Finite Group Databasebeta

← #18004967

Subgroups — #18004967

Order 4736.

484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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#14558088C211yesmaximal, characteristic, complemented
2#127×D37C211yesmaximal, characteristic
3#14557896C214yesmaximal, complemented
4#14557881C211yesmaximal, characteristic, complemented
5#14557880C211yesmaximal, characteristic, complemented
6#14557879C211yesmaximal, characteristic, complemented
7#14557536C214yesmaximal, complemented
8C4×#10596929C211yesmaximal, characteristic, complemented
9C37×#486C211yesmaximal, characteristic, complemented
10C2×D4×D37—21no—
11C2×D4×D37—21no—
12C2×D4×D37C2212yes—
13C2×#10596929C2212yes—
14#11924536C2211yescharacteristic, complemented
15#11924533C2211yescharacteristic
16#11924532—21no—
17#11924532—21no—
18#11924532C2212yes—
19#11924527C2212yescomplemented
20#11924516—21no—
21#11924512—21no—
22Q8×Dic37—21no—
23#11924501—21no—
24#11924494C2212yes—
25C42×D37C2211yescharacteristic
26#11924458C2214yescomplemented
27#11924457C2214yescomplemented
28#11924456C2214yescomplemented
29#11924446C2212yescomplemented
30C4×#64436C2211yescharacteristic, complemented
31C4⋊Q8×C37C2211yescharacteristic, complemented
32#127×C37C2211yescharacteristic
33#102×C37C2214yescomplemented
34C4×C8×C37C2211yescharacteristic, complemented
35C23×D37—22no—
36C2×Q8×C37—21no—
37C2×D4×C37—21no—
38C2×D4×C37—21no—
39C2×D4×C37C2312yes—
40C2×C22⋊D37—22no—
41C2×C22⋊D37—22no—
42C2×C22⋊D37—22no—
43D4×D37—28no—
44D4×D37—44no—
45D4×D37—44no—
46C2×D148—21no—
47C2×D148—21no—
48C2×D148C2312yes—
49C2×C4×D37D411yescharacteristic
50C2×C4×D37D411yescharacteristic
51C2×C4×D37C2311yescharacteristic
52C2×Dic74—21no—
53C2×C8×C37C2312yes—
54C4⋊C4×C37—21no—
55C4⋊C4×C37C2312yes—
56C42×C37C2311yescharacteristic
57#10596938—22no—
58C4⋊Dic37—21no—
59C4⋊Dic37—22no—
60C4⋊Dic37C2312yes—
61#10596936—22no—
62C4×Dic37—22no—
63C4×Dic37D411yescharacteristic
64C4×Dic37D411yescharacteristic
65C4×Dic37C2311yescharacteristic
66C2×#64436C2312yes—
67#10596929—24no—
68C23×C37—22no—
69C22×D37—22no—
70C22×D37—44no—
71C22×D37—44no—
72C22×D37—44no—
73C22×D37C2×D411yescharacteristic
74Q8×C37—42no—
75D4×C37—24no—
76D4×C37—42no—
77D4×C37—42no—
78C2×C4×C37—22no—
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2411yescharacteristic
82C22⋊D37—44no—
83C22⋊D37—44no—
84C22⋊D37—44no—
85C2×Dic37—22no—
86C2×Dic37C2×D411yescharacteristic
87C2×Dic37C2×D411yescharacteristic
88C2×Dic37C2×D411yescharacteristic
89D148—24no—
90D148—42no—
91D148—42no—
92C4×D37—22no—
93C4×D37—22no—
94C4×D37#4114yes—
95Dic74—42no—
96C8×C37—22no—
97#64436—22no—
98C22×C37—42no—
99C22×C37—42no—
100C22×C37—42no—
101C22×C37C22×D411yescharacteristic
102C2×D37—21no—
103C2×D37—21no—
104C2×D37—42no—
105C2×D37—42no—
106C2×D37—42no—
107C2×D37—88no—
108C2×D37#12412yes—
109C4×C37—42no—
110C4×C37AGL(1,ℤ/8)12yes—
111C4×C37AGL(1,ℤ/8)12yes—
112C4×C37C2×#4112yes—
113Dic37—21no—
114Dic37—21no—
115Dic37—42no—
116Dic37#12412yes—
117#3138—371nomaximal, Sylow
118C2×C37—82no—
119C2×C37C2×#12411yescharacteristic
120C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
122D37—22no—
123D37—82no—
