Finite Group Databasebeta

← #18006191

Subgroups — #18006191

Order 4736.

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

normal subgroups only

This group has 546 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
1C2×#11924560C212yesmaximal, complemented
2#14558187C211yesmaximal, characteristic, complemented
3#14558168C211yesmaximal, characteristic, complemented
4#14557905C211yesmaximal, characteristic, complemented
5#14557778C212yesmaximal, complemented
6#14557739C211yesmaximal, characteristic, complemented
7#14557685C212yesmaximal, complemented
8#14557675C212yesmaximal, complemented
9C4×#10596939C211yesmaximal, characteristic, complemented
10#14557610C211yesmaximal, characteristic, complemented
11C37×#459C211yesmaximal, characteristic, complemented
12C2×#10596964C2212yescomplemented
13C2×D4×D37—21no—
14C2×D4×D37C2212yes—
15#11924560—28no—
16C2×#10596930C2212yes—
17C2×#10596940C2212yescomplemented
18C2×#10596940C2212yescomplemented
19C2×#10596939C2211yescharacteristic
20C2×#10596929C2212yescomplemented
21#11924536C2211yescharacteristic, complemented
22#11924520—22no—
23#11924516C2212yescomplemented
24#11924510—21no—
25#11924507—21no—
26#11924507C2212yes—
27#11924504—22no—
28C4×D148C2211yescharacteristic
29C4×D148C2211yescharacteristic
30C2×C4⋊Dic37—21no—
31#11924469C2211yescharacteristic, complemented
32#11924461C2212yescomplemented
33#11924457C2211yescharacteristic, complemented
34#11924456C2211yescharacteristic
35#11924448C2212yescomplemented
36C4×#64436C2211yescharacteristic, complemented
37C2×D8×C37C2212yescomplemented
38#127×C37C2211yescharacteristic
39C4×D4×C37C2211yescharacteristic, complemented
40C4⋊C8×C37C2211yescharacteristic, complemented
41#102×C37C2212yescomplemented
42C23×D37—22no—
43C2×D4×C37—21no—
44C2×D4×C37—21no—
45C2×D4×C37C2312yes—
46C2×D4×C37C2311yescharacteristic
47C22×C4×C37—21no—
48C2×C22⋊D37—22no—
49C2×C22⋊D37—22no—
50C2×C22⋊D37—22no—
51C22×Dic37—22no—
52#10596964—24no—
53#10596964—42no—
54D4×D37—24no—
55D4×D37—42no—
56D4×D37—44no—
57C2×D148D411yescharacteristic
58C2×D148C2311yescharacteristic
59C2×C4×D37—21no—
60C2×C4×D37C2312yes—
61C2×Dic74C2312yes—
62D8×C37—24no—
63C2×C8×C37C2312yes—
64C4⋊C4×C37C2311yescharacteristic
65C22⋊C4×C37—21no—
66C42×C37C2311yescharacteristic
67C22⋊Dic37—22no—
68#10596940—24no—
69#10596940—42no—
70#10596939D414yescomplemented
71#10596938—22no—
72#10596938—21no—
73#10596938D412yes—
74C4⋊Dic37—21no—
75C4⋊Dic37—21no—
76C4⋊Dic37—22no—
77C4⋊Dic37D411yescharacteristic
78C4⋊Dic37C2311yescharacteristic
79C2×#64436C2311yescharacteristic
80C2×#64436C2311yescharacteristic
81#10596930—24no—
82#10596929—24no—
83C23×C37—21no—
84C23×C37—22no—
85C22×D37—21no—
86C22×D37—44no—
87C22×D37—44no—
88C22×D37—82no—
89C22×D37C2×D412yes—
90D4×C37—22no—
91D4×C37—21no—
92D4×C37—22no—
93D4×C37—42no—
94D4×C37—81no—
95D4×C37C2×D412yescomplemented
96C2×C4×C37—21no—
97C2×C4×C37—42no—
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37C2411yescharacteristic
101C22⋊D37—44no—
102C22⋊D37—44no—
103C22⋊D37—44no—
104C2×Dic37—22no—
105C2×Dic37—21no—
106C2×Dic37—44no—
107C2×Dic37C2×D412yes—
108D148—22no—
109D148—21no—
110D148C2×D412yes—
111C4×D37—22no—
112C4×D37—22no—
113C4×D37—42no—
114Dic74—22no—
115Dic74—22no—
116C8×C37—22no—
117#64436—21no—
118#64436C2×D412yescomplemented
119C22×C37—22no—
120C22×C37—41no—
121C22×C37—41no—
122C22×C37—42no—
123C22×C37—42no—
124C22×C37—42no—
125C22×C37C22×D411yescharacteristic
126C2×D37—22no—
127C2×D37—22no—
128C2×D37—22no—
129C2×D37—22no—
130C2×D37—41no—
131C2×D37—41no—
132C2×D37—88no—
133C4×C37—21no—
134C4×C37—41no—
135C4×C37AGL(1,ℤ/8)12yescomplemented
136C4×C37C22×D411yescharacteristic
137C4×C37H(5,𝔽2)11yescharacteristic
138Dic37—22no—
139Dic37—42no—
140Dic37—41no—
141#3272—371nomaximal, Sylow
142C2×C37—42no—
143C2×C37—82no—
144C2×C37D4211yescharacteristic
145C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C37#57711yescharacteristic
147D37—42no—
148D37—42no—
149C2×AGL(1,ℤ/8)—372no—
150#547—371no—
151D42—371no—
152#492—371no—
153#468—372no—
