Finite Group Databasebeta

← #18003452

Subgroups — #18003452

Order 4736.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D37C211yesmaximal, characteristic
2#14558009C211yesmaximal, characteristic, complemented
3#14558005C211yesmaximal, characteristic
4#14557635C211yesmaximal, characteristic, complemented
5#14557634C211yesmaximal, characteristic, complemented
6#14557632C211yesmaximal, characteristic, complemented
7#14557624C211yesmaximal, characteristic, complemented
8C4×#10596941C211yesmaximal, characteristic, complemented
9C4×#10596940C211yesmaximal, characteristic, complemented
10#14557618C211yesmaximal, characteristic, complemented
11#14557570C211yesmaximal, characteristic, complemented
12#14557540C211yesmaximal, characteristic, complemented
13#14557536C211yesmaximal, characteristic
14#14557490C211yesmaximal, characteristic, complemented
15C37×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596940C2211yescharacteristic
20C2×#10596941C2211yescharacteristic
21SD16×D37C418yescomplemented
22C2×#10596929C2211yescharacteristic
23C2×C8×D37C2211yescharacteristic
24Q8×Dic37C2211yescharacteristic, complemented
25C4×Dic74—21no—
26C4×Dic74C2211yescharacteristic, complemented
27#11924501—21no—
28#11924501C2211yescharacteristic, complemented
29C4×D148C2211yescharacteristic
30D4×Dic37C2211yescharacteristic
31#11924498C2211yescharacteristic
32C4×C22⋊D37—21no—
33#11924496—21no—
34#11924494—21no—
35#11924494C2211yescharacteristic
36#11924494C2211yescharacteristic
37#11924493—21no—
38#11924493C2211yescharacteristic
39C2×#10596938—21no—
40C22⋊C4×D37—21no—
41#11924470C2211yescharacteristic, complemented
42#11924467C2211yescharacteristic, complemented
43#11924467C2211yescharacteristic, complemented
44#11924461C2211yescharacteristic, complemented
45#11924460C2211yescharacteristic, complemented
46#11924459C2211yescharacteristic, complemented
47#11924458C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924446C2211yescharacteristic, complemented
51C4×#64436C2211yescharacteristic, complemented
52C8×Dic37C2211yescharacteristic, complemented
53C2×SD16×C37C2211yescharacteristic
54C4×Q8×C37C2211yescharacteristic, complemented
55C4×D4×C37C2211yescharacteristic
56#107×C37C2211yescharacteristic, complemented
57#103×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic
59#97×C37C2211yescharacteristic, complemented
60C23×D37—21no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37C2311yescharacteristic
63C22×C4×C37—21no—
64C2×C22⋊D37—21no—
65C22×Dic37—21no—
66Q8×D37—22no—
67Q8×D37C2×C414yescomplemented
68D4×D37—22no—
69D4×D37C2×C414yes—
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37C2311yescharacteristic
75C2×Dic74—21no—
76C2×Dic74C2311yescharacteristic
77SD16×C37C2×C414yescomplemented
78C2×C8×C37C2311yescharacteristic
79C2×C8×C37C2311yescharacteristic
80C4⋊C4×C37—21no—
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C22⋊C4×C37—21no—
84C42×C37—21no—
85C42×C37C2311yescharacteristic
86C22⋊Dic37—21no—
87#10596941C2×C414yescomplemented
88#10596940C2×C414yescomplemented
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938D411yescharacteristic
94#10596938D411yescharacteristic
95C4⋊Dic37—21no—
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37—21no—
105C4×Dic37—21no—
