Finite Group Databasebeta

← #17995039

Subgroups — #17995039

Order 4736.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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#14558044C211yesmaximal, characteristic
2C2×#11924464C212yesmaximal, complemented
3#14557497C211yesmaximal, characteristic, complemented
4#14557293C212yesmaximal, complemented
5C22×C42×C37C211yesmaximal, characteristic, complemented
6C2×#10596962C2211yescharacteristic
7C2×#10596934C2212yes—
8#11924519—21no—
9#11924515C412yescomplemented
10#11924510C412yescomplemented
11#11924505—21no—
12C4×C22⋊D37—22no—
13#11924495C2211yescharacteristic
14#11924464—24no—
15C22⋊#64436—22no—
16C23×C4×C37—21no—
17C23×C4×C37C2211yescharacteristic
18C2×C42×C37—21no—
19C2×C42×C37—24no—
20C2×C42×C37C2212yes—
21C24×C37D411yescharacteristic
22C22×C4×C37—24no—
23C22×C4×C37—28no—
24C22×C4×C37—22no—
25C22×C4×C37—22no—
26C22×C4×C37—22no—
27C22×C4×C37C2×C412yes—
28C22×C4×C37D412yes—
29C22×C4×C37D411yescharacteristic
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—22no—
32C2×C22⋊D37—21no—
33#10596962—22no—
34#10596962—22no—
35C2×D148C2×C411yescharacteristic, complemented
36C2×C4×D37—21no—
37C2×Dic74C2×C411yescharacteristic, complemented
38C42×C37—24no—
39C42×C37—22no—
40C42×C37D414yescomplemented
41C22⋊Dic37—22no—
42C22⋊Dic37—21no—
43#10596938—22no—
44C4⋊Dic37C2×C412yescomplemented
45#10596936—22no—
46C4×Dic37—21no—
47#10596934—22no—
48#10596934—22no—
49C2×#64436—22no—
50C23×C37—24no—
51C23×C37—21no—
52C23×C37—21no—
53C23×C37C22⋊C412yes—
54C23×C37C2×D411yescharacteristic
55C22×D37—21no—
56C2×C4×C37—216no—
57C2×C4×C37—28no—
58C2×C4×C37—21no—
59C2×C4×C37—24no—
60C2×C4×C37—21no—
61C2×C4×C37—24no—
62C2×C4×C37—24no—
63C2×C4×C37C22⋊C412yes—
64C2×C4×C37C22×C411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D412yes—
67C2×C4×C37#4112yes—
68C22⋊D37—44no—
69C22⋊D37—41no—
70C22⋊D37—41no—
71C2×Dic37—22no—
72C2×Dic37—21no—
73D148—22no—
74C4×D37—42no—
75Dic74—22no—
76#64436—42no—
77C22×C37—24no—
78C22×C37—24no—
79C22×C37—22no—
80C22×C37—22no—
81C22×C37—22no—
82C22×C37#10414yescomplemented
83C22×C37C2×C22⋊C411yescharacteristic
84C22×C37#12011yescharacteristic
85C22×C37#12311yescharacteristic
86C2×D37—41no—
87C2×D37—42no—
88C4×C37—28no—
89C4×C37—22no—
90C4×C37C4×D412yes—
91C4×C37#12112yes—
92Dic37—41no—
93Dic37—42no—
94#1896—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—24no—
97C2×C37—21no—
98C2×C37#38611yescharacteristic
99C2×C37C2×#10412yes—
100D37—81no—
101#525—371no—
102C22×C42D3711yescharacteristic, complemented
103C2×#104—372no—
104#407—371no—
105#339—372no—
106C37#189611yescharacteristic, complemented, Sylow
107C2×#41—371no—
108C23×C4—21no—
109C23×C4C2×D3711yescharacteristic
110C2×M16—372no—
111#123—741no—
112C22⋊Q8—372no—
113#121—372no—
114#120—741no—
115C4×D4—742no—
116#117—371no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D3712yes—
120#104—744no—
121C22⋊C8—742no—
122C24C22⋊D3711yescharacteristic
123#41—742no—
124#41—742no—
125C2×Q8—371no—
126C2×D4—371no—
127C2×D4—742no—
128C2×D4—741no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—741no—
135C22×C4C4×D3712yes—
136C22×C4D14812yes—
137C22×C4C22⋊D3711yescharacteristic
138C22×C4C22×D3711yescharacteristic
139M16—742no—
140M16—742no—
141C2×C8—742no—
142C4⋊C4—372no—
143C4⋊C4—742no—
144C22⋊C4—742no—
145C22⋊C4—741no—
146C22⋊C4—742no—
147C42—24no—
148C42—22no—
149C42—741no—
150C42C22⋊D3714yescomplemented
151C23—21no—
152C23—21no—
153C23—24no—
154C23—741no—
155C23#1059693812yes—
156C23C2×C22⋊D3711yescharacteristic
157Q8—742no—
158D4—742no—
159D4—1481no—
160D4—1481no—
161D4—1484no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—742no—
170C2×C4—741no—
171C2×C4—1482no—
172C2×C4#1059693812yes—
173C2×C4C2×C4×D3711yescharacteristic
174C2×C4C2×D14811yescharacteristic
175C2×C4#1059696212yes—
176C2×C4C2×C22⋊D3712yes—
177C8—1482no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—1482no—
184C22—1481no—
185C22#1192446414yescomplemented
186C22C2×#1059693811yescharacteristic
187C22#1192450511yescharacteristic
188C22#1192451911yescharacteristic
189C4—28no—
190C4—22no—
191C4—1482no—
192C4—1481no—
193C4C4×C22⋊D3712yes—
194C4#1192451012yes—
195C2—21no—
196C2—21no—
197C2—24no—
198C2—2961no—
199C2#1455741211yescharacteristic
200C2C2×#1192446412yes—
subgroupG/H
centerC2×C4C2×D148
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC22×C42×C37C2
socleC22×C37C2×C22⋊C4
prime radical#14558044C2
cosocleC22×C4×C37C23
hypercenterC22×C42D37
hypocenterC37#1896
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#11924464C2semidirect
3. #14557497C2semidirect
4. #14557293C2semidirect
5. C22×C42×C37C2semidirect
9. #11924515C4semidirect
10. #11924510C4semidirect
35. C2×D148C2×C4semidirect
37. C2×Dic74C2×C4semidirect
40. C42×C37D4semidirect
44. C4⋊Dic37C2×C4semidirect
82. C22×C37#104semidirect
102. C22×C42D37semidirect
106. C37#1896semidirect
150. C42C22⋊D37semidirect
185. C22#11924464semidirect

Maximal subgroups

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

subgroupindex
#145580442
C2×#119244642
#145574972
#145572932
C22×C42×C372
#189637