Finite Group Databasebeta

← #18006082

Subgroups — #18006082

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
2C2×D8×D37C211yesmaximal, characteristic, complemented
3#14558176C211yesmaximal, characteristic, complemented
4D4×D148C211yesmaximal, characteristic, complemented
5#14557923C211yesmaximal, characteristic, complemented
6#14557785C211yesmaximal, characteristic, complemented
7#14557765C211yesmaximal, characteristic, complemented
8#14557729C211yesmaximal, characteristic, complemented
9#14557682C211yesmaximal, characteristic, complemented
10#14557681C211yesmaximal, characteristic, complemented
11#14557668C211yesmaximal, characteristic, complemented
12#14557665C211yesmaximal, characteristic, complemented
13#14557643C211yesmaximal, characteristic, complemented
14#14557603C211yesmaximal, characteristic, complemented
15C37×#463C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic, complemented
17C22×D148—21no—
18C2×D4×D37C2211yescharacteristic
19C2×D4×D37C2211yescharacteristic, complemented
20C2×D4×D37C2211yescharacteristic, complemented
21#11924563—24no—
22C2×#10596941C2211yescharacteristic, complemented
23C2×#10596941C2211yescharacteristic, complemented
24C2×D296C2211yescharacteristic, complemented
25C2×D296C2211yescharacteristic, complemented
26C2×#10596939C2211yescharacteristic
27C2×#10596939C2211yescharacteristic, complemented
28C2×#10596939C2211yescharacteristic, complemented
29D8×D37—24no—
30C2×#10596929C2211yescharacteristic, complemented
31C2×C8×D37C2211yescharacteristic, complemented
32#11924533C2211yescharacteristic, complemented
33#11924518—21no—
34#11924512C2211yescharacteristic, complemented
35#11924511C2211yescharacteristic
36#11924511C2211yescharacteristic, complemented
37#11924510—21no—
38#11924509—21no—
39#11924507C2211yescharacteristic, complemented
40#11924506—21no—
41#11924506—21no—
42#11924506—21no—
43C4×D148C2211yescharacteristic
44C4×D148C2211yescharacteristic, complemented
45C22⋊C4×D37—21no—
46#11924467C2211yescharacteristic, complemented
47#11924458C2211yescharacteristic, complemented
48#11924458C2211yescharacteristic, complemented
49#11924457C2211yescharacteristic, complemented
50#11924456C2211yescharacteristic, complemented
51#11924448C2211yescharacteristic, complemented
52#11924448C2211yescharacteristic, complemented
53#11924447C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic, complemented
55C2×D8×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic, complemented
57C4×D4×C37C2211yescharacteristic, complemented
58C4⋊C8×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C23×D37—21no—
63C23×D37—21no—
64C2×Q8×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C2×D4×C37C2311yescharacteristic
67C22×C4×C37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72#10596966—22no—
73#10596966—41no—
74D4×D37—22no—
75D4×D37—22no—
76D4×D37—22no—
77D4×D37—41no—
78D4×D37—41no—
79D4×D37—41no—
80C2×D148—21no—
81C2×D148—21no—
82C2×D148—21no—
83C2×D148—21no—
84C2×D148—21no—
85C2×D148—44no—
86C2×D148D411yescharacteristic
87C2×D148C2311yescharacteristic
88C2×D148C2311yescharacteristic
89C2×D148C2311yescharacteristic
90C2×C4×D37—21no—
91C2×C4×D37—21no—
92C2×C4×D37C2311yescharacteristic
93C2×C4×D37C2311yescharacteristic
94SD16×C37—22no—
95D8×C37—22no—
96C2×C8×C37C2311yescharacteristic
97C2×C8×C37C2311yescharacteristic
98C4⋊C4×C37C2311yescharacteristic
99C22⋊C4×C37—21no—
100C22⋊C4×C37—21no—
101C22⋊C4×C37—21no—
102C42×C37C2311yescharacteristic
103C22⋊Dic37—21no—
104#10596941—22no—
105#10596941—41no—
106#10596939—22no—
107#10596939—41no—
