Finite Group Databasebeta

← #20254435

Subgroups — #20254435

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689724C211yesmaximal, characteristic, complemented
2#15689691C211yesmaximal, characteristic, complemented
3#15689509C211yesmaximal, characteristic, complemented
4#15689498C211yesmaximal, characteristic, complemented
5#15689486C211yesmaximal, characteristic, complemented
6#15689479C211yesmaximal, characteristic, complemented
7#15689335C211yesmaximal, characteristic, complemented
8#15689319C211yesmaximal, characteristic, complemented
9#15689318C211yesmaximal, characteristic, complemented
10#15689271C211yesmaximal, characteristic, complemented
11#15689267C211yesmaximal, characteristic, complemented
12#15689258C211yesmaximal, characteristic, complemented
13#15689255C211yesmaximal, characteristic, complemented
14#15689183C211yesmaximal, characteristic, complemented
15C47×#463C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625336C2211yescharacteristic, complemented
19C2×D376C2211yescharacteristic
20C2×D376C2211yescharacteristic, complemented
21C2×#10625334C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23C2×#10625334C2211yescharacteristic, complemented
24#13094021C2211yescharacteristic
25#13094020C2211yescharacteristic
26#13094020C2211yescharacteristic, complemented
27#13094015C2211yescharacteristic, complemented
28#13094013C2211yescharacteristic
29#13094007—21no—
30#13094006—21no—
31#13093999C2211yescharacteristic
32#13093998—21no—
33#13093997—21no—
34#13093997—21no—
35#13093997—21no—
36#13093995C2211yescharacteristic
37#13093994—21no—
38#13093994—21no—
39C4×D188C2211yescharacteristic, complemented
40#13093981C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic, complemented
48(C2×D47)⋊C8C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50#13093934C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic, complemented
53C2×D8×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70#10625354—41no—
71#10625354—41no—
72D4×D47—41no—
73D4×D47—41no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188C2311yescharacteristic
79C2×D188C2311yescharacteristic
80C2×D188C2311yescharacteristic
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47C2311yescharacteristic
84SD16×C47—41no—
85D8×C47—41no—
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C42×C47C2311yescharacteristic
93C22⋊Dic47—21no—
94#10625336—41no—
95#10625334—41no—
96#10625334—41no—
97#10625334—41no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4D411yescharacteristic
103(C2×D47)⋊C4D411yescharacteristic
104C4⋊Dic47—21no—
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4D411yescharacteristic
108Dic47⋊C4D411yescharacteristic
109C4×Dic47C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112D376—41no—
113D376—41no—
114C23×C47—21no—
115C23×C47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C22×D47C2×D411yescharacteristic
123Q8×C47—21no—
124Q8×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—81no—
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—42no—
136C22⋊D47—81no—
137C22⋊D47—81no—
138C22⋊D47—81no—
139C22⋊D47—81no—
140C22⋊D47—81no—
141C2×Dic47—21no—
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145D188—21no—
146D188—21no—
147D188—21no—
148D188—21no—
149D188—21no—
150D188—21no—
151D188—42no—
152D188—81no—
153D188—81no—
154D188—81no—
155C4×D47—21no—
156C4×D47—21no—
157C4×D47—42no—
158C4×D47—81no—
159C8×C47—21no—
160C8×C47—21no—
161C47⋊C8—21no—
162C47⋊C8—21no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47C22×D411yescharacteristic
170C2×D47—21no—
171C2×D47—21no—
172C2×D47—21no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—84no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47H(5,𝔽2)11yescharacteristic
188C4×C47H(5,𝔽2)11yescharacteristic
189Dic47—21no—
190Dic47—21no—
191Dic47—21no—
192Dic47—41no—
193#3220—471nomaximal, Sylow
194C2×C47—81no—
195C2×C47—81no—
196C2×C47#53511yescharacteristic
197C2×C47#57611yescharacteristic
198C2×C47#57611yescharacteristic
199D47—41no—
200D47—81no—
201D47—81no—
202D47—81no—
203#540—471no—
204#535—471no—
205#496—471no—
206#493—471no—
207#490—471no—
208#488—471no—
209#463—471no—
210#463D4711yescharacteristic, complemented
211#459—471no—
