Finite Group Databasebeta

← #20254912

Subgroups — #20254912

Order 6016.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094051C211yesmaximal, characteristic, complemented
2C2×#13094047C211yesmaximal, characteristic, complemented
3#15689776C211yesmaximal, characteristic, complemented
4#15689766C211yesmaximal, characteristic, complemented
5#15689378C211yesmaximal, characteristic, complemented
6#15689349C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689325C211yesmaximal, characteristic, complemented
9#15689284C211yesmaximal, characteristic, complemented
10#15689284C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689267C211yesmaximal, characteristic, complemented
13#15689236C211yesmaximal, characteristic, complemented
14#15689196C211yesmaximal, characteristic, complemented
15C47×#497C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625354C2211yescharacteristic
18C2×#10625354C2211yescharacteristic, complemented
19C2×D4×D47C2211yescharacteristic
20#13094051—24no—
21#13094047—24no—
22C2×#10625336C2211yescharacteristic
23C2×#10625336C2211yescharacteristic
24C2×#10625336C2211yescharacteristic, complemented
25C2×D376C2211yescharacteristic
26C2×#10625334C2211yescharacteristic
27C2×#10625324C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic, complemented
29#13094009—21no—
30#13094009—21no—
31#13094006—21no—
32#13094000C2211yescharacteristic
33#13094000C2211yescharacteristic
34#13094000C2211yescharacteristic, complemented
35#13093999—21no—
36#13093997—21no—
37#13093995C2211yescharacteristic
38#13093994—21no—
39C4×D188C2211yescharacteristic
40C4×D188C2211yescharacteristic
41C4×D188C2211yescharacteristic, complemented
42C4⋊C4×D47—21no—
43C22⋊C4×D47—21no—
44#13093956C2211yescharacteristic, complemented
45C4⋊(C47⋊C8)C2211yescharacteristic, complemented
46#13093948C2211yescharacteristic, complemented
47#13093948C2211yescharacteristic, complemented
48#13093948C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic
52(C2×D47)⋊C8C2211yescharacteristic
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54C2×Q16×C47C2211yescharacteristic, complemented
55C2×Q16×C47C2211yescharacteristic, complemented
56C2×SD16×C47C2211yescharacteristic
57C2×SD16×C47C2211yescharacteristic
58C4⋊Q8×C47C2211yescharacteristic, complemented
59#124×C47C2211yescharacteristic
60#97×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×Q8×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68#10625354—22no—
69#10625354—22no—
70#10625354—22no—
71#10625354—41no—
72#10625354—41no—
73#10625354—41no—
74D4×D47—22no—
75D4×D47—41no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188D411yescharacteristic
80C2×D188C2311yescharacteristic
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×C4×D47C2311yescharacteristic
88C2×C4×D47C2311yescharacteristic
89Q16×C47—22no—
90Q16×C47—41no—
91SD16×C47—22no—
92SD16×C47—41no—
93C2×C8×C47C2311yescharacteristic
94C2×C8×C47C2311yescharacteristic
95C4⋊C4×C47—21no—
96C4⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C22⋊C4×C47—21no—
99C42×C47C2311yescharacteristic
100C22⋊Dic47—21no—
101#10625336—22no—
102#10625336—22no—
103#10625336—22no—
104#10625334—22no—
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)⋊C4D411yescharacteristic
111(C2×D47)⋊C4D411yescharacteristic
112C4⋊Dic47D411yescharacteristic
113C4⋊Dic47C2311yescharacteristic
114C4⋊Dic47C2311yescharacteristic
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117Dic47⋊C4—21no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120D376D414yescomplemented
121#10625324—22no—
122C8×D47—22no—
123C23×C47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—42no—
127C22×D47—42no—
128C22×D47—81no—
129C22×D47C2×D411yescharacteristic
130C22×D47C2×D411yescharacteristic
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135Q8×C47—21no—
136Q8×C47—21no—
137D4×C47—21no—
138D4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2411yescharacteristic
145C22⋊D47—42no—
146C22⋊D47—81no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151D188—21no—
152D188—21no—
153D188—41no—
154D188—42no—
155D188—42no—
156D188—42no—
157D188C2×D412yes—
158D188C2×D412yes—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—21no—
162C4×D47—21no—
163C4×D47—42no—
164C4×D47—42no—
165C4×D47—42no—
166C4×D47—42no—
167C4×D47—81no—
168C8×C47—21no—
169C8×C47C2×D412yes—
170C47⋊C8—21no—
171C47⋊C8—21no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47C22×D411yescharacteristic
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—22no—
179C2×D47—22no—
180C2×D47—21no—
181C2×D47—21no—
182C2×D47—21no—
183C2×D47—21no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—84no—
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47C22×D411yescharacteristic
195C4×C47H(5,𝔽2)11yescharacteristic
196Dic47—21no—
197Dic47—21no—
198Dic47—41no—
199Dic47—41no—
200#3267—471nomaximal, Sylow
201C2×C47—81no—
