Finite Group Databasebeta

← #20254994

Subgroups — #20254994

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×#13094048C211yesmaximal, characteristic, complemented
3#15689768C211yesmaximal, characteristic, complemented
4#15689766C211yesmaximal, characteristic, complemented
5#15689505C211yesmaximal, characteristic, complemented
6#15689372C211yesmaximal, characteristic, complemented
7#15689368C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689288C211yesmaximal, characteristic, complemented
10#15689282C211yesmaximal, characteristic, complemented
11#15689258C211yesmaximal, characteristic, complemented
12#15689255C211yesmaximal, characteristic, complemented
13C4×#10625334C211yesmaximal, characteristic, complemented
14#15689200C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic, complemented
19C2×D4×D47C2211yescharacteristic, complemented
20#13094051—24no—
21#13094048—24no—
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625325C2211yescharacteristic, complemented
24C2×#10625335C2211yescharacteristic, complemented
25C2×#10625336C2211yescharacteristic, complemented
26C2×D376C2211yescharacteristic
27C2×#10625334C2211yescharacteristic
28C2×#10625334C2211yescharacteristic
29C2×#10625324C2211yescharacteristic, complemented
30C2×#10625324C2211yescharacteristic, complemented
31#13094012C2211yescharacteristic, complemented
32#13094008—21no—
33#13094006—21no—
34#13094004C2211yescharacteristic, complemented
35#13094000C2211yescharacteristic, complemented
36#13093999C2211yescharacteristic
37#13093998—21no—
38#13093997—21no—
39#13093995C2211yescharacteristic
40#13093994—21no—
41#13093994—21no—
42C4×D188C2211yescharacteristic
43C4×D188C2211yescharacteristic, complemented
44C2×(C2×D47)⋊C4—21no—
45C22⋊C4×D47—21no—
46#13093957C2211yescharacteristic, complemented
47#13093949C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic, complemented
49#13093945C2211yescharacteristic, complemented
50#13093944C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53C4×C47⋊C8C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic, complemented
55C2×D8×C47C2211yescharacteristic
56#124×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic, complemented
58C4⋊C8×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C23×D47—21no—
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C22×Dic47—21no—
72#10625354—22no—
73#10625354—41no—
74#10625352—22no—
75#10625352—41no—
76D4×D47—22no—
77D4×D47—22no—
78D4×D47—41no—
79D4×D47—41no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188D411yescharacteristic
83C2×D188C2311yescharacteristic
84C2×D188C2311yescharacteristic
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×C4×D47C2311yescharacteristic
88C2×C4×D47C2311yescharacteristic
89C2×Dic94C2311yescharacteristic
90SD16×C47—22no—
91D8×C47—22no—
92C2×C8×C47C2311yescharacteristic
93C2×C8×C47C2311yescharacteristic
94C4⋊C4×C47C2311yescharacteristic
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C42×C47C2311yescharacteristic
99C22⋊Dic47—21no—
100#10625337—41no—
101#10625336—22no—
102#10625335—22no—
103#10625334—41no—
104#10625334D414yescomplemented
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)⋊C4D411yescharacteristic
112(C2×D47)⋊C4D411yescharacteristic
113C4⋊Dic47—21no—
114C4⋊Dic47D411yescharacteristic
115C4⋊Dic47C2311yescharacteristic
116Dic47⋊C4—21no—
