Finite Group Databasebeta

← #18005355

Subgroups — #18005355

Order 4736.

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

normal subgroups only

This group has 468 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
1C2×#11924516C211yesmaximal, characteristic, complemented
2#121×D37C211yesmaximal, characteristic
3#14557865C212yesmaximal, complemented
4#14557851C211yesmaximal, characteristic, complemented
5#14557763C212yesmaximal, complemented
6#14557761C212yesmaximal, complemented
7#14557685C212yesmaximal, complemented
8#14557674C211yesmaximal, characteristic, complemented
9#14557671C211yesmaximal, characteristic, complemented
10C22⋊C8×D37C211yesmaximal, characteristic, complemented
11C37×#481C211yesmaximal, characteristic, complemented
12C22×Dic74C2211yescharacteristic, complemented
13C2×D4×D37—21no—
14C2×D4×D37C2211yescharacteristic
15C22×C4×D37C2211yescharacteristic
16C2×#10596930C2212yescomplemented
17C2×#10596940C2212yescomplemented
18C2×C8×D37C2212yescomplemented
19#11924516—21no—
20#11924516—21no—
21#11924516C2212yes—
22#11924516C2212yescomplemented
23#11924511C2211yescharacteristic
24#11924510C2211yescharacteristic
25#11924509—21no—
26#11924508—21no—
27#11924507C2211yescharacteristic
28C2×C4⋊Dic37—21no—
29C4⋊C4×D37C2211yescharacteristic
30C2×#10596938—21no—
31C22⋊C4×D37—21no—
32#11924467C2212yescomplemented
33#11924461C2212yescomplemented
34#11924459C2212yescomplemented
35#11924456C2212yescomplemented
36C22⋊#64436C2211yescharacteristic, complemented
37#11924448C2212yes—
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—42no—
55D4×D37—44no—
56C2×D148—21no—
57C2×D148C2311yescharacteristic
58C2×C4×D37—21no—
59C2×C4×D37—42no—
60C2×C4×D37D411yescharacteristic
61C2×C4×D37D411yescharacteristic
62C2×C4×D37C2311yescharacteristic
63C2×C4×D37C2311yescharacteristic
64C2×Dic74—21no—
65C2×Dic74—42no—
66C2×Dic74C2312yes—
67C2×C8×C37C2312yes—
68C4⋊C4×C37—21no—
69C4⋊C4×C37C2311yescharacteristic
70C4⋊C4×C37C2312yes—
71C22⋊C4×C37—21no—
72C22⋊Dic37—21no—
73#10596940—42no—
74#10596938—22no—
75#10596938—22no—
76#10596938—21no—
77#10596938—21no—
78C4⋊Dic37—22no—
79C4⋊Dic37—22no—
80C4⋊Dic37C2311yescharacteristic
81#10596936—21no—
82C2×#64436C2312yes—
83#10596930—42no—
84C8×D37—42no—
85C23×C37—21no—
86C23×C37C2×D411yescharacteristic
87C22×D37—21no—
88C22×D37—41no—
89C22×D37—41no—
90C22×D37—42no—
91C22×D37—42no—
92C22×D37—42no—
93C22×D37SD1614yescomplemented
94C22×D37C2×D411yescharacteristic
95C22×D37C2×D411yescharacteristic
96D4×C37—22no—
97D4×C37—42no—
98C2×C4×C37—22no—
99C2×C4×C37—21no—
100C2×C4×C37—22no—
101C2×C4×C37—42no—
102C2×C4×C37C2×D411yescharacteristic
103C2×C4×C37C2411yescharacteristic
104C22⋊D37—42no—
105C22⋊D37—42no—
106C22⋊D37—42no—
107C2×Dic37—21no—
108C2×Dic37—22no—
109C2×Dic37—41no—
110C2×Dic37—42no—
111C2×Dic37C2×D411yescharacteristic
112C2×Dic37C2×D411yescharacteristic
113D148—22no—
114D148—42no—
115C4×D37—22no—
116C4×D37—22no—
117C4×D37—41no—
118C4×D37—41no—
119C4×D37—42no—
120Dic74—22no—
121Dic74—22no—
122Dic74—42no—
123C8×C37—22no—
124#64436—22no—
125C22×C37—21no—
126C22×C37—21no—
127C22×C37—41no—
128C22×C37—41no—
129C22×C37—41no—
130C22×C37C2×SD1612yes—
131C22×C37C22×D411yescharacteristic
132C2×D37—21no—
133C2×D37—21no—
134C2×D37—21no—
135C2×D37—21no—
136C2×D37—44no—
137C2×D37—41no—
138C2×D37—41no—
139C2×D37—41no—
140C2×D37—84no—
141C2×D37C2×SD1612yes—
142C2×D37C2×SD1612yes—
143C4×C37—21no—
144C4×C37—41no—
145C4×C37—42no—
146C4×C37H(5,𝔽2)12yes—
147Dic37—21no—
148Dic37—21no—
149Dic37—42no—
150Dic37—41no—
151#3187—371nomaximal, Sylow
152C2×C37—22no—
153C2×C37—81no—
154C2×C37#53411yescharacteristic
155C2×C37C22×SD1611yescharacteristic
156C2×C37#57511yescharacteristic
157D37—22no—
158D37—22no—
159D37—81no—
160C2×C22⋊Q8—371no—
161C2×#121—371no—
162#483—372no—
163#481—371no—
164#481D3711yescharacteristic, complemented
165#465—372no—
166#465—372no—
