Finite Group Databasebeta

← #17996812

Subgroups — #17996812

Order 4736.

134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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#14557787C211yesmaximal, characteristic
2#14557580C211yesmaximal, characteristic, complemented
3#14557355C211yesmaximal, characteristic, complemented
4#14557347C211yesmaximal, characteristic, complemented
5#14557345C211yesmaximal, characteristic, complemented
6#14557314C211yesmaximal, characteristic, complemented
7C37×#365C211yesmaximal, characteristic, complemented
8C2×D296C2211yescharacteristic
9C2×#10596929C2211yescharacteristic
10M16×D37—21no—
11#11924511—21no—
12#11924476C2211yescharacteristic
13#11924472C2211yescharacteristic
14#11924471—21no—
15#11924456—21no—
16M32×C37C2211yescharacteristic
17#108×C37C2211yescharacteristic
18#106×C37C2211yescharacteristic
19C2×D148—21no—
20C2×D148—41no—
21C2×C4×D37D411yescharacteristic
22M16×C37—21no—
23C2×C8×C37C2311yescharacteristic
24C4⋊C4×C37—21no—
25#10596938—41no—
26#10596934—21no—
27C2×#64436D411yescharacteristic
28D296—21no—
29D296—21no—
30#10596929—21no—
31#10596929—21no—
32#10596929—41no—
33C8×D37—41no—
34C16×C37—21no—
35#10596925—21no—
36C22×D37—41no—
37C22×D37SD1611yescharacteristic
38C2×C4×C37—41no—
39C2×C4×C37C2×D411yescharacteristic
40C2×Dic37SD1611yescharacteristic
41D148—41no—
42D148—41no—
43D148—82no—
44C4×D37—21no—
45C4×D37—21no—
46C8×C37—41no—
47C8×C37#4111yescharacteristic
48C8×C37#4111yescharacteristic
49#64436—21no—
50#64436—41no—
51C22×C37C2×SD1611yescharacteristic
52C2×D37—21no—
53C2×D37—41no—
54C2×D37—81no—
55C2×D37—81no—
56C2×D37—81no—
57C4×C37—81no—
58C4×C37#12311yescharacteristic
59C4×C37AGL(1,ℤ/8)11yescharacteristic
60Dic37—21no—
61#2238—371nomaximal, Sylow
62C2×C37—21no—
63C2×C37#48111yescharacteristic
64D37—41no—
65D37—161no—
66#469—371no—
67#430—371no—
68#365—371no—
69#365D3711yescharacteristic, complemented
70#361—371no—
71#361—371no—
72#349—371no—
73C37#223811yescharacteristic, complemented, Sylow
74C2×D8—371no—
75C2×M16—371no—
76C2×M16—741no—
77#121—741no—
78M32—371no—
79M32C2×D3711yescharacteristic
80#108—371no—
81#108—741no—
82#108C2×D3711yescharacteristic
83#106C2×D3711yescharacteristic
84#102—741no—
85C2×D4—741no—
86C2×D4—1481no—
87C22×C4—371no—
88D8—741no—
89D8—741no—
90M16—21no—
91M16—741no—
92M16—741no—
93M16—741no—
94M16—1481no—
95C2×C8—371no—
96C2×C8—1481no—
97C2×C8C22×D3711yescharacteristic
98C4⋊C4—21no—
99C22⋊C4—1481no—
100C16—21no—
101C16—741no—
102C23—371no—
103C23—1481no—
104D4—2962no—
105D4—1481no—
106D4—1481no—
107C2×C4—41no—
108C2×C4—371no—
109C2×C4—741no—
110C2×C4—741no—
111C2×C4D4×D3711yescharacteristic
112C8—41no—
113C8—741no—
114C8—1481no—
115C8#1059696211yescharacteristic
116C8#1059696611yescharacteristic
117C22—2961no—
118C22—2961no—
119C22—2961no—
120C22—741no—
121C22—1481no—
122C22SD16×D3711yescharacteristic
123C4—81no—
124C4—741no—
125C4#1192452111yescharacteristic
126C4#1192456311yescharacteristic
127C2—21no—
128C2—5921no—
129C2—1481no—
130C2#1455785311yescharacteristic
subgroupG/H
centerC2#14557853
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#365C2
socleC2×C37#481
prime radical#14557787C2
hypercenter#365D37
hypocenterC37#2238
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
2. #14557580C2semidirect
3. #14557355C2semidirect
4. #14557347C2semidirect
5. #14557345C2semidirect
6. #14557314C2semidirect
7. C37×#365C2semidirect
69. #365D37semidirect
73. C37#2238semidirect

Maximal subgroups

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

subgroupindex
#145577872
#145575802
#145573552
#145573472
#145573452
#145573142
C37×#3652
#223837