202C2×C47D4211yescharacteristic
203C2×C47#57511yescharacteristic
204C2×C47#57711yescharacteristic
205D47—41no—
206D47—41no—
207D47—42no—
208D47—42no—
209C2×AGL(1,ℤ/8)—471no—
210C2×#135—471no—
211#547—471no—
212#546—471no—
213#497D4711yescharacteristic, complemented
214#470—471no—
215#465—471no—
216#463—471no—
217#461—471no—
218#452—471no—
219#452—471no—
220#450—471no—
221#449—471no—
222#442—471no—
223#435—471no—
224C47#326711yescharacteristic, complemented, Sylow
225C2×#41—471no—
226C2×#41—471no—
227C2×#41—471no—
228C22×D4—471no—
229AGL(1,ℤ/8)—944no—
230#135—944no—
231C2×Q16C2×D4711yescharacteristic, complemented
232C2×Q16C2×D4711yescharacteristic, complemented
233C2×SD16—471no—
234C2×SD16—471no—
235C2×SD16—471no—
236C2×SD16C2×D4711yescharacteristic
237C2×SD16C2×D4711yescharacteristic
238C2×D8—471no—
239C2×D8—471no—
240C2×M16—471no—
241C22×C8—471no—
242C4⋊Q8C2×D4711yescharacteristic, complemented
243#124C2×D4711yescharacteristic
244#123—941no—
245#123—941no—
246#123—941no—
247C22⋊Q8—471no—
248C22⋊Q8—471no—
249C22⋊Q8—471no—
250#121—471no—
251#121—941no—
252#121—941no—
253#120—941no—
254C4×D4—471no—
255C4×D4—471no—
256C4×D4—471no—
257C2×C4⋊C4—941no—
258C2×C22⋊C4—941no—
259#106—471no—
260C4⋊C8—471no—
261#103—471no—
262#103—471no—
263#103—471no—
264#102—471no—
265#102—471no—
266#102—471no—
267C22⋊C8—471no—
268C22⋊C8—471no—
269#97C2×D4711yescharacteristic, complemented
270C24—941no—
271#41—942no—
272#41—942no—
273#41—942no—
274#41—1881no—
275#41—1881no—
276#41—1881no—
277C2×Q8C22×D4711yescharacteristic
278C2×Q8C22×D4711yescharacteristic
279C2×Q8C22×D4711yescharacteristic
280C2×D4—471no—
281C2×D4—471no—
282C2×D4—471no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4—941no—
286C2×D4—941no—
287C2×D4—942no—
288C2×D4—941no—
289C2×D4—1881no—
290C2×D4C22×D4711yescharacteristic
291C22×C4—471no—
292C22×C4—471no—
293C22×C4—941no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4—941no—
297C22×C4—941no—
298Q16—22no—
299Q16—41no—
300SD16—22no—
301SD16—41no—
302SD16—942no—
303SD16—942no—
304SD16—942no—
305D8—474no—
306D8—942no—
307M16—942no—
308C2×C8—471no—
309C2×C8—471no—
310C2×C8—942no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—471no—
316C4⋊C4—471no—
317C4⋊C4—471no—
318C4⋊C4—941no—
319C4⋊C4—941no—
320C4⋊C4—941no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—471no—
324C22⋊C4—471no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C22⋊C4—941no—
331C42C22×D4711yescharacteristic
332C23—21no—
333C23—471no—
334C23—471no—
335C23—941no—
336C23—941no—
337C23—3761no—
338C23—1882no—
339C23—1882no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—21no—
346D4—21no—
347D4—21no—
348D4—472no—
349D4—472no—
350D4—941no—
351D4—941no—
352D4—3761no—
353D4—1881no—
354D4—1882no—
355D4—1882no—
356D4—1882no—
357D4—1882no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—471no—
362C2×C4—471no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—3761no—
370C2×C4—1882no—
371C2×C4—1882no—
372C2×C4—1882no—
373C2×C4—1882no—
374C2×C4D4×D4711yescharacteristic
375C2×C4D4×D4711yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C8—21no—
378C8—941no—
379C8—941no—
380C8D4×D4712yes—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—941no—
385C22—941no—
386C22—942no—
387C22—942no—
388C22—941no—
389C22—941no—
390C22—941no—
391C22—941no—
392C22—3764no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22C2×D4×D4711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—941no—
404C4—941no—
405C4—1881no—
406C4—1881no—
407C4C2×D4×D4711yescharacteristic
408C4#1309406911yescharacteristic
409C2—81no—
410C2—1881no—
411C2—1881no—
412C2—1882no—
413C2—1882no—
414C2#1568975811yescharacteristic
415C2#1568992211yescharacteristic
416C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#497C2
socleC22×C47C22×D4
hypercenter#497D47
hypocenterC47#3267
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. C2×#13094047C2semidirect
3. #15689776C2semidirect
4. #15689766C2semidirect
5. #15689378C2semidirect
6. #15689349C2semidirect
7. #15689335C2semidirect
8. #15689325C2semidirect
9. #15689284C2semidirect
10. #15689284C2semidirect
11. #15689272C2semidirect
12. #15689267C2semidirect
13. #15689236C2semidirect
14. #15689196C2semidirect
15. C47×#497C2semidirect
18. C2×#10625354C22semidirect
24. C2×#10625336C22semidirect
28. C2×C8×D47C22semidirect
34. #13094000C22semidirect
41. C4×D188C22semidirect
44. #13093956C22semidirect
45. C4⋊(C47⋊C8)C22semidirect
46. #13093948C22semidirect
47. #13093948C22semidirect
48. #13093948C22semidirect
50. #13093946C22semidirect
53. (C2×D47)⋊C8C22semidirect
54. C2×Q16×C47C22semidirect
55. C2×Q16×C47C22semidirect
58. C4⋊Q8×C47C22semidirect
60. #97×C47C22semidirect
120. D376D4semidirect
213. #497D47semidirect
224. C47#3267semidirect
231. C2×Q16C2×D47semidirect
232. C2×Q16C2×D47semidirect
242. C4⋊Q8C2×D47semidirect
269. #97C2×D47semidirect