Finite Group Databasebeta

← #20254992

Subgroups — #20254992

Order 6016.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094051C211yesmaximal, characteristic, complemented
2C2×#13094049C211yesmaximal, characteristic, complemented
3#15689764C211yesmaximal, characteristic, complemented
4#15689761C211yesmaximal, characteristic, complemented
5#15689508C211yesmaximal, characteristic, complemented
6#15689372C211yesmaximal, characteristic, complemented
7#15689371C211yesmaximal, characteristic, complemented
8#15689341C211yesmaximal, characteristic, complemented
9#15689340C211yesmaximal, characteristic, complemented
10#15689284C211yesmaximal, characteristic, complemented
11#15689259C211yesmaximal, characteristic, complemented
12#15689258C211yesmaximal, characteristic, complemented
13#15689203C211yesmaximal, characteristic, complemented
14#15689198C211yesmaximal, characteristic, complemented
15C47×#452C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C22×D188C2211yescharacteristic, complemented
18C2×D4×D47C2211yescharacteristic, complemented
19#13094051—24no—
20#13094049—24no—
21C2×#10625336C2211yescharacteristic, complemented
22C2×#10625336C2211yescharacteristic, complemented
23C2×#10625336C2211yescharacteristic, complemented
24C2×D376C2211yescharacteristic
25C2×D376C2211yescharacteristic
26C2×#10625334C2211yescharacteristic
27C2×#10625334C2211yescharacteristic
28C2×#10625329C2211yescharacteristic, complemented
29C2×#10625324C2211yescharacteristic, complemented
30#13094013C2211yescharacteristic, complemented
31#13094013C2211yescharacteristic, complemented
32#13094009—21no—
33#13094007—21no—
34#13094000C2211yescharacteristic, complemented
35#13093999—21no—
36#13093999C2211yescharacteristic
37#13093998C2211yescharacteristic
38#13093996—21no—
39#13093994—21no—
40#13093992—21no—
41D4×Dic47C2211yescharacteristic, complemented
42#13093986C2211yescharacteristic, complemented
43C4×C22⋊D47C2211yescharacteristic
44C2×(C2×D47)⋊C4—21no—
45C22⋊C4×D47—21no—
46#13093957C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093948C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic, complemented
50#13093946C2211yescharacteristic, complemented
51#13093944C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53C8×Dic47C2211yescharacteristic, complemented
54C2×#41×C47C2211yescharacteristic
55C2×Q16×C47C2211yescharacteristic, complemented
56C2×SD16×C47C2211yescharacteristic, complemented
57C22⋊Q8×C47C2211yescharacteristic, complemented
58#103×C47C2211yescharacteristic, complemented
59#102×C47C2211yescharacteristic, complemented
60C22⋊C8×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63#41×C47—22no—
64#41×C47—41no—
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C2×D4×C47—21no—
68C2×D4×C47C2311yescharacteristic
69C22×C4×C47—21no—
70C22×C4×C47C2311yescharacteristic
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47D411yescharacteristic
74C22×Dic47—21no—
75#10625354—22no—
76#10625354—41no—
77D4×D47—22no—
78D4×D47—41no—
79C2×D188—22no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188—41no—
84C2×D188C2311yescharacteristic
85C2×D188C2311yescharacteristic
86C2×D188C2311yescharacteristic
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47C2311yescharacteristic
90Q16×C47—41no—
91SD16×C47—22no—
92C2×C8×C47C2311yescharacteristic
93C2×C8×C47C2311yescharacteristic
94C4⋊C4×C47—21no—
95C4⋊C4×C47C2311yescharacteristic
96C22⋊C4×C47—21no—
97C22⋊Dic47—21no—
98C22⋊Dic47D411yescharacteristic
99#10625336—22no—
100#10625336—22no—
101#10625336—22no—
