Finite Group Databasebeta

← #18006192

Subgroups — #18006192

Order 4736.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#11924562C212yesmaximal, complemented
2#14558188C211yesmaximal, characteristic, complemented
3#14557905C211yesmaximal, characteristic, complemented
4#14557777C212yesmaximal, complemented
5#14557738C211yesmaximal, characteristic, complemented
6#14557725C211yesmaximal, characteristic, complemented
7#14557684C212yesmaximal, complemented
8#14557676C212yesmaximal, complemented
9C4×#10596939C211yesmaximal, characteristic, complemented
10#14557611C211yesmaximal, characteristic, complemented
11D42×C37C211yesmaximal, characteristic, complemented
12C2×#10596962C2212yescomplemented
13#11924562—28no—
14C2×#10596940C2212yes—
15C2×#10596940C2212yescomplemented
16C2×#10596940C2212yescomplemented
17C2×#10596939C2211yescharacteristic
18C2×#10596939C2212yescomplemented
19C2×#10596934C2212yescomplemented
20#11924536C2211yescharacteristic, complemented
21#11924518—22no—
22#11924515C2212yescomplemented
23#11924507—21no—
24C4×D148C2211yescharacteristic, complemented
25C4⋊C4×D37—21no—
26#11924469C2211yescharacteristic, complemented
27C4⋊#64436C2211yescharacteristic, complemented
28#11924459C2212yescomplemented
29#11924457C2211yescharacteristic
30#11924457C2212yescomplemented
31#11924456C2211yescharacteristic, complemented
32C22⋊#64436C2212yescomplemented
33C4×#64436C2211yescharacteristic, complemented
34C22×D4×C37—21no—
35C22×D4×C37C2212yes—
36#127×C37C2211yescharacteristic
37#121×C37—21no—
38#121×C37C2212yes—
39#120×C37—22no—
40C4×D4×C37C2211yescharacteristic
41C4×D4×C37C2211yescharacteristic
42C24×C37—22no—
43C2×D4×C37—24no—
44C2×D4×C37—22no—
45C2×D4×C37—22no—
46C2×D4×C37—21no—
47C2×D4×C37—21no—
48C2×D4×C37—42no—
49C2×D4×C37—44no—
50C2×D4×C37D411yescharacteristic
51C2×D4×C37C2312yes—
52C2×D4×C37C2311yescharacteristic
53C22×C4×C37—21no—
54C22×C4×C37C2312yes—
55C2×C22⋊D37—22no—
56#10596962—24no—
57#10596962—42no—
58C2×D148C2311yescharacteristic
59C2×C4×D37—21no—
60C2×C4×D37—22no—
61C2×Dic74C2312yes—
62C4⋊C4×C37D411yescharacteristic
63C4⋊C4×C37C2311yescharacteristic
64C22⋊C4×C37—21no—
65C22⋊C4×C37—22no—
66C22⋊C4×C37D412yes—
67C42×C37C2311yescharacteristic
68C22⋊Dic37—22no—
69#10596940—24no—
70#10596940—24no—
71#10596940—42no—
72#10596939—24no—
73#10596939D414yescomplemented
74#10596938—21no—
75C4⋊Dic37—21no—
76C4⋊Dic37—21no—
77C4⋊Dic37C2311yescharacteristic
78#10596936—22no—
79#10596934—24no—
80C2×#64436C2312yes—
81C2×#64436C2311yescharacteristic
82C2×#64436C2311yescharacteristic
83C23×C37—21no—
84C23×C37—22no—
85C23×C37—44no—
86C23×C37—44no—
87C23×C37—82no—
88C23×C37C2×D412yes—
89C22×D37—21no—
90D4×C37—22no—
91D4×C37—22no—
92D4×C37—21no—
93D4×C37—22no—
94D4×C37—44no—
95D4×C37—44no—
96D4×C37—42no—
97D4×C37—81no—
98D4×C37C2×D412yes—
99C2×C4×C37—22no—
100C2×C4×C37—22no—
101C2×C4×C37—21no—
102C2×C4×C37—42no—
103C2×C4×C37C2×D412yes—
104C2×C4×C37C2×D411yescharacteristic
105C2×C4×C37C2×D411yescharacteristic
106C2×C4×C37C2411yescharacteristic
107C22⋊D37—44no—
108C2×Dic37—21no—
109C2×Dic37—22no—
110D148—21no—
111D148C2×D412yescomplemented
112C4×D37—44no—
113C4×D37—42no—
114Dic74—22no—
115Dic74—22no—
116#64436—22no—
117#64436—21no—
118#64436C2×D412yescomplemented
119C22×C37—22no—
120C22×C37—22no—
121C22×C37—22no—
122C22×C37—22no—
123C22×C37—41no—
124C22×C37—41no—
125C22×C37—42no—
126C22×C37—42no—
127C22×C37—42no—
128C22×C37—88no—
129C22×C37C22×D411yescharacteristic
130C2×D37—22no—
131C2×D37—41no—
132C2×D37—41no—
133C4×C37—22no—
134C4×C37—21no—
135C4×C37—41no—
136C4×C37AGL(1,ℤ/8)12yescomplemented
137C4×C37C22×D411yescharacteristic
138C4×C37H(5,𝔽2)11yescharacteristic
139Dic37—42no—
140Dic37—41no—
141#3272—371nomaximal, Sylow
142C2×C37—42no—
143C2×C37—42no—
144C2×C37—82no—
145C2×C37D4211yescharacteristic
