Finite Group Databasebeta

← #18006552

Subgroups — #18006552

Order 4736.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558183C211yesmaximal, characteristic, complemented
2#14558180C211yesmaximal, characteristic, complemented
3#14557891C211yesmaximal, characteristic, complemented
4#14557865C211yesmaximal, characteristic, complemented
5#14557849C211yesmaximal, characteristic, complemented
6#14557822C211yesmaximal, characteristic, complemented
7#14557761C211yesmaximal, characteristic, complemented
8#14557746C211yesmaximal, characteristic, complemented
9#14557676C211yesmaximal, characteristic, complemented
10#14557665C211yesmaximal, characteristic, complemented
11#14557642C211yesmaximal, characteristic, complemented
12#14557602C211yesmaximal, characteristic, complemented
13#14557535C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#469C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596964—21no—
18C2×D4×D37C2211yescharacteristic
19C2×#10596940C2211yescharacteristic, complemented
20C2×#10596939C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22#11924535C2211yescharacteristic, complemented
23#11924523C2211yescharacteristic
24#11924518—21no—
25#11924518—21no—
26#11924517—21no—
27#11924516C2211yescharacteristic
28#11924513—21no—
29#11924507—21no—
30#11924507C2211yescharacteristic
31#11924504—21no—
32D4×Dic37C2211yescharacteristic, complemented
33#11924498C2211yescharacteristic
34C4×C22⋊D37C2211yescharacteristic
35C2×C4⋊Dic37C2211yescharacteristic, complemented
36C4⋊C4×D37C2211yescharacteristic
37C22⋊C4×D37—21no—
38#11924467C2211yescharacteristic, complemented
39#11924467C2211yescharacteristic, complemented
40#11924465C2211yescharacteristic, complemented
41#11924461C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924459C2211yescharacteristic, complemented
44#11924458C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924457C2211yescharacteristic
47#11924457C2211yescharacteristic
48#11924456C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic, complemented
50#11924448C2211yescharacteristic
51#11924446C2211yescharacteristic, complemented
52C2×D8×C37C2211yescharacteristic
53C2×M16×C37C2211yescharacteristic, complemented
54#121×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic, complemented
56#106×C37C2211yescharacteristic, complemented
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C2×D4×C37—21no—
61C2×D4×C37—21no—
62C2×D4×C37C2311yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37D411yescharacteristic
69C22×Dic37—21no—
70C22×Dic37—21no—
71#10596964—44no—
72D4×D37—22no—
73D4×D37—41no—
74#10596962—22no—
75#10596962—41no—
76C2×D148C2311yescharacteristic
77C2×C4×D37—21no—
78C2×C4×D37—21no—
79C2×C4×D37—21no—
80C2×C4×D37C2311yescharacteristic
81C2×Dic74—21no—
82C2×Dic74C2311yescharacteristic
83D8×C37—41no—
84M16×C37—41no—
85C2×C8×C37C2311yescharacteristic
86C2×C8×C37C2311yescharacteristic
87C4⋊C4×C37C2311yescharacteristic
88C4⋊C4×C37C2311yescharacteristic
89C22⋊C4×C37—21no—
90C22⋊C4×C37—21no—
91C22⋊Dic37—21no—
92C22⋊Dic37—21no—
93C22⋊Dic37—21no—
94C22⋊Dic37—21no—
95C22⋊Dic37D411yescharacteristic
96#10596940—41no—
97#10596939—22no—
98#10596938—21no—
99#10596938—21no—
100#10596938D411yescharacteristic
101C4⋊Dic37—21no—
102C4⋊Dic37—21no—
