Finite Group Databasebeta

← #18011006

Subgroups — #18011006

Order 4736.

154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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#14558580C211yesmaximal, characteristic, complemented
2#14558574C211yesmaximal, characteristic, complemented
3#14558458C211yesmaximal, characteristic, complemented
4#14558451C211yesmaximal, characteristic, complemented
5#14558449C211yesmaximal, characteristic, complemented
6#14558424C211yesmaximal, characteristic, complemented
7#14557967C211yesmaximal, characteristic
8#11924623—21no—
9D4×#3866—21no—
10#11924611C2211yescharacteristic
11#11924606C2211yescharacteristic
12#11924604C2211yescharacteristic
13#11924600—21no—
14#11924598—21no—
15#11924590C2211yescharacteristic
16#11924555C2211yescharacteristic
17D8×D37C2211yescharacteristic
18#11924481C411yescharacteristic, complemented
19#11924480C411yescharacteristic, complemented
20#11924477C411yescharacteristic, complemented
21#11924475C2211yescharacteristic
22D16×C37C411yescharacteristic, complemented
23C22×#3866—41no—
24#10596964—21no—
25D4×D37—21no—
26C22⋊#3866—41no—
27#10596957—41no—
28C2×#64438—41no—
29C4⋊#3866—21no—
30C4×#3866D411yescharacteristic
31#10596953—21no—
32D37⋊C8D411yescharacteristic
33D8×C37C2×C411yescharacteristic
34D8×C37C2×C411yescharacteristic, complemented
35#10596940—21no—
36#10596939—21no—
37Dic148C2×C411yescharacteristic, complemented
38D296C2×C411yescharacteristic
39C8×D37C2311yescharacteristic
40#10596927—21no—
41C16×C37C2×C411yescharacteristic, complemented
42#10596925C2×C411yescharacteristic, complemented
43C22×D37—41no—
44C2×#3866—21no—
45C2×#3866—41no—
46C2×#3866—82no—
47D4×C37—21no—
48D4×C37—21no—
49C22⋊D37—41no—
50C22⋊D37—41no—
51C2×Dic37—41no—
52D148—21no—
53C4×D37C2×D411yescharacteristic
54Dic74—21no—
55#64438—21no—
56#64438—41no—
57C8×C37C22×C411yescharacteristic
58#64436#4111yescharacteristic
59C22×C37—41no—
60C22×C37—41no—
61C2×D37—41no—
62C2×D37—81no—
63C2×D37—81no—
64C2×D37AGL(1,ℤ/8)11yescharacteristic
65#3866—41no—
66#3866—81no—
67C4×C37C4×D411yescharacteristic
68Dic37—41no—
69Dic37AGL(1,ℤ/8)11yescharacteristic
70AGL(1,ℤ/16)—371nomaximal, Sylow
71C2×C37—81no—
72C2×C37—81no—
73C2×C37#44211yescharacteristic
74D37—21no—
75D37—81no—
76#509—371no—
77#444—371no—
78#442—371no—
79#365—371no—
80#361—371no—
81#360—371no—
82#347—371no—
83C37AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
84#135—371no—
85C2×D8—371no—
86#131—741no—
87C4×D4—741no—
88SD32—371no—
89SD32—371no—
90D16—371no—
91D16#386611yescharacteristic, complemented
92M32—371no—
93M32—371no—
94#108—371no—
95#106—371no—
96#104—741no—
97#102—741no—
98#97—371no—
99#41—741no—
100C2×D4—741no—
101C22×C4—1481no—
102Q16—371no—
103SD16—741no—
104D8—371no—
105D8—741no—
106D8C2×#386611yescharacteristic
107D8C2×#386611yescharacteristic, complemented
108M16—741no—
109M16—1481no—
110C2×C8—371no—
111C2×C8—371no—
112C2×C8—1481no—
113C4⋊C4—741no—
114C22⋊C4—1481no—
115C42—371no—
116C16—371no—
117C16—741no—
118C16C2×#386611yescharacteristic, complemented
119C23—1481no—
120Q8—741no—
121D4—21no—
122D4—21no—
123D4—741no—
124D4—1481no—
125D4—1481no—
126C2×C4—371no—
127C2×C4—2962no—
128C2×C4—741no—
129C2×C4—1481no—
130C2×C4—1481no—
131C8—371no—
132C8—741no—
133C8—1481no—
134C8C22×#386611yescharacteristic
135C22—41no—
136C22—41no—
137C22—371no—
138C22—2961no—
139C22—2961no—
140C22—1481no—
141C4—371no—
142C4—2961no—
143C4—1481no—
144C4—1481no—
145C4D4×#386611yescharacteristic
146C2—81no—
147C2—81no—
148C2—2961no—
149C2—741no—
150C2#1455857411yescharacteristic
subgroupG/H
centerC2#14558574
commutatorC8×C37C22×C4
FrattiniC8C22×#3866
FittingD16×C37C4
socleC2×C37#442
prime radical#14557967C2
cosocleC8×D37C23
hypercenterD16#3866
hypocenterC37AGL(1,ℤ/16)
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

Complements

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

NH ≅ G/Ntype
1. #14558580C2semidirect
2. #14558574C2semidirect
3. #14558458C2semidirect
4. #14558451C2semidirect
5. #14558449C2semidirect
6. #14558424C2semidirect
18. #11924481C4semidirect
19. #11924480C4semidirect
20. #11924477C4semidirect
22. D16×C37C4semidirect
34. D8×C37C2×C4semidirect
37. Dic148C2×C4semidirect
41. C16×C37C2×C4semidirect
42. #10596925C2×C4semidirect
83. C37AGL(1,ℤ/16)semidirect
91. D16#3866semidirect
107. D8C2×#3866semidirect
118. C16C2×#3866semidirect

Maximal subgroups

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

subgroupindex
#145585802
#145585742
#145584582
#145584512
#145584492
#145584242
#145579672
AGL(1,ℤ/16)37