Finite Group Databasebeta

← #18006080

Subgroups — #18006080

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×#11924563C211yesmaximal, characteristic, complemented
2C22×#10596939C211yesmaximal, characteristic, complemented
3#14558174C211yesmaximal, characteristic, complemented
4D4×C22⋊D37C211yesmaximal, characteristic, complemented
5#14557919C211yesmaximal, characteristic, complemented
6#14557785C211yesmaximal, characteristic, complemented
7#14557764C211yesmaximal, characteristic, complemented
8#14557750C211yesmaximal, characteristic, complemented
9#14557727C211yesmaximal, characteristic, complemented
10#14557677C211yesmaximal, characteristic, complemented
11#14557669C211yesmaximal, characteristic, complemented
12#14557668C211yesmaximal, characteristic, complemented
13#14557642C211yesmaximal, characteristic, complemented
14#14557601C211yesmaximal, characteristic, complemented
15C37×#450C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic, complemented
17C22×D148C2211yescharacteristic, complemented
18C22×C22⋊D37—21no—
19C2×D4×D37C2211yescharacteristic, complemented
20#11924563—24no—
21C2×#10596941C2211yescharacteristic, complemented
22C2×D296C2211yescharacteristic, complemented
23C2×D296C2211yescharacteristic, complemented
24C2×#10596939—24no—
25C2×#10596939C2211yescharacteristic
26C2×#10596939C2211yescharacteristic
27C2×#10596939C2211yescharacteristic, complemented
28C2×#10596939C2211yescharacteristic, complemented
29C2×#10596929C2211yescharacteristic, complemented
30C22×#64436C2211yescharacteristic, complemented
31#11924532C2211yescharacteristic, complemented
32#11924525C2211yescharacteristic, complemented
33#11924521—21no—
34#11924511—21no—
35#11924511C2211yescharacteristic, complemented
36#11924510C2211yescharacteristic
37#11924508—21no—
38#11924507C2211yescharacteristic, complemented
39#11924506—21no—
40#11924505—21no—
41#11924504—21no—
42D4×Dic37C2211yescharacteristic, complemented
43#11924498C2211yescharacteristic, complemented
44C4×C22⋊D37C2211yescharacteristic
45C22⋊C4×D37—21no—
46#11924467C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924460C2211yescharacteristic, complemented
49#11924458C2211yescharacteristic, complemented
50#11924458C2211yescharacteristic, complemented
51#11924456C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic, complemented
53#11924446C2211yescharacteristic, complemented
54C22×D4×C37C2211yescharacteristic
55C2×SD16×C37C2211yescharacteristic, complemented
56C2×SD16×C37C2211yescharacteristic, complemented
57C22⋊Q8×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic, complemented
59#102×C37C2211yescharacteristic, complemented
60C22⋊C8×C37C2211yescharacteristic, complemented
61C24×C37—21no—
62C23×D37—21no—
63C23×D37—21no—
64C2×Q8×C37C2311yescharacteristic
65C2×D4×C37—22no—
66C2×D4×C37—21no—
67C2×D4×C37—41no—
68C2×D4×C37C2311yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37—21no—
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C2×C22⋊D37—44no—
77C2×C22⋊D37D411yescharacteristic
78C22×Dic37—21no—
79#10596966—22no—
80#10596966—41no—
81D4×D37—22no—
82D4×D37—41no—
83C2×D148—22no—
84C2×D148—21no—
85C2×D148—21no—
86C2×D148—21no—
87C2×D148—41no—
88C2×D148C2311yescharacteristic
89C2×D148C2311yescharacteristic
90C2×D148C2311yescharacteristic
91C2×C4×D37—21no—
92C2×C4×D37—21no—
93C2×C4×D37C2311yescharacteristic
94SD16×C37—22no—
95SD16×C37—41no—
96C2×C8×C37C2311yescharacteristic
97C2×C8×C37C2311yescharacteristic
98C4⋊C4×C37—21no—
99C4⋊C4×C37C2311yescharacteristic
100C22⋊C4×C37—21no—
101C22⋊Dic37—21no—
102C22⋊Dic37—21no—
103C22⋊Dic37D411yescharacteristic
104#10596941—22no—
105#10596939—22no—
106#10596939—22no—
107#10596939—22no—
108#10596939D414yescomplemented
109#10596938—21no—
110#10596938—21no—
111#10596938—21no—
112#10596938—21no—
113#10596938—21no—
114#10596938D411yescharacteristic
115C4⋊Dic37C2311yescharacteristic
116#10596936D411yescharacteristic