103C4⋊Dic37C2311yescharacteristic
104C4⋊Dic37C2311yescharacteristic
105#10596936—21no—
106#10596936—21no—
107#10596936D411yescharacteristic
108C4×Dic37C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C8×D37—41no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37C2×D411yescharacteristic
115C22×D37—21no—
116C22×D37—42no—
117C22×D37—42no—
118C22×D37—81no—
119C22×D37C2×D411yescharacteristic
120D4×C37—21no—
121D4×C37—21no—
122D4×C37—21no—
123D4×C37—21no—
124D4×C37—42no—
125D4×C37—81no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2411yescharacteristic
132C22⋊D37—22no—
133C22⋊D37—42no—
134C22⋊D37—42no—
135C22⋊D37—42no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—42no—
140C2×Dic37—42no—
141C2×Dic37C2×D411yescharacteristic
142C2×Dic37C2×D411yescharacteristic
143C2×Dic37C2×D411yescharacteristic
144D148—21no—
145D148#4112yescomplemented
146C4×D37—21no—
147C4×D37—21no—
148C4×D37—42no—
149C4×D37—42no—
150C4×D37—81no—
151Dic74—21no—
152Dic74—21no—
153Dic74—42no—
154C8×C37—21no—
155C8×C37—21no—
156#64436—21no—
157#64436—21no—
158C22×C37—21no—
159C22×C37—21no—
160C22×C37—21no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37C22×D411yescharacteristic
168C2×D37—21no—
169C2×D37—21no—
170C2×D37—22no—
171C2×D37—41no—
172C2×D37—41no—
173C2×D37—84no—
174C2×D37AGL(1,ℤ/8)12yes—
175C4×C37—21no—
176C4×C37—41no—
177C4×C37—41no—
178C4×C37C2×#4111yescharacteristic
179C4×C37H(5,𝔽2)11yescharacteristic
180Dic37—21no—
181Dic37—21no—
182Dic37—21no—
183Dic37—41no—
184Dic37—41no—
185Dic37—41no—
186#3306—371nomaximal, Sylow
187C2×C37—41no—
188C2×C37—81no—
189C2×C37—81no—
190C2×C37#54611yescharacteristic
191C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C37#57711yescharacteristic
193D37—22no—
194D37—42no—
195#547—371no—
196#546—371no—
197#489—371no—
198#483—371no—
199#481—371no—
200#476—371no—
201#469D3711yescharacteristic, complemented
202#465—371no—
203#463—371no—
204#449—371no—
205#447—371no—
206#442—371no—
207#435—371no—
208#417—371no—
209C2×#102—371no—
210C37#330611yescharacteristic, complemented, Sylow
211C2×#41—371no—
212C2×#41—741no—
213C22×D4—371no—
214C2×SD16—371no—
215C2×D8—371no—
216C2×D8C2×D3711yescharacteristic
217C2×M16C2×D3711yescharacteristic, complemented
218C22×C8—371no—
219C4⋊Q8—371no—
220#124—371no—
221#123—741no—
222#123—741no—
223#123—741no—
224C22⋊Q8—371no—
225C22⋊Q8—741no—
226#121—371no—
227#121—741no—
228#121C2×D3711yescharacteristic
229#121C2×D3711yescharacteristic, complemented
230#120—741no—
231C4×D4—371no—
232C4×D4—371no—
233C4×D4—371no—
234C2×C4⋊C4—371no—
235C2×C4⋊C4—371no—
236C2×C22⋊C4—741no—
237#106—371no—
238#106—371no—
239#106C2×D3711yescharacteristic, complemented
240C4⋊C8—371no—
241#103—371no—
242#103—371no—
243#103—371no—
244#102—371no—
245#102—371no—
246#102—371no—
247#102—371no—
248#102—371no—
249#102C2×D3711yescharacteristic
250#102C2×D3711yescharacteristic, complemented
251C22⋊C8—371no—
252C22⋊C8—371no—
253#97—371no—
254C24—741no—
255#41—742no—
256#41—1481no—
257#41—1484no—
258C2×Q8—371no—
259C2×Q8—741no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—371no—
263C2×D4—371no—
264C2×D4—741no—
265C2×D4—742no—
266C2×D4—741no—
267C2×D4—741no—
268C2×D4—1481no—
269C2×D4C22×D3711yescharacteristic
270C2×D4C22×D3711yescharacteristic