108#10596939D414yescomplemented
109#10596938—21no—
110#10596938—21no—
111#10596938—21no—
112#10596938—21no—
113#10596938D411yescharacteristic
114#10596938D411yescharacteristic
115C4⋊Dic37D411yescharacteristic
116C4⋊Dic37C2311yescharacteristic
117#10596936—21no—
118C2×#64436C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120D296—22no—
121D296—22no—
122#10596929—22no—
123C8×D37—22no—
124C23×C37—21no—
125C23×C37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—42no—
130C22×D37—42no—
131C22×D37—42no—
132C22×D37—42no—
133C22×D37—42no—
134C22×D37—42no—
135C22×D37—81no—
136C22×D37—81no—
137C22×D37—81no—
138C22×D37C2×D411yescharacteristic
139C22×D37C2×D411yescharacteristic
140Q8×C37—21no—
141Q8×C37—21no—
142D4×C37—21no—
143D4×C37—21no—
144D4×C37—21no—
145D4×C37C2×D412yes—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—42no—
149C2×C4×C37C2×D411yescharacteristic
150C2×C4×C37C2×D411yescharacteristic
151C2×C4×C37C2411yescharacteristic
152C22⋊D37—42no—
153C22⋊D37—42no—
154C22⋊D37—42no—
155C22⋊D37—81no—
156C2×Dic37—21no—
157C2×Dic37C2×D411yescharacteristic
158C2×Dic37C2×D411yescharacteristic
159D148—22no—
160D148—21no—
161D148—21no—
162D148—21no—
163D148—21no—
164D148—21no—
165D148—42no—
166D148—42no—
167D148—42no—
168D148—42no—
169D148—81no—
170D148C2×D412yescomplemented
171C4×D37—21no—
172C4×D37—21no—
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—22no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37C22×D411yescharacteristic
188C2×D37—21no—
189C2×D37—21no—
190C2×D37—21no—
191C2×D37—22no—
192C2×D37—21no—
193C2×D37—21no—
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—84no—
203C2×D37—84no—
204C2×D37—84no—
205C2×D37AGL(1,ℤ/8)12yescomplemented
206C4×C37—21no—
207C4×C37—21no—
208C4×C37—41no—
209C4×C37—41no—
210C4×C37C22×D411yescharacteristic
211C4×C37H(5,𝔽2)11yescharacteristic
212Dic37—21no—
213Dic37—21no—
214Dic37—41no—
215#3264—371nomaximal, Sylow
216C2×C37—42no—
217C2×C37—81no—
218C2×C37D4211yescharacteristic
219C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C37#57611yescharacteristic
221D37—22no—
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#463D3711yescharacteristic, complemented
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×SD16C2×D3711yescharacteristic, complemented
251C2×D8—371no—
252C2×D8—371no—
253C2×D8—371no—
254C2×D8—371no—
255C2×D8—371no—
256C2×D8—744no—
257C2×D8C2×D3711yescharacteristic
258C2×M16—371no—
259C22×C8—371no—
260#127—371no—
261#124C2×D3711yescharacteristic, complemented
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, complemented
275C2×C22⋊C4—741no—
276#106—371no—
277C4⋊C8C2×D3711yescharacteristic, complemented
278#103C2×D3711yescharacteristic, complemented
279#102—371no—
280#102—371no—
281#102—371no—
282#102—371no—
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×Q8C22×D3711yescharacteristic
293C2×D4—371no—
294C2×D4—371no—
295C2×D4—371no—
296C2×D4—371no—
297C2×D4—741no—
298C2×D4—741no—
299C2×D4—741no—
300C2×D4—741no—
301C2×D4—741no—
302C2×D4—741no—
303C2×D4—742no—
304C2×D4—741no—
305C2×D4—742no—
306C2×D4—742no—
307C2×D4—741no—
308C2×D4—741no—
309C2×D4—1484no—
310C2×D4—1481no—
311C2×D4—1481no—
312C2×D4—1481no—
313C2×D4C22×D3711yescharacteristic
314C2×D4C22×D3711yescharacteristic
315C22×C4—21no—
316C22×C4—371no—
317C22×C4—371no—
318C22×C4—741no—
319C22×C4—741no—
320SD16—22no—
321SD16—742no—
322SD16—1481no—
323D8—22no—
324D8—374no—
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—371no—
336C4⋊C4—371no—
337C4⋊C4—741no—
338C4⋊C4C22×D3711yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—371no—
