Finite Group Databasebeta

← #18006083

Subgroups — #18006083

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
2C2×D8×D37C211yesmaximal, characteristic, complemented
3#14558180C211yesmaximal, characteristic, complemented
4#14558167C211yesmaximal, characteristic, complemented
5#14557921C211yesmaximal, characteristic, complemented
6#14557763C211yesmaximal, characteristic, complemented
7#14557747C211yesmaximal, characteristic, complemented
8#14557727C211yesmaximal, characteristic, complemented
9#14557685C211yesmaximal, characteristic, complemented
10#14557676C211yesmaximal, characteristic, complemented
11#14557668C211yesmaximal, characteristic, complemented
12#14557666C211yesmaximal, characteristic, complemented
13#14557644C211yesmaximal, characteristic, complemented
14#14557602C211yesmaximal, characteristic, complemented
15C37×#469C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic, complemented
17C22×D148C2211yescharacteristic, complemented
18C2×D4×D37—21no—
19C2×D4×D37C2211yescharacteristic
20C2×D4×D37C2211yescharacteristic, complemented
21#11924564—24no—
22C2×#10596930C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic, complemented
24C2×#10596940C2211yescharacteristic, complemented
25C2×D296C2211yescharacteristic
26C2×D296C2211yescharacteristic, complemented
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic, complemented
29C2×#10596939C2211yescharacteristic, complemented
30D8×D37—24no—
31C2×C8×D37C2211yescharacteristic, complemented
32#11924532C2211yescharacteristic, complemented
33#11924523C2211yescharacteristic, complemented
34#11924518—21no—
35#11924516C2211yescharacteristic, complemented
36#11924511C2211yescharacteristic
37#11924509—21no—
38#11924507—21no—
39#11924506—21no—
40#11924504—21no—
41#11924504—21no—
42#11924498C2211yescharacteristic, complemented
43#11924498C2211yescharacteristic, complemented
44C4×C22⋊D37C2211yescharacteristic
45C22⋊C4×D37—21no—
46#11924465C2211yescharacteristic, complemented
47#11924459C2211yescharacteristic, complemented
48#11924456C2211yescharacteristic, complemented
49#11924456C2211yescharacteristic, complemented
50#11924456C2211yescharacteristic, complemented
51C22⋊#64436C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic, complemented
53#11924446C2211yescharacteristic, complemented
54C2×D8×C37C2211yescharacteristic, complemented
55C2×M16×C37C2211yescharacteristic, complemented
56#121×C37C2211yescharacteristic, complemented
57#121×C37C2211yescharacteristic, complemented
58#106×C37C2211yescharacteristic, complemented
59#102×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C23×D37—21no—
63C23×D37—21no—
64C2×D4×C37—21no—
65C2×D4×C37—21no—
66C2×D4×C37C2311yescharacteristic
67C2×D4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37—21no—
74C2×C22⋊D37D411yescharacteristic
75D4×D37—22no—
76D4×D37—22no—
77D4×D37—41no—
78D4×D37—41no—
79D4×D37—44no—
80#10596962—22no—
81#10596962—41no—
82C2×D148—22no—
83C2×D148—21no—
84C2×D148—21no—
85C2×D148—41no—
86C2×D148C2311yescharacteristic
87C2×D148C2311yescharacteristic
88C2×D148C2311yescharacteristic
89C2×C4×D37—21no—
90C2×C4×D37—21no—
91C2×C4×D37—21no—
92C2×C4×D37C2311yescharacteristic
93C2×Dic74C2311yescharacteristic
94D8×C37—22no—
95M16×C37—22no—
96C2×C8×C37C2311yescharacteristic
97C2×C8×C37C2311yescharacteristic
98C4⋊C4×C37C2311yescharacteristic
99C4⋊C4×C37C2311yescharacteristic
100C22⋊C4×C37—21no—
101C22⋊C4×C37—21no—
102C22⋊Dic37—21no—
103C22⋊Dic37—21no—
104C22⋊Dic37D411yescharacteristic
105#10596940—41no—
106#10596939—22no—
107#10596939—22no—
