Finite Group Databasebeta

← #18006428

Subgroups — #18006428

Order 4736.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558221C211yesmaximal, characteristic, complemented
2#14558178C211yesmaximal, characteristic
3#14557890C211yesmaximal, characteristic, complemented
4#14557865C211yesmaximal, characteristic, complemented
5#14557860C211yesmaximal, characteristic, complemented
6#14557775C211yesmaximal, characteristic, complemented
7#14557763C211yesmaximal, characteristic, complemented
8#14557756C211yesmaximal, characteristic, complemented
9#14557696C211yesmaximal, characteristic, complemented
10#14557685C211yesmaximal, characteristic, complemented
11C4×#10596940C211yesmaximal, characteristic, complemented
12#14557598C211yesmaximal, characteristic, complemented
13#14557526C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#478C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×Dic148C2211yescharacteristic, complemented
19C2×#10596930C2211yescharacteristic
20C2×#10596940C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic, complemented
23#11924531—21no—
24#11924527—21no—
25#11924524C2211yescharacteristic
26#11924521—21no—
27#11924520—21no—
28#11924516C2211yescharacteristic
29#11924516C2211yescharacteristic
30#11924516C2211yescharacteristic, complemented
31#11924511C2211yescharacteristic
32#11924510—21no—
33#11924506—21no—
34C4×Dic74C2211yescharacteristic, complemented
35C4×D148C2211yescharacteristic
36#11924494—21no—
37#11924494C2211yescharacteristic, complemented
38C4⋊C4×D37C2211yescharacteristic
39C2×#10596938—21no—
40#11924467C2211yescharacteristic, complemented
41#11924461C2211yescharacteristic, complemented
42#11924459C2211yescharacteristic, complemented
43#11924459C2211yescharacteristic, complemented
44#11924459C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic, complemented
51C4×#64436C2211yescharacteristic, complemented
52#125×C37C2211yescharacteristic, complemented
53C4×D4×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic, complemented
55#106×C37C2211yescharacteristic, complemented
56C4⋊C8×C37C2211yescharacteristic, complemented
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C23×D37—21no—
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C22×Dic37—21no—
65#10596964—22no—
66#10596964—41no—
67D4×D37—22no—
68D4×D37—41no—
69C2×D148—21no—
70C2×D148D411yescharacteristic
71C2×D148C2311yescharacteristic
72C2×C4×D37—21no—
73C2×C4×D37C2311yescharacteristic
74C2×C4×D37C2311yescharacteristic
75C2×Dic74C2311yescharacteristic
76C2×Dic74C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37—21no—
80C4⋊C4×C37—21no—
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C22⋊C4×C37—21no—
85C42×C37C2311yescharacteristic
86#10596940—22no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938D411yescharacteristic
95#10596938D411yescharacteristic
96C4⋊Dic37—21no—
97C4⋊Dic37—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37D411yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936—21no—
103C4×Dic37—21no—
104C4×Dic37—21no—
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107Dic148—41no—
108#10596930—41no—
109C8×D37—41no—
110C8×D37—41no—
111C23×C37—21no—
112C22×D37—21no—
113C22×D37—42no—
114C22×D37—42no—
115C22×D37—81no—
116C22×D37C2×D411yescharacteristic
117C22×D37C2×D411yescharacteristic
118D4×C37—21no—
119D4×C37#4112yes—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—81no—
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2411yescharacteristic
127C22⋊D37—42no—
128C22⋊D37—42no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—42no—
133C2×Dic37C2×D411yescharacteristic
134C2×Dic37C2×D411yescharacteristic
135D148—22no—
136D148—21no—
137D148—21no—
138D148—81no—
139C4×D37—21no—
140C4×D37—21no—
141C4×D37—21no—
142C4×D37—21no—
143C4×D37—42no—
144Dic74—21no—
145Dic74—21no—
146Dic74—21no—
147Dic74—21no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—22no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37C22×D411yescharacteristic
156C2×D37—21no—
157C2×D37—21no—
158C2×D37—21no—
159C2×D37—21no—
160C2×D37—21no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—84no—
165C2×D37#13512yes—
166C4×C37—21no—
167C4×C37—21no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37—41no—
171C4×C37C2×#4111yescharacteristic
172C4×C37H(5,𝔽2)11yescharacteristic
173Dic37—21no—
174Dic37—21no—
175Dic37—41no—
176Dic37—41no—
177Dic37—41no—
178#3296—371nomaximal, Sylow
179C2×C37—42no—
180C2×C37#54611yescharacteristic
181C2×C37C2×#13511yescharacteristic
182C2×C37#57711yescharacteristic
183D37—22no—
184D37—41no—
