Finite Group Databasebeta

← #20254241

Subgroups — #20254241

Order 6016.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689703C211yesmaximal, characteristic, complemented
2#15689689C211yesmaximal, characteristic, complemented
3#15689462C211yesmaximal, characteristic, complemented
4#15689450C211yesmaximal, characteristic, complemented
5#15689440C211yesmaximal, characteristic, complemented
6#15689438C211yesmaximal, characteristic, complemented
7#15689376C211yesmaximal, characteristic, complemented
8#15689357C211yesmaximal, characteristic, complemented
9#15689354C211yesmaximal, characteristic, complemented
10#15689272C211yesmaximal, characteristic, complemented
11#15689271C211yesmaximal, characteristic, complemented
12#15689267C211yesmaximal, characteristic, complemented
13#15689258C211yesmaximal, characteristic, complemented
14#15689091C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic, complemented
17C2×#10625350C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×D376C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic, complemented
23#13094020—21no—
24#13094010—21no—
25#13094002—21no—
26#13094000C2211yescharacteristic
27#13093999—21no—
28#13093999C2211yescharacteristic
29#13093999C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093998C2211yescharacteristic, complemented
32#13093997—21no—
33#13093997—21no—
34#13093995C2211yescharacteristic
35#13093994—21no—
36#13093992—21no—
37#13093982C2211yescharacteristic
38C4⋊C4×D47C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40#13093956C2211yescharacteristic, complemented
41#13093955C2211yescharacteristic, 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(C2×D47)⋊C8C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic, complemented
54C22⋊Q8×C47C2211yescharacteristic, complemented
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69C2×C22⋊D47D411yescharacteristic
70#10625354—41no—
71#10625354—41no—
72D4×D47—41no—
73D4×D47—41no—
74#10625350—41no—
75#10625350—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×D47C2311yescharacteristic
85C2×C4×D47C2311yescharacteristic
86C2×Dic94D411yescharacteristic
87SD16×C47—41no—
88M16×C47—41no—
89C2×C8×C47C2311yescharacteristic
90C2×C8×C47C2311yescharacteristic
91C4⋊C4×C47—21no—
92C4⋊C4×C47C2311yescharacteristic
93C4⋊C4×C47C2311yescharacteristic
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊Dic47—21no—
97#10625336—41no—
98#10625334—41no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107Dic47⋊C4—21no—
108Dic47⋊C4—21no—
109C4×Dic47—21no—
110C2×C47⋊C8—41no—
111C2×C47⋊C8C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113D376—41no—
114C23×C47—21no—
115C23×C47C2×D411yescharacteristic
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—42no—
119C22×D47—81no—
120C22×D47—81no—
121C22×D47C2×D411yescharacteristic
122C22×D47C2×D411yescharacteristic
123Q8×C47—21no—
124Q8×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—81no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—41no—
136C22⋊D47—41no—
137C22⋊D47—42no—
138C22⋊D47—81no—
139C22⋊D47—81no—
140C22⋊D47—81no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47C2×D411yescharacteristic
144C2×Dic47C2×D411yescharacteristic
145D188—21no—
146D188—21no—
147D188—21no—
148D188—21no—
149D188—41no—
150D188—42no—
151D188—81no—
152D188—81no—
153C4×D47—21no—
154C4×D47—21no—
155C4×D47—21no—
156C4×D47—21no—
157C4×D47—42no—
158C4×D47—81no—
159Dic94—41no—
160C8×C47—21no—
161C8×C47—21no—
162C47⋊C8—21no—
163C47⋊C8—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47C22×D411yescharacteristic
171C2×D47—21no—
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—84no—
184C4×C47—21no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47H(5,𝔽2)11yescharacteristic
189C4×C47H(5,𝔽2)11yescharacteristic
190Dic47—21no—
191Dic47—21no—
192Dic47—41no—
193Dic47—41no—
194#3198—471nomaximal, Sylow
195C2×C47—41no—
196C2×C47—81no—
197C2×C47#53411yescharacteristic
198C2×C47#57611yescharacteristic
199C2×C47#57711yescharacteristic
200D47—41no—
201D47—41no—
202D47—81no—
203D47—81no—
204#537—471no—
205#535—471no—
206#485—471no—
207#482—471no—
208#481—471no—
209#480—471no—
210#469—471no—
211#468D4711yescharacteristic, complemented
212#466—471no—
213#465—471no—
214#450—471no—
