Finite Group Databasebeta

← #14557724

Subgroups — #14557724

Order 2368.

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#11924581C211yesmaximal, characteristic
2#11924520C212yesmaximal, complemented
3#11924517C211yesmaximal, characteristic, complemented
4#11924450C212yesmaximal, complemented
5#99×C37C211yesmaximal, characteristic, complemented
6C2×D4×C37C2211yescharacteristic
7C2×C22⋊D37—21no—
8C2×C22⋊D37C2212yes—
9C22×Dic37C2211yescharacteristic, complemented
10#10596964—22no—
11D4×D37—22no—
12#10596962—21no—
13C22⋊C4×C37C2212yescomplemented
14C22⋊Dic37—21no—
15C22⋊Dic37C2211yescharacteristic, complemented
16#10596938—22no—
17C4⋊Dic37—22no—
18#10596936—21no—
19C23×C37D411yescharacteristic
20C23×C37C2311yescharacteristic
21C22×D37—21no—
22C22×D37D412yes—
23D4×C37—22no—
24C2×C4×C37—22no—
25C2×C4×C37D411yescharacteristic
26C22⋊D37—22no—
27C22⋊D37—22no—
28C22⋊D37—22no—
29C2×Dic37—21no—
30C2×Dic37—21no—
31C2×Dic37—21no—
32C2×Dic37—22no—
33C2×Dic37D412yes—
34D148—21no—
35C4×D37—22no—
36Dic74—21no—
37C22×C37—21no—
38C22×C37—41no—
39C22×C37—41no—
40C22×C37C2×D411yescharacteristic
41C22×C37C2×D412yes—
42C2×D37—22no—
43C2×D37—42no—
44C2×D37—81no—
45C4×C37—21no—
46C4×C37—42no—
47Dic37—22no—
48Dic37—41no—
49Dic37—41no—
50C2×C37—21no—
51C2×C37—22no—
52C2×C37—41no—
53C2×C37#12011yescharacteristic
54D37—42no—
55#458—371nomaximal, Sylow
56C37#45811yescharacteristic, complemented, Sylow
57H(5,𝔽2)—371no—
58#123—371no—
59#123—372no—
60#99—372no—
61#99D3711yescharacteristic, complemented
62#41—742no—
63#41—741no—
64C2×D4—372no—
65C2×D4—742no—
66C2×D4—741no—
67C2×D4C2×D3711yescharacteristic
68C22×C4—371no—
69C4⋊C4—742no—
70C4⋊C4—741no—
71C22⋊C4—371no—
72C22⋊C4—742no—
73C22⋊C4—741no—
74C22⋊C4C2×D3712yescomplemented
75C23—372no—
76C23—741no—
77C23D14811yescharacteristic
78C23C22×D3711yescharacteristic
79Q8—741no—
80D4—22no—
81D4—741no—
82D4—742no—
83D4—742no—
84D4—742no—
85C2×C4—22no—
86C2×C4—372no—
87C2×C4—742no—
88C2×C4—741no—
89C2×C4—741no—
90C2×C4—741no—
91C2×C4—742no—
92C2×C4D14811yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—2961no—
97C22—742no—
98C22—1482no—
99C22C2×D14811yescharacteristic
100C22D4×D3712yes—
101C4—21no—
102C4—42no—
103C4—742no—
104C4—1481no—
105C4—1481no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—1482no—
110C2#1192450611yescharacteristic
subgroupG/H
centerC2#11924506
commutator, cosocleC23×C37C23
FrattiniC23C22×D37
Fitting#99×C37C2
socleC2×C37#120
prime radical#11924581C2
hypercenter#99D37
hypocenterC37#458
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #11924520C2semidirect
3. #11924517C2semidirect
4. #11924450C2semidirect
5. #99×C37C2semidirect
9. C22×Dic37C22semidirect
13. C22⋊C4×C37C22semidirect
15. C22⋊Dic37C22semidirect
56. C37#458semidirect
61. #99D37semidirect
74. C22⋊C4C2×D37semidirect

Maximal subgroups

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

subgroupindex
#119245812
#119245202
#119245172
#119244502
#99×C372
#45837