124#533—371no—
125C2×#127—371no—
126#490—374no—
127#486—371no—
128#486—371no—
129#486—371no—
130#486D3711yescharacteristic, complemented
131#418—374no—
132C4×M16—371no—
133C37#313811yescharacteristic, complemented, Sylow
134C22×D4—372no—
135C22×D4—741no—
136C22×D4—741no—
137C2×M16—372no—
138C4⋊Q8—371no—
139C4⋊Q8C2×D3711yescharacteristic, complemented
140#127—372no—
141#127—371no—
142#127—741no—
143#127—741no—
144#127C2×D3711yescharacteristic
145#125—372no—
146C22⋊Q8—741no—
147C22⋊Q8—741no—
148C4×Q8—741no—
149C4×Q8—741no—
150#117—372no—
151C2×C42—371no—
152#102—374no—
153#102—374no—
154#102—374no—
155#102C2×D3714yescomplemented
156#97—372no—
157C4×C8—371no—
158C4×C8C2×D3711yescharacteristic, complemented
159C24—742no—
160C2×Q8—21no—
161C2×Q8—741no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—372no—
165C2×D4—748no—
166C2×D4—742no—
167C2×D4—742no—
168C2×D4—742no—
169C2×D4—741no—
170C2×D4—741no—
171C2×D4—1484no—
172C2×D4—1484no—
173C2×D4C22×D3712yes—
174C22×C4—371no—
175C22×C4—371no—
176C22×C4—371no—
177M16—744no—
178C2×C8—372no—
179C2×C8C22×D3712yes—
180C4⋊C4—21no—
181C4⋊C4—372no—
182C4⋊C4—742no—
183C4⋊C4—742no—
184C4⋊C4—741no—
185C4⋊C4C22×D3712yes—
186C22⋊C4—742no—
187C42—371no—
188C42—371no—
189C42—371no—
190C42—742no—
191C42C22×D3711yescharacteristic
192C23—22no—
193C23—371no—
194C23—742no—
195C23—1484no—
196C23—1484no—
197C23—1484no—
198Q8—42no—
199Q8—1482no—
200D4—24no—
201D4—42no—
202D4—42no—
203D4—744no—
204D4—1484no—
205D4—1484no—
206D4—1484no—
207D4—1482no—
208D4—1482no—
209C2×C4—22no—
210C2×C4—371no—
211C2×C4—374no—
212C2×C4—371no—
213C2×C4—371no—
214C2×C4—742no—
215C2×C4—742no—
216C2×C4—742no—
217C2×C4D4×D3711yescharacteristic
218C2×C4D4×D3711yescharacteristic
219C2×C4C23×D3711yescharacteristic
220C8—22no—
221C8—742no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—372no—
226C22—2968no—
227C22—741no—
228C22—741no—
229C22—1482no—
230C22—1482no—
231C22—1482no—
232C22C2×D4×D3711yescharacteristic
233C4—42no—
234C4—372no—
235C4—741no—
236C4—741no—
237C4—1482no—
238C4#1192456012yes—
239C4#1192456312yes—
240C4#41×D3712yes—
241C2—82no—
242C2—2962no—
243C2—742no—
244C2#124×D3711yescharacteristic
245C2C2×#1192456011yescharacteristic
246C2C2×#1192456311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#486C2
socleC22×C37C22×D4
prime radical#127×D37C2
hypercenter#486D37
hypocenterC37#3138
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14558088C2semidirect
3. #14557896C2semidirect
4. #14557881C2semidirect
5. #14557880C2semidirect
6. #14557879C2semidirect
7. #14557536C2semidirect
8. C4×#10596929C2semidirect
9. C37×#486C2semidirect
14. #11924536C22semidirect
19. #11924527C22semidirect
26. #11924458C22semidirect
27. #11924457C22semidirect
28. #11924456C22semidirect
29. #11924446C22semidirect
30. C4×#64436C22semidirect
31. C4⋊Q8×C37C22semidirect
33. #102×C37C22semidirect
34. C4×C8×C37C22semidirect
130. #486D37semidirect
133. C37#3138semidirect
139. C4⋊Q8C2×D37semidirect
155. #102C2×D37semidirect
158. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580882
#127×D372
#145578962
#145578812
#145578802
#145578792
#145575362
C4×#105969292
C37×#4862
#313837