Finite Group Databasebeta

← #17996723

Subgroups — #17996723

Order 4736.

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

normal subgroups only

This group has 144 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#14557949C211yesmaximal, characteristic, complemented
2#14557805C211yesmaximal, characteristic, complemented
3#14557800C211yesmaximal, characteristic
4#14557363C211yesmaximal, characteristic, complemented
5#14557349C211yesmaximal, characteristic, complemented
6#14557346C211yesmaximal, characteristic, complemented
7C2×SD32×C37C211yesmaximal, characteristic, complemented
8#11924567—21no—
9#11924562—21no—
10#11924542C2211yescharacteristic
11#11924476C2211yescharacteristic
12#11924475—21no—
13C16×D37—21no—
14#11924472C2211yescharacteristic
15#11924472C2211yescharacteristic
16#11924455—21no—
17#11924453—21no—
18C2×Q16×C37C2211yescharacteristic
19C2×D8×C37C2211yescharacteristic
20SD32×C37—21no—
21SD32×C37—21no—
22C2×C16×C37C2211yescharacteristic
23C2×Q8×C37—21no—
24C2×D4×C37—21no—
25#10596962D411yescharacteristic
26Q16×C37—21no—
27Q16×C37—21no—
28D8×C37—21no—
29D8×C37—21no—
30C2×C8×C37C2311yescharacteristic
31#10596942—41no—
32#10596941—41no—
33#10596940—41no—
34#10596939—41no—
35#10596934—21no—
36#10596934—21no—
37#10596934D411yescharacteristic
38#10596929—21no—
39C8×D37—21no—
40C16×C37D411yescharacteristic
41C16×C37D411yescharacteristic
42#10596925—21no—
43C23×C37—41no—
44Q8×C37—41no—
45Q8×C37—41no—
46D4×C37—41no—
47D4×C37—41no—
48C2×C4×C37—41no—
49C2×C4×C37C2×D411yescharacteristic
50C22⋊D37—21no—
51D148D811yescharacteristic
52C4×D37—21no—
53Dic74D811yescharacteristic
54C8×C37C2×D411yescharacteristic
55C8×C37#4111yescharacteristic
56#64436—21no—
57#64436—41no—
58#64436—41no—
59C22×C37—81no—
60C22×C37—161no—
61C22×C37#13511yescharacteristic
62C2×D37—21no—
63C4×C37—81no—
64C4×C37#12111yescharacteristic
65C4×C37C2×D811yescharacteristic
66Dic37—21no—
67#2223—371nomaximal, Sylow
68C2×C37—21no—
69C2×C37—161no—
70C2×C37#46611yescharacteristic
71D37—41no—
72C2×SD32D3711yescharacteristic, complemented
73#504—371no—
74#473—371no—
75#472—371no—
76#368—371no—
77#362—371no—
78#361—371no—
79C37#222311yescharacteristic, complemented, Sylow
80#137—741no—
81AGL(1,ℤ/8)—741no—
82C2×Q16C2×D3711yescharacteristic
83C2×D8C2×D3711yescharacteristic
84#131—371no—
85SD32—21no—
86SD32—21no—
87M32—371no—
88M32—741no—
89C2×C16—741no—
90C2×C16C2×D3711yescharacteristic
91#108—371no—
92#108—371no—
93#101—741no—
94#100—741no—
95#41—371no—
96C2×Q8—21no—
97C2×D4—21no—
98Q16—21no—
99Q16—21no—
100Q16—1481no—
101SD16—1481no—
102SD16—1481no—
103D8—21no—
104D8—21no—
105D8—1481no—
106M16—371no—
107M16—741no—
108M16—741no—
109M16—741no—
110C2×C8—741no—
111C2×C8C22×D3711yescharacteristic
112C16—741no—
113C16C22⋊D3711yescharacteristic
114C16C22⋊D3711yescharacteristic
115C23—41no—
116Q8—41no—
117Q8—41no—
118Q8—371no—
119D4—41no—
120D4—41no—
121D4—371no—
122D4—741no—
123C2×C4—41no—
124C2×C4—741no—
125C2×C4D4×D3711yescharacteristic
126C8—741no—
127C8—1481no—
128C8—1481no—
129C8#1059696411yescharacteristic
130C8C2×C22⋊D3711yescharacteristic
131C22—81no—
132C22—161no—
133C22—741no—
134C22#1192455511yescharacteristic
135C4—81no—
136C4—741no—
137C4#1192450711yescharacteristic
138C4D8×D3711yescharacteristic
139C2—21no—
140C2—161no—
141C2—1481no—
142C2#1455776611yescharacteristic
subgroupG/H
centerC2#14557766
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC2×SD32×C37C2
socleC2×C37#466
prime radical#14557800C2
hypercenterC2×SD32D37
hypocenterC37#2223
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #14557949C2semidirect
2. #14557805C2semidirect
4. #14557363C2semidirect
5. #14557349C2semidirect
6. #14557346C2semidirect
7. C2×SD32×C37C2semidirect
72. C2×SD32D37semidirect
79. C37#2223semidirect

Maximal subgroups

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

subgroupindex
#145579492
#145578052
#145578002
#145573632
#145573492
#145573462
C2×SD32×C372
#222337