154#461—371no—
155#459D3711yescharacteristic, complemented
156#450—372no—
157#449—372no—
158C4×D8—371no—
159#436—371no—
160C37#327211yescharacteristic, complemented, Sylow
161C2×#41—372no—
162C22×D4—372no—
163C22×D4—741no—
164AGL(1,ℤ/8)—748no—
165C2×SD16—372no—
166C2×SD16—372no—
167C2×SD16—372no—
168C2×D8—371no—
169C2×D8C2×D3712yescomplemented
170C2×M16—372no—
171C4⋊Q8—371no—
172#127C2×D3711yescharacteristic
173#123—742no—
174C22⋊Q8—372no—
175#121—372no—
176#121—741no—
177#121—741no—
178#120—742no—
179C4×D4—371no—
180C4×D4—371no—
181C4×D4C2×D3711yescharacteristic, complemented
182C2×C4⋊C4—741no—
183#107—371no—
184C4⋊C8C2×D3711yescharacteristic, complemented
185#103—372no—
186#102—371no—
187#102—371no—
188#102C2×D3712yescomplemented
189C22⋊C8—372no—
190C4×C8—371no—
191C24—742no—
192#41—744no—
193#41—1482no—
194C2×Q8—372no—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—371no—
198C2×D4—371no—
199C2×D4—742no—
200C2×D4—744no—
201C2×D4—742no—
202C2×D4—742no—
203C2×D4—1482no—
204C2×D4—1484no—
205C2×D4C22×D3712yes—
206C2×D4C22×D3711yescharacteristic
207C22×C4—21no—
208C22×C4—372no—
209C22×C4—742no—
210C22×C4—741no—
211SD16—744no—
212SD16—744no—
213SD16—1482no—
214D8—24no—
215D8—374no—
216M16—744no—
217C2×C8—371no—
218C2×C8—371no—
219C2×C8C22×D3712yes—
220C4⋊C4—371no—
221C4⋊C4—371no—
222C4⋊C4—742no—
223C4⋊C4—741no—
224C4⋊C4—741no—
225C4⋊C4C22×D3711yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—372no—
228C22⋊C4—742no—
229C22⋊C4—742no—
230C22⋊C4—741no—
231C42C22×D3711yescharacteristic
232C23—21no—
233C23—22no—
234C23—372no—
235C23—2962no—
236C23—741no—
237C23—1484no—
238C23—1484no—
239Q8—742no—
240Q8—742no—
241D4—22no—
242D4—21no—
243D4—22no—
244D4—42no—
245D4—81no—
246D4—372no—
247D4—742no—
248D4—741no—
249D4—1484no—
250D4—1484no—
251D4—1484no—
252D4D4×D3712yescomplemented
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—372no—
256C2×C4—742no—
257C2×C4—742no—
258C2×C4—741no—
259C2×C4—742no—
260C2×C4—1484no—
261C2×C4—1482no—
262C2×C4D4×D3711yescharacteristic
263C2×C4D4×D3711yescharacteristic
264C2×C4C23×D3711yescharacteristic
265C8—22no—
266C8—372no—
267C8—741no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—2968no—
275C22—742no—
276C22—742no—
277C22—742no—
278C22—742no—
279C22—1481no—
280C22—1481no—
281C22C2×D4×D3711yescharacteristic
282C4—21no—
283C4—41no—
284C4—742no—
285C4—1481no—
286C4—1482no—
287C4#1192456012yescomplemented
288C4C2×D4×D3711yescharacteristic
289C4#1192458211yescharacteristic
290C2—42no—
291C2—82no—
292C2—1482no—
293C2—1482no—
294C2#1455816711yescharacteristic
295C2C2×#1192456011yescharacteristic
296C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#459C2
socleC22×C37C22×D4
hypercenter#459D37
hypocenterC37#3272
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#11924560C2semidirect
2. #14558187C2semidirect
3. #14558168C2semidirect
4. #14557905C2semidirect
5. #14557778C2semidirect
6. #14557739C2semidirect
7. #14557685C2semidirect
8. #14557675C2semidirect
9. C4×#10596939C2semidirect
10. #14557610C2semidirect
11. C37×#459C2semidirect
12. C2×#10596964C22semidirect
17. C2×#10596940C22semidirect
18. C2×#10596940C22semidirect
20. C2×#10596929C22semidirect
21. #11924536C22semidirect
23. #11924516C22semidirect
31. #11924469C22semidirect
32. #11924461C22semidirect
33. #11924457C22semidirect
35. #11924448C22semidirect
36. C4×#64436C22semidirect
37. C2×D8×C37C22semidirect
39. C4×D4×C37C22semidirect
40. C4⋊C8×C37C22semidirect
41. #102×C37C22semidirect
70. #10596939D4semidirect
95. D4×C37C2×D4semidirect
118. #64436C2×D4semidirect
135. C4×C37AGL(1,ℤ/8)semidirect
155. #459D37semidirect
160. C37#3272semidirect
169. C2×D8C2×D37semidirect
181. C4×D4C2×D37semidirect
184. C4⋊C8C2×D37semidirect
188. #102C2×D37semidirect
252. D4D4×D37semidirect
287. C4#11924560semidirect

Maximal subgroups

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

subgroupindex
C2×#119245602
#145581872
#145581682
#145579052
#145577782
#145577392
#145576852
#145576752
C4×#105969392
#145576102
C37×#4592
#327237