Finite Group Databasebeta

← #18004531

Subgroups — #18004531

Order 4736.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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#121×D37C211yesmaximal, characteristic
2C2×#11924494C211yesmaximal, characteristic, complemented
3#14557860C212yesmaximal, complemented
4#14557856C212yesmaximal, complemented
5#14557852C211yesmaximal, characteristic, complemented
6#14557849C211yesmaximal, characteristic, complemented
7#14557846C211yesmaximal, characteristic, complemented
8#14557574C212yesmaximal, complemented
9#14557536C212yesmaximal, complemented
10#14557495C211yesmaximal, characteristic, complemented
11C37×#480C211yesmaximal, characteristic, complemented
12C2×D4×D37—21no—
13C2×D4×D37C2211yescharacteristic
14C22×C4×D37C2211yescharacteristic
15C2×#10596929C2212yes—
16#11924511C2211yescharacteristic
17#11924510C2211yescharacteristic
18#11924509—21no—
19#11924508—21no—
20#11924507C2211yescharacteristic
21#11924494—21no—
22#11924494—21no—
23#11924494C2212yes—
24#11924494C2212yescomplemented
25C2×C4⋊Dic37C2211yescharacteristic, complemented
26C4⋊C4×D37C2211yescharacteristic
27C2×#10596938—21no—
28C22⋊C4×D37—21no—
29C2×C4×Dic37—21no—
30#11924469C2212yescomplemented
31#11924468C2212yescomplemented
32#11924467C2212yescomplemented
33#11924458C2212yescomplemented
34#11924457C2212yescomplemented
35#11924456C2212yescomplemented
36C22⋊#64436C2211yescharacteristic, complemented
37#11924448C2212yescomplemented
38#121×C37C2211yescharacteristic
39C2×C4⋊C4×C37C2211yescharacteristic, complemented
40#107×C37C2212yescomplemented
41#102×C37C2212yescomplemented
42C22⋊C8×C37C2211yescharacteristic, complemented
43C23×D37—21no—
44C23×D37D411yescharacteristic
45C2×D4×C37—21no—
46C2×D4×C37C2311yescharacteristic
47C22×C4×C37—21no—
48C22×C4×C37C2311yescharacteristic
49C2×C22⋊D37—21no—
50C2×C22⋊D37—21no—
51C2×C22⋊D37—21no—
52C22×Dic37—21no—
53C22×Dic37D411yescharacteristic
54D4×D37—24no—
55D4×D37—44no—
56C2×D148—21no—
57C2×D148C2311yescharacteristic
58C2×C4×D37—24no—
59C2×C4×D37—21no—
60C2×C4×D37D411yescharacteristic
61C2×C4×D37D411yescharacteristic
62C2×C4×D37C2311yescharacteristic
63C2×C4×D37C2311yescharacteristic
64C2×C8×C37C2312yes—
65C4⋊C4×C37—21no—
66C4⋊C4×C37C2311yescharacteristic
67C4⋊C4×C37C2312yes—
68C22⋊C4×C37—21no—
69C22⋊Dic37—21no—
70#10596938—22no—
71#10596938—22no—
72#10596938—21no—
73#10596938—21no—
74C4⋊Dic37—21no—
75C4⋊Dic37C2311yescharacteristic
76C4⋊Dic37C2312yes—
77#10596936—21no—
78C4×Dic37—22no—
79C4×Dic37—22no—
80C2×#64436C2312yes—
81#10596929—24no—
82C23×C37—21no—
83C23×C37C2×D411yescharacteristic
84C22×D37—22no—
85C22×D37—22no—
86C22×D37—21no—
87C22×D37—41no—
88C22×D37—42no—
89C22×D37—42no—
90C22×D37—42no—
91C22×D37C2×D411yescharacteristic
92C22×D37C2×D411yescharacteristic
93D4×C37—22no—
94D4×C37—42no—
95C2×C4×C37—22no—
96C2×C4×C37—22no—
97C2×C4×C37—21no—
98C2×C4×C37—42no—
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37C2411yescharacteristic
101C22⋊D37—42no—
102C22⋊D37—42no—
103C22⋊D37—42no—
104C2×Dic37—22no—
105C2×Dic37—22no—
106C2×Dic37—21no—
107C2×Dic37—42no—
108C2×Dic37C2×D411yescharacteristic
109C2×Dic37C2×D411yescharacteristic
110D148—22no—
111D148—42no—
112C4×D37—22no—
113C4×D37—22no—
114C4×D37—22no—
115C4×D37—42no—
116C4×D37#4114yes—
117C8×C37—22no—
118#64436—22no—
119C22×C37—21no—
120C22×C37—21no—
121C22×C37—41no—
122C22×C37—41no—
123C22×C37—41no—
124C22×C37AGL(1,ℤ/8)12yes—
125C22×C37C22×D411yescharacteristic
126C2×D37—21no—
127C2×D37—21no—
128C2×D37—21no—
129C2×D37—21no—
130C2×D37—21no—
131C2×D37—44no—
132C2×D37—41no—
133C2×D37—41no—
134C2×D37—41no—
135C2×D37—84no—
136C2×D37#12312yes—
137C4×C37—21no—
138C4×C37—41no—
139C4×C37—42no—
140C4×C37C2×#4112yes—
141Dic37—21no—
142Dic37—41no—
143Dic37—42no—
144Dic37#12312yes—
145#3094—371nomaximal, Sylow
146C2×C37—22no—
147C2×C37—81no—
148C2×C37C2×#12311yescharacteristic
149C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C37#57511yescharacteristic
