Finite Group Databasebeta

← #18006072

Subgroups — #18006072

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×#11924562C211yesmaximal, characteristic, complemented
2C22×#10596939C211yesmaximal, characteristic, complemented
3#14558179C211yesmaximal, characteristic, complemented
4#14557920C211yesmaximal, characteristic, complemented
5#14557784C211yesmaximal, characteristic, complemented
6#14557760C211yesmaximal, characteristic, complemented
7#14557748C211yesmaximal, characteristic, complemented
8#14557725C211yesmaximal, characteristic, complemented
9#14557684C211yesmaximal, characteristic, complemented
10#14557676C211yesmaximal, characteristic, complemented
11#14557667C211yesmaximal, characteristic, complemented
12#14557666C211yesmaximal, characteristic, complemented
13#14557643C211yesmaximal, characteristic, complemented
14#14557605C211yesmaximal, characteristic, complemented
15D42×C37C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic, complemented
17C22×D148C2211yescharacteristic, complemented
18#11924562—24no—
19C2×#10596940C2211yescharacteristic, complemented
20C2×#10596940C2211yescharacteristic, complemented
21C2×#10596940C2211yescharacteristic, complemented
22C2×#10596939—24no—
23C2×#10596939C2211yescharacteristic
24C2×#10596939C2211yescharacteristic
25C2×#10596939C2211yescharacteristic, complemented
26C2×#10596939C2211yescharacteristic, complemented
27C2×#10596939C2211yescharacteristic, complemented
28C2×#10596939C2211yescharacteristic, complemented
29C2×#10596934C2211yescharacteristic, complemented
30C22×#64436C2211yescharacteristic, complemented
31#11924524C2211yescharacteristic, complemented
32#11924521—21no—
33#11924515C2211yescharacteristic, complemented
34#11924510C2211yescharacteristic, complemented
35#11924509—21no—
36#11924504—21no—
37C4×D148C2211yescharacteristic, complemented
38C22⋊C4×D37—21no—
39#11924467C2211yescharacteristic, complemented
40C4⋊#64436C2211yescharacteristic, complemented
41#11924459C2211yescharacteristic, complemented
42#11924457C2211yescharacteristic, complemented
43#11924457C2211yescharacteristic, complemented
44#11924457C2211yescharacteristic, complemented
45#11924456C2211yescharacteristic, complemented
46#11924456C2211yescharacteristic, complemented
47C22⋊#64436C2211yescharacteristic, complemented
48C22⋊#64436C2211yescharacteristic, complemented
49#11924447C2211yescharacteristic, complemented
50C22×D4×C37—21no—
51C22×D4×C37C2211yescharacteristic
52C22×D4×C37C2211yescharacteristic, complemented
53#127×C37C2211yescharacteristic, complemented
54#121×C37—21no—
55#121×C37C2211yescharacteristic
56#121×C37C2211yescharacteristic, complemented
57#120×C37—21no—
58#120×C37—21no—
59C4×D4×C37C2211yescharacteristic
60C4×D4×C37C2211yescharacteristic, complemented
61C24×C37—21no—
62C24×C37—21no—
63C23×D37—21no—
64C2×D4×C37—22no—
65C2×D4×C37—22no—
66C2×D4×C37—21no—
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37—21no—
70C2×D4×C37—21no—
71C2×D4×C37—21no—
72C2×D4×C37—41no—
73C2×D4×C37—41no—
74C2×D4×C37—44no—
75C2×D4×C37D411yescharacteristic
76C2×D4×C37C2311yescharacteristic
77C2×D4×C37C2311yescharacteristic
78C2×D4×C37C2311yescharacteristic
79C22×C4×C37—21no—
80C22×C4×C37C2311yescharacteristic
81C22×C4×C37C2311yescharacteristic
82C2×C22⋊D37—21no—
83C2×C22⋊D37—21no—
84#10596962—22no—
85#10596962—41no—
86C2×D148—22no—
87C2×D148—21no—
88C2×D148—41no—
89C2×D148C2311yescharacteristic
90C2×D148C2311yescharacteristic
91C2×C4×D37—21no—
92C2×C4×D37—21no—
93C2×Dic74C2311yescharacteristic
94C4⋊C4×C37D411yescharacteristic
95C4⋊C4×C37C2311yescharacteristic
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊C4×C37—21no—
99C22⋊C4×C37D411yescharacteristic
100C22⋊C4×C37D411yescharacteristic
101C42×C37C2311yescharacteristic
102C22⋊Dic37—21no—
