Finite Group Databasebeta

← #17993905

Subgroups — #17993905

Order 4736.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#14558283C211yesmaximal, characteristic
2#14557939C212yesmaximal, complemented
3#14557274C212yesmaximal, complemented
4#14557273C211yesmaximal, characteristic
5C37×#497C211yesmaximal, characteristic
6#11924534—21no—
7#11924529—22no—
8#11924528C2212yes—
9#11924517—21no—
10#11924513—22no—
11#11924469—22no—
12#11924467—22no—
13#11924447C2212yes—
14C2×Q16×C37—21no—
15C2×SD16×C37—21no—
16C4⋊Q8×C37C2211yescharacteristic
17#124×C37C2211yescharacteristic
18#97×C37C2211yescharacteristic
19C2×Q8×C37—21no—
20C2×Q8×C37D411yescharacteristic
21C2×D4×C37D411yescharacteristic
22C22×Dic37—21no—
23C2×Dic74—21no—
24Q16×C37—42no—
25SD16×C37—42no—
26C2×C8×C37—21no—
27C4⋊C4×C37—22no—
28C22⋊C4×C37—22no—
29C42×C37C2311yescharacteristic
30C22⋊Dic37—22no—
31C22⋊Dic37—21no—
32C4⋊Dic37D412yes—
33C4⋊Dic37D412yes—
34#10596936—22no—
35#10596936—22no—
36#10596936—22no—
37C4×Dic37—21no—
38C2×#64436—22no—
39C23×C37—21no—
40Q8×C37—41no—
41Q8×C37—41no—
42Q8×C37—41no—
43D4×C37—41no—
44C2×C4×C37—21no—
45C2×C4×C37—41no—
46C2×C4×C37C2×D412yes—
47C2×C4×C37C2×D411yescharacteristic
48C2×Dic37—22no—
49C2×Dic37—22no—
50C2×Dic37—81no—
51Dic74—81no—
52C8×C37—22no—
53#64436—24no—
54C22×C37—41no—
55C22×C37—42no—
56C22×C37#12011yescharacteristic
57C4×C37—21no—
58C4×C37—22no—
59C4×C37—41no—
60C4×C37—81no—
61Dic37—42no—
62Dic37—42no—
63#1660—371nomaximal, Sylow
64C2×C37—81no—
65C2×C37#45311yescharacteristic
66C2×C37#45612yes—
67#563—371no—
68#501—372no—
69#497D3711yescharacteristic
70#330—372no—
71#329—371no—
72C37#166011yescharacteristic, complemented, Sylow
73C2×Q16—21no—
74C2×SD16—21no—
75C4⋊Q8—741no—
76C4⋊Q8C2×D3711yescharacteristic
77#126—742no—
78#125—372no—
79#124C2×D3711yescharacteristic
80#123—741no—
81C22⋊Q8—742no—
82#107—742no—
83#106—742no—
84#97—372no—
85#97C2×D3711yescharacteristic
86C2×Q8—21no—
87C2×Q8—741no—
88C2×Q8C22⋊D3711yescharacteristic
89C2×D4C22⋊D3711yescharacteristic
90C22×C4—741no—
91Q16—42no—
92SD16—42no—
93C2×C8—21no—
94C2×C8—742no—
95C4⋊C4—22no—
96C4⋊C4—372no—
97C4⋊C4—372no—
98C4⋊C4—742no—
99C4⋊C4—742no—
100C4⋊C4—742no—
101C22⋊C4—22no—
102C22⋊C4—742no—
103C22⋊C4—741no—
104C42—741no—
105C42C22×D3711yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—41no—
109Q8—41no—
110Q8—2961no—
111D4—41no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—2961no—
115C2×C4—742no—
116C2×C4—742no—
117C2×C4D4×D3712yes—
118C2×C4C2×C22⋊D3711yescharacteristic
119C8—22no—
120C8—744no—
121C22—41no—
122C22—42no—
123C22#1192450411yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—81no—
128C4—1482no—
129C4—1482no—
130C2—81no—
131C2#1455770011yescharacteristic
132C2#1455771412yes—
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#497C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenter#497D37
hypocenterC37#1660
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #14557939C2semidirect
3. #14557274C2semidirect
72. C37#1660semidirect

Maximal subgroups

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

subgroupindex
#145582832
#145579392
#145572742
#145572732
C37×#4972
#166037