Finite Group Databasebeta

← #18006419

Subgroups — #18006419

Order 4736.

462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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#14558244C211yesmaximal, characteristic, complemented
2#14558168C211yesmaximal, characteristic
3#14557850C212yesmaximal, complemented
4#14557820C211yesmaximal, characteristic, complemented
5#14557761C212yesmaximal, complemented
6#14557730C211yesmaximal, characteristic, complemented
7#14557685C212yesmaximal, complemented
8C4×#10596930C211yesmaximal, characteristic, complemented
9C8×D148C211yesmaximal, characteristic, complemented
10#102×D37C212yesmaximal, complemented
11C37×#486C211yesmaximal, characteristic, complemented
12C2×D4×D37—21no—
13C2×D4×D37C2212yes—
14C2×#10596930C2211yescharacteristic
15C2×#10596940C2212yescomplemented
16C2×C8×D37C2212yescomplemented
17#11924527—21no—
18#11924516C2212yescomplemented
19#11924512—22no—
20#11924507—21no—
21#11924507C2212yes—
22#11924504—22no—
23C4×Dic74C2211yescharacteristic, complemented
24C4×D148C2211yescharacteristic
25C4×D148C2211yescharacteristic
26#11924498—21no—
27C4⋊C4×D37C2212yescomplemented
28#11924468C2211yescharacteristic, complemented
29#11924467C2212yescomplemented
30C4⋊#64436C2211yescharacteristic, complemented
31#11924461C2211yescharacteristic, complemented
32#11924458C2211yescharacteristic
33#11924457C2212yescomplemented
34#11924456C2212yes—
35#11924448C2212yescomplemented
36C4⋊Q8×C37C2211yescharacteristic, complemented
37#127×C37C2211yescharacteristic
38#102×C37C2212yescomplemented
39#102×C37C2212yescomplemented
40C4×C8×C37C2211yescharacteristic, complemented
41C23×D37—22no—
42C2×Q8×C37—21no—
43C2×D4×C37—21no—
44C2×D4×C37—21no—
45C2×D4×C37C2312yes—
46C2×C22⋊D37—22no—
47C2×C22⋊D37—22no—
48D4×D37—24no—
49D4×D37—42no—
50D4×D37—44no—
51C2×D148D411yescharacteristic
52C2×D148C2311yescharacteristic
53C2×C4×D37—21no—
54C2×C4×D37—22no—
55C2×C4×D37C2312yes—
56C2×Dic74C2311yescharacteristic
57C2×C8×C37C2311yescharacteristic
58C2×C8×C37C2311yescharacteristic
59C4⋊C4×C37—21no—
60C4⋊C4×C37C2312yes—
61C42×C37C2311yescharacteristic
62C22⋊Dic37—22no—
63#10596940—42no—
64#10596938—22no—
65#10596938—21no—
66#10596938D412yes—
67C4⋊Dic37—22no—
68C4⋊Dic37D411yescharacteristic
69C4⋊Dic37C2311yescharacteristic
70C4⋊Dic37C2311yescharacteristic
71#10596936—21no—
72#10596936—22no—
73C4×Dic37—21no—
74C2×#64436C2312yes—
75#10596930—22no—
76C8×D37—42no—
77C23×C37—22no—
78C22×D37—21no—
79C22×D37—44no—
80C22×D37—44no—
81C22×D37—82no—
82C22×D37C2×D412yes—
83Q8×C37—81no—
84D4×C37—22no—
85D4×C37—22no—
86D4×C37—42no—
87D4×C37—81no—
88C2×C4×C37—22no—
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2411yescharacteristic
92C22⋊D37—44no—
93C22⋊D37—44no—
94C2×Dic37—21no—
95C2×Dic37—21no—
96C2×Dic37—21no—
97C2×Dic37C2×D412yes—
98D148—21no—
99D148SD1614yescomplemented
100D148#4112yes—
101C4×D37—22no—
102C4×D37—22no—
103C4×D37—42no—
104C4×D37—82no—
105Dic74—21no—
106Dic74—21no—
107C8×C37—21no—
108C8×C37—21no—
109#64436—22no—
110C22×C37—42no—
111C22×C37—42no—
112C22×C37—42no—
113C22×C37C22×D411yescharacteristic
114C2×D37—22no—
115C2×D37—22no—
116C2×D37—22no—
117C2×D37—41no—
118C2×D37—41no—
119C2×D37—88no—
120C2×D37C2×SD1614yes—
121C4×C37—21no—
122C4×C37—42no—
123C4×C37C2×SD1612yes—
124C4×C37C2×#4111yescharacteristic
125C4×C37H(5,𝔽2)11yescharacteristic
126Dic37—22no—
127Dic37—41no—
128Dic37—41no—
129Dic37—41no—
130#3295—371nomaximal, Sylow
131C2×C37—82no—
132C2×C37#54611yescharacteristic
133C2×C37C22×SD1611yescharacteristic
134C2×C37#57611yescharacteristic
135D37—24no—
136D37—42no—
137#554—371no—
138D42—371no—
139#486D3711yescharacteristic, complemented
