Finite Group Databasebeta

← #17996497

Subgroups — #17996497

Order 4736.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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#14557969C211yesmaximal, characteristic
2#14557654C211yesmaximal, characteristic, complemented
3#14557645C211yesmaximal, characteristic, complemented
4#14557357C211yesmaximal, characteristic, complemented
5#14557344C211yesmaximal, characteristic, complemented
6#14557310C211yesmaximal, characteristic, complemented
7C37×#361C211yesmaximal, characteristic, complemented
8#11924558C2211yescharacteristic
9#11924544—21no—
10D4×Dic37—21no—
11#11924480C412yescomplemented
12#11924477C412yescomplemented
13#11924476C2211yescharacteristic
14#11924468C2211yescharacteristic
15#11924462—21no—
16#11924457—21no—
17#11924446C2211yescharacteristic
18C2×D8×C37C2211yescharacteristic
19M32×C37C2211yescharacteristic
20#108×C37C2211yescharacteristic
21C2×D4×C37—21no—
22C22×Dic37—41no—
23#10596962—21no—
24D8×C37—21no—
25D8×C37C2×C412yes—
26M16×C37—21no—
27C2×C8×C37C2311yescharacteristic
28C22⋊Dic37—41no—
29C4⋊Dic37—21no—
30C4×Dic37D411yescharacteristic
31C2×#64436D411yescharacteristic
32Dic148C2×C411yescharacteristic, complemented
33D296C2×C411yescharacteristic, complemented
34#10596930—21no—
35#10596929—41no—
36C8×D37—41no—
37C16×C37—21no—
38#10596925C2×C412yescomplemented
39C23×C37—41no—
40D4×C37—22no—
41D4×C37—41no—
42C2×C4×C37C2×D411yescharacteristic
43C22⋊D37—41no—
44C2×Dic37—21no—
45C2×Dic37—41no—
46C2×Dic37—82no—
47D148—21no—
48C4×D37—41no—
49Dic74—21no—
50C8×C37—41no—
51C8×C37C22×C411yescharacteristic
52C8×C37#4111yescharacteristic
53#64436—21no—
54C22×C37—42no—
55C22×C37—81no—
56C22×C37—81no—
57C22×C37AGL(1,ℤ/8)11yescharacteristic
58C2×D37—41no—
59C4×C37C4×D411yescharacteristic
60C4×C37AGL(1,ℤ/8)11yescharacteristic
61Dic37—41no—
62Dic37—41no—
63Dic37—81no—
64AGL(1,ℤ/16)—371nomaximal, Sylow
65C2×C37—21no—
66C2×C37—82no—
67C2×C37#44211yescharacteristic
68D37—81no—
69#509—371no—
70#444—371no—
71#442—371no—
72#365—371no—
73#361D3711yescharacteristic, complemented
74#360—371no—
75#347—371no—
76C37AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
77#135—371no—
78C2×D8C2×D3711yescharacteristic
79#131—741no—
80C4×D4—741no—
81SD32—372no—
82D16—372no—
83M32—371no—
84M32C2×D3711yescharacteristic
85#108C2×D3711yescharacteristic
86#106—371no—
87#104—741no—
88#102—741no—
89#97—371no—
90#41—741no—
91C2×D4—21no—
92C22×C4—1481no—
93Q16—371no—
94SD16—741no—
95D8—21no—
96D8—371no—
97D8C4×D3712yes—
98M16—21no—
99M16—1481no—
100C2×C8—371no—
101C2×C8—1481no—
102C2×C8C22×D3711yescharacteristic
103C4⋊C4—741no—
104C22⋊C4—1481no—
105C42—371no—
106C16—21no—
107C16—372no—
108C23—41no—
109Q8—741no—
110D4—22no—
111D4—41no—
112D4—741no—
113D4—1481no—
114C2×C4—2962no—
115C2×C4—741no—
116C2×C4—1481no—
117C2×C4—1481no—
118C2×C4D4×D3711yescharacteristic
119C8—41no—
120C8—741no—
121C8C2×C4×D3711yescharacteristic
122C8#1059696411yescharacteristic
123C22—42no—
124C22—81no—
125C22—81no—
126C22—1481no—
127C22#1192456311yescharacteristic
128C4—2961no—
129C4—1481no—
130C4—1481no—
131C4#1192449611yescharacteristic
132C4#1192456011yescharacteristic
133C2—21no—
134C2—82no—
135C2—2961no—
136C2#1455764211yescharacteristic
subgroupG/H
centerC2#14557642
commutatorC8×C37C22×C4
FrattiniC2×C8C22×D37
FittingC37×#361C2
socleC2×C37#442
prime radical#14557969C2
cosocleC2×C8×C37C23
hypercenter#361D37
hypocenterC37AGL(1,ℤ/16)
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. #14557654C2semidirect
3. #14557645C2semidirect
4. #14557357C2semidirect
5. #14557344C2semidirect
6. #14557310C2semidirect
7. C37×#361C2semidirect
11. #11924480C4semidirect
12. #11924477C4semidirect
32. Dic148C2×C4semidirect
33. D296C2×C4semidirect
38. #10596925C2×C4semidirect
73. #361D37semidirect
76. C37AGL(1,ℤ/16)semidirect

Maximal subgroups

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

subgroupindex
#145579692
#145576542
#145576452
#145573572
#145573442
#145573102
C37×#3612
AGL(1,ℤ/16)37