102#10625334—22no—
103#10625334D414yescomplemented
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
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×Dic47C2311yescharacteristic
117#10625329—22no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120D376—22no—
121D376—41no—
122#10625324—22no—
123C23×C47—21no—
124C23×C47C2×D411yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—81no—
133C22×D47—81no—
134C22×D47C2×D411yescharacteristic
135Q8×C47—21no—
136Q8×C47—21no—
137Q8×C47—21no—
138Q8×C47—21no—
139D4×C47—21no—
140D4×C47—42no—
141D4×C47C2×D412yes—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—42no—
148C2×C4×C47C2×D411yescharacteristic
149C2×C4×C47C2411yescharacteristic
150C22⋊D47—41no—
151C22⋊D47—42no—
152C22⋊D47—81no—
153C2×Dic47—21no—
154C2×Dic47—81no—
155C2×Dic47C2×D411yescharacteristic
156C2×Dic47C2×D411yescharacteristic
157C2×Dic47C2×D411yescharacteristic
158D188—21no—
159D188—21no—
160D188—21no—
161D188—21no—
162D188—21no—
163D188—42no—
164D188—42no—
165D188—81no—
166D188C2×D412yes—
167C4×D47—21no—
168C4×D47—21no—
169C4×D47—42no—
170C4×D47—81no—
171C8×C47—21no—
172C8×C47—21no—
173C47⋊C8—21no—
174C47⋊C8C2×D412yes—
175C22×C47—22no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47C22×D411yescharacteristic
182C2×D47—21no—
183C2×D47—22no—
184C2×D47—21no—
185C2×D47—21no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—84no—
195C2×D47—84no—
196C4×C47—21no—
197C4×C47—41no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47C22×D411yescharacteristic
201C4×C47H(5,𝔽2)11yescharacteristic
202Dic47—21no—
203Dic47—21no—
204Dic47—21no—
205Dic47—41no—
206#3273—471nomaximal, Sylow
207C2×C47—41no—
208C2×C47—42no—
209C2×C47D4211yescharacteristic
210C2×C47#57511yescharacteristic
211C2×C47#57611yescharacteristic
212D47—41no—
213D47—42no—
214D47—81no—
215D47—81no—
216C2×AGL(1,ℤ/8)—471no—
217C2×AGL(1,ℤ/8)—471no—
218#546—471no—
219#546—471no—
220#495—471no—
221#468—471no—
222#468—471no—
223#463—471no—
224#463—471no—
225#452—471no—
226#452D4711yescharacteristic, complemented
227#447—471no—
228#447—471no—
229C4×D8—471no—
230#436—471no—
231C47#327311yescharacteristic, complemented, Sylow
232C2×#41—471no—
233C2×#41C2×D4711yescharacteristic
234C22×D4—471no—
235C22×D4—471no—
236AGL(1,ℤ/8)—944no—
237AGL(1,ℤ/8)—944no—
238C2×Q16C2×D4711yescharacteristic, complemented
239C2×SD16—471no—
240C2×SD16—471no—
241C2×SD16—471no—
242C2×SD16C2×D4711yescharacteristic, complemented
243C2×D8—471no—
244C2×D8—471no—
245C2×D8—471no—
246C2×D8—471no—
247C2×M16—471no—
248C2×M16—471no—
249#124—471no—
250#124—471no—
251#123—941no—
252#123—941no—
253C22⋊Q8—471no—
254C22⋊Q8C2×D4711yescharacteristic, complemented
255#121—471no—
256#121—471no—
257#121—941no—
258#121—941no—
259#120—941no—
260#120—941no—
261C4×D4—471no—
262C4×D4—471no—
263C4×D4—471no—
264C2×C22⋊C4—941no—
265C2×C22⋊C4—941no—
266#107—471no—
267C4⋊C8—471no—
268#103—471no—
269#103C2×D4711yescharacteristic, complemented
270#102—471no—
271#102—471no—
272#102—471no—
273#102C2×D4711yescharacteristic, complemented
274C22⋊C8—471no—
275C22⋊C8C2×D4711yescharacteristic, complemented
276C4×C8—471no—
277C24—941no—
278C24—941no—
279#41—22no—
280#41—41no—
281#41—942no—
282#41—1881no—
283C2×Q8C22×D4711yescharacteristic
284C2×Q8C22×D4711yescharacteristic
285C2×D4—21no—
286C2×D4—471no—
287C2×D4—471no—
288C2×D4—471no—
289C2×D4—471no—
290C2×D4—942no—
291C2×D4—941no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—942no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—1881no—
298C2×D4—1881no—
299C2×D4C22×D4711yescharacteristic
