Finite Group Databasebeta

← #20253063

Subgroups — #20253063

Order 6016.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094051C211yesmaximal, characteristic, complemented
2C2×#13094032C211yesmaximal, characteristic, complemented
3#15689703C211yesmaximal, characteristic, complemented
4#15689689C211yesmaximal, characteristic, complemented
5#15689376C211yesmaximal, characteristic, complemented
6#15689375C211yesmaximal, characteristic, complemented
7#15689372C211yesmaximal, characteristic, complemented
8#15689360C211yesmaximal, characteristic, complemented
9#15689357C211yesmaximal, characteristic, complemented
10#15689354C211yesmaximal, characteristic, complemented
11#15689349C211yesmaximal, characteristic, complemented
12#15689164C211yesmaximal, characteristic, complemented
13#15689118C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625350C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19#13094051—24no—
20C2×#10625336C2211yescharacteristic
21C2×D376C2211yescharacteristic
22C2×#10625334C2211yescharacteristic
23#13094032—24no—
24C2×#10625324C2211yescharacteristic
25C2×#10625324C2211yescharacteristic, complemented
26C22×C47⋊C8C2211yescharacteristic, complemented
27C2×C8×D47C2211yescharacteristic
28C2×C8×D47C2211yescharacteristic, complemented
29#13094020—21no—
30#13094010—21no—
31#13094002—21no—
32#13094000C2211yescharacteristic, complemented
33#13093999—21no—
34#13093999C2211yescharacteristic
35#13093999C2211yescharacteristic, complemented
36#13093998C2211yescharacteristic
37#13093998C2211yescharacteristic, complemented
38#13093997—21no—
39#13093997—21no—
40#13093995C2211yescharacteristic
41#13093994—21no—
42#13093992—21no—
43#13093982C2211yescharacteristic
44C4⋊C4×D47C2211yescharacteristic
45#13093957C2211yescharacteristic, complemented
46#13093956C2211yescharacteristic, complemented
47#13093955C2211yescharacteristic, complemented
48#13093948C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic
52#13093944C2211yescharacteristic
53#13093944C2211yescharacteristic, complemented
54C2×SD16×C47C2211yescharacteristic
55C2×M16×C47C2211yescharacteristic, complemented
56C22⋊Q8×C47C2211yescharacteristic, complemented
57#121×C47C2211yescharacteristic
58#107×C47C2211yescharacteristic, complemented
59#103×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic
61C23×D47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47D411yescharacteristic
71C2×C22⋊D47D411yescharacteristic
72#10625354—22no—
73#10625354—22no—
74D4×D47—22no—
75D4×D47—22no—
76#10625350—22no—
77#10625350—22no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188D411yescharacteristic
82C2×D188C2311yescharacteristic
83C2×D188C2311yescharacteristic
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47C2311yescharacteristic
87C2×C4×D47C2311yescharacteristic
88C2×Dic94D411yescharacteristic
89SD16×C47—22no—
90M16×C47—22no—
91C2×C8×C47C2311yescharacteristic
92C2×C8×C47C2311yescharacteristic
93C4⋊C4×C47—21no—
94C4⋊C4×C47C2311yescharacteristic
95C4⋊C4×C47C2311yescharacteristic
96C22⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C22⋊Dic47—21no—
99#10625336—22no—
100#10625334—22no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107C4⋊Dic47C2311yescharacteristic
108C4⋊Dic47C2311yescharacteristic
109Dic47⋊C4—21no—
110Dic47⋊C4—21no—
111C4×Dic47—21no—
112C2×C47⋊C8—22no—
113C2×C47⋊C8C2311yescharacteristic
114C2×C47⋊C8C2311yescharacteristic
115D376—22no—
116#10625324—22no—
117#10625324D414yescomplemented
118C8×D47—22no—
119C8×D47—22no—
120C23×C47—21no—
121C23×C47C2×D411yescharacteristic
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—42no—
125C22×D47—81no—
126C22×D47—81no—
127C22×D47C2×D411yescharacteristic
128C22×D47C2×D411yescharacteristic
129Q8×C47—21no—
130Q8×C47—21no—
131D4×C47—21no—
132D4×C47—21no—
133D4×C47—81no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2411yescharacteristic
141C22⋊D47—22no—
142C22⋊D47—22no—
143C22⋊D47—42no—
144C22⋊D47—81no—
145C22⋊D47—81no—
146C22⋊D47—81no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47C2×D411yescharacteristic
150C2×Dic47C2×D411yescharacteristic
151D188—22no—
152D188—21no—
153D188—21no—
154D188—21no—
155D188—21no—
156D188—42no—
157D188—81no—
158D188—81no—
159C4×D47—21no—
160C4×D47—21no—
161C4×D47—42no—
162C4×D47—81no—
163C4×D47C2×D412yes—
164C4×D47#4112yes—
165Dic94—22no—
166C8×C47—21no—
167C8×C47C2×D412yes—
168C47⋊C8—21no—
169C47⋊C8C2×D412yes—
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47C22×D411yescharacteristic
177C2×D47—21no—
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—21no—
181C2×D47—21no—
182C2×D47—41no—
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—84no—
189C2×D47#12112yes—
190C4×C47—21no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47C22×D411yescharacteristic
195C4×C47C2×#4111yescharacteristic
196Dic47—21no—
197Dic47—41no—
