Finite Group Databasebeta

← #18004949

Subgroups — #18004949

Order 4736.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558163C211yesmaximal, characteristic, complemented
2#14558101C211yesmaximal, characteristic
3#14557899C211yesmaximal, characteristic, complemented
4#14557896C211yesmaximal, characteristic, complemented
5#14557894C211yesmaximal, characteristic, complemented
6#14557892C211yesmaximal, characteristic, complemented
7#14557889C211yesmaximal, characteristic, complemented
8#14557880C211yesmaximal, characteristic, complemented
9#14557878C211yesmaximal, characteristic, complemented
10#14557536C211yesmaximal, characteristic, complemented
11#14557533C211yesmaximal, characteristic, complemented
12#14557528C211yesmaximal, characteristic, complemented
13#102×D37C211yesmaximal, characteristic, complemented
14#14557487C211yesmaximal, characteristic, complemented
15C37×#488C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18C2×#10596929C2211yescharacteristic
19C2×C8×D37C2211yescharacteristic
20#11924536C2211yescharacteristic, complemented
21#11924535—21no—
22#11924535C2211yescharacteristic, complemented
23#11924533C2211yescharacteristic
24#11924532C2211yescharacteristic
25#11924527C2211yescharacteristic, complemented
26#11924526—21no—
27#11924525C2211yescharacteristic
28#11924516—21no—
29#11924514—21no—
30#11924509—21no—
31#11924509—21no—
32#11924506—21no—
33#11924506—21no—
34#11924494C2211yescharacteristic
35#11924493C2211yescharacteristic
36C4⋊C4×D37C2211yescharacteristic
37#11924460C2211yescharacteristic, complemented
38#11924460C2211yescharacteristic, complemented
39#11924458C2211yescharacteristic
40#11924458C2211yescharacteristic
41#11924458C2211yescharacteristic, complemented
42#11924458C2211yescharacteristic, complemented
43#11924457C2211yescharacteristic
44#11924457C2211yescharacteristic
45#11924456C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic, complemented
48#11924456C2211yescharacteristic, complemented
49#11924447C2211yescharacteristic, complemented
50#11924446C2211yescharacteristic, complemented
51C8×Dic37C2211yescharacteristic, complemented
52#125×C37C2211yescharacteristic, complemented
53#124×C37C2211yescharacteristic
54#103×C37C2211yescharacteristic, complemented
55#103×C37C2211yescharacteristic, complemented
56#102×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58C4×C8×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×Q8×C37C2311yescharacteristic
61C2×D4×C37C2311yescharacteristic
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65#10596966—22no—
66#10596966—22no—
67D4×D37—22no—
68D4×D37—22no—
69C2×D148—21no—
70C2×D148—21no—
71C2×D148—21no—
72C2×D148C2311yescharacteristic
73C2×D148C2311yescharacteristic
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37C2311yescharacteristic
77C2×Dic74—21no—
78C2×Dic74—21no—
79C2×C8×C37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C4⋊C4×C37—21no—
82C4⋊C4×C37—21no—
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊C4×C37—21no—
86C22⋊C4×C37—21no—
87C42×C37C2311yescharacteristic
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938D411yescharacteristic
92#10596938D411yescharacteristic
93C4⋊Dic37—21no—
94C4⋊Dic37—21no—
95C4⋊Dic37C2311yescharacteristic
96C4⋊Dic37C2311yescharacteristic
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106#10596929—22no—
107C8×D37—22no—
108C23×C37—21no—
109C22×D37—21no—
110C22×D37—21no—
111C22×D37—42no—
112C22×D37—81no—
113C22×D37—81no—
114C22×D37C2×D411yescharacteristic
115Q8×C37—21no—
116Q8×C37—21no—
117D4×C37—21no—
118D4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2411yescharacteristic
125C22⋊D37—42no—
126C22⋊D37—81no—
127C22⋊D37—81no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133D148—21no—
134D148—21no—
135D148—21no—
136D148—21no—
137D148—42no—
138D148—81no—
139D148—81no—
140C4×D37—42no—
141C4×D37—81no—
142C4×D37#4112yes—
143C4×D37#4112yes—
144Dic74—81no—
145Dic74—81no—
146C8×C37—21no—
147C8×C37—21no—
148#64436—21no—
149#64436—21no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37C22×D411yescharacteristic
154C2×D37—21no—
155C2×D37—21no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—84no—
163C2×D37#12412yes—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37C2×#4111yescharacteristic
170C4×C37C2×#4111yescharacteristic
171Dic37—21no—
172Dic37—21no—
173Dic37—41no—
174Dic37—41no—
175Dic37#12412yes—
176#3136—371nomaximal, Sylow
177C2×C37—81no—
178C2×C37C2×#12411yescharacteristic
179C2×C37#57611yescharacteristic
180C2×C37#57711yescharacteristic
181D37—22no—
