Finite Group Databasebeta

← #481×D37 #18004492

Subgroups — #481×D37 #18004492

Order 4736.

512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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×C4⋊C4×D37C211yesmaximal, characteristic, complemented
3#14557853C212yesmaximal, complemented
4#14557852C211yesmaximal, characteristic, complemented
5#14557851C211yesmaximal, characteristic, complemented
6#14557850C212yesmaximal, complemented
7#14557849C211yesmaximal, characteristic, complemented
8#106×D37C212yesmaximal, complemented
9#102×D37C212yesmaximal, complemented
10C22⋊C8×D37C211yesmaximal, characteristic, complemented
11C37×#481C211yesmaximal, characteristic, complemented
12C2×D4×D37—21no—
13C2×D4×D37C2211yescharacteristic
14C22×C4×D37—21no—
15C22×C4×D37C2211yescharacteristic
16C2×C8×D37C2212yes—
17#11924511C2211yescharacteristic
18#11924510C2211yescharacteristic
19#11924509—21no—
20#11924508—21no—
21#11924507C2211yescharacteristic
22C2×C4⋊Dic37C2211yescharacteristic, complemented
23C2×#10596936—21no—
24C4⋊C4×D37—21no—
25C4⋊C4×D37—21no—
26C4⋊C4×D37C2212yes—
27C4⋊C4×D37C2211yescharacteristic
28C4⋊C4×D37C2212yescomplemented
29C22⋊C4×D37—21no—
30#11924468C2212yescomplemented
31#11924467C2212yescomplemented
32#11924467C2212yescomplemented
33#11924458C2212yescomplemented
34#11924457C2212yescomplemented
35#11924456C2212yescomplemented
36C22⋊#64436C2211yescharacteristic, complemented
37#11924448C2212yescomplemented
38#121×C37C2211yescharacteristic
39C2×C4⋊C4×C37C2211yescharacteristic, complemented
40#106×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×D37—22no—
61C2×C4×D37—22no—
62C2×C4×D37—44no—
63C2×C4×D37D411yescharacteristic
64C2×C4×D37D411yescharacteristic
65C2×C4×D37C2311yescharacteristic
66C2×C4×D37C2311yescharacteristic
67C2×C8×C37C2312yes—
68C4⋊C4×C37—21no—
69C4⋊C4×C37C2312yes—
70C4⋊C4×C37C2311yescharacteristic
71C22⋊C4×C37—21no—
72C22⋊Dic37—21no—
73#10596938—21no—
74#10596938—21no—
75C4⋊Dic37—21no—
76C4⋊Dic37C2312yes—
77C4⋊Dic37C2311yescharacteristic
78#10596936—22no—
79#10596936—22no—
80#10596936—21no—
81C2×#64436C2312yes—
82C8×D37—24no—
83C23×C37—21no—
84C23×C37C2×D411yescharacteristic
85C22×D37—22no—
86C22×D37—22no—
87C22×D37—21no—
88C22×D37—42no—
89C22×D37—42no—
90C22×D37—42no—
91C22×D37SD1614yes—
92C22×D37C2×D411yescharacteristic
93C22×D37C2×D411yescharacteristic
94D4×C37—22no—
95D4×C37—42no—
96C2×C4×C37—22no—
97C2×C4×C37—22no—
98C2×C4×C37—21no—
99C2×C4×C37—42no—
100C2×C4×C37C2×D411yescharacteristic
101C2×C4×C37C2411yescharacteristic
102C22⋊D37—42no—
103C22⋊D37—42no—
104C22⋊D37—42no—
105C2×Dic37—22no—
106C2×Dic37—22no—
107C2×Dic37—21no—
108C2×Dic37—42no—
109C2×Dic37C2×D411yescharacteristic
110C2×Dic37C2×D411yescharacteristic
111D148—22no—
112D148—42no—
113C4×D37—22no—
114C4×D37—22no—
115C4×D37—22no—
116C4×D37—44no—
117C4×D37—42no—
118C4×D37—44no—
119C4×D37#4114yes—
120C8×C37—22no—
121#64436—22no—
122C22×C37—21no—
123C22×C37—21no—
124C22×C37—41no—
125C22×C37—41no—
126C22×C37—41no—
127C22×C37C2×SD1612yes—
128C22×C37C22×D411yescharacteristic
129C2×D37—21no—
130C2×D37—21no—
131C2×D37—28no—
132C2×D37—41no—
133C2×D37—41no—
134C2×D37—41no—
135C2×D37—84no—
136C2×D37#12312yes—
137C2×D37C2×SD1612yes—
138C2×D37C2×SD1612yes—
139C2×D37AGL(1,ℤ/8)12yes—
140C4×C37—21no—
141C4×C37—41no—
142C4×C37—42no—
143C4×C37C2×#4112yes—
144Dic37—21no—
145Dic37—41no—
146Dic37—42no—
147Dic37#12312yes—
148C2×#481—371nomaximal, Sylow
149C2×C37—22no—
150C2×C37—81no—
151C2×C37C2×#12311yescharacteristic
152C2×C37C22×SD1611yescharacteristic
153C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
154D37—22no—
155D37—81no—
156D37#48114yesdirect product factor
157C2×#121—371no—
158C22×C4⋊C4—371no—
159#481—371no—
160#481—371no—
161#481—372no—
162#481—372no—
163#481—371no—
164#481D3711yescharacteristic, direct product factor
