Finite Group Databasebeta

← #17993853

Subgroups — #17993853

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#14558257C211yesmaximal, characteristic
2#14557936C211yesmaximal, characteristic, complemented
3#14557819C211yesmaximal, characteristic, complemented
4#14557739C211yesmaximal, characteristic
5#14557263C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic
7C37×#332C211yesmaximal, characteristic, complemented
8C2×#10596930—21no—
9#11924536C2211yescharacteristic
10#11924531—22no—
11#11924525—21no—
12#11924516—21no—
13Q8×Dic37—21no—
14C4×Dic74C2211yescharacteristic
15C4×D148C2211yescharacteristic
16#11924494—21no—
17#11924469—22no—
18#11924468—21no—
19#11924461—21no—
20#11924461—21no—
21C4×#64436C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26C2×D148D411yescharacteristic
27C2×C4×D37—21no—
28C2×Dic74—21no—
29C2×Dic74D411yescharacteristic
30C2×C8×C37—21no—
31C2×C8×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37D412yes—
34C42×C37C2311yescharacteristic
35#10596938—22no—
36#10596938—22no—
37#10596938—21no—
38C4⋊Dic37—22no—
39C4⋊Dic37—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37D411yescharacteristic
42C4⋊Dic37D411yescharacteristic
43#10596936—21no—
44C4×Dic37—22no—
45C4×Dic37—21no—
46C2×#64436—21no—
47#10596930—42no—
48C22×D37—21no—
49Q8×C37—41no—
50Q8×C37—41no—
51C2×C4×C37—22no—
52C2×C4×C37C2×D411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×Dic37—21no—
56C2×Dic37—21no—
57C2×Dic37—21no—
58C2×Dic37—41no—
59D148—21no—
60D148—21no—
61C4×D37—41no—
62C4×D37—41no—
63Dic74—21no—
64Dic74—21no—
65Dic74—41no—
66Dic74—41no—
67C8×C37—41no—
68C8×C37—41no—
69#64436—22no—
70C22×C37#12011yescharacteristic
71C2×D37—41no—
72C2×D37—41no—
73C2×D37—41no—
74C4×C37—21no—
75C4×C37—42no—
76C4×C37#13511yescharacteristic
77C4×C37#13511yescharacteristic
78C4×C37AGL(1,ℤ/8)11yescharacteristic
79C4×C37#13711yescharacteristic
80Dic37—41no—
81Dic37—41no—
82Dic37—41no—
83Dic37—81no—
84#1650—371nomaximal, Sylow
85C2×C37#44911yescharacteristic
86C2×C37#45211yescharacteristic
87C2×C37#45611yescharacteristic
88D37—81no—
89#556—371no—
90#500—371no—
91#475—371no—
92#461—371no—
93#332D3711yescharacteristic, complemented
94Q8⋊C8—371no—
95D4⋊C8—371no—
96C37#165011yescharacteristic, complemented, Sylow
97C2×SD16—741no—
98C4⋊Q8—371no—
99C4⋊Q8C2×D3711yescharacteristic
100#126—742no—
101#124—741no—
102C22⋊Q8—741no—
103C4×Q8—371no—
104C4×Q8—741no—
105C4×D4—371no—
106#117—741no—
107#107—742no—
108#106—741no—
109C4⋊C8C2×D3711yescharacteristic
110C4⋊C8C2×D3711yescharacteristic
111#103—741no—
112#103—741no—
113C4×C8—371no—
114C2×Q8—21no—
115C2×Q8—371no—
116C2×Q8—741no—
117C2×D4—371no—
118C22×C4—741no—
119SD16—1482no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—741no—
123C4⋊C4—21no—
124C4⋊C4—371no—
125C4⋊C4—371no—
126C4⋊C4—742no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4D14812yes—
131C22⋊C4—742no—
132C22⋊C4—742no—
133C22⋊C4—741no—
134C42—742no—
135C42—741no—
136C42C22×D3711yescharacteristic
137C23—741no—
138Q8—41no—
139Q8—41no—
140Q8—741no—
141Q8—741no—
142Q8—1481no—
143Q8—1481no—
144D4—741no—
145D4—741no—
146C2×C4—22no—
147C2×C4—741no—
148C2×C4—741no—
149C2×C4—741no—
150C2×C4—1481no—
151C2×C4—1481no—
152C2×C4—1481no—
153C2×C4C2×D14811yescharacteristic
154C2×C4D4×D3711yescharacteristic
155C2×C4D4×D3711yescharacteristic
156C8—41no—
157C8—41no—
158C8—742no—
159C22—1481no—
160C22—1481no—
161C22—1481no—
162C22#1192450611yescharacteristic
163C4—21no—
164C4—42no—
165C4—2961no—
166C4—1481no—
167C4—1481no—
168C4—1481no—
169C4#1192455711yescharacteristic
170C4#1192455711yescharacteristic
171C4#1192456011yescharacteristic
172C4#1192456811yescharacteristic
173C2—2961no—
174C2#1455767911yescharacteristic
175C2#1455769811yescharacteristic
176C2#1455771811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenter#332D37
hypocenterC37#1650
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #14557936C2semidirect
3. #14557819C2semidirect
5. #14557263C2semidirect
7. C37×#332C2semidirect
93. #332D37semidirect
96. C37#1650semidirect

Maximal subgroups

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

subgroupindex
#145582572
#145579362
#145578192
#145577392
#145572632
#145572602
C37×#3322
#165037