117C4×Dic37C2311yescharacteristic
118C2×#64436—22no—
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121D296—22no—
122D296—41no—
123#10596929—22no—
124C23×C37—21no—
125C23×C37—21no—
126C23×C37—42no—
127C23×C37—42no—
128C23×C37—81no—
129C23×C37C2×D411yescharacteristic
130C22×D37—21no—
131C22×D37—21no—
132C22×D37—21no—
133C22×D37—42no—
134C22×D37—42no—
135C22×D37—42no—
136C22×D37—42no—
137C22×D37—81no—
138C22×D37—81no—
139C22×D37C2×D411yescharacteristic
140Q8×C37—21no—
141Q8×C37—21no—
142D4×C37—21no—
143D4×C37—21no—
144D4×C37—21no—
145D4×C37—42no—
146D4×C37C2×D412yes—
147C2×C4×C37—21no—
148C2×C4×C37—21no—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37C2×D411yescharacteristic
152C2×C4×C37C2411yescharacteristic
153C22⋊D37—22no—
154C22⋊D37—42no—
155C22⋊D37—42no—
156C22⋊D37—42no—
157C22⋊D37—42no—
158C22⋊D37—81no—
159C2×Dic37—21no—
160C2×Dic37—42no—
161C2×Dic37C2×D411yescharacteristic
162C2×Dic37C2×D411yescharacteristic
163C2×Dic37C2×D411yescharacteristic
164D148—21no—
165D148—21no—
166D148—21no—
167D148—21no—
168D148—21no—
169D148—42no—
170D148—42no—
171D148—81no—
172D148C2×D412yescomplemented
173C4×D37—21no—
174C4×D37—21no—
175C4×D37—42no—
176C4×D37—81no—
177C8×C37—21no—
178C8×C37—21no—
179#64436—21no—
180#64436C2×D412yescomplemented
181C22×C37—21no—
182C22×C37—21no—
183C22×C37—22no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—41no—
188C22×C37—41no—
189C22×C37—84no—
190C22×C37AGL(1,ℤ/8)12yescomplemented
191C22×C37C22×D411yescharacteristic
192C2×D37—21no—
193C2×D37—22no—
194C2×D37—21no—
195C2×D37—21no—
196C2×D37—41no—
197C2×D37—41no—
198C2×D37—41no—
199C2×D37—41no—
200C2×D37—41no—
201C2×D37—41no—
202C2×D37—41no—
203C2×D37—41no—
204C2×D37—84no—
205C2×D37—84no—
206C4×C37—21no—
207C4×C37—41no—
208C4×C37—41no—
209C4×C37C22×D411yescharacteristic
210C4×C37H(5,𝔽2)11yescharacteristic
211Dic37—21no—
212Dic37—21no—
213Dic37—21no—
214Dic37—41no—
215#3264—371nomaximal, Sylow
216C2×C37—22no—
217C2×C37—42no—
218C2×C37—81no—
219C2×C37D4211yescharacteristic
220C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
221C2×C37#57611yescharacteristic
222D37—41no—
223D37—42no—
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#450D3711yescharacteristic, complemented
236#449—371no—
237#447—371no—
238#447—371no—
239#442—371no—
240#435—371no—
241C37#326411yescharacteristic, complemented, Sylow
242C2×#41—371no—
243C22×D4—371no—
244C22×D4—371no—
245C22×D4—741no—
246C22×D4C2×D3711yescharacteristic
247AGL(1,ℤ/8)—744no—
248C2×SD16—371no—
249C2×SD16C2×D3711yescharacteristic, complemented
250C2×SD16C2×D3711yescharacteristic, complemented
251C2×D8—371no—
252C2×D8—371no—
253C2×D8—371no—
254C2×D8—371no—
255C2×D8—371no—
256C2×D8—371no—
257C2×D8—744no—
258C2×M16—371no—
259C22×C8—371no—
260#127—371no—
261#124—371no—
262#123—741no—
263C22⋊Q8C2×D3711yescharacteristic, complemented
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×D4—371no—
275C2×C22⋊C4—741no—
276#106—371no—
277C4⋊C8—371no—
278#103—371no—
279#102—371no—
280#102—371no—
281#102—371no—
282#102C2×D3711yescharacteristic, complemented
283#102C2×D3711yescharacteristic, complemented
284C22⋊C8—371no—
285C22⋊C8C2×D3711yescharacteristic, complemented
286#97—371no—
287C24—21no—
288C24—741no—
289C24—741no—
290#41—742no—
291#41—1481no—
292C2×Q8C22×D3711yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—371no—
297C2×D4—371no—
298C2×D4—371no—
299C2×D4—371no—
300C2×D4—742no—
301C2×D4—741no—
302C2×D4—741no—
303C2×D4—741no—
304C2×D4—741no—
305C2×D4—741no—
306C2×D4—742no—
307C2×D4—741no—
308C2×D4—741no—
309C2×D4—741no—
310C2×D4—1481no—
311C2×D4—1481no—
312C2×D4—1484no—
313C2×D4C22×D3711yescharacteristic
314C2×D4C22×D3711yescharacteristic
315C22×C4—371no—
316C22×C4—741no—
317C22×C4—741no—
318C22×C4—741no—
319C22×C4C22×D3711yescharacteristic
320SD16—22no—
321SD16—41no—
322SD16—742no—
323D8—374no—
324D8—742no—
325D8—742no—
326D8—742no—
327D8—742no—
328D8—1481no—
329M16—742no—
