Finite Group Databasebeta

← #18006081

Subgroups — #18006081

Order 4736.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924564C211yesmaximal, characteristic, complemented
2C22×D296C211yesmaximal, characteristic, complemented
3#14558179C211yesmaximal, characteristic, complemented
4D4×D148C211yesmaximal, characteristic, complemented
5#14557922C211yesmaximal, characteristic, complemented
6#14557786C211yesmaximal, characteristic, complemented
7#14557762C211yesmaximal, characteristic, complemented
8#14557749C211yesmaximal, characteristic, complemented
9#14557729C211yesmaximal, characteristic, complemented
10#14557686C211yesmaximal, characteristic, complemented
11#14557680C211yesmaximal, characteristic, complemented
12#14557669C211yesmaximal, characteristic, complemented
13#14557669C211yesmaximal, characteristic, complemented
14#14557646C211yesmaximal, characteristic, complemented
15C37×#435C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic, complemented
17C22×D148C2211yescharacteristic
18C22×D148C2211yescharacteristic, complemented
19C22×D148C2211yescharacteristic, complemented
20C2×D4×D37—21no—
21#11924564—24no—
22C2×#10596930C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic, complemented
24C2×#10596930C2211yescharacteristic, complemented
25C2×D296—24no—
26C2×D296C2211yescharacteristic
27C2×D296C2211yescharacteristic
28C2×D296C2211yescharacteristic, complemented
29C2×D296C2211yescharacteristic, complemented
30C2×D296C2211yescharacteristic, complemented
31C2×D296C2211yescharacteristic, complemented
32#11924533C2211yescharacteristic, complemented
33#11924524C2211yescharacteristic, complemented
34#11924521—21no—
35#11924515C2211yescharacteristic, complemented
36#11924511—21no—
37#11924510C2211yescharacteristic
38#11924510C2211yescharacteristic, complemented
39#11924510C2211yescharacteristic, complemented
40#11924509—21no—
41#11924506—21no—
42#11924506—21no—
43#11924504—21no—
44C4×D148C2211yescharacteristic, complemented
45C4×D148C2211yescharacteristic, complemented
46C22⋊C4×D37—21no—
47#11924468C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924458C2211yescharacteristic, complemented
50#11924458C2211yescharacteristic, complemented
51#11924458C2211yescharacteristic, complemented
52#11924458C2211yescharacteristic, complemented
53#11924458C2211yescharacteristic, complemented
54C2×M16×C37C2211yescharacteristic, complemented
55C22×C8×C37C2211yescharacteristic, complemented
56C4×D4×C37C2211yescharacteristic
57C4⋊C8×C37C2211yescharacteristic, complemented
58C22⋊C8×C37C2211yescharacteristic, complemented
59C22⋊C8×C37C2211yescharacteristic, complemented
60#97×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C23×D37—21no—
63C23×D37—21no—
64C2×D4×C37D411yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71D4×D37—44no—
72#10596962—22no—
73#10596962—41no—
74C2×D148—22no—
75C2×D148—22no—
76C2×D148—22no—
77C2×D148—21no—
78C2×D148—21no—
79C2×D148—21no—
80C2×D148—21no—
81C2×D148—21no—