146C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C37#57711yescharacteristic
148D37—42no—
149C2×AGL(1,ℤ/8)—372no—
150#547—371no—
151D42D3711yescharacteristic, complemented
152#492—371no—
153#468—372no—
154#461—371no—
155#459—371no—
156#450—372no—
157#449—372no—
158C4×D8—371no—
159#436—371no—
160C37#327211yescharacteristic, complemented, Sylow
161C2×#41—372no—
162C22×D4—21no—
163C22×D4C2×D3712yes—
164AGL(1,ℤ/8)—748no—
165C2×SD16—372no—
166C2×SD16—372no—
167C2×SD16—372no—
168C2×D8—371no—
169C2×D8—372no—
170C2×M16—372no—
171C4⋊Q8—371no—
172#127C2×D3711yescharacteristic
173#123—742no—
174C22⋊Q8—372no—
175#121—21no—
176#121—741no—
177#121C2×D3712yes—
178#120—22no—
179C4×D4—371no—
180C4×D4C2×D3711yescharacteristic
181C4×D4C2×D3711yescharacteristic
182C2×C4⋊C4—741no—
183#107—371no—
184C4⋊C8—371no—
185#103—372no—
186#102—371no—
187#102—372no—
188#102—371no—
189C22⋊C8—372no—
190C4×C8—371no—
191C24—22no—
192#41—744no—
193#41—1482no—
194C2×Q8—372no—
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—44no—
202C2×D4—371no—
203C2×D4—742no—
204C2×D4C22⋊D3711yescharacteristic
205C2×D4C22×D3712yes—
206C2×D4C22×D3711yescharacteristic
207C22×C4—21no—
208C22×C4—741no—
209C22×C4—742no—
210C22×C4C22×D3712yes—
211SD16—744no—
212SD16—744no—
213SD16—1482no—
214D8—374no—
215D8—744no—
216M16—744no—
217C2×C8—371no—
218C2×C8—371no—
219C2×C8—372no—
220C4⋊C4—371no—
221C4⋊C4—742no—
222C4⋊C4—741no—
223C4⋊C4—741no—
224C4⋊C4C22⋊D3711yescharacteristic
225C4⋊C4C22×D3711yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—22no—
228C22⋊C4—742no—
229C22⋊C4—741no—
230C22⋊C4C22⋊D3712yes—
231C42C22×D3711yescharacteristic
232C23—21no—
233C23—22no—
234C23—44no—
235C23—44no—
236C23—82no—
237C23—741no—
238C23C2×C22⋊D3712yes—
239Q8—742no—
240Q8—742no—
241D4—22no—
242D4—22no—
243D4—21no—
244D4—22no—
245D4—44no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—372no—
250D4—741no—
251D4—1484no—
252D4D4×D3712yes—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—741no—
258C2×C4—742no—
259C2×C4—1484no—
260C2×C4—1482no—
261C2×C4C2×C22⋊D3711yescharacteristic
262C2×C4C2×C22⋊D3712yes—
263C2×C4C2×C22⋊D3711yescharacteristic
264C2×C4C23×D3711yescharacteristic
265C8—372no—
266C8—742no—
267C8—741no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—88no—
278C22—742no—
279C22—1481no—
280C22—1481no—
281C22C22×C22⋊D3711yescharacteristic
282C4—21no—
283C4—22no—
284C4—41no—
285C4—1481no—
286C4—1482no—
287C4#1192456212yescomplemented
288C4C2×D4×D3711yescharacteristic
289C4#1192458111yescharacteristic
290C2—42no—
291C2—42no—
292C2—82no—
293C2—1482no—
294C2D4×C22⋊D3711yescharacteristic
295C2C2×#1192456211yescharacteristic
296C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingD42×C37C2
socleC22×C37C22×D4
hypercenterD42D37
hypocenterC37#3272
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. #14558188C2semidirect
3. #14557905C2semidirect
4. #14557777C2semidirect
5. #14557738C2semidirect
6. #14557725C2semidirect
7. #14557684C2semidirect
8. #14557676C2semidirect
9. C4×#10596939C2semidirect
10. #14557611C2semidirect
11. D42×C37C2semidirect
12. C2×#10596962C22semidirect
15. C2×#10596940C22semidirect
16. C2×#10596940C22semidirect
18. C2×#10596939C22semidirect
19. C2×#10596934C22semidirect
20. #11924536C22semidirect
22. #11924515C22semidirect
24. C4×D148C22semidirect
26. #11924469C22semidirect
27. C4⋊#64436C22semidirect
28. #11924459C22semidirect
30. #11924457C22semidirect
31. #11924456C22semidirect
32. C22⋊#64436C22semidirect
33. C4×#64436C22semidirect
73. #10596939D4semidirect
111. D148C2×D4semidirect
118. #64436C2×D4semidirect
136. C4×C37AGL(1,ℤ/8)semidirect
151. D42D37semidirect
160. C37#3272semidirect
287. C4#11924562semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
#145581882
#145579052
#145577772
#145577382
#145577252
#145576842
#145576762
C4×#105969392
#145576112
D42×C372
#327237