Finite Group Databasebeta

← #17996494

Subgroups — #17996494

Order 4736.

154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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#14557968C211yesmaximal, characteristic
2#14557646C211yesmaximal, characteristic, complemented
3#14557357C211yesmaximal, characteristic, complemented
4#14557345C211yesmaximal, characteristic, complemented
5#14557343C211yesmaximal, characteristic, complemented
6#14557311C211yesmaximal, characteristic, complemented
7C37×#444C211yesmaximal, characteristic, complemented
8C2×D296C2211yescharacteristic
9C4×D148—21no—
10#11924479C412yescomplemented
11#11924477C412yescomplemented
12#11924476C2211yescharacteristic
13#11924476C2211yescharacteristic
14#11924468C2211yescharacteristic
15#11924458—21no—
16#135×C37C2211yescharacteristic
17#131×C37—21no—
18#108×C37C2211yescharacteristic
19#104×C37—21no—
20#97×C37C2211yescharacteristic
21#41×C37—21no—
22C2×D148—21no—
23C2×C4×D37—41no—
24Q16×C37C2×C411yescharacteristic, complemented
25SD16×C37—21no—
26D8×C37C2×C411yescharacteristic, complemented
27M16×C37—21no—
28M16×C37—41no—
29C2×C8×C37—41no—
30C2×C8×C37D411yescharacteristic
31C2×C8×C37C2311yescharacteristic
32C42×C37D411yescharacteristic
33#10596938—41no—
34C4⋊Dic37—21no—
35D296—21no—
36D296C2×C412yes—
37#10596925—21no—
38#10596925C2×C412yescomplemented
39C22×D37—41no—
40Q8×C37—21no—
41D4×C37—21no—
42D4×C37—41no—
43C2×C4×C37—21no—
44C2×C4×C37—41no—
45C2×C4×C37C2×D411yescharacteristic
46C2×Dic37—41no—
47D148—22no—
48D148—41no—
49C4×D37—82no—
50C8×C37—21no—
51C8×C37—41no—
52C8×C37C22×C411yescharacteristic
53C8×C37#4111yescharacteristic
54C22×C37—41no—
55C22×C37AGL(1,ℤ/8)11yescharacteristic
56C2×D37—42no—
57C2×D37—81no—
58C2×D37—81no—
59C4×C37—41no—
60C4×C37—41no—
61C4×C37C4×D411yescharacteristic
62C4×C37AGL(1,ℤ/8)11yescharacteristic
63Dic37—81no—
64AGL(1,ℤ/16)—371nomaximal, Sylow
65C2×C37—21no—
66C2×C37—81no—
67C2×C37#44211yescharacteristic
68D37—82no—
69#509—371no—
70#444D3711yescharacteristic, complemented
71#442—371no—
72#365—371no—
73#361—371no—
74#360—371no—
75#347—371no—
76C37AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
77#135C2×D3711yescharacteristic
78C2×D8—371no—
79#131—21no—
80C4×D4—741no—
81SD32—372no—
82D16—372no—
83M32—371no—
84M32—371no—
85#108C2×D3711yescharacteristic
86#106—371no—
87#104—21no—
88#102—741no—
89#97C2×D3711yescharacteristic
90#41—21no—
91C2×D4—741no—
92C22×C4—1481no—
93Q16C4×D3711yescharacteristic, complemented
94SD16—21no—
95D8—372no—
96D8—741no—
97D8C4×D3711yescharacteristic, complemented
98M16—21no—
99M16—41no—
100C2×C8—41no—
101C2×C8C22⋊D3711yescharacteristic
102C2×C8C22×D3711yescharacteristic
103C4⋊C4—741no—
104C22⋊C4—1481no—
105C42C22⋊D3711yescharacteristic
106C16—372no—
107C16—741no—
108C23—1481no—
109Q8—21no—
110D4—21no—
111D4—41no—
112D4—742no—
113D4—1481no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—2962no—
117C2×C4—1481no—
118C2×C4C2×C22⋊D3711yescharacteristic
119C8—21no—
120C8—41no—
121C8C2×C4×D3711yescharacteristic
122C8#1059696211yescharacteristic
123C22—41no—
124C22—2961no—
125C22—2961no—
126C22—1482no—
127C22#1192456111yescharacteristic
128C4—41no—
129C4—41no—
130C4—2961no—
131C4C4×C22⋊D3711yescharacteristic
132C4#1192456211yescharacteristic
133C2—21no—
134C2—81no—
135C2—2962no—
136C2#1455764311yescharacteristic
subgroupG/H
centerC2#14557643
commutatorC8×C37C22×C4
FrattiniC2×C8C22×D37
FittingC37×#444C2
socleC2×C37#442
prime radical#14557968C2
cosocleC2×C8×C37C23
hypercenter#444D37
hypocenterC37AGL(1,ℤ/16)
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #444

Complements

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

NH ≅ G/Ntype
2. #14557646C2semidirect
3. #14557357C2semidirect
4. #14557345C2semidirect
5. #14557343C2semidirect
6. #14557311C2semidirect
7. C37×#444C2semidirect
10. #11924479C4semidirect
11. #11924477C4semidirect
24. Q16×C37C2×C4semidirect
26. D8×C37C2×C4semidirect
38. #10596925C2×C4semidirect
70. #444D37semidirect
76. C37AGL(1,ℤ/16)semidirect
93. Q16C4×D37semidirect
97. D8C4×D37semidirect

Maximal subgroups

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

subgroupindex
#145579682
#145576462
#145573572
#145573452
#145573432
#145573112
C37×#4442
AGL(1,ℤ/16)37