Finite Group Databasebeta

← #17993121

Subgroups — #17993121

Order 4736.

242 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 81 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#14557590C211yesmaximal, characteristic, complemented
2C4×C4⋊Dic37C211yesmaximal, characteristic, complemented
3#14557270C212yesmaximal, complemented
4#14557267C212yesmaximal
5C37×#529C211yesmaximal, characteristic
6C2×C4⋊Dic37—21no—
7C2×C4×Dic37—21no—
8C4⋊#64436—21no—
9C22⋊#64436C2212yes—
10#11924447—21no—
11#11924443C2212yes—
12#126×C37—21no—
13#125×C37C411yescharacteristic, complemented
14#124×C37C411yescharacteristic, complemented
15#123×C37—21no—
16C22⋊Q8×C37C2211yescharacteristic
17#121×C37C2211yescharacteristic
18C4×Q8×C37C411yescharacteristic, complemented
19C4×D4×C37—21no—
20C4×D4×C37C411yescharacteristic, complemented
21#117×C37—21no—
22C2×C42×C37C2211yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24C2×D4×C37—21no—
25C2×D4×C37C2×C411yescharacteristic
26C22×C4×C37—21no—
27C22×C4×C37D411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×C4×C37C2311yescharacteristic
30C22×Dic37—22no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37C2×C411yescharacteristic
36C4⋊C4×C37C2×C411yescharacteristic
37C22⋊C4×C37—21no—
38C22⋊C4×C37—21no—
39C22⋊C4×C37—21no—
40C22⋊C4×C37—21no—
41C22⋊C4×C37—21no—
42C42×C37—21no—
43C42×C37C2×C411yescharacteristic
44C42×C37C2×C411yescharacteristic
45C42×C37D411yescharacteristic
46C42×C37D411yescharacteristic
47C4⋊Dic37—24no—
48C4×Dic37—42no—
49C2×#64436—22no—
50C23×C37—21no—
51C23×C37C2×D411yescharacteristic
52Q8×C37—41no—
53D4×C37—41no—
54D4×C37—41no—
55D4×C37—41no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—22no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—41no—
63C2×C4×C37—42no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22⋊C411yescharacteristic
67C2×C4×C37C22⋊C411yescharacteristic
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×Dic37—24no—
71C2×Dic37—42no—
72C2×Dic37—42no—
73#64436—42no—
74C22×C37—21no—
75C22×C37—21no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37C2×C22⋊C411yescharacteristic
80C22×C37AGL(1,ℤ/8)11yescharacteristic
81C22×C37#13711yescharacteristic
82C4×C37—21no—
83C4×C37—21no—
84C4×C37—21no—
85C4×C37—21no—
86C4×C37—21no—
87C4×C37—41no—
88C4×C37—41no—
89C4×C37—41no—
90C4×C37#10412yes—
91Dic37—44no—
92#1509—371nomaximal, Sylow
93C2×C37—21no—
94C2×C37—21no—
95C2×C37—81no—
96C2×C37#41011yescharacteristic
97C2×C37#41711yescharacteristic
98C2×C37C2×#10411yescharacteristic
99#529D3711yescharacteristic
100#432—371no—
101C4×C4⋊C4—371no—
102#328—372no—
103#327—372no—
104C37#150911yescharacteristic, complemented, Sylow
105#126—21no—
106#125Dic3711yescharacteristic, complemented
107#124Dic3711yescharacteristic, complemented
108#123—21no—
109C22⋊Q8C2×D3711yescharacteristic
110#121C2×D3711yescharacteristic
111C4×Q8Dic3711yescharacteristic, complemented
112C4×D4—21no—
113C4×D4Dic3711yescharacteristic, complemented
114#117—21no—
115C2×C4⋊C4—741no—
116C2×C42—741no—
117C2×C42C2×D3711yescharacteristic
118C4⋊C8—741no—
119C22⋊C8—372no—
120#97—741no—
121#95—372no—
122C2×Q8C2×Dic3711yescharacteristic
123C2×D4—21no—
124C2×D4C2×Dic3711yescharacteristic
125C22×C4—21no—
126C22×C4—742no—
127C22×C4C22⋊D3711yescharacteristic
128C22×C4C22⋊D3711yescharacteristic
129C22×C4C22×D3711yescharacteristic
130C2×C8—742no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—744no—
136C4⋊C4C2×Dic3711yescharacteristic
137C4⋊C4C2×Dic3711yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C22⋊C4—21no—
143C42—21no—
144C42—1482no—
145C42C2×Dic3711yescharacteristic
146C42C2×Dic3711yescharacteristic
147C42C22⋊D3711yescharacteristic
148C42C22⋊D3711yescharacteristic
149C23—21no—
150C23C2×C22⋊D3711yescharacteristic
151Q8—41no—
152D4—41no—
153D4—41no—
154D4—41no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—744no—
164C2×C4—1482no—
165C2×C4—1482no—
166C2×C4C22⋊Dic3711yescharacteristic
167C2×C4C22⋊Dic3711yescharacteristic
168C2×C4C22⋊Dic3711yescharacteristic
169C2×C4C22⋊Dic3711yescharacteristic
170C2×C4C22×Dic3711yescharacteristic
171C2×C4C2×C22⋊D3711yescharacteristic
172C8—1482no—
173C22—21no—
174C22—21no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22C2×C22⋊Dic3711yescharacteristic
179C22#1192456111yescharacteristic
180C22#1192456611yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—41no—
189C4—1484no—
190C4#1192446312yes—
191C2—21no—
192C2—21no—
193C2—81no—
194C2#1455750711yescharacteristic
195C2#1455753411yescharacteristic
196C2C2×#1192446311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#529C2
socleC22×C37C2×C22⋊C4
prime radical#121×C37C22
cosocleC22×C4×C37C23
hypercenter#529D37
hypocenterC37#1509
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #14557590C2semidirect
2. C4×C4⋊Dic37C2semidirect
3. #14557270C2semidirect
13. #125×C37C4semidirect
14. #124×C37C4semidirect
18. C4×Q8×C37C4semidirect
20. C4×D4×C37C4semidirect
104. C37#1509semidirect
106. #125Dic37semidirect
107. #124Dic37semidirect
111. C4×Q8Dic37semidirect
113. C4×D4Dic37semidirect

Maximal subgroups

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

subgroupindex
#145575902
C4×C4⋊Dic372
#145572702
#145572672
C37×#5292
#150937