82C2×D148—41no—
83C2×D148—41no—
84C2×D148—41no—
85C2×D148C2311yescharacteristic
86C2×D148C2311yescharacteristic
87C2×D148C2311yescharacteristic
88C2×D148C2311yescharacteristic
89C2×D148C2311yescharacteristic
90C2×C4×D37—21no—
91C2×C4×D37—21no—
92C2×C4×D37—21no—
93C2×Dic74C2311yescharacteristic
94M16×C37—22no—
95C2×C8×C37—22no—
96C2×C8×C37C2311yescharacteristic
97C2×C8×C37C2311yescharacteristic
98C2×C8×C37C2311yescharacteristic
99C2×C8×C37C2311yescharacteristic
100C4⋊C4×C37D411yescharacteristic
101C22⋊C4×C37D411yescharacteristic
102C22⋊C4×C37D411yescharacteristic
103C42×C37C2311yescharacteristic
104C22⋊Dic37—21no—
105#10596938—21no—
106#10596938—21no—
107#10596938—21no—
108#10596938—21no—
109#10596938—21no—
110#10596938—21no—
111#10596938—21no—
112C4⋊Dic37C2311yescharacteristic
113C4⋊Dic37C2311yescharacteristic
114#10596936—21no—
115D296—22no—
116D296—22no—
117D296—22no—
118D296—22no—
119D296—41no—
120D296D414yescomplemented
121#10596930—22no—
122#10596930—22no—
123#10596930—41no—
124C23×C37C2×D411yescharacteristic
125C23×C37C2×D411yescharacteristic
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—21no—
130C22×D37—21no—
131C22×D37—42no—
132C22×D37—42no—
133C22×D37—42no—
134C22×D37—42no—
135C22×D37—42no—
136C22×D37—42no—
137C22×D37—81no—
138C22×D37—81no—
139C22×D37—81no—
140D4×C37—22no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2×D411yescharacteristic
147C2×C4×C37C2×D411yescharacteristic
148C2×C4×C37C2×D411yescharacteristic
149C2×C4×C37C2411yescharacteristic
150C22⋊D37—42no—
151C22⋊D37—42no—
152C22⋊D37—42no—
153C22⋊D37—81no—
154C2×Dic37—21no—
155C2×Dic37—21no—
156C2×Dic37—21no—
157D148—21no—
158D148—21no—
159D148—21no—
160D148—21no—
161D148—21no—
162D148—21no—
163D148—21no—
164D148—21no—
165D148—42no—
166D148—42no—
167D148—42no—
168D148—42no—
169D148—81no—
170D148C2×D412yes—
171D148C2×D412yescomplemented
172C4×D37—42no—
173C4×D37—42no—
174C4×D37—81no—
175Dic74—21no—
176Dic74—21no—
177C8×C37—21no—
178C8×C37—21no—
179C8×C37—21no—
180C8×C37C2×D412yescomplemented
181C22×C37—21no—
182C22×C37—21no—
183C22×C37—21no—
184C22×C37—21no—
185C22×C37—21no—
186C22×C37AGL(1,ℤ/8)12yescomplemented
187C22×C37C22×D411yescharacteristic
188C2×D37—22no—
189C2×D37—22no—
190C2×D37—41no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—41no—
195C2×D37—41no—
196C2×D37—41no—
197C2×D37—41no—
198C2×D37—41no—
199C2×D37—41no—
200C2×D37—41no—
201C2×D37—41no—
202C2×D37—41no—
203C2×D37—84no—
204C2×D37—84no—
205C2×D37—84no—
206C4×C37—21no—
207C4×C37—21no—
208C4×C37—21no—
209C4×C37—21no—
210C4×C37C22×D411yescharacteristic
211C4×C37H(5,𝔽2)11yescharacteristic
212Dic37—41no—
213Dic37—41no—
214Dic37—41no—
215#3264—371nomaximal, Sylow
216C2×C37—22no—
217C2×C37—41no—
218C2×C37D4211yescharacteristic
219C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C37#57611yescharacteristic
221D37—42no—
222D37—42no—
223D37—81no—
224D37—81no—
225D37—81no—
226C2×AGL(1,ℤ/8)—371no—
227C22×D8—371no—
228#546—371no—
229D42—371no—
