no—
87C2×C4—6262no—
88C2×C4—6261no—
89C2×C4—6262no—
90C2×C4—6261no—
91C2×C4—6261no—
92C2×C4D125211yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—6262no—
97C22—25041no—
98C22—12522no—
99C22D4×D31312yes—
100C22C2×D125211yescharacteristic
101C4—21no—
102C4—42no—
103C4—6262no—
104C4—12521no—
105C4—12521no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—12522no—
110C2#2375646711yescharacteristic
subgroupG/H
centerC2#23756467
commutator, cosocleC23×C313C23
FrattiniC23C22×D313
Fitting#99×C313C2
socleC2×C313#120
prime radical#23756542C2
hypercenter#99D313
hypocenterC313#458
LCSG ▷ C23×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #23756481C2semidirect
3. #23756478C2semidirect
4. #23756411C2semidirect
5. #99×C313C2semidirect
11. C22×Dic313C22semidirect
15. C22⋊Dic313C22semidirect
18. C22⋊C4×C313C22semidirect
55. C313#458semidirect
61. #99D313semidirect
74. C22⋊C4C2×D313semidirect

Maximal subgroups

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

subgroupindex
#237565422
#237564812
#237564782
#237564112
#99×C3132
#458313