Finite Group Databasebeta

← #20254927

Subgroups — #20254927

Order 6016.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094048C211yesmaximal, characteristic, complemented
2C2×#13094045C211yesmaximal, characteristic, complemented
3#15689793C211yesmaximal, characteristic, complemented
4#15689766C211yesmaximal, characteristic, complemented
5#15689366C211yesmaximal, characteristic, complemented
6#15689356C211yesmaximal, characteristic, complemented
7#15689342C211yesmaximal, characteristic, complemented
8#15689315C211yesmaximal, characteristic, complemented
9#15689282C211yesmaximal, characteristic, complemented
10#15689267C211yesmaximal, characteristic, complemented
11#15689265C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13#15689225C211yesmaximal, characteristic, complemented
14#15689196C211yesmaximal, characteristic, complemented
15C47×#496C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×#10625352C2211yescharacteristic, complemented
19C2×D4×D47C2211yescharacteristic
20#13094048—24no—
21#13094045—24no—
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic
24C2×#10625335C2211yescharacteristic
25C2×#10625334C2211yescharacteristic
26C2×#10625334C2211yescharacteristic
27C2×#10625324C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic, complemented
29#13094020—21no—
30#13094006—21no—
31#13094000C2211yescharacteristic
32#13093997—21no—
33#13093996—21no—
34#13093996—21no—
35#13093995C2211yescharacteristic
36#13093995C2211yescharacteristic
37#13093995C2211yescharacteristic, complemented
38#13093994—21no—
39C4×Dic94C2211yescharacteristic, complemented
40C4×D188C2211yescharacteristic
41C4×D188C2211yescharacteristic
42D4×Dic47—21no—
43C22⋊C4×D47—21no—
44#13093958C2211yescharacteristic, complemented
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46#13093949C2211yescharacteristic, complemented
47#13093948C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic
49#13093945C2211yescharacteristic
50#13093945C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×SD16×C47C2211yescharacteristic, complemented
56C2×D8×C47C2211yescharacteristic
57C2×D8×C47C2211yescharacteristic
58#127×C47C2211yescharacteristic, complemented
59#124×C47C2211yescharacteristic
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76#10625354—22no—
77#10625354—41no—
78#10625352—22no—
79#10625352—22no—
80#10625352—41no—
81#10625352—41no—
82D4×D47—22no—
83D4×D47—41no—
84C2×D188—21no—
85C2×D188D411yescharacteristic
86C2×D188C2311yescharacteristic
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47C2311yescharacteristic
90C2×C4×D47C2311yescharacteristic
91C2×Dic94C2311yescharacteristic
92SD16×C47—22no—
93SD16×C47—41no—
94D8×C47—22no—
95D8×C47—41no—
96C2×C8×C47C2311yescharacteristic
97C2×C8×C47C2311yescharacteristic
98C22⋊C4×C47—21no—
99C22⋊C4×C47—21no—
100C42×C47C2311yescharacteristic
101C22⋊Dic47—21no—
102C22⋊Dic47—21no—
103C22⋊Dic47—21no—
104#10625337—22no—
105#10625335—22no—
106#10625334—22no—
107#10625334—22no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110(C2×D47)⋊C4D411yescharacteristic
111(C2×D47)⋊C4D411yescharacteristic
112C4⋊Dic47D411yescharacteristic
113C4⋊Dic47C2311yescharacteristic
114C4⋊Dic47C2311yescharacteristic
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117C4×Dic47—21no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120#10625325D414yescomplemented