106C4×Dic37—21no—
107C4×Dic37C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110#10596930C2×C414yescomplemented
111#10596929—22no—
112C8×D37C2×C414yescomplemented
113C23×C37—21no—
114C22×D37—21no—
115C22×D37—24no—
116C22×D37—81no—
117C22×D37—81no—
118C22×D37C2×D411yescharacteristic
119Q8×C37—21no—
120Q8×C37C22×C412yes—
121D4×C37—21no—
122D4×C37C22×C412yes—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—81no—
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2411yescharacteristic
130C22⋊D37—24no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—81no—
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138D148—21no—
139D148C22×C412yes—
140C4×D37—24no—
141C4×D37—81no—
142C4×D37—81no—
143C4×D37C22×C412yes—
144C4×D37#4112yes—
145Dic74—21no—
146Dic74—24no—
147Dic74C22×C412yes—
148C8×C37—21no—
149C8×C37C22×C412yes—
150#64436—21no—
151#64436C22×C412yes—
152C22×C37—22no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37C22×D411yescharacteristic
156C2×D37—21no—
157C2×D37—21no—
158C2×D37—22no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—84no—
162C2×D37C4×D412yes—
163C4×C37—22no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37C23×C411yescharacteristic
169C4×C37C2×#4111yescharacteristic
170Dic37—22no—
171Dic37—21no—
172Dic37—21no—
173Dic37—41no—
174Dic37—41no—
175Dic37C4×D412yes—
176#2949—371nomaximal, Sylow
177C2×C37—42no—
178C2×C37C2×C4×D411yescharacteristic
179C2×C37#57711yescharacteristic
180C2×C37#57711yescharacteristic
181D37—22no—
182D37—42no—
183C22×SD16—371no—
184#519—371no—
185#518—371no—
186#440—371no—
187#440—371no—
188#440—371no—
189#440D3711yescharacteristic, complemented
190C4×SD16—371no—
191C4×SD16—371no—
192C4×SD16—371no—
193C4×SD16—371no—
194#427—371no—
195#419—371no—
196#418—371no—
197#405—371no—
198C37#294911yescharacteristic, complemented, Sylow
199C22×Q8—371no—
200C22×D4—371no—
201C2×SD16—371no—
202C2×SD16—371no—
203C2×SD16—378no—
204C2×SD16—371no—
205C2×SD16C2×D3711yescharacteristic
206C2×M16—371no—
207C22×C8—371no—
208C4×Q8—371no—
209C4×Q8—371no—
210C4×Q8—371no—
211C4×Q8—741no—
212C4×Q8—741no—
213C4×Q8C2×D3711yescharacteristic, complemented
214C4×D4—371no—
215C4×D4—371no—
216C4×D4—371no—
217C4×D4—741no—
218C4×D4—741no—
219C4×D4C2×D3711yescharacteristic
220#117—371no—
221#117—371no—
222#117—371no—
223#117—741no—
224#117—741no—
225C2×C22⋊C4—741no—
226C2×C22⋊C4—741no—
227#107—371no—
228#107C2×D3711yescharacteristic, complemented
229#106—371no—
230#106—371no—
231#103—371no—
232#103—371no—
233#103—371no—
234#103C2×D3711yescharacteristic, complemented
235#102—371no—
236#102—371no—
237#102—371no—
238#102C2×D3711yescharacteristic
239#97—371no—
240#97C2×D3711yescharacteristic, complemented
241C4×C8—371no—
242C4×C8—371no—
243C24—741no—
244C2×Q8—374no—
245C2×Q8—371no—
246C2×Q8—741no—
247C2×Q8—742no—
248C2×Q8C22×D3711yescharacteristic
249C2×D4—374no—
250C2×D4—371no—
251C2×D4—742no—
252C2×D4—741no—
253C2×D4C22×D3711yescharacteristic
254C22×C4—21no—
255C22×C4—371no—
256C22×C4—741no—
257C22×C4—741no—
258C22×C4—741no—
259C22×C4—741no—
260SD16—374no—
261SD16—374no—
262SD16—374no—
263SD16C4×D3714yescomplemented
264M16—742no—
265C2×C8—371no—
266C2×C8—374no—
267C2×C8—371no—
268C2×C8C22×D3711yescharacteristic
