Finite Group Databasebeta

← #20254881

Subgroups — #20254881

Order 6016.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094050C211yesmaximal, characteristic, complemented
2C2×SD16×D47C211yesmaximal, characteristic, complemented
3#15689783C211yesmaximal, characteristic, complemented
4D4×C22⋊D47C211yesmaximal, characteristic, complemented
5#15689509C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689358C211yesmaximal, characteristic, complemented
8#15689340C211yesmaximal, characteristic, complemented
9#15689322C211yesmaximal, characteristic, complemented
10#15689270C211yesmaximal, characteristic, complemented
11#15689260C211yesmaximal, characteristic, complemented
12#15689258C211yesmaximal, characteristic, complemented
13#15689220C211yesmaximal, characteristic, complemented
14#15689197C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic, complemented
17C2×Q8×D47C2211yescharacteristic, complemented
18C22×C22⋊D47—21no—
19C2×D4×D47C2211yescharacteristic
20#13094050—24no—
21C2×#10625325C2211yescharacteristic, complemented
22C2×#10625335C2211yescharacteristic
23C2×#10625335C2211yescharacteristic, complemented
24C2×#10625336C2211yescharacteristic, complemented
25SD16×D47—24no—
26C2×D376C2211yescharacteristic, complemented
27C2×#10625334C2211yescharacteristic
28C2×#10625334C2211yescharacteristic, complemented
29C2×#10625329C2211yescharacteristic, complemented
30C2×C8×D47C2211yescharacteristic, complemented
31#13094020C2211yescharacteristic
32#13094013C2211yescharacteristic, complemented
33#13094010—21no—
34#13094002—21no—
35#13093999C2211yescharacteristic, complemented
36#13093998C2211yescharacteristic
37#13093997—21no—
38#13093996—21no—
39#13093995C2211yescharacteristic
40#13093993—21no—
41#13093992—21no—
42#13093989C2211yescharacteristic, complemented
43D4×Dic47C2211yescharacteristic
44#13093986—21no—
45C4×C22⋊D47C2211yescharacteristic
46#13093957C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093948C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic, complemented
51#13093944C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53#13093934C2211yescharacteristic, complemented
54C22×D4×C47C2211yescharacteristic
55C2×SD16×C47C2211yescharacteristic
56C2×SD16×C47C2211yescharacteristic, complemented
57C22⋊Q8×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59#102×C47C2211yescharacteristic, complemented
60C22⋊C8×C47C2211yescharacteristic, complemented
61C24×C47—21no—
62C23×D47—21no—
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47—22no—
65C2×D4×C47—21no—
66C2×D4×C47—41no—
67C2×D4×C47C2311yescharacteristic
68C2×D4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C2×C22⋊D47—44no—
77C2×C22⋊D47D411yescharacteristic
78C22×Dic47—21no—
79Q8×D47—22no—
80Q8×D47—41no—
81D4×D47—22no—
82D4×D47—41no—
83#10625350—22no—
84#10625350—41no—
85C2×D188—21no—
86C2×D188C2311yescharacteristic
87C2×D188C2311yescharacteristic
88C2×C4×D47—21no—
89C2×C4×D47—21no—
90C2×C4×D47C2311yescharacteristic
91C2×Dic94—21no—
92C2×Dic94C2311yescharacteristic
93SD16×C47—22no—
94SD16×C47—41no—
95C2×C8×C47C2311yescharacteristic
96C2×C8×C47C2311yescharacteristic
97C4⋊C4×C47—21no—
98C4⋊C4×C47C2311yescharacteristic
99C22⋊C4×C47—21no—
100C22⋊Dic47—21no—
101C22⋊Dic47—21no—
102C22⋊Dic47D411yescharacteristic
103#10625336—22no—
104#10625335—22no—
105#10625335D414yescomplemented
106#10625334—22no—
107#10625334—22no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4D411yescharacteristic
113C4⋊Dic47C2311yescharacteristic
114Dic47⋊C4—21no—
115Dic47⋊C4D411yescharacteristic