140#481—372no—
141#476—371no—
142#465—372no—
143#460—371no—
144#450—372no—
145C4×SD16—371no—
146C8×D4—371no—
147C2×#102—372no—
148C37#329511yescharacteristic, complemented, Sylow
149C22×D4—372no—
150C22×D4—741no—
151C2×SD16—372no—
152C2×SD16—371no—
153C22×C8—372no—
154C4⋊Q8C2×D3711yescharacteristic, complemented
155#127C2×D3711yescharacteristic
156#125—741no—
157C22⋊Q8—372no—
158C22⋊Q8—742no—
159#121—372no—
160#121—741no—
161#120—742no—
162C4×Q8—371no—
163C4×D4—371no—
164C4×D4—371no—
165C4×D4—741no—
166C2×C4⋊C4—372no—
167#106—371no—
168#106—372no—
169C4⋊C8—371no—
170#103—371no—
171#102—372no—
172#102—371no—
173#102—372no—
174#102C2×D3712yescomplemented
175#102C2×D3712yescomplemented
176C22⋊C8—372no—
177C4×C8C2×D3711yescharacteristic, complemented
178C24—742no—
179C2×Q8—21no—
180C2×Q8—371no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—371no—
184C2×D4—371no—
185C2×D4—742no—
186C2×D4—744no—
187C2×D4—742no—
188C2×D4—1482no—
189C2×D4—1484no—
190C2×D4C22×D3712yes—
191C22×C4—372no—
192C22×C4—742no—
193C22×C4—741no—
194SD16—742no—
195SD16—1482no—
196C2×C8—372no—
197C2×C8—1482no—
198C2×C8C22×D3711yescharacteristic
199C2×C8C22×D3711yescharacteristic
200C4⋊C4—21no—
201C4⋊C4—371no—
202C4⋊C4—371no—
203C4⋊C4—371no—
204C4⋊C4—742no—
205C4⋊C4—742no—
206C4⋊C4—741no—
207C4⋊C4C22×D3712yes—
208C22⋊C4—372no—
209C22⋊C4—742no—
210C22⋊C4—742no—
211C22⋊C4—741no—
212C42—741no—
213C42C22×D3711yescharacteristic
214C23—22no—
215C23—372no—
216C23—2962no—
217C23—741no—
218C23—1484no—
219C23—1484no—
220Q8—81no—
221Q8—741no—
222Q8—741no—
223D4—22no—
224D4—22no—
225D4—42no—
226D4—81no—
227D4—374no—
228D4—372no—
229D4—741no—
230D4—1484no—
231D4—1484no—
232C2×C4—22no—
233C2×C4—372no—
234C2×C4—2962no—
235C2×C4—742no—
236C2×C4—742no—
237C2×C4—741no—
238C2×C4—741no—
239C2×C4—741no—
240C2×C4—1482no—
241C2×C4D4×D3711yescharacteristic
242C2×C4D4×D3711yescharacteristic
243C2×C4C23×D3711yescharacteristic
244C8—21no—
245C8—21no—
246C8—742no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—374no—
251C22—2968no—
252C22—742no—
253C22—742no—
254C22—742no—
255C22—1481no—
256C22—1481no—
257C22C2×D4×D3711yescharacteristic
258C4—21no—
259C4—42no—
260C4—742no—
261C4—1481no—
262C4—1481no—
263C4—1481no—
264C4SD16×D3712yes—
265C4#41×D3711yescharacteristic
266C4#1192458211yescharacteristic
267C2—82no—
268C2—744no—
269C2—1482no—
270C2#1455817611yescharacteristic
271C2C2×SD16×D3711yescharacteristic
272C2#1455833411yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#486C2
socleC22×C37C22×D4
prime radical#14558168C2
hypercenter#486D37
hypocenterC37#3295
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. #14558244C2semidirect
3. #14557850C2semidirect
4. #14557820C2semidirect
5. #14557761C2semidirect
6. #14557730C2semidirect
7. #14557685C2semidirect
8. C4×#10596930C2semidirect
9. C8×D148C2semidirect
10. #102×D37C2semidirect
11. C37×#486C2semidirect
15. C2×#10596940C22semidirect
16. C2×C8×D37C22semidirect
18. #11924516C22semidirect
23. C4×Dic74C22semidirect
27. C4⋊C4×D37C22semidirect
28. #11924468C22semidirect
29. #11924467C22semidirect
30. C4⋊#64436C22semidirect
31. #11924461C22semidirect
33. #11924457C22semidirect
35. #11924448C22semidirect
36. C4⋊Q8×C37C22semidirect
38. #102×C37C22semidirect
39. #102×C37C22semidirect
40. C4×C8×C37C22semidirect
99. D148SD16semidirect
139. #486D37semidirect
148. C37#3295semidirect
154. C4⋊Q8C2×D37semidirect
174. #102C2×D37semidirect
175. #102C2×D37semidirect
177. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582442
#145581682
#145578502
#145578202
#145577612
#145577302
#145576852
C4×#105969302
C8×D1482
#102×D372
C37×#4862
#329537