Finite Group Databasebeta

← #17993710

Subgroups — #17993710

Order 4736.

314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558168C211yesmaximal, characteristic
2#14557820C212yesmaximal, complemented
3#14557277C211yesmaximal, characteristic, complemented
4#14557262C212yesmaximal, complemented
5C37×#492C211yesmaximal, characteristic, complemented
6C2×D4×D37—22no—
7#11924507—22no—
8#11924504—22no—
9C4×D148C2212yes—
10#11924467—22no—
11C4⋊#64436C2212yescomplemented
12#11924456—22no—
13C2×SD16×C37—22no—
14C4⋊Q8×C37C2211yescharacteristic, complemented
15#127×C37C2211yescharacteristic
16C4×C8×C37C2211yescharacteristic, complemented
17C23×D37—22no—
18C2×Q8×C37—21no—
19C2×D4×C37—22no—
20C2×D4×C37D412yes—
21C2×C22⋊D37—24no—
22D4×D37—44no—
23D4×D37—44no—
24C2×D148D412yes—
25C2×C4×D37—22no—
26SD16×C37—44no—
27C2×C8×C37—21no—
28C4⋊C4×C37—22no—
29C42×C37C2311yescharacteristic
30C22⋊Dic37—22no—
31#10596938—22no—
32C4⋊Dic37D412yes—
33C2×#64436—22no—
34C23×C37—22no—
35C22×D37—22no—
36C22×D37—48no—
37C22×D37—82no—
38Q8×C37—42no—
39D4×C37—42no—
40D4×C37—42no—
41D4×C37—42no—
42C2×C4×C37—41no—
43C2×C4×C37C2×D412yes—
44C2×C4×C37C2×D411yescharacteristic
45C22⋊D37—48no—
46C2×Dic37—22no—
47D148—22no—
48D148SD1614yescomplemented
49C4×D37—42no—
50C4×D37—42no—
51C8×C37—22no—
52#64436—42no—
53C22×C37—44no—
54C22×C37—42no—
55C22×C37#12011yescharacteristic
56C2×D37—24no—
57C2×D37—42no—
58C2×D37—42no—
59C2×D37—88no—
60C4×C37—21no—
61C4×C37—81no—
62C4×C37C2×SD1612yes—
63C4×C37AGL(1,ℤ/8)12yes—
64Dic37—42no—
65#1629—371nomaximal, Sylow
66C2×C37—82no—
67C2×C37#45012yes—
68C2×C37#45311yescharacteristic
69D37—44no—
70D42—371no—
71#492D3711yescharacteristic, complemented
72#476—372no—
73#331—371no—
74D4⋊C8—372no—
75C37#162911yescharacteristic, complemented, Sylow
76C22×D4—742no—
77C2×SD16—22no—
78C4⋊Q8C2×D3711yescharacteristic, complemented
79#127C2×D3711yescharacteristic
80#121—742no—
81#120—742no—
82C4×D4—372no—
83#106—742no—
84C4⋊C8—372no—
85#102—742no—
86C4×C8C2×D3711yescharacteristic, complemented
87C24—742no—
88C2×Q8—21no—
89C2×D4—22no—
90C2×D4—372no—
91C2×D4—744no—
92C2×D4—1484no—
93C2×D4—1484no—
94C2×D4C22⋊D3712yes—
95C22×C4—742no—
96SD16—44no—
97C2×C8—21no—
98C2×C8—742no—
99C4⋊C4—22no—
100C4⋊C4—372no—
101C22⋊C4—742no—
102C22⋊C4—742no—
103C42C22×D3711yescharacteristic
104C23—22no—
105C23—2962no—
106C23—742no—
107C23—1488no—
108Q8—42no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—374no—
113D4—742no—
114D4—1488no—
115C2×C4—41no—
116C2×C4—742no—
117C2×C4—1482no—
118C2×C4—1482no—
119C2×C4D4×D3712yes—
120C2×C4C2×C22⋊D3711yescharacteristic
121C8—22no—
122C8—1482no—
123C22—42no—
124C22—44no—
125C22—2968no—
126C22—744no—
127C22—1482no—
128C22—1482no—
129C22#1192450411yescharacteristic
130C4—21no—
131C4—81no—
132C4—1482no—
133C4SD16×D3712yes—
134C4#1192456312yes—
135C2—82no—
136C2—1484no—
137C2#1455768212yes—
138C2#1455770011yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#492C2
socleC22×C37#120
prime radical#14558168C2
hypercenter#492D37
hypocenterC37#1629
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #14557820C2semidirect
3. #14557277C2semidirect
4. #14557262C2semidirect
5. C37×#492C2semidirect
11. C4⋊#64436C22semidirect
14. C4⋊Q8×C37C22semidirect
16. C4×C8×C37C22semidirect
48. D148SD16semidirect
71. #492D37semidirect
75. C37#1629semidirect
78. C4⋊Q8C2×D37semidirect
86. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581682
#145578202
#145572772
#145572622
C37×#4922
#162937