271C22×C4—371no—
272C22×C4—741no—
273C22×C4—741no—
274C22×C4—741no—
275C22×C4—741no—
276C22×C4—741no—
277C22×C4C22×D3711yescharacteristic
278SD16—1481no—
279D8—41no—
280D8—742no—
281M16—41no—
282C2×C8—371no—
283C2×C8—371no—
284C2×C8—1481no—
285C2×C8C22×D3711yescharacteristic
286C2×C8C22×D3711yescharacteristic
287C4⋊C4—371no—
288C4⋊C4—371no—
289C4⋊C4—371no—
290C4⋊C4—741no—
291C4⋊C4—741no—
292C4⋊C4—741no—
293C4⋊C4—741no—
294C4⋊C4C22×D3711yescharacteristic
295C4⋊C4C22×D3711yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—371no—
299C22⋊C4—371no—
300C22⋊C4—741no—
301C22⋊C4—741no—
302C22⋊C4—741no—
303C22⋊C4—741no—
304C22⋊C4—741no—
305C22⋊C4—741no—
306C42—371no—
307C23—21no—
308C23—21no—
309C23—371no—
310C23—2961no—
311C23—741no—
312C23—1482no—
313C23—1482no—
314C23D4×D3711yescharacteristic
315Q8—741no—
316Q8—741no—
317Q8—1482no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—81no—
324D4—372no—
325D4—742no—
326D4—741no—
327D4—1482no—
328D4—1482no—
329D4—1482no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—371no—
335C2×C4—371no—
336C2×C4—371no—
337C2×C4—2961no—
338C2×C4—741no—
339C2×C4—741no—
340C2×C4—741no—
341C2×C4—741no—
342C2×C4—741no—
343C2×C4—1482no—
344C2×C4—1482no—
345C2×C4—1482no—
346C2×C4—1482no—
347C2×C4D4×D3711yescharacteristic
348C2×C4C23×D3711yescharacteristic
349C8—21no—
350C8—21no—
351C8—741no—
352C8—741no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—372no—
363C22—2964no—
364C22—741no—
365C22—741no—
366C22—742no—
367C22—1481no—
368C22—1481no—
369C22C2×D4×D3711yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—741no—
374C4—741no—
375C4—741no—
376C4—1481no—
377C4—1481no—
378C4—1481no—
379C4#41×D3711yescharacteristic
380C4#1192458111yescharacteristic
381C2—41no—
382C2—81no—
383C2—81no—
384C2—742no—
385C2—1482no—
386C2#1455817211yescharacteristic
387C2AGL(1,ℤ/8)×D3711yescharacteristic
388C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#469C2
socleC22×C37C22×D4
hypercenter#469D37
hypocenterC37#3306
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14558183C2semidirect
2. #14558180C2semidirect
3. #14557891C2semidirect
4. #14557865C2semidirect
5. #14557849C2semidirect
6. #14557822C2semidirect
7. #14557761C2semidirect
8. #14557746C2semidirect
9. #14557676C2semidirect
10. #14557665C2semidirect
11. #14557642C2semidirect
12. #14557602C2semidirect
13. #14557535C2semidirect
14. #102×D37C2semidirect
15. C37×#469C2semidirect
19. C2×#10596940C22semidirect
22. #11924535C22semidirect
32. D4×Dic37C22semidirect
35. C2×C4⋊Dic37C22semidirect
38. #11924467C22semidirect
39. #11924467C22semidirect
40. #11924465C22semidirect
41. #11924461C22semidirect
42. #11924461C22semidirect
43. #11924459C22semidirect
49. C22⋊#64436C22semidirect
51. #11924446C22semidirect
53. C2×M16×C37C22semidirect
55. #121×C37C22semidirect
56. #106×C37C22semidirect
58. #102×C37C22semidirect
145. D148#41semidirect
201. #469D37semidirect
210. C37#3306semidirect
217. C2×M16C2×D37semidirect
229. #121C2×D37semidirect
239. #106C2×D37semidirect
250. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581832
#145581802
#145578912
#145578652
#145578492
#145578222
#145577612
#145577462
#145576762
#145576652
#145576422
#145576022
#145575352
#102×D372
C37×#4692
#330637