185D37—81no—
186#552—371no—
187#546—371no—
188#488—371no—
189#483—371no—
190#482—371no—
191#478D3711yescharacteristic, complemented
192#467—371no—
193#465—371no—
194#464—371no—
195#452—371no—
196#450—371no—
197C4×SD16—371no—
198C8×D4—371no—
199#416—371no—
200C2×#102—371no—
201C37#329611yescharacteristic, complemented, Sylow
202C2×#41—371no—
203C22×D4—371no—
204C2×Q16—371no—
205C2×SD16—371no—
206C2×SD16—371no—
207C22×C8—371no—
208C22×C8—371no—
209#126—741no—
210#125—741no—
211#125C2×D3711yescharacteristic, complemented
212#124—371no—
213#123—741no—
214#123—741no—
215C22⋊Q8—371no—
216C22⋊Q8—371no—
217C22⋊Q8—371no—
218#121—371no—
219#121—741no—
220#120—741no—
221C4×Q8—371no—
222C4×D4—371no—
223C4×D4C2×D3711yescharacteristic
224#117—371no—
225#117—741no—
226C2×C4⋊C4—371no—
227C2×C22⋊C4—741no—
228#107C2×D3711yescharacteristic, complemented
229#106—371no—
230#106C2×D3711yescharacteristic, complemented
231C4⋊C8C2×D3711yescharacteristic, complemented
232#103—371no—
233#103—371no—
234#103—371no—
235#103—371no—
236#102—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102C2×D3711yescharacteristic
241#102C2×D3711yescharacteristic
242C22⋊C8—371no—
243C22⋊C8—371no—
244C4×C8—371no—
245C24—741no—
246#41—742no—
247#41—1481no—
248C2×Q8—371no—
249C2×Q8—371no—
250C2×D4—371no—
251C2×D4—371no—
252C2×D4—741no—
253C2×D4—741no—
254C2×D4—742no—
255C2×D4—741no—
256C2×D4—1481no—
257C2×D4C22×D3711yescharacteristic
258C22×C4—21no—
259C22×C4—371no—
260C22×C4—371no—
261C22×C4—741no—
262C22×C4—741no—
263Q16—1481no—
264SD16—742no—
265SD16—1481no—
266C2×C8—371no—
267C2×C8—371no—
268C2×C8—1481no—
269C2×C8—1481no—
270C2×C8C22×D3711yescharacteristic
271C2×C8C22×D3711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—741no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4C22×D3711yescharacteristic
282C4⋊C4C22×D3711yescharacteristic
283C4⋊C4C22×D3711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—371no—
286C22⋊C4—371no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C22⋊C4—741no—
294C42—741no—
295C42—741no—
296C42C22×D3711yescharacteristic
297C23—21no—
298C23—371no—
299C23—371no—
300C23—2961no—
301C23—741no—
302C23—1482no—
303C23—1482no—
304Q8—741no—
305Q8—741no—
306Q8—741no—
307Q8—741no—
308D4—21no—
309D4—2961no—
310D4—742no—
311D4—741no—
312D4—741no—
313D4—1482no—
314D4—1482no—
315D4#1059696612yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—371no—
321C2×C4—371no—
322C2×C4—741no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—741no—
329C2×C4—1482no—
330C2×C4—1482no—
331C2×C4D4×D3711yescharacteristic
332C2×C4D4×D3711yescharacteristic
333C2×C4C23×D3711yescharacteristic
334C8—21no—
335C8—21no—
336C8—741no—
337C8—741no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—372no—
342C22—2964no—
343C22—741no—
344C22—741no—
345C22—741no—
346C22—741no—
347C22—741no—
348C22—1481no—
349C22—1481no—
350C22—1481no—
351C22C2×D4×D3711yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—741no—
358C4—741no—
359C4—1481no—
360C4—1481no—
361C4—1481no—
362C4C2×#1059696611yescharacteristic
363C4#1192458211yescharacteristic
364C2—42no—
365C2—2961no—
366C2—742no—
367C2—1481no—
368C2#1455817411yescharacteristic
369C2#135×D3711yescharacteristic
370C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#478C2
socleC22×C37C22×D4
prime radical#14558178C2
hypercenter#478D37
hypocenterC37#3296
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14558221C2semidirect
3. #14557890C2semidirect
4. #14557865C2semidirect
5. #14557860C2semidirect
6. #14557775C2semidirect
7. #14557763C2semidirect
8. #14557756C2semidirect
9. #14557696C2semidirect
10. #14557685C2semidirect
11. C4×#10596940C2semidirect
12. #14557598C2semidirect
13. #14557526C2semidirect
14. #102×D37C2semidirect
15. C37×#478C2semidirect
18. C2×Dic148C22semidirect
22. C2×C8×D37C22semidirect
30. #11924516C22semidirect
34. C4×Dic74C22semidirect
37. #11924494C22semidirect
40. #11924467C22semidirect
41. #11924461C22semidirect
42. #11924459C22semidirect
43. #11924459C22semidirect
44. #11924459C22semidirect
50. #11924448C22semidirect
51. C4×#64436C22semidirect
52. #125×C37C22semidirect
54. #107×C37C22semidirect
55. #106×C37C22semidirect
56. C4⋊C8×C37C22semidirect
191. #478D37semidirect
201. C37#3296semidirect
211. #125C2×D37semidirect
228. #107C2×D37semidirect
230. #106C2×D37semidirect
231. C4⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145582212
#145581782
#145578902
#145578652
#145578602
#145577752
#145577632
#145577562
#145576962
#145576852
C4×#105969402
#145575982
#145575262
#102×D372
C37×#4782
#329637