300C22×C4—21no—
301C22×C4—471no—
302C22×C4—941no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4C22×D4711yescharacteristic
306Q16—41no—
307SD16—22no—
308SD16—942no—
309SD16—942no—
310SD16—942no—
311D8—474no—
312D8—942no—
313D8—942no—
314D8—1881no—
315M16—942no—
316M16—942no—
317C2×C8—471no—
318C2×C8—471no—
319C2×C8C22×D4711yescharacteristic
320C2×C8C22×D4711yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—471no—
323C4⋊C4—471no—
324C4⋊C4—941no—
325C4⋊C4C22×D4711yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—471no—
328C22⋊C4—471no—
329C22⋊C4—941no—
330C22⋊C4—941no—
331C22⋊C4—941no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C42—471no—
339C23—21no—
340C23—471no—
341C23—941no—
342C23—941no—
343C23—941no—
344C23—3761no—
345C23—3761no—
346C23—1882no—
347C23—1882no—
348C23—1882no—
349C23—1882no—
350C23D4×D4711yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—21no—
354Q8—21no—
355D4—21no—
356D4—42no—
357D4—472no—
358D4—941no—
359D4—941no—
360D4—941no—
361D4—941no—
362D4—941no—
363D4—3761no—
364D4—3761no—
365D4—1882no—
366D4—1882no—
367D4—1881no—
368D4—1882no—
369D4D4×D4712yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—471no—
377C2×C4—471no—
378C2×C4—471no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—3761no—
383C2×C4—3761no—
384C2×C4—1882no—
385C2×C4D4×D4711yescharacteristic
386C2×C4C23×D4711yescharacteristic
387C8—21no—
388C8—21no—
389C8—472no—
390C8—941no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—941no—
398C22—942no—
399C22—941no—
400C22—941no—
401C22—3764no—
402C22—3764no—
403C22—1881no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22—1881no—
409C22—1881no—
410C22—1881no—
411C22C2×D4×D4711yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—941no—
417C4—941no—
418C4—941no—
419C4—1881no—
420C4C2×D4×D4711yescharacteristic
421C4#1309406911yescharacteristic
422C2—41no—
423C2—42no—
424C2—3761no—
425C2—3761no—
426C2—1881no—
427C2—1882no—
428C2#1568975511yescharacteristic
429C2#1568992211yescharacteristic
430C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#452C2
socleC22×C47C22×D4
hypercenter#452D47
hypocenterC47#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. C2×#13094049C2semidirect
3. #15689764C2semidirect
4. #15689761C2semidirect
5. #15689508C2semidirect
6. #15689372C2semidirect
7. #15689371C2semidirect
8. #15689341C2semidirect
9. #15689340C2semidirect
10. #15689284C2semidirect
11. #15689259C2semidirect
12. #15689258C2semidirect
13. #15689203C2semidirect
14. #15689198C2semidirect
15. C47×#452C2semidirect
17. C22×D188C22semidirect
18. C2×D4×D47C22semidirect
21. C2×#10625336C22semidirect
22. C2×#10625336C22semidirect
23. C2×#10625336C22semidirect
28. C2×#10625329C22semidirect
29. C2×#10625324C22semidirect
30. #13094013C22semidirect
31. #13094013C22semidirect
34. #13094000C22semidirect
41. D4×Dic47C22semidirect
42. #13093986C22semidirect
46. #13093957C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093948C22semidirect
49. #13093946C22semidirect
50. #13093946C22semidirect
51. #13093944C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. C8×Dic47C22semidirect
55. C2×Q16×C47C22semidirect
56. C2×SD16×C47C22semidirect
57. C22⋊Q8×C47C22semidirect
58. #103×C47C22semidirect
59. #102×C47C22semidirect
60. C22⋊C8×C47C22semidirect
103. #10625334D4semidirect
226. #452D47semidirect
231. C47#3273semidirect
238. C2×Q16C2×D47semidirect
242. C2×SD16C2×D47semidirect
254. C22⋊Q8C2×D47semidirect
269. #103C2×D47semidirect
273. #102C2×D47semidirect
275. C22⋊C8C2×D47semidirect