117C2×C47⋊C8C2311yescharacteristic
118C2×C47⋊C8C2311yescharacteristic
119D376—22no—
120#10625325—22no—
121#10625324—22no—
122#10625324—22no—
123C23×C47—21no—
124C23×C47—21no—
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—42no—
128C22×D47—42no—
129C22×D47—42no—
130C22×D47—42no—
131C22×D47—81no—
132C22×D47—81no—
133C22×D47C2×D411yescharacteristic
134C22×D47C2×D411yescharacteristic
135Q8×C47—21no—
136Q8×C47—21no—
137D4×C47—21no—
138D4×C47—21no—
139D4×C47—21no—
140D4×C47C2×D412yes—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—81no—
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2411yescharacteristic
147C22⋊D47—42no—
148C22⋊D47—42no—
149C22⋊D47—42no—
150C22⋊D47—81no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—42no—
154C2×Dic47C2×D411yescharacteristic
155C2×Dic47C2×D411yescharacteristic
156D188—21no—
157D188—21no—
158D188—21no—
159D188—41no—
160D188—42no—
161D188—81no—
162D188C2×D412yes—
163C4×D47—21no—
164C4×D47—21no—
165C4×D47—21no—
166C4×D47—21no—
167C4×D47—42no—
168C4×D47—81no—
169Dic94—21no—
170Dic94—21no—
171C8×C47—21no—
172C8×C47—21no—
173C47⋊C8—21no—
174C47⋊C8C2×D412yes—
175C22×C47—22no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47C22×D411yescharacteristic
182C2×D47—21no—
183C2×D47—21no—
184C2×D47—22no—
185C2×D47—21no—
186C2×D47—21no—
187C2×D47—21no—
188C2×D47—21no—
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—21no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47C22×D411yescharacteristic
201C4×C47H(5,𝔽2)11yescharacteristic
202Dic47—21no—
203Dic47—21no—
204Dic47—41no—
205Dic47—41no—
206#3273—471nomaximal, Sylow
207C2×C47—42no—
208C2×C47—81no—
209C2×C47D4211yescharacteristic
210C2×C47#57511yescharacteristic
211C2×C47#57611yescharacteristic
212D47—41no—
213D47—41no—
214D47—42no—
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#463D4711yescharacteristic, complemented
225#452—471no—
226#452—471no—
227#447—471no—
228#447—471no—
229C4×D8—471no—
230#436—471no—
231C47#327311yescharacteristic, complemented, Sylow
232C2×#41—471no—
233C2×#41—471no—
234C22×D4—471no—
235C22×D4—471no—
236AGL(1,ℤ/8)—944no—
237AGL(1,ℤ/8)—944no—
238C2×Q16—471no—
239C2×SD16—471no—
240C2×SD16—471no—
241C2×SD16—471no—
242C2×SD16C2×D4711yescharacteristic, complemented
243C2×D8—471no—
244C2×D8—471no—
245C2×D8—471no—
246C2×D8C2×D4711yescharacteristic
247C2×M16—471no—
248C2×M16—471no—
249#124—471no—
250#124C2×D4711yescharacteristic, complemented
251#123—941no—
252#123—941no—
253C22⋊Q8—471no—
254C22⋊Q8—471no—
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×D4C2×D4711yescharacteristic, complemented
264C2×C22⋊C4—941no—
265C2×C22⋊C4—941no—
266#107—471no—
267C4⋊C8C2×D4711yescharacteristic, complemented
268#103—471no—
269#103C2×D4711yescharacteristic, complemented
270#102—471no—
271#102—471no—
272#102—471no—
273#102C2×D4711yescharacteristic, complemented
274C22⋊C8—471no—
275C22⋊C8—471no—
276C4×C8—471no—
277C24—941no—
278C24—941no—
279#41—942no—
280#41—942no—
281#41—1881no—
282#41—1881no—
283C2×Q8—471no—
284C2×Q8C22×D4711yescharacteristic
285C2×D4—471no—
286C2×D4—471no—
287C2×D4—471no—
288C2×D4—941no—
289C2×D4—941no—
290C2×D4—941no—
291C2×D4—941no—
292C2×D4—942no—
293C2×D4—942no—
294C2×D4—941no—
295C2×D4—941no—
296C2×D4—1881no—
297C2×D4—1881no—
298C2×D4C22×D4711yescharacteristic
299C2×D4C22×D4711yescharacteristic