230#496—371no—
231#469—371no—
232#465—371no—
233#463—371no—
234#459—371no—
235#450—371no—
236#449—371no—
237#447—371no—
238#447—371no—
239#442—371no—
240#435D3711yescharacteristic, complemented
241C37#326411yescharacteristic, complemented, Sylow
242C2×#41—371no—
243C22×D4—371no—
244C22×D4—371no—
245C22×D4—371no—
246C22×D4—741no—
247AGL(1,ℤ/8)—744no—
248C2×SD16—371no—
249C2×SD16—371no—
250C2×SD16—371no—
251C2×D8—371no—
252C2×D8—371no—
253C2×D8—371no—
254C2×D8—371no—
255C2×D8—371no—
256C2×D8—371no—
257C2×D8—744no—
258C2×M16C2×D3711yescharacteristic, complemented
259C22×C8C2×D3711yescharacteristic, complemented
260#127—371no—
261#124—371no—
262#123—741no—
263C22⋊Q8—371no—
264#121—371no—
265#121—371no—
266#121—371no—
267#121—741no—
268#121—741no—
269#120—741no—
270#120—741no—
271#120—741no—
272C4×D4—371no—
273C4×D4—371no—
274C4×D4C2×D3711yescharacteristic
275C2×C22⋊C4—741no—
276#106—371no—
277C4⋊C8C2×D3711yescharacteristic, complemented
278#103—371no—
279#102—371no—
280#102—371no—
281#102—371no—
282#102—371no—
283#102—371no—
284C22⋊C8C2×D3711yescharacteristic, complemented
285C22⋊C8C2×D3711yescharacteristic, complemented
286#97C2×D3711yescharacteristic, complemented
287C24—741no—
288C24—741no—
289C24—741no—
290#41—742no—
291#41—1481no—
292C2×Q8—371no—
293C2×D4—371no—
294C2×D4—371no—
295C2×D4—371no—
296C2×D4—371no—
297C2×D4—371no—
298C2×D4—742no—
299C2×D4—742no—
300C2×D4—742no—
301C2×D4—741no—
302C2×D4—741no—
303C2×D4—741no—
304C2×D4—741no—
305C2×D4—741no—
306C2×D4—741no—
307C2×D4—741no—
308C2×D4—741no—
309C2×D4—741no—
310C2×D4—1481no—
311C2×D4—1481no—
312C2×D4—1481no—
313C2×D4—1484no—
314C2×D4D14811yescharacteristic
315C22×C4—741no—
316C22×C4—741no—
317C22×C4—741no—
318C22×C4C22×D3711yescharacteristic
319C22×C4C22×D3711yescharacteristic
320SD16—742no—
321SD16—742no—
322SD16—1481no—
323D8—374no—
324D8—742no—
325D8—742no—
326D8—742no—
327D8—742no—
328D8—1481no—
329M16—22no—
330C2×C8—22no—
331C2×C8C22×D3711yescharacteristic
332C2×C8C22×D3711yescharacteristic
333C2×C8C22×D3711yescharacteristic
334C2×C8C22×D3711yescharacteristic
335C4⋊C4—371no—
336C4⋊C4—371no—
337C4⋊C4—741no—
338C4⋊C4D14811yescharacteristic
339C22⋊C4—741no—
340C22⋊C4—741no—
341C22⋊C4—741no—
342C22⋊C4—741no—
343C22⋊C4—741no—
344C22⋊C4—741no—
345C22⋊C4—741no—
346C22⋊C4—741no—
347C22⋊C4D14811yescharacteristic
348C22⋊C4D14811yescharacteristic
349C42C22×D3711yescharacteristic
350C23—2961no—
351C23—2961no—
352C23—2961no—
353C23—741no—
354C23—741no—
355C23—741no—
356C23—741no—
357C23—741no—
358C23—1482no—
359C23—1482no—
360C23—1482no—
361C23—1482no—
362C23—1482no—
363C23—1482no—
364C23C2×D14811yescharacteristic
365C23C2×D14811yescharacteristic
366Q8—741no—
367Q8—741no—
368D4—22no—
369D4—372no—
370D4—372no—
371D4—2961no—
372D4—2961no—
373D4—741no—
374D4—741no—
375D4—741no—
376D4—741no—
377D4—741no—
378D4—741no—
379D4—741no—
380D4—741no—
381D4—1482no—
382D4—1482no—
383D4—1482no—
384D4—1482no—
385D4—1482no—
386D4—1482no—