212#459—471no—
213#449—471no—
214#449—471no—
215#447—471no—
216#447—471no—
217#433—471no—
218C47#322011yescharacteristic, complemented, Sylow
219C2×#41—471no—
220C22×D4—471no—
221C2×SD16—471no—
222C2×SD16C2×D4711yescharacteristic, complemented
223C2×D8—471no—
224C2×D8—471no—
225C2×D8—471no—
226C2×D8—471no—
227C2×D8—471no—
228C2×D8C2×D4711yescharacteristic
229#127—471no—
230#127—471no—
231#127—471no—
232#125—471no—
233#124—471no—
234#124C2×D4711yescharacteristic
235#123—941no—
236#123—941no—
237#121—471no—
238#121—471no—
239#121—941no—
240#121—941no—
241#121—941no—
242#121—941no—
243#120—941no—
244#120—941no—
245C4×D4—471no—
246C4×D4C2×D4711yescharacteristic, complemented
247#117—471no—
248C4⋊C8—471no—
249C4⋊C8C2×D4711yescharacteristic, complemented
250#103—471no—
251#103C2×D4711yescharacteristic, complemented
252#102—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102—471no—
257#102C2×D4711yescharacteristic
258C22⋊C8—471no—
259C22⋊C8—471no—
260#97—471no—
261C4×C8—471no—
262C24—941no—
263#41—1881no—
264#41—1881no—
265C2×Q8C22×D4711yescharacteristic
266C2×D4—471no—
267C2×D4—471no—
268C2×D4—471no—
269C2×D4—941no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C2×D4—1881no—
280C2×D4—1881no—
281C2×D4C22×D4711yescharacteristic
282C2×D4C22×D4711yescharacteristic
283C22×C4—21no—
284C22×C4—471no—
285C22×C4—941no—
286C22×C4—941no—
287SD16—41no—
288SD16—1881no—
289D8—41no—
290D8—1881no—
291D8—1881no—
292D8—1881no—
293D8—1881no—
294D8—1881no—
295C2×C8—471no—
296C2×C8—471no—
297C2×C8C22×D4711yescharacteristic
298C2×C8C22×D4711yescharacteristic
299C4⋊C4—471no—
300C4⋊C4—471no—
301C4⋊C4—471no—
302C4⋊C4—941no—
303C4⋊C4—941no—
304C4⋊C4C22×D4711yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—471no—
309C22⋊C4—471no—
310C22⋊C4—941no—
311C22⋊C4—941no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C42—471no—
316C42C22×D4711yescharacteristic
317C23—21no—
318C23—21no—
319C23—471no—
320C23—941no—
321C23—941no—
322C23—941no—
323C23—3761no—
324C23—3761no—
325C23—1882no—
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—941no—
333D4—941no—
334D4—941no—
335D4—941no—
336D4—941no—
337D4—941no—
338D4—3761no—
339D4—3761no—
340D4—3761no—
341D4—3761no—
342D4—3761no—
343D4—3761no—
344D4—3761no—
345D4—3761no—
346D4—1882no—
347D4—1882no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—471no—
352C2×C4—471no—
353C2×C4—471no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—3761no—
358C2×C4—1882no—
359C2×C4D4×D4711yescharacteristic
360C2×C4D4×D4711yescharacteristic
361C2×C4C23×D4711yescharacteristic
362C8—21no—
363C8—21no—
364C8—941no—
365C8—941no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—941no—
373C22—941no—
374C22—941no—
375C22—3764no—
376C22—1881no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22—1881no—
385C22C2×D4×D4711yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—941no—
391C4—941no—
392C4—941no—
393C4—1881no—
394C4#1309406911yescharacteristic
395C4#1309407011yescharacteristic
396C2—81no—
397C2—81no—
398C2—3761no—
399C2—3761no—
400C2—3761no—
401C2—1881no—
402C2#1568968911yescharacteristic
403C2#1568992511yescharacteristic
404C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3220
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. #15689724C2semidirect
2. #15689691C2semidirect
3. #15689509C2semidirect
4. #15689498C2semidirect
5. #15689486C2semidirect
6. #15689479C2semidirect
7. #15689335C2semidirect
8. #15689319C2semidirect
9. #15689318C2semidirect
10. #15689271C2semidirect
11. #15689267C2semidirect
12. #15689258C2semidirect
13. #15689255C2semidirect
14. #15689183C2semidirect
15. C47×#463C2semidirect
18. C2×#10625336C22semidirect
20. C2×D376C22semidirect
23. C2×#10625334C22semidirect
26. #13094020C22semidirect
27. #13094015C22semidirect
39. C4×D188C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093948C22semidirect
44. #13093946C22semidirect
47. #13093944C22semidirect
50. #13093934C22semidirect
51. C8×Dic47C22semidirect
52. C2×SD16×C47C22semidirect
55. C4×D4×C47C22semidirect
56. C4⋊C8×C47C22semidirect
57. #103×C47C22semidirect
210. #463D47semidirect
218. C47#3220semidirect
222. C2×SD16C2×D47semidirect
246. C4×D4C2×D47semidirect
249. C4⋊C8C2×D47semidirect
251. #103C2×D47semidirect