121#10625324—22no—
122C8×D47—22no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C22×D47—21no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—81no—
130C22×D47C2×D411yescharacteristic
131C22×D47C2×D411yescharacteristic
132Q8×C47—21no—
133Q8×C47—21no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—21no—
137D4×C47—21no—
138D4×C47—21no—
139D4×C47—21no—
140D4×C47—42no—
141D4×C47—81no—
142C2×C4×C47—21no—
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2411yescharacteristic
146C22⋊D47—42no—
147C22⋊D47—42no—
148C22⋊D47—42no—
149C22⋊D47—81no—
150C22⋊D47—81no—
151C22⋊D47—81no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—42no—
156C2×Dic47—42no—
157C2×Dic47C2×D411yescharacteristic
158C2×Dic47C2×D411yescharacteristic
159D188—21no—
160D188—41no—
161D188—42no—
162D188C2×D412yes—
163C4×D47—21no—
164C4×D47—21no—
165C4×D47—21no—
166C4×D47—21no—
167C4×D47—42no—
168C4×D47—81no—
169Dic94—21no—
170Dic94C2×D412yes—
171C8×C47—21no—
172C8×C47C2×D412yes—
173C47⋊C8—21no—
174C47⋊C8—21no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47C22×D411yescharacteristic
185C2×D47—21no—
186C2×D47—21no—
187C2×D47—22no—
188C2×D47—21no—
189C2×D47—21no—
190C2×D47—21no—
191C2×D47—21no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—84no—
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—41no—
198C4×C47C22×D411yescharacteristic
199C4×C47H(5,𝔽2)11yescharacteristic
200Dic47—22no—
201Dic47—21no—
202Dic47—21no—
203Dic47—41no—
204Dic47—41no—
205#3268—471nomaximal, Sylow
206C2×C47—81no—
207C2×C47—81no—
208C2×C47—81no—
209C2×C47D4211yescharacteristic
210C2×C47#57511yescharacteristic
211C2×C47#57611yescharacteristic
212D47—41no—
213D47—41no—
214D47—42no—
215C2×AGL(1,ℤ/8)—471no—
216C2×#135—471no—
217#550—471no—
218#546—471no—
219#496D4711yescharacteristic, complemented
220#468—471no—
221#466—471no—
222#464—471no—
223#459—471no—
224#452—471no—
225#449—471no—
226#449—471no—
227#447—471no—
228#440—471no—
229#435—471no—
230C47#326811yescharacteristic, complemented, Sylow
231C2×#41—471no—
232C2×#41—471no—
233C2×#41—471no—
234C22×D4—471no—
235AGL(1,ℤ/8)—944no—
236#135—944no—
237C2×Q16—471no—
238C2×SD16—471no—
239C2×SD16—471no—
240C2×SD16C2×D4711yescharacteristic, complemented
241C2×SD16C2×D4711yescharacteristic, complemented
242C2×D8—471no—
243C2×D8—471no—
244C2×D8C2×D4711yescharacteristic
245C2×D8C2×D4711yescharacteristic
246C2×M16—471no—
247C22×C8—471no—
248#127—941no—
249#127C2×D4711yescharacteristic, complemented
250#124C2×D4711yescharacteristic
251#123—941no—
252C22⋊Q8—471no—
253#121—471no—
254#121—471no—
255#121—471no—
256#121—941no—
257#121—941no—
258#121—941no—
259#120—941no—
260C4×Q8—471no—
261C4×D4—471no—
262C4×D4—471no—
263C4×D4—941no—
264C2×C22⋊C4—941no—
265#107—471no—
266C4⋊C8—471no—
267#103—471no—
268#103—471no—
269#102—471no—
270#102—471no—
271#102—471no—
272#102—471no—
273C22⋊C8—471no—
274C22⋊C8—471no—
275#97C2×D4711yescharacteristic, complemented
276C24—941no—
277#41—942no—
278#41—942no—
279#41—942no—
280#41—1881no—
281#41—1881no—
282#41—1881no—
283C2×Q8—471no—
284C2×Q8C22×D4711yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—471no—
288C2×D4—471no—
289C2×D4—941no—
290C2×D4—941no—
291C2×D4—942no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4—941no—