215#449—471no—
216#449—471no—
217#447—471no—
218#408—471no—
219C47#319811yescharacteristic, complemented, Sylow
220C2×#41—471no—
221C2×#41—471no—
222C22×D4—471no—
223C2×SD16—471no—
224C2×SD16C2×D4711yescharacteristic
225C2×D8—471no—
226C2×D8—471no—
227C2×M16C2×D4711yescharacteristic, complemented
228C22×C8—471no—
229#127—941no—
230#124—941no—
231C22⋊Q8—471no—
232C22⋊Q8—941no—
233C22⋊Q8C2×D4711yescharacteristic, complemented
234#121—471no—
235#121—471no—
236#121—471no—
237#121—471no—
238#121—471no—
239#121—941no—
240#121—941no—
241#121—941no—
242#121C2×D4711yescharacteristic
243#120—941no—
244#120—941no—
245#117—471no—
246C2×C4⋊C4—471no—
247#107—471no—
248#107C2×D4711yescharacteristic, complemented
249#106—471no—
250#106—471no—
251#103—471no—
252#103C2×D4711yescharacteristic, complemented
253#102—471no—
254#102—471no—
255#102—471no—
256#102—471no—
257#102—471no—
258#102C2×D4711yescharacteristic
259C22⋊C8—471no—
260C22⋊C8—471no—
261C22⋊C8—471no—
262C22⋊C8—471no—
263C24—941no—
264#41—1881no—
265#41—1881no—
266#41—1881no—
267#41—1881no—
268C2×Q8—471no—
269C2×Q8C22×D4711yescharacteristic
270C2×D4—21no—
271C2×D4—471no—
272C2×D4—471no—
273C2×D4—471no—
274C2×D4—471no—
275C2×D4—471no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C2×D4—941no—
280C2×D4—941no—
281C2×D4—941no—
282C2×D4—941no—
283C2×D4—1881no—
284C2×D4—1881no—
285C2×D4C22×D4711yescharacteristic
286C22×C4—471no—
287C22×C4—471no—
288C22×C4—941no—
289C22×C4—941no—
290C22×C4C22×D4711yescharacteristic
291SD16—41no—
292SD16—1881no—
293D8—1881no—
294D8—1881no—
295M16—41no—
296C2×C8—471no—
297C2×C8—471no—
298C2×C8—1881no—
299C2×C8C22×D4711yescharacteristic
300C2×C8C22×D4711yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—471no—
303C4⋊C4—471no—
304C4⋊C4—941no—
305C4⋊C4—941no—
306C4⋊C4C22×D4711yescharacteristic
307C4⋊C4C22×D4711yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—941no—
311C22⋊C4—941no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C42—941no—
318C23—21no—
319C23—471no—
320C23—471no—
321C23—941no—
322C23—941no—
323C23—3761no—
324C23—3761no—
325C23—1882no—
326C23D4×D4711yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—1881no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—941no—
334D4—941no—
335D4—941no—
336D4—941no—
337D4—3761no—
338D4—3761no—
339D4—3761no—
340D4—3761no—
341D4—3761no—
342D4—1881no—
343D4—1882no—
344D4—1881no—
345D4—1881no—
346D4—1882no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—471no—
353C2×C4—471no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—3761no—
361C2×C4—1882no—
362C2×C4D4×D4711yescharacteristic
363C2×C4C23×D4711yescharacteristic
364C8—21no—
365C8—21no—
366C8—941no—
367C8—941no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—941no—
375C22—941no—
376C22—941no—
377C22—941no—
378C22—941no—
379C22—941no—
380C22—3764no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22C2×D4×D4711yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—941no—
393C4—941no—
394C4—1881no—
395C4—1881no—
396C4#1309406911yescharacteristic
397C4#1309407011yescharacteristic
398C2—41no—
399C2—81no—
400C2—3761no—
401C2—3761no—
402C2—1881no—
403C2—1881no—
404C2#1568968111yescharacteristic
405C2#1568992711yescharacteristic
406C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #15689703C2semidirect
2. #15689689C2semidirect
3. #15689462C2semidirect
4. #15689450C2semidirect
5. #15689440C2semidirect
6. #15689438C2semidirect
7. #15689376C2semidirect
8. #15689357C2semidirect
9. #15689354C2semidirect
10. #15689272C2semidirect
11. #15689271C2semidirect
12. #15689267C2semidirect
13. #15689258C2semidirect
14. #15689091C2semidirect
15. C47×#468C2semidirect
16. C2×#10625354C22semidirect
22. C22×C47⋊C8C22semidirect
31. #13093998C22semidirect
38. C4⋊C4×D47C22semidirect
39. #13093957C22semidirect
40. #13093956C22semidirect
41. #13093955C22semidirect
42. #13093948C22semidirect
44. #13093946C22semidirect
47. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. (C2×D47)⋊C8C22semidirect
53. C2×M16×C47C22semidirect
54. C22⋊Q8×C47C22semidirect
56. #107×C47C22semidirect
57. #103×C47C22semidirect
211. #468D47semidirect
219. C47#3198semidirect
227. C2×M16C2×D47semidirect
233. C22⋊Q8C2×D47semidirect
248. #107C2×D47semidirect
252. #103C2×D47semidirect