330C2×C8—371no—
331C2×C8—371no—
332C2×C8—742no—
333C2×C8C22×D3711yescharacteristic
334C2×C8C22×D3711yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—371no—
337C4⋊C4—371no—
338C4⋊C4C22×D3711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—371no—
341C22⋊C4—371no—
342C22⋊C4—741no—
343C22⋊C4—741no—
344C22⋊C4—741no—
345C22⋊C4—741no—
346C22⋊C4—741no—
347C22⋊C4—741no—
348C22⋊C4—741no—
349C42—371no—
350C23—21no—
351C23—21no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—371no—
356C23—2961no—
357C23—2961no—
358C23—741no—
359C23—741no—
360C23—741no—
361C23—1482no—
362C23—1482no—
363C23—1482no—
364C23—1482no—
365C23D4×D3711yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—42no—
372D4—372no—
373D4—2961no—
374D4—2961no—
375D4—742no—
376D4—741no—
377D4—741no—
378D4—741no—
379D4—741no—
380D4—741no—
381D4—1482no—
382D4—1482no—
383D4—1482no—
384D4—1482no—
385D4—1482no—
386D4—1482no—
387D4D4×D3712yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—371no—
393C2×C4—371no—
394C2×C4—371no—
395C2×C4—2961no—
396C2×C4—741no—
397C2×C4—741no—
398C2×C4—741no—
399C2×C4—1482no—
400C2×C4—1482no—
401C2×C4D4×D3711yescharacteristic
402C2×C4C23×D3711yescharacteristic
403C8—21no—
404C8—21no—
405C8—372no—
406C8—741no—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—84no—
416C22—2964no—
417C22—2964no—
418C22—741no—
419C22—741no—
420C22—741no—
421C22—742no—
422C22—1481no—
423C22—1481no—
424C22—1481no—
425C22—1481no—
426C22—1481no—
427C22—1481no—
428C22—1481no—
429C22—1481no—
430C22#1192456312yescomplemented
431C22C2×D4×D3711yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—741no—
436C4—741no—
437C4—741no—
438C4—1481no—
439C4C2×D4×D3711yescharacteristic
440C4#1192458111yescharacteristic
441C2—22no—
442C2—42no—
443C2—81no—
444C2—2961no—
445C2—2961no—
446C2—1481no—
447C2—1482no—
448C2#1455816511yescharacteristic
449C2C2×#1192456311yescharacteristic
450C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#450C2
socleC22×C37C22×D4
hypercenter#450D37
hypocenterC37#3264
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#11924563C2semidirect
2. C22×#10596939C2semidirect
3. #14558174C2semidirect
4. D4×C22⋊D37C2semidirect
5. #14557919C2semidirect
6. #14557785C2semidirect
7. #14557764C2semidirect
8. #14557750C2semidirect
9. #14557727C2semidirect
10. #14557677C2semidirect
11. #14557669C2semidirect
12. #14557668C2semidirect
13. #14557642C2semidirect
14. #14557601C2semidirect
15. C37×#450C2semidirect
16. C2×#10596966C22semidirect
17. C22×D148C22semidirect
19. C2×D4×D37C22semidirect
21. C2×#10596941C22semidirect
22. C2×D296C22semidirect
23. C2×D296C22semidirect
27. C2×#10596939C22semidirect
28. C2×#10596939C22semidirect
29. C2×#10596929C22semidirect
30. C22×#64436C22semidirect
31. #11924532C22semidirect
32. #11924525C22semidirect
35. #11924511C22semidirect
38. #11924507C22semidirect
42. D4×Dic37C22semidirect
43. #11924498C22semidirect
46. #11924467C22semidirect
47. #11924465C22semidirect
48. #11924460C22semidirect
49. #11924458C22semidirect
50. #11924458C22semidirect
51. #11924456C22semidirect
52. #11924448C22semidirect
53. #11924446C22semidirect
55. C2×SD16×C37C22semidirect
56. C2×SD16×C37C22semidirect
57. C22⋊Q8×C37C22semidirect
58. #102×C37C22semidirect
59. #102×C37C22semidirect
60. C22⋊C8×C37C22semidirect
108. #10596939D4semidirect
172. D148C2×D4semidirect
180. #64436C2×D4semidirect
190. C22×C37AGL(1,ℤ/8)semidirect
235. #450D37semidirect
241. C37#3264semidirect
249. C2×SD16C2×D37semidirect
250. C2×SD16C2×D37semidirect
263. C22⋊Q8C2×D37semidirect
282. #102C2×D37semidirect
283. #102C2×D37semidirect
285. C22⋊C8C2×D37semidirect
430. C22#11924563semidirect

Maximal subgroups

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

subgroupindex
C2×#119245632
C22×#105969392
#145581742
D4×C22⋊D372
#145579192
#145577852
#145577642
#145577502
#145577272
#145576772
#145576692
#145576682
#145576422
#145576012
C37×#4502
#326437