Finite Group Databasebeta

← #17993850

Subgroups — #17993850

Order 4736.

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

normal subgroups only

This group has 200 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#14558253C211yesmaximal, characteristic
2#14557936C211yesmaximal, characteristic, complemented
3#14557815C211yesmaximal, characteristic, complemented
4#14557280C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic
7C37×#461C211yesmaximal, characteristic
8#11924536C2211yescharacteristic
9#11924529—22no—
10#11924523—21no—
11#11924515—21no—
12C4×Dic74C2211yescharacteristic
13#11924501—21no—
14#11924495—21no—
15#11924469—22no—
16#11924467—21no—
17C4⋊#64436C2211yescharacteristic
18#11924459—21no—
19C4×#64436C2211yescharacteristic
20C2×SD16×C37—21no—
21C4⋊Q8×C37C2211yescharacteristic
22C4×D4×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#103×C37—21no—
25C2×Q8×C37—21no—
26C2×D4×C37D411yescharacteristic
27C22×C4×C37—21no—
28C2×Dic74—21no—
29C2×Dic74D411yescharacteristic
30SD16×C37—42no—
31C2×C8×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37D411yescharacteristic
35C22⋊C4×C37—21no—
36C42×C37C2311yescharacteristic
37C22⋊Dic37—22no—
38C22⋊Dic37—22no—
39C4⋊Dic37—21no—
40C4⋊Dic37D411yescharacteristic
41C4⋊Dic37D412yes—
42#10596936—22no—
43#10596936—21no—
44C4×Dic37—22no—
45C4×Dic37—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48C23×C37—21no—
49Q8×C37—41no—
50Q8×C37—41no—
51D4×C37—21no—
52D4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37—41no—
55C2×C4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×Dic37—21no—
61C2×Dic37—21no—
62C2×Dic37—22no—
63Dic74—21no—
64Dic74—21no—
65Dic74—41no—
66Dic74—41no—
67C8×C37—41no—
68#64436—22no—
69#64436—41no—
70C22×C37—41no—
71C22×C37—41no—
72C22×C37—41no—
73C22×C37#12011yescharacteristic
74C4×C37—21no—
75C4×C37—41no—
76C4×C37—81no—
77C4×C37#13511yescharacteristic
78C4×C37#13511yescharacteristic
79C4×C37AGL(1,ℤ/8)11yescharacteristic
80C4×C37#13711yescharacteristic
81Dic37—42no—
82Dic37—41no—
83Dic37—41no—
84#1650—371nomaximal, Sylow
85C2×C37—81no—
86C2×C37#44911yescharacteristic
87C2×C37#45211yescharacteristic
88C2×C37#45611yescharacteristic
89#556—371no—
90#500—371no—
91#475—371no—
92#461D3711yescharacteristic
93#332—371no—
94Q8⋊C8—371no—
95D4⋊C8—371no—
96C37#165011yescharacteristic, complemented, Sylow
97C2×SD16—21no—
98C4⋊Q8—371no—
99C4⋊Q8C2×D3711yescharacteristic
100#126—742no—
101#124—741no—
102C22⋊Q8—741no—
103C4×Q8—371no—
104C4×Q8—741no—
105C4×D4C2×D3711yescharacteristic
106#117—741no—
107#107—742no—
108#106—741no—
109C4⋊C8—371no—
110C4⋊C8C2×D3711yescharacteristic
111#103—21no—
112#103—741no—
113C4×C8—371no—
114C2×Q8—21no—
115C2×Q8—371no—
116C2×Q8—741no—
117C2×D4C22⋊D3711yescharacteristic
118C22×C4—21no—
119SD16—42no—
120C2×C8—21no—
121C2×C8—741no—
122C2×C8—741no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—371no—
126C4⋊C4—372no—
127C4⋊C4—742no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4C22⋊D3711yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—742no—
133C22⋊C4—742no—
134C42—742no—
135C42—741no—
136C42C22×D3711yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—741no—
141Q8—741no—
142Q8—1481no—
143Q8—1481no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—741no—
151C2×C4—742no—
152C2×C4—741no—
153C2×C4D4×D3711yescharacteristic
154C2×C4D4×D3711yescharacteristic
155C2×C4C2×C22⋊D3711yescharacteristic
156C8—41no—
157C8—742no—
158C8—1481no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1192450411yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—1481no—
167C4—1482no—
168C4—1481no—
169C4#1192455611yescharacteristic
170C4#1192455711yescharacteristic
171C4#1192456211yescharacteristic
172C4#1192456511yescharacteristic
173C2—81no—
174C2#1455767611yescharacteristic
175C2#1455769211yescharacteristic
176C2#1455771411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#461C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenter#461D37
hypocenterC37#1650
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #14557936C2semidirect
3. #14557815C2semidirect
4. #14557280C2semidirect
5. #14557263C2semidirect
96. C37#1650semidirect

Maximal subgroups

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

subgroupindex
#145582532
#145579362
#145578152
#145572802
#145572632
D4⋊#644362
C37×#4612
#165037