297C2×D4—1881no—
298C2×D4C22×D4711yescharacteristic
299C2×D4C22×D4711yescharacteristic
300C2×D4C22×D4711yescharacteristic
301C22×C4—471no—
302C22×C4—471no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4—941no—
306C22×C4—941no—
307Q16—942no—
308SD16—22no—
309SD16—41no—
310SD16—474no—
311SD16—942no—
312D8—22no—
313D8—41no—
314D8—942no—
315D8—942no—
316M16—942no—
317C2×C8—471no—
318C2×C8—471no—
319C2×C8—942no—
320C2×C8C22×D4711yescharacteristic
321C2×C8C22×D4711yescharacteristic
322C4⋊C4—471no—
323C4⋊C4—471no—
324C4⋊C4—471no—
325C4⋊C4—941no—
326C4⋊C4—941no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—471no—
330C22⋊C4—471no—
331C22⋊C4—941no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C42—941no—
337C42C22×D4711yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—471no—
342C23—471no—
343C23—941no—
344C23—3761no—
345C23—1882no—
346C23—1882no—
347Q8—21no—
348Q8—21no—
349Q8—472no—
350Q8—941no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—42no—
358D4—81no—
359D4—472no—
360D4—941no—
361D4—3761no—
362D4—3761no—
363D4—3761no—
364D4—1881no—
365D4—1882no—
366D4—1882no—
367D4—1882no—
368D4—1882no—
369C2×C4—21no—
370C2×C4—471no—
371C2×C4—471no—
372C2×C4—941no—
373C2×C4—941no—
374C2×C4—941no—
375C2×C4—941no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—3761no—
380C2×C4—1882no—
381C2×C4—1882no—
382C2×C4—1882no—
383C2×C4D4×D4711yescharacteristic
384C2×C4D4×D4711yescharacteristic
385C2×C4C23×D4711yescharacteristic
386C8—21no—
387C8—941no—
388C8—941no—
389C8D4×D4712yes—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—941no—
400C22—941no—
401C22—942no—
402C22—941no—
403C22—941no—
404C22—941no—
405C22—941no—
406C22—3764no—
407C22—1881no—
408C22—1881no—
409C22C2×D4×D4711yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—941no—
414C4—941no—
415C4—942no—
416C4—1881no—
417C4—1881no—
418C4C2×D4×D4711yescharacteristic
419C4#1309406911yescharacteristic
420C2—81no—
421C2—81no—
422C2—81no—
423C2—1881no—
424C2—1881no—
425C2—1882no—
426C2#1568975811yescharacteristic
427C2#1568991911yescharacteristic
428C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#496C2
socleC22×C47C22×D4
hypercenter#496D47
hypocenterC47#3268
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#13094048C2semidirect
2. C2×#13094045C2semidirect
3. #15689793C2semidirect
4. #15689766C2semidirect
5. #15689366C2semidirect
6. #15689356C2semidirect
7. #15689342C2semidirect
8. #15689315C2semidirect
9. #15689282C2semidirect
10. #15689267C2semidirect
11. #15689265C2semidirect
12. #15689255C2semidirect
13. #15689225C2semidirect
14. #15689196C2semidirect
15. C47×#496C2semidirect
18. C2×#10625352C22semidirect
22. C2×#10625337C22semidirect
28. C2×C8×D47C22semidirect
37. #13093995C22semidirect
39. C4×Dic94C22semidirect
44. #13093958C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. #13093949C22semidirect
47. #13093948C22semidirect
50. #13093945C22semidirect
51. #13093945C22semidirect
53. (C2×D47)⋊C8C22semidirect
54. C2×SD16×C47C22semidirect
55. C2×SD16×C47C22semidirect
58. #127×C47C22semidirect
60. #97×C47C22semidirect
120. #10625325D4semidirect
219. #496D47semidirect
230. C47#3268semidirect
240. C2×SD16C2×D47semidirect
241. C2×SD16C2×D47semidirect
249. #127C2×D47semidirect
275. #97C2×D47semidirect