387D4—1482no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—2961no—
393C2×C4—741no—
394C2×C4—741no—
395C2×C4—741no—
396C2×C4—1482no—
397C2×C4—1482no—
398C2×C4C2×D14811yescharacteristic
399C2×C4C2×D14811yescharacteristic
400C2×C4C2×D14811yescharacteristic
401C2×C4C2×D14811yescharacteristic
402C2×C4C23×D3711yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8D4×D3712yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—2964no—
413C22—2964no—
414C22—2964no—
415C22—742no—
416C22—742no—
417C22—1481no—
418C22—1481no—
419C22—1481no—
420C22—1481no—
421C22—1481no—
422C22—1481no—
423C22—1481no—
424C22—1481no—
425C22—1481no—
426C22—1481no—
427C22—1481no—
428C22—1481no—
429C22—1481no—
430C22#1192456412yescomplemented
431C22C22×D14811yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—1481no—
437C4—1481no—
438C4—1481no—
439C4C2×D4×D3711yescharacteristic
440C4#1192458211yescharacteristic
441C2—22no—
442C2—41no—
443C2—2961no—
444C2—2961no—
445C2—2961no—
446C2—1482no—
447C2—1482no—
448C2D4×D14811yescharacteristic
449C2C2×#1192456411yescharacteristic
450C2#1455833811yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#435C2
socleC22×C37C22×D4
hypercenter#435D37
hypocenterC37#3264
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. C22×D296C2semidirect
3. #14558179C2semidirect
4. D4×D148C2semidirect
5. #14557922C2semidirect
6. #14557786C2semidirect
7. #14557762C2semidirect
8. #14557749C2semidirect
9. #14557729C2semidirect
10. #14557686C2semidirect
11. #14557680C2semidirect
12. #14557669C2semidirect
13. #14557669C2semidirect
14. #14557646C2semidirect
15. C37×#435C2semidirect
16. C2×#10596962C22semidirect
18. C22×D148C22semidirect
19. C22×D148C22semidirect
22. C2×#10596930C22semidirect
23. C2×#10596930C22semidirect
24. C2×#10596930C22semidirect
28. C2×D296C22semidirect
29. C2×D296C22semidirect
30. C2×D296C22semidirect
31. C2×D296C22semidirect
32. #11924533C22semidirect
33. #11924524C22semidirect
35. #11924515C22semidirect
38. #11924510C22semidirect
39. #11924510C22semidirect
44. C4×D148C22semidirect
45. C4×D148C22semidirect
47. #11924468C22semidirect
48. #11924461C22semidirect
49. #11924458C22semidirect
50. #11924458C22semidirect
51. #11924458C22semidirect
52. #11924458C22semidirect
53. #11924458C22semidirect
54. C2×M16×C37C22semidirect
55. C22×C8×C37C22semidirect
57. C4⋊C8×C37C22semidirect
58. C22⋊C8×C37C22semidirect
59. C22⋊C8×C37C22semidirect
60. #97×C37C22semidirect
120. D296D4semidirect
171. D148C2×D4semidirect
180. C8×C37C2×D4semidirect
186. C22×C37AGL(1,ℤ/8)semidirect
240. #435D37semidirect
241. C37#3264semidirect
258. C2×M16C2×D37semidirect
259. C22×C8C2×D37semidirect
277. C4⋊C8C2×D37semidirect
284. C22⋊C8C2×D37semidirect
285. C22⋊C8C2×D37semidirect
286. #97C2×D37semidirect
406. C8D4×D37semidirect
430. C22#11924564semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
C22×D2962
#145581792
D4×D1482
#145579222
#145577862
#145577622
#145577492
#145577292
#145576862
#145576802
#145576692
#145576462
C37×#4352
#326437