182D37—81no—
183D37—81no—
184#544—371no—
185#535—371no—
186#490—371no—
187#490—371no—
188#489—371no—
189#489—371no—
190#488—371no—
191#488D3711yescharacteristic, complemented
192#486—371no—
193#486—371no—
194#418—371no—
195#417—371no—
196#416—371no—
197C2×#102—371no—
198#405—371no—
199C37#313611yescharacteristic, complemented, Sylow
200C2×#41—371no—
201C22×D4—371no—
202C2×M16—371no—
203C22×C8—371no—
204C4⋊Q8—371no—
205C4⋊Q8—371no—
206C4⋊Q8—741no—
207#127—371no—
208#127—371no—
209#125—371no—
210#125—741no—
211#125C2×D3711yescharacteristic, complemented
212#124—371no—
213#124C2×D3711yescharacteristic
214C22⋊Q8—741no—
215C22⋊Q8—741no—
216#121—741no—
217#121—741no—
218#120—741no—
219#120—741no—
220#117—371no—
221#117—371no—
222C2×C4⋊C4—371no—
223#103—371no—
224#103—371no—
225#103C2×D3711yescharacteristic, complemented
226#103C2×D3711yescharacteristic, complemented
227#102—371no—
228#102—371no—
229#102—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235#102—371no—
236#102—371no—
237#102C2×D3711yescharacteristic
238#102C2×D3711yescharacteristic
239#97—371no—
240#97—371no—
241C4×C8—371no—
242C4×C8C2×D3711yescharacteristic, complemented
243C24—741no—
244#41—742no—
245#41—742no—
246C2×Q8—741no—
247C2×Q8—741no—
248C2×Q8C22×D3711yescharacteristic
249C2×D4—371no—
250C2×D4—371no—
251C2×D4—741no—
252C2×D4—742no—
253C2×D4—742no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4—741no—
257C2×D4—741no—
258C2×D4—741no—
259C2×D4C22×D3711yescharacteristic
260C22×C4—371no—
261C22×C4—741no—
262C22×C4—741no—
263M16—742no—
264C2×C8—371no—
265C2×C8—371no—
266C2×C8—742no—
267C2×C8C22×D3711yescharacteristic
268C2×C8C22×D3711yescharacteristic
269C4⋊C4—21no—
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⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4C22×D3711yescharacteristic
281C4⋊C4C22×D3711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—371no—
285C22⋊C4—371no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C42—371no—
290C42—741no—
291C42C22×D3711yescharacteristic
292C23—21no—
293C23—371no—
294C23—2961no—
295C23—2961no—
296C23—741no—
297C23—741no—
298C23—1482no—
299Q8—21no—
300Q8—21no—
301Q8—2961no—
302Q8—2961no—
303D4—21no—
304D4—21no—
305D4—2961no—
306D4—2961no—
307D4—2961no—
308D4—2961no—
309D4—741no—
310D4—741no—
311D4—741no—
312D4—741no—
313D4—1482no—
314D4—1482no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—371no—
319C2×C4—372no—
320C2×C4—372no—
321C2×C4—371no—
322C2×C4—371no—
323C2×C4—2961no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—1482no—
327C2×C4D4×D3711yescharacteristic
328C2×C4D4×D3711yescharacteristic
329C2×C4C23×D3711yescharacteristic
330C8—21no—
331C8—21no—
332C8—741no—
333C8—741no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—372no—
338C22—2964no—
339C22—741no—
340C22—741no—
341C22—1481no—
342C22—1481no—
343C22—1481no—
344C22—1481no—
345C22—1481no—
346C22—1481no—
347C22C2×D4×D3711yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—372no—
354C4—741no—
355C4—741no—
356C4—1481no—
357C4—1481no—
358C4#41×D3711yescharacteristic
359C4#41×D3711yescharacteristic
360C2—81no—
361C2—2961no—
362C2—2961no—
363C2—742no—
364C2#124×D3711yescharacteristic
365C2#1455833511yescharacteristic
366C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#488C2
socleC22×C37C22×D4
prime radical#14558101C2
hypercenter#488D37
hypocenterC37#3136
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #14558163C2semidirect
3. #14557899C2semidirect
4. #14557896C2semidirect
5. #14557894C2semidirect
6. #14557892C2semidirect
7. #14557889C2semidirect
8. #14557880C2semidirect
9. #14557878C2semidirect
10. #14557536C2semidirect
11. #14557533C2semidirect
12. #14557528C2semidirect
13. #102×D37C2semidirect
14. #14557487C2semidirect
15. C37×#488C2semidirect
20. #11924536C22semidirect
22. #11924535C22semidirect
25. #11924527C22semidirect
37. #11924460C22semidirect
38. #11924460C22semidirect
41. #11924458C22semidirect
42. #11924458C22semidirect
47. #11924456C22semidirect
48. #11924456C22semidirect
49. #11924447C22semidirect
50. #11924446C22semidirect
51. C8×Dic37C22semidirect
52. #125×C37C22semidirect
54. #103×C37C22semidirect
55. #103×C37C22semidirect
58. C4×C8×C37C22semidirect
191. #488D37semidirect
199. C37#3136semidirect
211. #125C2×D37semidirect
225. #103C2×D37semidirect
226. #103C2×D37semidirect
242. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581632
#145581012
#145578992
#145578962
#145578942
#145578922
#145578892
#145578802
#145578782
#145575362
#145575332
#145575282
#102×D372
#145574872
C37×#4882
#313637