343C22⋊C4—371no—
344C22⋊C4—741no—
345C22⋊C4—741no—
346C22⋊C4—741no—
347C22⋊C4—741no—
348C22⋊C4—741no—
349C42C22×D3711yescharacteristic
350C23—21no—
351C23—21no—
352C23—371no—
353C23—371no—
354C23—2961no—
355C23—2961no—
356C23—2961no—
357C23—741no—
358C23—741no—
359C23—741no—
360C23—1482no—
361C23—1482no—
362C23—1482no—
363C23—1482no—
364C23—1482no—
365C23—1482no—
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—372no—
372D4—2961no—
373D4—2961no—
374D4—742no—
375D4—741no—
376D4—741no—
377D4—741no—
378D4—741no—
379D4—741no—
380D4—1482no—
381D4—1482no—
382D4—1482no—
383D4—1482no—
384D4—1482no—
385D4—1482no—
386D4—1482no—
387D4D4×D3712yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—371no—
392C2×C4—371no—
393C2×C4—2961no—
394C2×C4—741no—
395C2×C4—741no—
396C2×C4—741no—
397C2×C4—741no—
398C2×C4—741no—
399C2×C4—1482no—
400C2×C4D4×D3711yescharacteristic
401C2×C4D4×D3711yescharacteristic
402C2×C4C23×D3711yescharacteristic
403C8—21no—
404C8—21no—
405C8—372no—
406C8—741no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—372no—
414C22—2964no—
415C22—2964no—
416C22—2964no—
417C22—741no—
418C22—741no—
419C22—741no—
420C22—741no—
421C22—741no—
422C22—742no—
423C22—1481no—
424C22—1481no—
425C22—1481no—
426C22—1481no—
427C22—1481no—
428C22—1481no—
429C22—1481no—
430C22—1481no—
431C22C2×D4×D3711yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—741no—
437C4—741no—
438C4—1481no—
439C4C2×D4×D3711yescharacteristic
440C4#1192458211yescharacteristic
441C2—42no—
442C2—81no—
443C2—2961no—
444C2—2961no—
445C2—742no—
446C2—1481no—
447C2—1482no—
448C2#1455816711yescharacteristic
449C2AGL(1,ℤ/8)×D3711yescharacteristic
450C2#1455833511yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#463C2
socleC22×C37C22×D4
hypercenter#463D37
hypocenterC37#3264
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#11924563C2semidirect
2. C2×D8×D37C2semidirect
3. #14558176C2semidirect
4. D4×D148C2semidirect
5. #14557923C2semidirect
6. #14557785C2semidirect
7. #14557765C2semidirect
8. #14557729C2semidirect
9. #14557682C2semidirect
10. #14557681C2semidirect
11. #14557668C2semidirect
12. #14557665C2semidirect
13. #14557643C2semidirect
14. #14557603C2semidirect
15. C37×#463C2semidirect
16. C2×#10596966C22semidirect
19. C2×D4×D37C22semidirect
20. C2×D4×D37C22semidirect
22. C2×#10596941C22semidirect
23. C2×#10596941C22semidirect
24. C2×D296C22semidirect
25. C2×D296C22semidirect
27. C2×#10596939C22semidirect
28. C2×#10596939C22semidirect
30. C2×#10596929C22semidirect
31. C2×C8×D37C22semidirect
32. #11924533C22semidirect
34. #11924512C22semidirect
36. #11924511C22semidirect
39. #11924507C22semidirect
44. C4×D148C22semidirect
46. #11924467C22semidirect
47. #11924458C22semidirect
48. #11924458C22semidirect
49. #11924457C22semidirect
50. #11924456C22semidirect
51. #11924448C22semidirect
52. #11924448C22semidirect
53. #11924447C22semidirect
54. C2×SD16×C37C22semidirect
56. #124×C37C22semidirect
57. C4×D4×C37C22semidirect
58. C4⋊C8×C37C22semidirect
59. #103×C37C22semidirect
60. #102×C37C22semidirect
108. #10596939D4semidirect
170. D148C2×D4semidirect
180. #64436C2×D4semidirect
205. C2×D37AGL(1,ℤ/8)semidirect
233. #463D37semidirect
241. C37#3264semidirect
250. C2×SD16C2×D37semidirect
261. #124C2×D37semidirect
274. C4×D4C2×D37semidirect
277. C4⋊C8C2×D37semidirect
278. #103C2×D37semidirect
283. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245632
C2×D8×D372
#145581762
D4×D1482
#145579232
#145577852
#145577652
#145577292
#145576822
#145576812
#145576682
#145576652
#145576432
#145576032
C37×#4632
#326437