Finite Group Databasebeta

← #17995037

Subgroups — #17995037

Order 4736.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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
2C22×C4×Dic37C211yesmaximal, characteristic, complemented
3C2×#11924462C212yesmaximal, complemented
4#14557294C212yesmaximal, complemented
5C37×#407C211yesmaximal, characteristic, complemented
6C2×#10596962C2211yescharacteristic
7C23×Dic37—21no—
8#11924519—21no—
9#11924515C412yescomplemented
10#11924510C412yescomplemented
11#11924505—21no—
12C4×C22⋊D37—22no—
13#11924495C2211yescharacteristic
14C2×C4×Dic37—21no—
15C2×C4×Dic37—24no—
16C2×C4×Dic37C2212yes—
17#11924462—24no—
18C23×C4×C37C2211yescharacteristic
19C2×M16×C37C2212yes—
20C22⋊C8×C37—22no—
21C24×C37D411yescharacteristic
22C22×C4×C37—22no—
23C22×C4×C37—22no—
24C22×C4×C37C2×C412yes—
25C22×C4×C37D411yescharacteristic
26C22×C4×C37D412yes—
27C22×C4×C37C2311yescharacteristic
28C2×C22⋊D37—22no—
29C2×C22⋊D37—21no—
30C22×Dic37—24no—
31C22×Dic37—28no—
32C22×Dic37—22no—
33#10596962—22no—
34#10596962—22no—
35C2×D148C2×C411yescharacteristic, complemented
36C2×C4×D37—21no—
37C2×Dic74C2×C411yescharacteristic, complemented
38M16×C37—22no—
39M16×C37—22no—
40C2×C8×C37—22no—
41C22⋊Dic37—22no—
42C22⋊Dic37—21no—
43#10596938—22no—
44C4⋊Dic37C2×C412yescomplemented
45#10596936—22no—
46C4×Dic37—24no—
47C4×Dic37—22no—
48C4×Dic37—21no—
49C4×Dic37D414yescomplemented
50C23×C37—24no—
51C23×C37—21no—
52C23×C37—21no—
53C23×C37C22⋊C412yes—
54C23×C37C2×D411yescharacteristic
55C22×D37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—24no—
59C2×C4×C37—24no—
60C2×C4×C37C22⋊C412yes—
61C2×C4×C37C22×C411yescharacteristic
62C2×C4×C37C2×D412yes—
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37#4112yes—
65C22⋊D37—44no—
66C22⋊D37—41no—
67C22⋊D37—41no—
68C2×Dic37—216no—
69C2×Dic37—28no—
70C2×Dic37—24no—
71C2×Dic37—22no—
72C2×Dic37—21no—
73D148—22no—
74C4×D37—42no—
75Dic74—22no—
76C8×C37—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—22no—
89C4×C37C4×D412yes—
90C4×C37#12112yes—
91Dic37—28no—
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×C42—371no—
103C2×#104—372no—
104#407D3711yescharacteristic, complemented
105#339—372no—
106C37#189611yescharacteristic, complemented, Sylow
107C2×#41—371no—
108C23×C4—741no—
109C23×C4C2×D3711yescharacteristic
110C2×M16C2×D3712yes—
111#123—741no—
112C22⋊Q8—372no—
113#121—372no—
114#120—741no—
115C4×D4—742no—
116#117—371no—
117C2×C42—372no—
118C2×C42—744no—
119C2×C42—741no—
120#104—744no—
121C22⋊C8—22no—
122C24D14811yescharacteristic
123#41—742no—
124#41—742no—
125C2×Q8—371no—
126C2×D4—371no—
127C2×D4—742no—
128C2×D4—741no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—744no—
132C22×C4—748no—
133C22×C4—742no—
134C22×C4—741no—
135C22×C4C4×D3712yes—
136C22×C4D14811yescharacteristic
137C22×C4C22⋊D3712yes—
138C22×C4C22×D3711yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—372no—
143C4⋊C4—742no—
144C22⋊C4—742no—
145C22⋊C4—741no—
146C22⋊C4—742no—
147C42—374no—
148C42—744no—
149C42—742no—
150C42—741no—
151C23—21no—
152C23—21no—
153C23—24no—
154C23—741no—
155C23#1059693812yes—
156C23C2×D14811yescharacteristic
157Q8—742no—
158D4—742no—
159D4—1481no—
160D4—1481no—
161D4—1484no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—7416no—
167C2×C4—748no—
168C2×C4—744no—
169C2×C4—742no—
170C2×C4—741no—
171C2×C4—1482no—
172C2×C4#1059693812yes—
173C2×C4C2×C4×D3711yescharacteristic
174C2×C4D4×D3712yes—
175C2×C4#1059696412yes—
176C2×C4C2×C22⋊D3711yescharacteristic
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—1482no—
184C22—1481no—
185C22#1192446214yescomplemented
186C22C2×#1059693811yescharacteristic
187C22#1192450611yescharacteristic
188C22#1192452011yescharacteristic
189C4—22no—
190C4—748no—
191C4—1482no—
192C4—1481no—
193C4#1192449612yes—
194C4#1192450812yes—
195C2—21no—
196C2—21no—
197C2—24no—
198C2—2961no—
199C2#1455741011yescharacteristic
200C2C2×#1192446212yes—
subgroupG/H
centerC2×C4C2×C22⋊D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#407C2
socleC22×C37C2×C22⋊C4
prime radical#14558044C2
cosocleC22×C4×C37C23
hypercenter#407D37
hypocenterC37#1896
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic37C2semidirect
3. C2×#11924462C2semidirect
4. #14557294C2semidirect
5. C37×#407C2semidirect
9. #11924515C4semidirect
10. #11924510C4semidirect
35. C2×D148C2×C4semidirect
37. C2×Dic74C2×C4semidirect
44. C4⋊Dic37C2×C4semidirect
49. C4×Dic37D4semidirect
82. C22×C37#104semidirect
104. #407D37semidirect
106. C37#1896semidirect
185. C22#11924462semidirect

Maximal subgroups

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

subgroupindex
#145580442
C22×C4×Dic372
C2×#119244622
#145572942
C37×#4072
#189637