116C4×Dic47—21no—
117C4×Dic47C2311yescharacteristic
118#10625329—22no—
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121D376—41no—
122#10625325—22no—
123C8×D47—22no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—42no—
127C23×C47—42no—
128C23×C47—81no—
129C23×C47C2×D411yescharacteristic
130C22×D47—21no—
131C22×D47—21no—
132C22×D47—42no—
133C22×D47—42no—
134C22×D47—81no—
135C22×D47C2×D411yescharacteristic
136Q8×C47—21no—
137Q8×C47—21no—
138D4×C47—21no—
139D4×C47—21no—
140D4×C47—21no—
141D4×C47—42no—
142D4×C47C2×D412yes—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2411yescharacteristic
149C22⋊D47—22no—
150C22⋊D47—42no—
151C22⋊D47—42no—
152C22⋊D47—42no—
153C22⋊D47—42no—
154C22⋊D47—42no—
155C22⋊D47—81no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—42no—
159C2×Dic47C2×D411yescharacteristic
160C2×Dic47C2×D411yescharacteristic
161C2×Dic47C2×D411yescharacteristic
162D188—21no—
163D188—21no—
164D188—21no—
165D188—21no—
166D188—42no—
167C4×D47—21no—
168C4×D47—21no—
169C4×D47—42no—
170C4×D47—42no—
171Dic94—21no—
172Dic94—42no—
173Dic94C2×D412yescomplemented
174C8×C47—21no—
175C8×C47—21no—
176C47⋊C8—21no—
177C47⋊C8C2×D412yescomplemented
178C22×C47—21no—
179C22×C47—22no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—84no—
188C22×C47C22×D411yescharacteristic
189C2×D47—21no—
190C2×D47—21no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—84no—
198C2×D47AGL(1,ℤ/8)12yescomplemented
199C4×C47—21no—
200C4×C47—41no—
201C4×C47—41no—
202C4×C47C22×D411yescharacteristic
203C4×C47H(5,𝔽2)11yescharacteristic
204Dic47—22no—
205Dic47—21no—
206Dic47—21no—
207Dic47—21no—
208Dic47—41no—
209#3265—471nomaximal, Sylow
210C2×C47—42no—
211C2×C47—41no—
212C2×C47—81no—
213C2×C47D4211yescharacteristic
214C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C47#57711yescharacteristic
216D47—22no—
217D47—81no—
218D47—81no—
219C2×AGL(1,ℤ/8)—471no—
220C22×SD16—471no—
221#548—471no—
222D42—471no—
223#496—471no—
224#468—471no—
225#466—471no—
226#463—471no—
227#460—471no—
228#450D4711yescharacteristic, complemented
229#449—471no—
230#448—471no—
231#447—471no—
232#440—471no—
233#435—471no—
234C47#326511yescharacteristic, complemented, Sylow
235C2×#41—471no—
236C22×Q8—471no—
237C22×D4—471no—
238C22×D4—941no—
239C22×D4C2×D4711yescharacteristic
240AGL(1,ℤ/8)—944no—
241C2×SD16—471no—
242C2×SD16—471no—
243C2×SD16—471no—
244C2×SD16—471no—
245C2×SD16—944no—
246C2×SD16C2×D4711yescharacteristic
247C2×SD16C2×D4711yescharacteristic, complemented
248C2×D8—471no—
249C2×D8—471no—
250C2×D8—471no—
251C2×M16—471no—
252C22×C8—471no—
253#127—471no—
254#124—471no—
255#124—941no—
256C22⋊Q8—941no—
257C22⋊Q8C2×D4711yescharacteristic, complemented
258#121—471no—
259#121—471no—
260#121—471no—
261#121—941no—
262#121—941no—
263#120—941no—
264#120—941no—
265C4×Q8—471no—
266C4×D4—471no—
267C4×D4—471no—
268C4×D4—941no—
269#107—471no—
270C4⋊C8—471no—
271#103—471no—
272#103—471no—
273#102—471no—
274#102—471no—
275#102C2×D4711yescharacteristic
276#102C2×D4711yescharacteristic, complemented
277C22⋊C8—471no—
278C22⋊C8C2×D4711yescharacteristic, complemented
279#97—471no—
280C24—21no—
281C24—941no—
282#41—942no—
283#41—1881no—
284C2×Q8—471no—
285C2×Q8—941no—
286C2×Q8—942no—
287C2×Q8—1881no—
288C2×Q8C22×D4711yescharacteristic
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—471no—
293C2×D4—471no—
294C2×D4—471no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—941no—
298C2×D4—941no—
299C2×D4—942no—
300C2×D4—941no—
301C2×D4—941no—
302C2×D4—941no—
303C2×D4—1881no—
304C2×D4—1884no—