103#10596940—22no—
104#10596940—22no—
105#10596940—41no—
106#10596939—22no—
107#10596939—22no—
108#10596939—22no—
109#10596939—22no—
110#10596939—41no—
111#10596939D414yescomplemented
112#10596938—21no—
113#10596938—21no—
114#10596938—21no—
115#10596938—21no—
116C4⋊Dic37C2311yescharacteristic
117#10596936—21no—
118#10596934—22no—
119C2×#64436—22no—
120C2×#64436C2311yescharacteristic
121C2×#64436C2311yescharacteristic
122C2×#64436C2311yescharacteristic
123C2×#64436C2311yescharacteristic
124C23×C37—21no—
125C23×C37—21no—
126C23×C37—21no—
127C23×C37—42no—
128C23×C37—42no—
129C23×C37—42no—
130C23×C37—42no—
131C23×C37—81no—
132C23×C37—81no—
133C23×C37C2×D411yescharacteristic
134C23×C37C2×D411yescharacteristic
135C22×D37—21no—
136C22×D37—21no—
137C22×D37—42no—
138C22×D37—42no—
139C22×D37—81no—
140D4×C37—22no—
141D4×C37—21no—
142D4×C37—21no—
143D4×C37—21no—
144D4×C37—21no—
145D4×C37—21no—
146D4×C37—42no—
147D4×C37—42no—
148D4×C37—42no—
149D4×C37—42no—
150D4×C37—42no—
151D4×C37—81no—
152D4×C37C2×D412yes—
153C2×C4×C37—21no—
154C2×C4×C37—21no—
155C2×C4×C37—21no—
156C2×C4×C37—21no—
157C2×C4×C37—21no—
158C2×C4×C37—42no—
159C2×C4×C37C2×D411yescharacteristic
160C2×C4×C37C2×D411yescharacteristic
161C2×C4×C37C2×D411yescharacteristic
162C2×C4×C37C2×D411yescharacteristic
163C2×C4×C37C2411yescharacteristic
164C22⋊D37—42no—
165C22⋊D37—81no—
166C2×Dic37—21no—
167C2×Dic37—21no—
168D148—21no—
169D148—21no—
170D148—21no—
171D148—42no—
172D148C2×D412yescomplemented
173C4×D37—42no—
174C4×D37—81no—
175Dic74—21no—
176Dic74—21no—
177#64436—21no—
178#64436—21no—
179#64436—21no—
180#64436C2×D412yescomplemented
181C22×C37—21no—
182C22×C37—21no—
183C22×C37—21no—
184C22×C37—22no—
185C22×C37—21no—
186C22×C37—21no—
187C22×C37—41no—
188C22×C37—41no—
189C22×C37—41no—
190C22×C37—41no—
191C22×C37—41no—
192C22×C37—41no—
193C22×C37—41no—
194C22×C37—41no—
195C22×C37—84no—
196C22×C37—84no—
197C22×C37AGL(1,ℤ/8)12yescomplemented
198C22×C37C22×D411yescharacteristic
199C2×D37—22no—
200C2×D37—41no—
201C2×D37—41no—
202C2×D37—41no—
203C2×D37—41no—
204C2×D37—41no—
205C2×D37—84no—
206C4×C37—21no—
207C4×C37—21no—
208C4×C37—21no—
209C4×C37—21no—
210C4×C37—41no—
211C4×C37C22×D411yescharacteristic
212C4×C37H(5,𝔽2)11yescharacteristic
213Dic37—41no—
214Dic37—41no—
215#3264—371nomaximal, Sylow
216C2×C37—22no—
217C2×C37—41no—
218C2×C37—42no—
219C2×C37—81no—
220C2×C37—81no—
221C2×C37D4211yescharacteristic
222C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
223C2×C37#57611yescharacteristic
224D37—42no—
225D37—81no—
226C2×AGL(1,ℤ/8)—371no—
227C22×D8—371no—
228#546—371no—
229D42D3711yescharacteristic, complemented
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#435—371no—
241C37#326411yescharacteristic, complemented, Sylow
242C2×#41—371no—
243C22×D4—21no—
244C22×D4—371no—
245C22×D4C2×D3711yescharacteristic
246C22×D4C2×D3711yescharacteristic, complemented
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×M16—371no—
259C22×C8—371no—
260#127C2×D3711yescharacteristic, complemented
261#124—371no—
262#123—741no—
263C22⋊Q8—371no—
264#121—21no—
265#121—371no—
266#121—741no—
267#121C2×D3711yescharacteristic
268#121C2×D3711yescharacteristic, complemented
269#120—21no—
270#120—21no—
271#120—741no—
272C4×D4—371no—
273C4×D4C2×D3711yescharacteristic
274C4×D4C2×D3711yescharacteristic, complemented
275C2×C22⋊C4—741no—
276#106—371no—
277C4⋊C8—371no—
278#103—371no—
279#102—371no—
280#102—371no—
281#102—371no—
282#102—371no—
283#102—371no—
284C22⋊C8—371no—
285C22⋊C8—371no—
286#97—371no—
287C24—21no—
288C24—21no—
289C24—741no—
290#41—742no—
291#41—1481no—
292C2×Q8—371no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—44no—
304C2×D4—371no—
305C2×D4—371no—
306C2×D4—742no—
307C2×D4—741no—
308C2×D4—741no—
309C2×D4—741no—
310C2×D4—1481no—