198Dic47—41no—
199Dic47#12112yes—
200#3062—471nomaximal, Sylow
201C2×C47—41no—
202C2×C47—81no—
203C2×C47C2×#12111yescharacteristic
204C2×C47#57611yescharacteristic
205C2×C47#57711yescharacteristic
206D47—22no—
207D47—41no—
208D47—81no—
209D47—81no—
210C2×AGL(1,ℤ/8)—471no—
211C2×#131—471no—
212#537—471no—
213#535—471no—
214#469—471no—
215#469—471no—
216#468—471no—
217#468D4711yescharacteristic, complemented
218#466—471no—
219#466—471no—
220#465—471no—
221#465—471no—
222#428—471no—
223#416—471no—
224C2×#102—471no—
225C47#306211yescharacteristic, complemented, Sylow
226C2×#41—471no—
227C2×#41—471no—
228C22×D4—471no—
229AGL(1,ℤ/8)—944no—
230C2×SD16—471no—
231C2×SD16C2×D4711yescharacteristic
232C2×D8—471no—
233C2×D8—471no—
234#131—944no—
235C2×M16—471no—
236C2×M16—471no—
237C2×M16C2×D4711yescharacteristic, complemented
238C22×C8—471no—
239C22×C8—471no—
240C22×C8—471no—
241#127—941no—
242#124—941no—
243C22⋊Q8—471no—
244C22⋊Q8—941no—
245C22⋊Q8C2×D4711yescharacteristic, complemented
246#121—471no—
247#121—471no—
248#121—471no—
249#121—471no—
250#121—471no—
251#121—941no—
252#121—941no—
253#121—941no—
254#121C2×D4711yescharacteristic
255#120—941no—
256#120—941no—
257#117—471no—
258C2×C4⋊C4—471no—
259#107—471no—
260#107C2×D4711yescharacteristic, complemented
261#106—471no—
262#106—471no—
263#103—471no—
264#103C2×D4711yescharacteristic, complemented
265#102—471no—
266#102—471no—
267#102—471no—
268#102—471no—
269#102—471no—
270#102C2×D4711yescharacteristic
271C24—941no—
272#41—942no—
273#41—942no—
274#41—942no—
275#41—942no—
276C2×Q8—471no—
277C2×Q8C22×D4711yescharacteristic
278C2×D4—21no—
279C2×D4—471no—
280C2×D4—471no—
281C2×D4—471no—
282C2×D4—471no—
283C2×D4—471no—
284C2×D4—941no—
285C2×D4—941no—
286C2×D4—941no—
287C2×D4—942no—
288C2×D4—942no—
289C2×D4—941no—
290C2×D4—941no—
291C2×D4—941no—
292C2×D4—941no—
293C2×D4C22×D4711yescharacteristic
294C22×C4—471no—
295C22×C4—471no—
296C22×C4—941no—
297C22×C4—941no—
298C22×C4C22×D4711yescharacteristic
299SD16—22no—
300SD16—942no—
301D8—942no—
302D8—942no—
303M16—22no—
304M16—474no—
305M16—942no—
306C2×C8—471no—
307C2×C8—471no—
308C2×C8—942no—
309C2×C8—942no—
310C2×C8—942no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—471no—
315C4⋊C4—471no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4C22×D4711yescharacteristic
319C4⋊C4C22×D4711yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C42—941no—
330C23—21no—
331C23—471no—
332C23—471no—
333C23—941no—
334C23—941no—
335C23—3761no—
336C23—3761no—
337C23—1882no—
338C23D4×D4711yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—942no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—942no—
346D4—942no—
347D4—942no—
348D4—941no—
349D4—941no—
350D4—941no—
351D4—941no—
352D4—3761no—
353D4—3761no—
354D4—3761no—
355D4—3761no—
356D4—3761no—
357D4—1882no—
358D4—1882no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—471no—
365C2×C4—472no—
366C2×C4—472no—
367C2×C4—471no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—3761no—
373C2×C4—1882no—
374C2×C4D4×D4711yescharacteristic
375C2×C4C23×D4711yescharacteristic
376C8—21no—
377C8—472no—
378C8—941no—
379C8D4×D4712yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—472no—
387C22—941no—
388C22—941no—
389C22—941no—
390C22—941no—
391C22—941no—
392C22—3764no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22—1881no—
398C22—1881no—
399C22C2×D4×D4711yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—472no—
405C4—941no—
406C4—1881no—
407C4—1881no—
408C4C2×D4×D4711yescharacteristic
409C4#41×D4711yescharacteristic
410C2—41no—
411C2—81no—
412C2—942no—
413C2—3761no—
414C2—3761no—
415C2—1881no—
416C2#121×D4711yescharacteristic
417C2#1568992711yescharacteristic
418C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3062
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. C2×#13094051C2semidirect
2. C2×#13094032C2semidirect
3. #15689703C2semidirect
4. #15689689C2semidirect
5. #15689376C2semidirect
6. #15689375C2semidirect
7. #15689372C2semidirect
8. #15689360C2semidirect
9. #15689357C2semidirect
10. #15689354C2semidirect
11. #15689349C2semidirect
12. #15689164C2semidirect
13. #15689118C2semidirect
14. #102×D47C2semidirect
15. C47×#468C2semidirect
25. C2×#10625324C22semidirect
26. C22×C47⋊C8C22semidirect
28. C2×C8×D47C22semidirect
32. #13094000C22semidirect
35. #13093999C22semidirect
37. #13093998C22semidirect
45. #13093957C22semidirect
46. #13093956C22semidirect
47. #13093955C22semidirect
48. #13093948C22semidirect
50. #13093946C22semidirect
53. #13093944C22semidirect
55. C2×M16×C47C22semidirect
56. C22⋊Q8×C47C22semidirect
58. #107×C47C22semidirect
59. #103×C47C22semidirect
117. #10625324D4semidirect
217. #468D47semidirect
225. C47#3062semidirect
237. C2×M16C2×D47semidirect
245. C22⋊Q8C2×D47semidirect
260. #107C2×D47semidirect
264. #103C2×D47semidirect