108#10596939—41no—
109#10596938—21no—
110#10596938—21no—
111#10596938—21no—
112#10596938—21no—
113#10596938D411yescharacteristic
114C4⋊Dic37—21no—
115#10596936D411yescharacteristic
116C4×Dic37C2311yescharacteristic
117C2×#64436C2311yescharacteristic
118C2×#64436C2311yescharacteristic
119D296—22no—
120D296D414yescomplemented
121#10596930—22no—
122#10596930—22no—
123C8×D37—22no—
124C23×C37—21no—
125C23×C37—21no—
126C23×C37C2×D411yescharacteristic
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—21no—
130C22×D37—42no—
131C22×D37—42no—
132C22×D37—42no—
133C22×D37—42no—
134C22×D37—42no—
135C22×D37—42no—
136C22×D37—81no—
137C22×D37—81no—
138C22×D37—81no—
139C22×D37C2×D411yescharacteristic
140D4×C37—21no—
141D4×C37—21no—
142D4×C37—21no—
143D4×C37—21no—
144D4×C37—42no—
145D4×C37—81no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—21no—
149C2×C4×C37—21no—
150C2×C4×C37C2×D411yescharacteristic
151C2×C4×C37C2411yescharacteristic
152C22⋊D37—22no—
153C22⋊D37—42no—
154C22⋊D37—42no—
155C22⋊D37—42no—
156C22⋊D37—42no—
157C22⋊D37—81no—
158C2×Dic37—21no—
159C2×Dic37C2×D411yescharacteristic
160C2×Dic37C2×D411yescharacteristic
161C2×Dic37C2×D411yescharacteristic
162D148—21no—
163D148—21no—
164D148—21no—
165D148—21no—
166D148—42no—
167D148—42no—
168D148C2×D412yes—
169D148C2×D412yescomplemented
170C4×D37—21no—
171C4×D37—21no—
172C4×D37—42no—
173C4×D37—42no—
174C4×D37—81no—
175Dic74—21no—
176Dic74—21no—
177C8×C37—21no—
178C8×C37C2×D412yescomplemented
179#64436—21no—
180#64436—21no—
181C22×C37—21no—
182C22×C37—21no—
183C22×C37—21no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—41no—
188C22×C37—41no—
189C22×C37—41no—
190C22×C37C22×D411yescharacteristic
191C2×D37—21no—
192C2×D37—21no—
193C2×D37—22no—
194C2×D37—22no—
195C2×D37—41no—
196C2×D37—41no—
197C2×D37—41no—
198C2×D37—41no—
199C2×D37—41no—
200C2×D37—41no—
201C2×D37—41no—
202C2×D37—84no—
203C2×D37—84no—
204C2×D37—84no—
205C2×D37AGL(1,ℤ/8)12yescomplemented
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—41no—
217C2×C37—81no—
218C2×C37—81no—
219C2×C37D4211yescharacteristic
220C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
221C2×C37#57611yescharacteristic
222D37—22no—
223D37—42no—
224D37—42no—
225D37—81no—
226C2×AGL(1,ℤ/8)—371no—
227C22×D8—371no—
228#546—371no—
229D42—371no—
230#496—371no—
231#469D3711yescharacteristic, complemented
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#435—371no—
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—744no—
257C2×D8C2×D3711yescharacteristic, complemented
258C2×M16C2×D3711yescharacteristic, complemented
259C22×C8—371no—
260#127—371no—
261#124—371no—
262#123—741no—
263C22⋊Q8—371no—
264#121—371no—
265#121—741no—
266#121—741no—
267#121C2×D3711yescharacteristic, complemented
268#121C2×D3711yescharacteristic, complemented
269#120—741no—
270#120—741no—
271#120—741no—
272C4×D4—371no—
273C4×D4—371no—
274C4×D4—371no—
275C2×C22⋊C4—741no—
276#106C2×D3711yescharacteristic, complemented
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⋊C8—371no—
286#97—371no—
287C24—741no—
288C24—741no—
289C24—741no—
290#41—742no—
291#41—1481no—
292C2×Q8—371no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—371no—
296C2×D4—371no—
297C2×D4—371no—
298C2×D4—371no—
299C2×D4—742no—
300C2×D4—741no—
301C2×D4—741no—
302C2×D4—741no—
303C2×D4—741no—
304C2×D4—741no—
305C2×D4—742no—
306C2×D4—742no—
307C2×D4—741no—
308C2×D4—741no—
309C2×D4—1481no—
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—742no—
321SD16—742no—
322SD16—1481no—
323D8—22no—
324D8—374no—