165C2×#106—372no—
166C2×#102—372no—
167C2×C22⋊C8—371no—
168C37C2×#48111yescharacteristic, complemented, Sylow
169C22×D4—371no—
170C22×D4—741no—
171C23×C4—371no—
172C23×C4—741no—
173C22×C8—372no—
174#121—371no—
175#121—371no—
176#121—371no—
177#121—741no—
178#121—741no—
179#121C2×D3711yescharacteristic
180C2×C4⋊C4—371no—
181C2×C4⋊C4—372no—
182C2×C4⋊C4—372no—
183C2×C4⋊C4—371no—
184C2×C4⋊C4—741no—
185C2×C4⋊C4—741no—
186C2×C4⋊C4—741no—
187C2×C4⋊C4C2×D3711yescharacteristic, complemented
188C2×C22⋊C4—741no—
189#106—372no—
190#106—372no—
191#106—372no—
192#106C2×D3712yescomplemented
193#102—372no—
194#102—372no—
195#102—372no—
196#102C2×D3712yescomplemented
197C22⋊C8—371no—
198C22⋊C8—372no—
199C22⋊C8C2×D3711yescharacteristic, complemented
200C24—371no—
201C24—741no—
202C2×D4—21no—
203C2×D4—371no—
204C2×D4—741no—
205C2×D4—744no—
206C2×D4—741no—
207C2×D4—741no—
208C2×D4—741no—
209C2×D4—1484no—
210C2×D4C22×D3711yescharacteristic
211C22×C4—21no—
212C22×C4—371no—
213C22×C4—371no—
214C22×C4—371no—
215C22×C4—371no—
216C22×C4—371no—
217C22×C4—744no—
218C22×C4—741no—
219C22×C4—742no—
220C22×C4—742no—
221C22×C4—741no—
222C22×C4—1484no—
223C22×C4C22×D3711yescharacteristic
224C2×C8—372no—
225C2×C8—744no—
226C2×C8C22×D3712yes—
227C4⋊C4—21no—
228C4⋊C4—372no—
229C4⋊C4—371no—
230C4⋊C4—742no—
231C4⋊C4—742no—
232C4⋊C4—741no—
233C4⋊C4—741no—
234C4⋊C4C22×D3712yes—
235C4⋊C4C22×D3711yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—741no—
238C22⋊C4—741no—
239C22⋊C4—741no—
240C23—21no—
241C23—371no—
242C23—374no—
243C23—371no—
244C23—742no—
245C23—742no—
246C23—741no—
247C23—1482no—
248C23—1482no—
249C23—1482no—
250C23D4×D3711yescharacteristic
251D4—22no—
252D4—42no—
253D4—742no—
254D4—1482no—
255D4—1482no—
256D4—1482no—
257D4—1482no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—371no—
263C2×C4—374no—
264C2×C4—371no—
265C2×C4—742no—
266C2×C4—742no—
267C2×C4—742no—
268C2×C4—742no—
269C2×C4—741no—
270C2×C4—742no—
271C2×C4—1484no—
272C2×C4—1482no—
273C2×C4—1484no—
274C2×C4—1482no—
275C2×C4D4×D3711yescharacteristic
276C2×C4C23×D3711yescharacteristic
277C8—22no—
278C8—742no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—372no—
285C22—372no—
286C22—372no—
287C22—372no—
288C22—2964no—
289C22—748no—
290C22—741no—
291C22—741no—
292C22—1481no—
293C22—1481no—
294C22—1481no—
295C22SD16×D3712yes—
296C22C2×D4×D3711yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—372no—
301C4—741no—
302C4—1481no—
303C4—1482no—
304C4#41×D3712yes—
305C2—22no—
306C2—81no—
307C2—374no—
308C2—2961no—
309C2—742no—
310C2#123×D3711yescharacteristic
311C2C2×SD16×D3711yescharacteristic
312C2AGL(1,ℤ/8)×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#481C2
socleC22×C37C22×D4
prime radical#121×D37C2
hypercenter#481D37
hypocenterC37C2×#481
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D37C2semidirect
3. #14557853C2semidirect
4. #14557852C2semidirect
5. #14557851C2semidirect
6. #14557850C2semidirect
7. #14557849C2semidirect
8. #106×D37C2semidirect
9. #102×D37C2semidirect
10. C22⋊C8×D37C2semidirect
11. C37×#481C2semidirect
22. C2×C4⋊Dic37C22semidirect
28. C4⋊C4×D37C22semidirect
30. #11924468C22semidirect
31. #11924467C22semidirect
32. #11924467C22semidirect
33. #11924458C22semidirect
34. #11924457C22semidirect
35. #11924456C22semidirect
36. C22⋊#64436C22semidirect
37. #11924448C22semidirect
39. C2×C4⋊C4×C37C22semidirect
40. #106×C37C22semidirect
41. #102×C37C22semidirect
42. C22⋊C8×C37C22semidirect
156. D37#481direct (N × H)
164. #481D37direct (N × H)
168. C37C2×#481semidirect
187. C2×C4⋊C4C2×D37semidirect
192. #106C2×D37semidirect
196. #102C2×D37semidirect
199. 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×C4⋊C4×D372
#145578532
#145578522
#145578512
#145578502
#145578492
#106×D372
#102×D372
C22⋊C8×D372
C37×#4812
C2×#48137