269C2×C8C22×D3711yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—371no—
272C4⋊C4—371no—
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—741no—
276C4⋊C4—741no—
277C4⋊C4—741no—
278C4⋊C4C22×D3711yescharacteristic
279C4⋊C4C22×D3711yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—371no—
282C22⋊C4—371no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C22⋊C4—741no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C42—21no—
289C42—371no—
290C42—741no—
291C42—741no—
292C42—741no—
293C42—741no—
294C42—741no—
295C42C22×D3711yescharacteristic
296C23—21no—
297C23—371no—
298C23—2961no—
299C23—2961no—
300C23—744no—
301C23—741no—
302Q8—21no—
303Q8—372no—
304Q8—744no—
305Q8—741no—
306Q8C2×C4×D3712yes—
307D4—21no—
308D4—372no—
309D4—744no—
310D4—741no—
311D4C2×C4×D3712yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—371no—
317C2×C4—372no—
318C2×C4—372no—
319C2×C4—371no—
320C2×C4—371no—
321C2×C4—2961no—
322C2×C4—2961no—
323C2×C4—2961no—
324C2×C4—744no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4D4×D3711yescharacteristic
329C2×C4D4×D3711yescharacteristic
330C2×C4C23×D3711yescharacteristic
331C8—21no—
332C8—372no—
333C8—741no—
334C8C2×C4×D3712yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—372no—
339C22—2964no—
340C22—741no—
341C22—741no—
342C22—742no—
343C22—1481no—
344C22—1481no—
345C22C2×D4×D3711yescharacteristic
346C4—22no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—372no—
352C4—742no—
353C4—741no—
354C4—741no—
355C4—1481no—
356C4—1481no—
357C4C22×C4×D3711yescharacteristic
358C4#41×D3711yescharacteristic
359C2—42no—
360C2—742no—
361C2—1482no—
362C2C4×D4×D3711yescharacteristic
363C2#1455834211yescharacteristic
364C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutatorC4×C37C23×C4
FrattiniC2×C4C23×D37
FittingC37×#440C2
socleC22×C37C22×D4
prime radicalC2×D4×D37C22
cosocleC2×C4×C37C24
hypercenter#440D37
hypocenterC37#2949
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #14558009C2semidirect
4. #14557635C2semidirect
5. #14557634C2semidirect
6. #14557632C2semidirect
7. #14557624C2semidirect
8. C4×#10596941C2semidirect
9. C4×#10596940C2semidirect
10. #14557618C2semidirect
11. #14557570C2semidirect
12. #14557540C2semidirect
14. #14557490C2semidirect
15. C37×#440C2semidirect
21. SD16×D37C4semidirect
24. Q8×Dic37C22semidirect
26. C4×Dic74C22semidirect
28. #11924501C22semidirect
41. #11924470C22semidirect
42. #11924467C22semidirect
43. #11924467C22semidirect
44. #11924461C22semidirect
45. #11924460C22semidirect
46. #11924459C22semidirect
50. #11924446C22semidirect
51. C4×#64436C22semidirect
52. C8×Dic37C22semidirect
54. C4×Q8×C37C22semidirect
56. #107×C37C22semidirect
57. #103×C37C22semidirect
59. #97×C37C22semidirect
67. Q8×D37C2×C4semidirect
77. SD16×C37C2×C4semidirect
87. #10596941C2×C4semidirect
88. #10596940C2×C4semidirect
110. #10596930C2×C4semidirect
112. C8×D37C2×C4semidirect
189. #440D37semidirect
198. C37#2949semidirect
213. C4×Q8C2×D37semidirect
228. #107C2×D37semidirect
234. #103C2×D37semidirect
240. #97C2×D37semidirect
263. SD16C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D372
#145580092
#145580052
#145576352
#145576342
#145576322
#145576242
C4×#105969412
C4×#105969402
#145576182
#145575702
#145575402
#145575362
#145574902
C37×#4402
#294937