151D37—22no—
152D37—41no—
153D37—81no—
154C2×#121—371no—
155C2×#117—371no—
156#482—372no—
157#482—372no—
158#481—371no—
159#481—371no—
160#480—371no—
161#480D3711yescharacteristic, complemented
162#428—372no—
163#418—372no—
164#407—371no—
165C37#309411yescharacteristic, complemented, Sylow
166C22×D4—371no—
167C22×D4—741no—
168C23×C4—371no—
169C2×M16—372no—
170#121—371no—
171#121—371no—
172#121—371no—
173#121—741no—
174#121—741no—
175#121C2×D3711yescharacteristic
176#117—372no—
177#117—372no—
178#117—741no—
179#117—741no—
180C2×C4⋊C4—371no—
181C2×C4⋊C4—371no—
182C2×C4⋊C4C2×D3711yescharacteristic, complemented
183C2×C22⋊C4—741no—
184C2×C22⋊C4—741no—
185C2×C42—741no—
186#107—372no—
187#107C2×D3712yescomplemented
188#106—372no—
189#106—372no—
190#102—372no—
191#102—372no—
192#102—372no—
193#102C2×D3712yescomplemented
194C22⋊C8—371no—
195C22⋊C8—372no—
196C22⋊C8C2×D3711yescharacteristic, complemented
197C24—371no—
198C24—741no—
199C2×D4—21no—
200C2×D4—371no—
201C2×D4—741no—
202C2×D4—744no—
203C2×D4—741no—
204C2×D4—741no—
205C2×D4—741no—
206C2×D4—1484no—
207C2×D4C22×D3711yescharacteristic
208C22×C4—21no—
209C22×C4—371no—
210C22×C4—371no—
211C22×C4—371no—
212C22×C4—371no—
213C22×C4—371no—
214C22×C4—744no—
215C22×C4—741no—
216C22×C4—741no—
217C22×C4C22×D3711yescharacteristic
218M16—744no—
219C2×C8—372no—
220C2×C8C22×D3712yes—
221C4⋊C4—21no—
222C4⋊C4—372no—
223C4⋊C4—371no—
224C4⋊C4—741no—
225C4⋊C4—741no—
226C4⋊C4C22×D3712yes—
227C4⋊C4C22×D3711yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—741no—
230C22⋊C4—742no—
231C22⋊C4—742no—
232C22⋊C4—741no—
233C22⋊C4—741no—
234C42—742no—
235C42—742no—
236C23—21no—
237C23—371no—
238C23—371no—
239C23—742no—
240C23—742no—
241C23—741no—
242C23—1481no—
243C23—1482no—
244C23—1482no—
245C23—1482no—
246C23D4×D3711yescharacteristic
247D4—22no—
248D4—42no—
249D4—742no—
250D4—1482no—
251D4—1482no—
252D4—1482no—
253D4—1482no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—371no—
259C2×C4—374no—
260C2×C4—371no—
261C2×C4—742no—
262C2×C4—742no—
263C2×C4—742no—
264C2×C4—742no—
265C2×C4—742no—
266C2×C4—741no—
267C2×C4—1482no—
268C2×C4—1482no—
269C2×C4D4×D3711yescharacteristic
270C2×C4C23×D3711yescharacteristic
271C8—22no—
272C8—742no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—372no—
279C22—2964no—
280C22—741no—
281C22—741no—
282C22—741no—
283C22—741no—
284C22—741no—
285C22—1484no—
286C22—1481no—
287C22—1481no—
288C22—1481no—
289C22#1192456012yes—
290C22C2×D4×D3711yescharacteristic
291C4—21no—
292C4—42no—
293C4—41no—
294C4—372no—
295C4—741no—
296C4—1481no—
297C4—1482no—
298C4#41×D3712yes—
299C2—22no—
300C2—81no—
301C2—2961no—
302C2—742no—
303C2—1481no—
304C2#123×D3711yescharacteristic
305C2C2×#1192456011yescharacteristic
306C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#480C2
socleC22×C37C22×D4
prime radical#121×D37C2
hypercenter#480D37
hypocenterC37#3094
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#11924494C2semidirect
3. #14557860C2semidirect
4. #14557856C2semidirect
5. #14557852C2semidirect
6. #14557849C2semidirect
7. #14557846C2semidirect
8. #14557574C2semidirect
9. #14557536C2semidirect
10. #14557495C2semidirect
11. C37×#480C2semidirect
24. #11924494C22semidirect
25. C2×C4⋊Dic37C22semidirect
30. #11924469C22semidirect
31. #11924468C22semidirect
32. #11924467C22semidirect
33. #11924458C22semidirect
34. #11924457C22semidirect
35. #11924456C22semidirect
36. C22⋊#64436C22semidirect
37. #11924448C22semidirect
39. C2×C4⋊C4×C37C22semidirect
40. #107×C37C22semidirect
41. #102×C37C22semidirect
42. C22⋊C8×C37C22semidirect
161. #480D37semidirect
165. C37#3094semidirect
182. C2×C4⋊C4C2×D37semidirect
187. #107C2×D37semidirect
193. #102C2×D37semidirect
196. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#121×D372
C2×#119244942
#145578602
#145578562
#145578522
#145578492
#145578462
#145575742
#145575362
#145574952
C37×#4802
#309437