167#450—372no—
168#448—371no—
169#448—371no—
170C2×C22⋊C8—371no—
171C37#318711yescharacteristic, complemented, Sylow
172C22×Q8—371no—
173C22×D4—371no—
174C22×D4—741no—
175C23×C4—371no—
176C2×SD16—372no—
177C2×SD16—372no—
178C22×C8—372no—
179C22⋊Q8—372no—
180C22⋊Q8—372no—
181C22⋊Q8—741no—
182C22⋊Q8—741no—
183#121—371no—
184#121—371no—
185#121—371no—
186#121—741no—
187#121—741no—
188#121C2×D3711yescharacteristic
189C2×C4⋊C4—371no—
190C2×C4⋊C4—741no—
191C2×C4⋊C4C2×D3711yescharacteristic, complemented
192C2×C22⋊C4—741no—
193C2×C22⋊C4—741no—
194#106—372no—
195#106C2×D3712yescomplemented
196#103—372no—
197#103—372no—
198#102—372no—
199#102C2×D3712yescomplemented
200C22⋊C8—371no—
201C22⋊C8—372no—
202C22⋊C8C2×D3711yescharacteristic, complemented
203C24—371no—
204C24—741no—
205C2×Q8—372no—
206C2×Q8—741no—
207C2×Q8—1482no—
208C2×D4—21no—
209C2×D4—371no—
210C2×D4—741no—
211C2×D4—741no—
212C2×D4—741no—
213C2×D4—741no—
214C2×D4—1482no—
215C2×D4—1484no—
216C2×D4C22×D3711yescharacteristic
217C22×C4—21no—
218C22×C4—371no—
219C22×C4—371no—
220C22×C4—371no—
221C22×C4—371no—
222C22×C4—371no—
223C22×C4—741no—
224C22×C4—741no—
225C22×C4—1482no—
226C22×C4C22×D3711yescharacteristic
227SD16—1482no—
228SD16—1482no—
229C2×C8—372no—
230C2×C8—1482no—
231C2×C8C22×D3712yes—
232C4⋊C4—21no—
233C4⋊C4—371no—
234C4⋊C4—741no—
235C4⋊C4—742no—
236C4⋊C4—742no—
237C4⋊C4C22×D3712yes—
238C4⋊C4C22×D3711yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—741no—
241C22⋊C4—742no—
242C22⋊C4—742no—
243C22⋊C4—741no—
244C22⋊C4—741no—
245C23—21no—
246C23—371no—
247C23—371no—
248C23—374no—
249C23—741no—
250C23—1481no—
251C23—1481no—
252C23—1482no—
253C23—1482no—
254C23—1482no—
255C23D4×D3711yescharacteristic
256Q8—742no—
257Q8—742no—
258Q8—1482no—
259D4—22no—
260D4—42no—
261D4—742no—
262D4—1482no—
263D4—1482no—
264D4—1482no—
265D4—1482no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—371no—
271C2×C4—371no—
272C2×C4—742no—
273C2×C4—742no—
274C2×C4—741no—
275C2×C4—742no—
276C2×C4—1481no—
277C2×C4—1481no—
278C2×C4—1482no—
279C2×C4—1481no—
280C2×C4—1482no—
281C2×C4D4×D3711yescharacteristic
282C2×C4C23×D3711yescharacteristic
283C8—22no—
284C8—742no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—372no—
291C22—372no—
292C22—2964no—
293C22—741no—
294C22—741no—
295C22—741no—
296C22—741no—
297C22—1484no—
298C22—1481no—
299C22—1481no—
300C22—1481no—
301C22SD16×D3712yes—
302C22C2×D4×D3711yescharacteristic
303C4—21no—
304C4—41no—
305C4—42no—
306C4—741no—
307C4—741no—
308C4—1481no—
309C4—1482no—
310C4#1192458212yes—
311C2—22no—
312C2—81no—
313C2—2961no—
314C2—742no—
315C2—742no—
316C2#1455809411yescharacteristic
317C2C2×SD16×D3711yescharacteristic
318C2#1455832911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#481C2
socleC22×C37C22×D4
prime radical#121×D37C2
hypercenter#481D37
hypocenterC37#3187
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
1. C2×#11924516C2semidirect
3. #14557865C2semidirect
4. #14557851C2semidirect
5. #14557763C2semidirect
6. #14557761C2semidirect
7. #14557685C2semidirect
8. #14557674C2semidirect
9. #14557671C2semidirect
10. C22⋊C8×D37C2semidirect
11. C37×#481C2semidirect
12. C22×Dic74C22semidirect
16. C2×#10596930C22semidirect
17. C2×#10596940C22semidirect
18. C2×C8×D37C22semidirect
22. #11924516C22semidirect
32. #11924467C22semidirect
33. #11924461C22semidirect
34. #11924459C22semidirect
35. #11924456C22semidirect
36. C22⋊#64436C22semidirect
39. C2×C4⋊C4×C37C22semidirect
40. #106×C37C22semidirect
41. #102×C37C22semidirect
42. C22⋊C8×C37C22semidirect
93. C22×D37SD16semidirect
164. #481D37semidirect
171. C37#3187semidirect
191. C2×C4⋊C4C2×D37semidirect
195. #106C2×D37semidirect
199. #102C2×D37semidirect
202. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245162
#121×D372
#145578652
#145578512
#145577632
#145577612
#145576852
#145576742
#145576712
C22⋊C8×D372
C37×#4812
#318737