305C2×D4C22×D4711yescharacteristic
306C2×D4C22×D4711yescharacteristic
307C22×C4—471no—
308C22×C4—941no—
309C22×C4—941no—
310C22×C4—941no—
311C22×C4C22×D4711yescharacteristic
312SD16—22no—
313SD16—41no—
314SD16—474no—
315SD16—942no—
316SD16—942no—
317SD16—942no—
318D8—942no—
319D8—942no—
320D8—1881no—
321M16—942no—
322C2×C8—471no—
323C2×C8—471no—
324C2×C8—942no—
325C2×C8C22×D4711yescharacteristic
326C2×C8C22×D4711yescharacteristic
327C4⋊C4—21no—
328C4⋊C4—471no—
329C4⋊C4—471no—
330C4⋊C4—941no—
331C4⋊C4C22×D4711yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—471no—
334C22⋊C4—471no—
335C22⋊C4—941no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C22⋊C4—941no—
339C22⋊C4—941no—
340C22⋊C4—941no—
341C42—471no—
342C42—941no—
343C23—21no—
344C23—21no—
345C23—42no—
346C23—42no—
347C23—81no—
348C23—471no—
349C23—941no—
350C23—941no—
351C23—3761no—
352C23—1882no—
353C23—1882no—
354C23D4×D4711yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—472no—
358Q8—941no—
359Q8—1882no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—942no—
365D4—941no—
366D4—941no—
367D4—941no—
368D4—941no—
369D4—3761no—
370D4—1882no—
371D4—1882no—
372D4—1882no—
373D4—1882no—
374D4—1882no—
375D4—1882no—
376D4D4×D4712yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—471no—
382C2×C4—471no—
383C2×C4—471no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—1882no—
389C2×C4—1882no—
390C2×C4—1882no—
391C2×C4D4×D4711yescharacteristic
392C2×C4C23×D4711yescharacteristic
393C8—21no—
394C8—21no—
395C8—472no—
396C8—941no—
397C22—21no—
398C22—22no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—84no—
407C22—472no—
408C22—941no—
409C22—941no—
410C22—3764no—
411C22—1881no—
412C22—1881no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22—1881no—
417C22C2×D4×D4711yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—941no—
422C4—942no—
423C4—941no—
424C4—941no—
425C4—1881no—
426C4C2×D4×D4711yescharacteristic
427C4#1309406911yescharacteristic
428C2—41no—
429C2—42no—
430C2—81no—
431C2—942no—
432C2—3761no—
433C2—3761no—
434C2#1568975511yescharacteristic
435C2AGL(1,ℤ/8)×D4711yescharacteristic
436C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3265
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#13094050C2semidirect
2. C2×SD16×D47C2semidirect
3. #15689783C2semidirect
4. D4×C22⋊D47C2semidirect
5. #15689509C2semidirect
6. #15689371C2semidirect
7. #15689358C2semidirect
8. #15689340C2semidirect
9. #15689322C2semidirect
10. #15689270C2semidirect
11. #15689260C2semidirect
12. #15689258C2semidirect
13. #15689220C2semidirect
14. #15689197C2semidirect
15. C47×#450C2semidirect
16. C2×#10625350C22semidirect
17. C2×Q8×D47C22semidirect
21. C2×#10625325C22semidirect
23. C2×#10625335C22semidirect
24. C2×#10625336C22semidirect
26. C2×D376C22semidirect
28. C2×#10625334C22semidirect
29. C2×#10625329C22semidirect
30. C2×C8×D47C22semidirect
32. #13094013C22semidirect
35. #13093999C22semidirect
42. #13093989C22semidirect
46. #13093957C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093948C22semidirect
50. #13093946C22semidirect
51. #13093944C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. #13093934C22semidirect
56. C2×SD16×C47C22semidirect
57. C22⋊Q8×C47C22semidirect
59. #102×C47C22semidirect
60. C22⋊C8×C47C22semidirect
105. #10625335D4semidirect
173. Dic94C2×D4semidirect
177. C47⋊C8C2×D4semidirect
198. C2×D47AGL(1,ℤ/8)semidirect
228. #450D47semidirect
234. C47#3265semidirect
247. C2×SD16C2×D47semidirect
257. C22⋊Q8C2×D47semidirect
276. #102C2×D47semidirect
278. C22⋊C8C2×D47semidirect