300C22×C4—21no—
301C22×C4—471no—
302C22×C4—471no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4—941no—
306Q16—1881no—
307SD16—22no—
308SD16—942no—
309SD16—942no—
310SD16—942no—
311D8—22no—
312D8—474no—
313D8—942no—
314D8—1881no—
315M16—942no—
316M16—942no—
317C2×C8—471no—
318C2×C8—471no—
319C2×C8C22×D4711yescharacteristic
320C2×C8C22×D4711yescharacteristic
321C4⋊C4—471no—
322C4⋊C4—471no—
323C4⋊C4—941no—
324C4⋊C4—941no—
325C4⋊C4C22×D4711yescharacteristic
326C22⋊C4—21no—
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—
336C22⋊C4—941no—
337C22⋊C4—941no—
338C42C22×D4711yescharacteristic
339C23—21no—
340C23—21no—
341C23—471no—
342C23—471no—
343C23—941no—
344C23—941no—
345C23—3761no—
346C23—3761no—
347C23—1882no—
348C23—1882no—
349C23—1882no—
350C23—1882no—
351Q8—21no—
352Q8—21no—
353Q8—941no—
354Q8—941no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—472no—
359D4—941no—
360D4—941no—
361D4—941no—
362D4—3761no—
363D4—3761no—
364D4—1881no—
365D4—1882no—
366D4—1882no—
367D4—1882no—
368D4—1882no—
369D4D4×D4712yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—471no—
374C2×C4—471no—
375C2×C4—941no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—3761no—
382C2×C4—1882no—
383C2×C4—1882no—
384C2×C4D4×D4711yescharacteristic
385C2×C4D4×D4711yescharacteristic
386C2×C4C23×D4711yescharacteristic
387C8—21no—
388C8—21no—
389C8—472no—
390C8—941no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—941no—
398C22—941no—
399C22—942no—
400C22—941no—
401C22—941no—
402C22—941no—
403C22—941no—
404C22—3764no—
405C22—3764no—
406C22—1881no—
407C22—1881no—
408C22—1881no—
409C22—1881no—
410C22—1881no—
411C22C2×D4×D4711yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—941no—
417C4—941no—
418C4—1881no—
419C4—1881no—
420C4C2×D4×D4711yescharacteristic
421C4#1309407011yescharacteristic
422C2—42no—
423C2—81no—
424C2—3761no—
425C2—1881no—
426C2—1881no—
427C2—1882no—
428C2#1568975711yescharacteristic
429C2#1568992011yescharacteristic
430C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. C2×#13094048C2semidirect
3. #15689768C2semidirect
4. #15689766C2semidirect
5. #15689505C2semidirect
6. #15689372C2semidirect
7. #15689368C2semidirect
8. #15689339C2semidirect
9. #15689288C2semidirect
10. #15689282C2semidirect
11. #15689258C2semidirect
12. #15689255C2semidirect
13. C4×#10625334C2semidirect
14. #15689200C2semidirect
15. C47×#463C2semidirect
18. C2×D4×D47C22semidirect
19. C2×D4×D47C22semidirect
22. C2×#10625337C22semidirect
23. C2×#10625325C22semidirect
24. C2×#10625335C22semidirect
25. C2×#10625336C22semidirect
29. C2×#10625324C22semidirect
30. C2×#10625324C22semidirect
31. #13094012C22semidirect
34. #13094004C22semidirect
35. #13094000C22semidirect
43. C4×D188C22semidirect
46. #13093957C22semidirect
47. #13093949C22semidirect
48. #13093946C22semidirect
49. #13093945C22semidirect
50. #13093944C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. C4×C47⋊C8C22semidirect
54. C2×SD16×C47C22semidirect
56. #124×C47C22semidirect
57. C4×D4×C47C22semidirect
58. C4⋊C8×C47C22semidirect
59. #103×C47C22semidirect
60. #102×C47C22semidirect
104. #10625334D4semidirect
224. #463D47semidirect
231. C47#3273semidirect
242. C2×SD16C2×D47semidirect
250. #124C2×D47semidirect
263. C4×D4C2×D47semidirect
267. C4⋊C8C2×D47semidirect
269. #103C2×D47semidirect
273. #102C2×D47semidirect