311C2×D4C22⋊D3711yescharacteristic
312C2×D4C22×D3711yescharacteristic
313C2×D4C22×D3711yescharacteristic
314C2×D4C22×D3711yescharacteristic
315C22×C4—21no—
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—742no—
330C2×C8—371no—
331C2×C8—371no—
332C2×C8—371no—
333C2×C8—371no—
334C2×C8—742no—
335C4⋊C4—371no—
336C4⋊C4—741no—
337C4⋊C4C22⋊D3711yescharacteristic
338C4⋊C4C22×D3711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—741no—
343C22⋊C4—741no—
344C22⋊C4—741no—
345C22⋊C4—741no—
346C22⋊C4—741no—
347C22⋊C4C22⋊D3711yescharacteristic
348C22⋊C4C22⋊D3711yescharacteristic
349C42C22×D3711yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—81no—
358C23—81no—
359C23—2961no—
360C23—741no—
361C23—741no—
362C23—1482no—
363C23—1482no—
364C23C2×C22⋊D3711yescharacteristic
365C23C2×C22⋊D3711yescharacteristic
366Q8—741no—
367Q8—741no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—42no—
379D4—81no—
380D4—372no—
381D4—2961no—
382D4—741no—
383D4—741no—
384D4—741no—
385D4—1482no—
386D4—1482no—
387D4D4×D3712yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—42no—
394C2×C4—2961no—
395C2×C4—741no—
396C2×C4—741no—
397C2×C4—1482no—
398C2×C4C2×C22⋊D3711yescharacteristic
399C2×C4C2×C22⋊D3711yescharacteristic
400C2×C4C2×C22⋊D3711yescharacteristic
401C2×C4C2×C22⋊D3711yescharacteristic
402C2×C4C23×D3711yescharacteristic
403C8—372no—
404C8—741no—
405C8—741no—
406C8—741no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—2964no—
424C22—742no—
425C22—1481no—
426C22—1481no—
427C22—1481no—
428C22—1481no—
429C22—1481no—
430C22#1192456212yescomplemented
431C22C22×C22⋊D3711yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—1481no—
438C4—1481no—
439C4C2×D4×D3711yescharacteristic
440C4#1192458111yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—2961no—
447C2—1482no—
448C2D4×C22⋊D3711yescharacteristic
449C2C2×#1192456211yescharacteristic
450C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingD42×C37C2
socleC22×C37C22×D4
hypercenterD42D37
hypocenterC37#3264
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C22×#10596939C2semidirect
3. #14558179C2semidirect
4. #14557920C2semidirect
5. #14557784C2semidirect
6. #14557760C2semidirect
7. #14557748C2semidirect
8. #14557725C2semidirect
9. #14557684C2semidirect
10. #14557676C2semidirect
11. #14557667C2semidirect
12. #14557666C2semidirect
13. #14557643C2semidirect
14. #14557605C2semidirect
15. D42×C37C2semidirect
16. C2×#10596962C22semidirect
17. C22×D148C22semidirect
19. C2×#10596940C22semidirect
20. C2×#10596940C22semidirect
21. C2×#10596940C22semidirect
25. C2×#10596939C22semidirect
26. C2×#10596939C22semidirect
27. C2×#10596939C22semidirect
28. C2×#10596939C22semidirect
29. C2×#10596934C22semidirect
30. C22×#64436C22semidirect
31. #11924524C22semidirect
33. #11924515C22semidirect
34. #11924510C22semidirect
37. C4×D148C22semidirect
39. #11924467C22semidirect
40. C4⋊#64436C22semidirect
41. #11924459C22semidirect
42. #11924457C22semidirect
43. #11924457C22semidirect
44. #11924457C22semidirect
45. #11924456C22semidirect
46. #11924456C22semidirect
47. C22⋊#64436C22semidirect
48. C22⋊#64436C22semidirect
49. #11924447C22semidirect
52. C22×D4×C37C22semidirect
53. #127×C37C22semidirect
56. #121×C37C22semidirect
60. C4×D4×C37C22semidirect
111. #10596939D4semidirect
172. D148C2×D4semidirect
180. #64436C2×D4semidirect
197. C22×C37AGL(1,ℤ/8)semidirect
229. D42D37semidirect
241. C37#3264semidirect
246. C22×D4C2×D37semidirect
260. #127C2×D37semidirect
268. #121C2×D37semidirect
274. C4×D4C2×D37semidirect
430. C22#11924562semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C22×#105969392
#145581792
#145579202
#145577842
#145577602
#145577482
#145577252
#145576842
#145576762
#145576672
#145576662
#145576432
#145576052
D42×C372
#326437