325D8—742no—
326D8—742no—
327D8—742no—
328D8—1481no—
329M16—22no—
330C2×C8—371no—
331C2×C8—371no—
332C2×C8—742no—
333C2×C8C22×D3711yescharacteristic
334C2×C8C22×D3711yescharacteristic
335C4⋊C4—371no—
336C4⋊C4—741no—
337C4⋊C4C22×D3711yescharacteristic
338C4⋊C4C22×D3711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—371no—
342C22⋊C4—371no—
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—371no—
353C23—2961no—
354C23—2961no—
355C23—2961no—
356C23—741no—
357C23—741no—
358C23—741no—
359C23—1482no—
360C23—1482no—
361C23—1482no—
362C23—1482no—
363C23—1482no—
364C23—1482no—
365C23D4×D3711yescharacteristic
366Q8—741no—
367Q8—741no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—42no—
373D4—81no—
374D4—372no—
375D4—372no—
376D4—2961no—
377D4—742no—
378D4—741no—
379D4—741no—
380D4—741no—
381D4—741no—
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—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—741no—
405C8—741no—
406C8D4×D3712yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—372no—
417C22—2964no—
418C22—2964no—
419C22—2964no—
420C22—741no—
421C22—741no—
422C22—742no—
423C22—742no—
424C22—1481no—
425C22—1481no—
426C22—1481no—
427C22—1481no—
428C22—1481no—
429C22—1481no—
430C22—1481no—
431C22C2×D4×D3711yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—741no—
436C4—741no—
437C4—741no—
438C4—1481no—
439C4C2×D4×D3711yescharacteristic
440C4#1192458211yescharacteristic
441C2—41no—
442C2—81no—
443C2—81no—
444C2—2961no—
445C2—742no—
446C2—1482no—
447C2—1482no—
448C2#1455816711yescharacteristic
449C2AGL(1,ℤ/8)×D3711yescharacteristic
450C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#469C2
socleC22×C37C22×D4
hypercenter#469D37
hypocenterC37#3264
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. C2×#11924564C2semidirect
2. C2×D8×D37C2semidirect
3. #14558180C2semidirect
4. #14558167C2semidirect
5. #14557921C2semidirect
6. #14557763C2semidirect
7. #14557747C2semidirect
8. #14557727C2semidirect
9. #14557685C2semidirect
10. #14557676C2semidirect
11. #14557668C2semidirect
12. #14557666C2semidirect
13. #14557644C2semidirect
14. #14557602C2semidirect
15. C37×#469C2semidirect
16. C2×#10596962C22semidirect
17. C22×D148C22semidirect
20. C2×D4×D37C22semidirect
22. C2×#10596930C22semidirect
23. C2×#10596930C22semidirect
24. C2×#10596940C22semidirect
26. C2×D296C22semidirect
28. C2×#10596939C22semidirect
29. C2×#10596939C22semidirect
31. C2×C8×D37C22semidirect
32. #11924532C22semidirect
33. #11924523C22semidirect
35. #11924516C22semidirect
42. #11924498C22semidirect
43. #11924498C22semidirect
46. #11924465C22semidirect
47. #11924459C22semidirect
48. #11924456C22semidirect
49. #11924456C22semidirect
50. #11924456C22semidirect
51. C22⋊#64436C22semidirect
52. #11924448C22semidirect
53. #11924446C22semidirect
54. C2×D8×C37C22semidirect
55. C2×M16×C37C22semidirect
56. #121×C37C22semidirect
57. #121×C37C22semidirect
58. #106×C37C22semidirect
59. #102×C37C22semidirect
60. #102×C37C22semidirect
120. D296D4semidirect
169. D148C2×D4semidirect
178. C8×C37C2×D4semidirect
205. C2×D37AGL(1,ℤ/8)semidirect
231. #469D37semidirect
241. C37#3264semidirect
257. C2×D8C2×D37semidirect
258. C2×M16C2×D37semidirect
267. #121C2×D37semidirect
268. #121C2×D37semidirect
276. #106C2×D37semidirect
282. #102C2×D37semidirect
283. #102C2×D37semidirect
406. C8D4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
C2×D8×D372
#145581802
#145581672
#145579212
#145577632
#145577472
#145577272
#145576852
#145576762
#145576682
#145576662
#145576442
#145576022
C37×#4692
#326437